**Design and Development of Ultrasonic Process Tomography**

Mohd Hafiz Fazalul Rahiman1, Ruzairi Abdul Rahim2, Herlina Abdul Rahim2 and Nor Muzakkir Nor Ayob2 *1Universiti Malaysia Perlis (UniMAP) 2Universiti Teknologi Malaysia (UTM) 1,2Malaysia* 

## **1. Introduction**

210 Ultrasonic Waves

Zhang F., Krishnaswamy S., Fei D., Rebinsky D. & Feng B., (2006), Ultrasonic

Zou, D.H. S., Cheng J., Yue, R. & Sun X., (October 2010), Grout quality and its impact on

carbon hard coatings, *Thin Solid Films*, Vol. 503, No. 1-2, pp.250-258

characterization of mechanical properties of Cr- and W- doped diamond like

guided ultrasonic waves in grouted rock bolts, *International Journal of Rock Mechanics and Mining Sciences & Geomechanics*, Volume 19, Issue 5, Pages 221-228

> Process tomography is a process of obtaining the plane-section images of a threedimensional object. Process tomography techniques produce cross-section images of the distribution of flow components in a pipeline, and it offers great potential for the development, and verification of flow models, and also for process diagnostic.

> The measurement of two-component flow such as liquid or oil flow through a pipe is increasingly important in a wide range of applications, for example, pipeline control in oil exploitation, and chemical process monitoring. Knowledge of the flow component distribution is required for the determination of flow parameters such as the void fraction, and the flow regime.

> Real-time reconstruction of the flow image is needed in order to estimate the flow regime when it is continuously evolving. This flow image is important in many areas of industry, and scientific research concerning liquid/gas two-phase flow. The operation efficiency of such a process is closely related to accurate measurement, and control of hydrodynamic parameters such as flow regime, and flow rate (Rahiman et al., 2010). Commonly, the monitoring in the process industry is limited to either visual inspection or a single-point product sampling assuming the product is uniformed. This approach for the determination of fluid flow parameters of two-component flow is also known as flow imaging.

## **1.1 Principle overview**

Ultrasonic sensors have been successfully applied in flow measurement, non-destructive testing, and it is widely used in medical imaging. The method involves in using ultrasonic is through transmitting, and receiving sensors that are axially spaced along the flow stream. The sensors do not obstruct the flow. As the suspended solids' concentration fluctuates, the ultrasonic beam is scattered, and the received signal fluctuates in a random manner about a mean value. This type of sensor can be used for measuring the flow velocity. Two pairs of sensors are required in order to obtain the velocity using a cross- correlation method. Ultrasonic sensor propagates acoustic waves within the range of 18 kHz to 20 MHz.

Design and Development of Ultrasonic Process Tomography 213

vi. A mutually compatible range of techniques can be used to determine a wide range of parameters: these include liquid level, interface position, concentration (or density),

Besides, those benefits have a significant impact, and lead to the development of Ultrasonic tomography. Ultrasonic tomography offers the advantage of imaging two-component flows, and gives the opportunity of providing quantitative and real-time data on chemical media within a full-scale industrial process, such as filtration, without the need of process

The major potential benefits are; it is possible to gain an insight into the actual process; secondly, since ultrasonic tomography is capable of on-line monitoring, it has the opportunity to develop closed-loop control systems, and finally, it can be a non-invasive, and possibly nonintrusive system. The overall anticipated effects are improvements in product yield, and uniformity, minimized input process material, reduced energy consumption, and

The popular ultrasonic sensing system is the transmission-mode, and the reflection-mode. The transmission-mode technique is based on the measurement of the changed in the properties of the transmitted acoustic wave, which are influenced by the material of the medium in the measuring volume. The change of the physical properties can be the intensity, and/or transmission time (time-of-flight). The reflection-mode technique is based on the measurement of the position, and the change of the physical properties of wave or a particle reflected on an interface. Similar to the reflection-mode technique there are some techniques based on diffraction or refraction of wave at a discrete or continuous interface in

Utilizing attenuation or time-of-flight of a transmitted energy beam such as light or acoustic waves to produce an image of multiphase flow has been attempted at an early stage. In transparent media, optical methods based on light transmission technique, and the photographical techniques has proven quite effective (Rahim et al., 2011). However, since many real reaction systems are optically opaque, an application of the elegant optical

Techniques based on reflection or the scattering of optical or acoustical waves were realized by measuring the Doppler shift-frequency of the reflected or scattered signals. An example is the use of laser Doppler anemometry for in-situ measurements of velocity, fluctuating velocity, size, and concentration of particles, bubbles or droplets in multiphase systems. A corresponding example of the Doppler technique utilizing ultrasonic wave is the measurements of bubble velocity in a stirred tank, and a ferment or vessel by Broring et al.,

A combination of the transmission and the reflection modes is found in acoustical imaging techniques, which are widely used in medical, and ocean engineering fields from early stages. An application of ultrasonic imaging velocimetry has been attempted by Kytomaa & Corrington (1994) to investigate a transient liquefaction phenomenon of cohesion-less particulate media. More advanced particle imaging velocimetry techniques were developed by combining the photographic technique and image processing technique or using radioactive particle tracking techniques. Examples are using particle image velocimetry

environmental impact, and the lowering of occupational exposure to plant personnel.

temperature, and flow-rate. Hence multiplexed electronics are feasible.

interruption (Warsito et al., 1999).

the object space.

(1991).

method is severely limited.

Ultrasonic wave is strongly reflected at the interface between one substance, and another. However, it is difficult to collimate, and problems occur due to reflections within enclosed spaces, such as metal pipes. There are two types of ultrasonic signals that are usually used. They are the continuous signal, and the pulsed signal. Using a continuous signal will provide continuous impact on the crystal whereas by using pulses the interval of the transmission and reception signal can be estimated. Using the ultrasonic method in the air is very inefficient due to the mismatch of the sensors' impedance as compared with air's acoustic impedance. New types of sensors are continually being developed, but the effective ones are expensive. The design of this sensor is critical when it needs to reduce the sensor's ringing.

## **1.2 The tomography technique**

The first step of a tomographic process is to generate the integral measurements using a selected sensor. The second step is to reconstruct the property field (the cross-sectional distribution of the physical properties of the multiphase media) from the measured integral values. This process is called tomographic reconstruction (Warsito et al., 1999).

There are numerous reconstruction algorithms available for tomographic reconstruction. The algorithms based on Fourier's techniques, and the algebraic reconstruction technique (ART) has been widely used in the field of medicine. However, the choice of the reconstruction algorithm is also dependent on the sensor system selected. In engineering related applications, the number of measurement is usually very small to perform a realtime measurement or limited by constraints on the sensor employed. Therefore, the reconstruction results are then further corrected using a mathematical approximation to obtain a better reconstruction.

In contrast to light or other electromagnetic waves, ultrasound needs medium to transmit through, and interrogates the physical properties (i.e. density, compressibility) of the media. Therefore, it is speculated that such a method would be appropriate for application in a medium with relatively homogeneous but high density, which is poorly penetrated by light or other electromagnetic radiation. In addition, in comparison with high-energy electromagnetic radiation, ultrasonic technique consumes much lower energy, low-cost, and simpler to use, and suitable for applications from laboratory scale to industrial plants (Williams & Beck, 1995).

## **2. Ultrasonic process tomography – An overview**

Instrumentation systems employing a variety of ultrasonic techniques have been applied to a wide range of measurements in the chemical, and process industries (Asher, 1983). At least, eight categories of ultrasonic flow meter can be identified with flow meters of time-of-flight type now being employed in single-phase liquid, and gas flow measurement with a great deal of success. It is favoured by most industries due to the benefits as follows (Asher, 1983):


Ultrasonic wave is strongly reflected at the interface between one substance, and another. However, it is difficult to collimate, and problems occur due to reflections within enclosed spaces, such as metal pipes. There are two types of ultrasonic signals that are usually used. They are the continuous signal, and the pulsed signal. Using a continuous signal will provide continuous impact on the crystal whereas by using pulses the interval of the transmission and reception signal can be estimated. Using the ultrasonic method in the air is very inefficient due to the mismatch of the sensors' impedance as compared with air's acoustic impedance. New types of sensors are continually being developed, but the effective ones are expensive. The

The first step of a tomographic process is to generate the integral measurements using a selected sensor. The second step is to reconstruct the property field (the cross-sectional distribution of the physical properties of the multiphase media) from the measured integral

There are numerous reconstruction algorithms available for tomographic reconstruction. The algorithms based on Fourier's techniques, and the algebraic reconstruction technique (ART) has been widely used in the field of medicine. However, the choice of the reconstruction algorithm is also dependent on the sensor system selected. In engineering related applications, the number of measurement is usually very small to perform a realtime measurement or limited by constraints on the sensor employed. Therefore, the reconstruction results are then further corrected using a mathematical approximation to

In contrast to light or other electromagnetic waves, ultrasound needs medium to transmit through, and interrogates the physical properties (i.e. density, compressibility) of the media. Therefore, it is speculated that such a method would be appropriate for application in a medium with relatively homogeneous but high density, which is poorly penetrated by light or other electromagnetic radiation. In addition, in comparison with high-energy electromagnetic radiation, ultrasonic technique consumes much lower energy, low-cost, and simpler to use, and suitable for applications from laboratory scale to industrial plants

Instrumentation systems employing a variety of ultrasonic techniques have been applied to a wide range of measurements in the chemical, and process industries (Asher, 1983). At least, eight categories of ultrasonic flow meter can be identified with flow meters of time-of-flight type now being employed in single-phase liquid, and gas flow measurement with a great deal of success. It is favoured by most industries due to the benefits as follows (Asher, 1983):

v. The energy levels required to excite the transducers are very low, and have no

detrimental effect on the plant or the materials being interrogated.

design of this sensor is critical when it needs to reduce the sensor's ringing.

values. This process is called tomographic reconstruction (Warsito et al., 1999).

**1.2 The tomography technique** 

obtain a better reconstruction.

(Williams & Beck, 1995).

ii. It has 'no moving parts'.

**2. Ultrasonic process tomography – An overview** 

i. Ultrasonic techniques can usually be truly non-invasive.

iv. The rapid response usually in a fraction of a second.

iii. The radioactive materials are not involved.

vi. A mutually compatible range of techniques can be used to determine a wide range of parameters: these include liquid level, interface position, concentration (or density), temperature, and flow-rate. Hence multiplexed electronics are feasible.

Besides, those benefits have a significant impact, and lead to the development of Ultrasonic tomography. Ultrasonic tomography offers the advantage of imaging two-component flows, and gives the opportunity of providing quantitative and real-time data on chemical media within a full-scale industrial process, such as filtration, without the need of process interruption (Warsito et al., 1999).

The major potential benefits are; it is possible to gain an insight into the actual process; secondly, since ultrasonic tomography is capable of on-line monitoring, it has the opportunity to develop closed-loop control systems, and finally, it can be a non-invasive, and possibly nonintrusive system. The overall anticipated effects are improvements in product yield, and uniformity, minimized input process material, reduced energy consumption, and environmental impact, and the lowering of occupational exposure to plant personnel.

The popular ultrasonic sensing system is the transmission-mode, and the reflection-mode. The transmission-mode technique is based on the measurement of the changed in the properties of the transmitted acoustic wave, which are influenced by the material of the medium in the measuring volume. The change of the physical properties can be the intensity, and/or transmission time (time-of-flight). The reflection-mode technique is based on the measurement of the position, and the change of the physical properties of wave or a particle reflected on an interface. Similar to the reflection-mode technique there are some techniques based on diffraction or refraction of wave at a discrete or continuous interface in the object space.

Utilizing attenuation or time-of-flight of a transmitted energy beam such as light or acoustic waves to produce an image of multiphase flow has been attempted at an early stage. In transparent media, optical methods based on light transmission technique, and the photographical techniques has proven quite effective (Rahim et al., 2011). However, since many real reaction systems are optically opaque, an application of the elegant optical method is severely limited.

Techniques based on reflection or the scattering of optical or acoustical waves were realized by measuring the Doppler shift-frequency of the reflected or scattered signals. An example is the use of laser Doppler anemometry for in-situ measurements of velocity, fluctuating velocity, size, and concentration of particles, bubbles or droplets in multiphase systems. A corresponding example of the Doppler technique utilizing ultrasonic wave is the measurements of bubble velocity in a stirred tank, and a ferment or vessel by Broring et al., (1991).

A combination of the transmission and the reflection modes is found in acoustical imaging techniques, which are widely used in medical, and ocean engineering fields from early stages. An application of ultrasonic imaging velocimetry has been attempted by Kytomaa & Corrington (1994) to investigate a transient liquefaction phenomenon of cohesion-less particulate media. More advanced particle imaging velocimetry techniques were developed by combining the photographic technique and image processing technique or using radioactive particle tracking techniques. Examples are using particle image velocimetry

Design and Development of Ultrasonic Process Tomography 215

The relationship of the simplified ultrasonic transmission model is depicted in Equation (3),

where *VG* is the sensor loss voltage due to the gas opacity, *VC* is the calibration voltage, and *VR* is the receiving voltage. For measuring the concentration profile, the parameter *VG* is to

Ultrasound Transmission

*VG VR*

One of the most important parts in an ultrasonic tomography system is the front-end, which is the transducer array, and associated electronic hardware. This is important for acquiring the data needed to produce a meaningful image. This is fundamental to the success or failure of an acoustic imaging system. Therefore, given the object to be imaged, and the specifications to be achieved, the design of the front-end of an acoustic imaging system

Ultrasonic transducer is a device capable of converting electrical energy into highfrequency sound waves, and also converting sound waves back into electrical energy. Ultrasonic transducer contains piezoelectric crystal materials that have the ability to transform mechanical energy into electrical energy, and vice versa. In reality, when a crystal element is pulsed with a voltage profile, a wave starts travelling from each face of the crystal element. The vibrational mode of the crystal can therefore, only be considered from a transient wave propagation viewpoint. Resolution and penetrating power of an ultrasonic wave depends on the resulting wavelength of excitation inside the material in question. Greater wavelengths or lower frequencies generally penetrate much further into a material (Kannath & Dewhurst, 2004). Higher frequency ultrasonic excitations with smaller wavelengths generally decay more rapidly inside a material, but resolution

For the presented systems, the active element for the transducers is the wide-angle beam ceramic piezoelectric with resonance frequency of 333 kHz. Transducer elements employed in ultrasonic imaging arrays may be designed to produce either a narrow focused beam or a divergent beam. The beam pattern used for two-dimensional imaging is the cylindrically diverging or 'fan-shaped' beam pattern. This is to ensure a maximum number of transducers located around the pipe circumference, which receive the directly

*VVV GCR* (3)

Receiver

*VC*

and shown graphically in Figure 2.

**3. The measurement system** 

should be regarded as a first priority.

capability is improved.

transmitted wave.

Fig. 2. The simplified ultrasound transmission model

Transmitter Gas cavity

be resolved.

(PIV), particle streak velocimetry (PSV), and particle tracking velocimetry (PTV) for visualizing the flow pattern of multiphase flows (Rashidi, 1997).

#### **2.1 The attenuation model**

The attenuation process may be modelled by Lambert's exponential law of absorption, where the ultrasonic energy intensity of transmitter and receiver are related as in Figure 1 and Equation (1), where *L* represents the total path length.

Fig. 1. The ultrasonic attenuation model

$$P = P\_o \exp\left(-\int\_L f(\mathbf{x}\_\prime, y)dP\right) \tag{1}$$

where *P* = the measured sound pressure (dB), *Po* = the initial sound pressure (dB), *L* = path length in the object field (m), and *f (x,y)* = the attenuation function of the object field (dB/m). Because the pressure is proportional to the voltage measured by the transducer, Equation (1) can be written as Equation (2).

$$
\upsilon\_{Rx} = \upsilon\_{Tx} e^{-\alpha L} \tag{2}
$$

where *vRx* = the ultrasonic receiver voltage (V), *vTx* = the ultrasonic transmitted voltage (V), and = the attenuation coefficient of the object field (Np/m).

As introduced above, the attenuation will critically depend upon the material through which the ultrasonic wave travels.

#### **2.2 Scattering issues**

Acoustic impedance is a ratio of acoustic pressure to acoustic volume flow, and is frequency dependent. The greater the difference in acoustic impedance at the interface, the greater will be the amount of energy reflected. At a water, and gas interface, about 99.94% of the ultrasonic energy will be reflected (Rahiman et al., 2008). However, in some cases, scattering occurs on small gas hold-ups. Small was defined as a sphere with a radius of *a* where the circumference of the sphere, *2πa*, divided by the wavelength *λ* is much less than 1 (i.e. ka = *2πa*/*λ* << 1) where *k* is the wave number = *2πf/c*.

If ultrasonic waves propagate in a bubbly air/water with a wavelength much shorter than the gas radius a, i.e. ka >> 1, the diffraction can be ignored, and these hold-ups will act as many acoustics opacities. This is because when ka >> 1, the surface of the sphere appears as a flat surface with respect to the wavelength, and the scattering becomes the same as a reflection from a flat surface.

(PIV), particle streak velocimetry (PSV), and particle tracking velocimetry (PTV) for

The attenuation process may be modelled by Lambert's exponential law of absorption, where the ultrasonic energy intensity of transmitter and receiver are related as in Figure 1

> *Po P L*

> > Object field

*f (x,y)* 

where *P* = the measured sound pressure (dB), *Po* = the initial sound pressure (dB), *L* = path length in the object field (m), and *f (x,y)* = the attenuation function of the object field (dB/m). Because the pressure is proportional to the voltage measured by the transducer, Equation (1)

*Rx Tx v ve*

= the attenuation coefficient of the object field (Np/m).

where *vRx* = the ultrasonic receiver voltage (V), *vTx* = the ultrasonic transmitted voltage (V),

As introduced above, the attenuation will critically depend upon the material through

Acoustic impedance is a ratio of acoustic pressure to acoustic volume flow, and is frequency dependent. The greater the difference in acoustic impedance at the interface, the greater will be the amount of energy reflected. At a water, and gas interface, about 99.94% of the ultrasonic energy will be reflected (Rahiman et al., 2008). However, in some cases, scattering occurs on small gas hold-ups. Small was defined as a sphere with a radius of *a* where the circumference of the sphere, *2πa*, divided by the wavelength *λ* is much less than 1 (i.e. ka =

If ultrasonic waves propagate in a bubbly air/water with a wavelength much shorter than the gas radius a, i.e. ka >> 1, the diffraction can be ignored, and these hold-ups will act as many acoustics opacities. This is because when ka >> 1, the surface of the sphere appears as a flat surface with respect to the wavelength, and the scattering becomes the same as a

*L*

*<sup>o</sup>* exp ( , ) *<sup>L</sup> P P f x y dP* (1)

(2)

visualizing the flow pattern of multiphase flows (Rashidi, 1997).

and Equation (1), where *L* represents the total path length.

**2.1 The attenuation model** 

Fig. 1. The ultrasonic attenuation model

can be written as Equation (2).

which the ultrasonic wave travels.

*2πa*/*λ* << 1) where *k* is the wave number = *2πf/c*.

**2.2 Scattering issues** 

reflection from a flat surface.

and  The relationship of the simplified ultrasonic transmission model is depicted in Equation (3), and shown graphically in Figure 2.

$$V\_G = V\_C - V\_R \tag{3}$$

where *VG* is the sensor loss voltage due to the gas opacity, *VC* is the calibration voltage, and *VR* is the receiving voltage. For measuring the concentration profile, the parameter *VG* is to be resolved.

Fig. 2. The simplified ultrasound transmission model

## **3. The measurement system**

One of the most important parts in an ultrasonic tomography system is the front-end, which is the transducer array, and associated electronic hardware. This is important for acquiring the data needed to produce a meaningful image. This is fundamental to the success or failure of an acoustic imaging system. Therefore, given the object to be imaged, and the specifications to be achieved, the design of the front-end of an acoustic imaging system should be regarded as a first priority.

Ultrasonic transducer is a device capable of converting electrical energy into highfrequency sound waves, and also converting sound waves back into electrical energy. Ultrasonic transducer contains piezoelectric crystal materials that have the ability to transform mechanical energy into electrical energy, and vice versa. In reality, when a crystal element is pulsed with a voltage profile, a wave starts travelling from each face of the crystal element. The vibrational mode of the crystal can therefore, only be considered from a transient wave propagation viewpoint. Resolution and penetrating power of an ultrasonic wave depends on the resulting wavelength of excitation inside the material in question. Greater wavelengths or lower frequencies generally penetrate much further into a material (Kannath & Dewhurst, 2004). Higher frequency ultrasonic excitations with smaller wavelengths generally decay more rapidly inside a material, but resolution capability is improved.

For the presented systems, the active element for the transducers is the wide-angle beam ceramic piezoelectric with resonance frequency of 333 kHz. Transducer elements employed in ultrasonic imaging arrays may be designed to produce either a narrow focused beam or a divergent beam. The beam pattern used for two-dimensional imaging is the cylindrically diverging or 'fan-shaped' beam pattern. This is to ensure a maximum number of transducers located around the pipe circumference, which receive the directly transmitted wave.

Design and Development of Ultrasonic Process Tomography 217

Fig. 4. The discontinuous component viewed by the ultrasonic receiver

Transmitting signal

Time-of-Flight (TOF)

*Voltage, V* 

Fig. 5. An example of transmitting, and receiving an ultrasonic signal

had travelled (Moore *et al*. 2000).

In our work, a transmission-mode method emphasizing the receiver amplitude, and the arrival time analysis has been used. Arrival time analysis is based on the simple fact that it takes some finite time for an ultrasonic disturbance to move from one position to another inside the experimental pipe. In Figure 5, the *observation time* denoted by *ts* was the first peak after the time-of-flight corresponding to a straight path. By sampling amplitude of this observation time for every receiving sensor due to projection of transmitters, the information via transmission-mode method can be obtained. As the distance between the transmitting sensor, and the receiving sensor increases, the ultrasound will consume longer time-of flight to reach to the point of interest, and therefore, set out a longer observation time. This time-of-flight may then be assumed to be proportional to the distance that they

Multiple reflection signals

Receiving signal

*ts*

*Time, t* 

## **3.1 Fan-shaped beam sensor array**

An example of a fan-shaped beam sensor array is shown in Figure 3, which consists of 32 ultrasonic transceivers that is mounted on an experimental column. The transceivers enable the transmission, and reception on the same sensor. The transmission and reception of ultrasonic waves are, however, controlled by the electronic analogue-switches which direct the signal to the corresponding channels.

Fig. 3. Ultrasonic transceiver sensor array

One of the significant advantages in employing ultrasonic techniques is it enables measurement to be made without breaking into the process vessel, and therefore, measurements can be made where for a reason of safety hygiene, continuity of supply or cost it is not possible to break into the process vessel. However, the invasive transducers actually contact the flow inside the pipe, for obvious reasons it is not favoured by most industries (Sanderson & Yeung, 2002).

In Figure 3, the transmitter is modelled as a point source, which propagates within angle *a* in the image plane, and the receiver is modelled as a circular arc with radius of curvature *r*. The wavefronts are taken to be circular arcs of uniform ultrasonic energy. When ultrasound is propagating in the flow medium, areas occupied by the discontinuous component block the transmitted ultrasound. As a result, an effect analogous to the shadowing of visible light by an opaque object can be seen in Figure 4. An example of transmitting, and receiving ultrasonic signals is shown in Figure 5.

An example of a fan-shaped beam sensor array is shown in Figure 3, which consists of 32 ultrasonic transceivers that is mounted on an experimental column. The transceivers enable the transmission, and reception on the same sensor. The transmission and reception of ultrasonic waves are, however, controlled by the electronic analogue-switches which direct

One of the significant advantages in employing ultrasonic techniques is it enables measurement to be made without breaking into the process vessel, and therefore, measurements can be made where for a reason of safety hygiene, continuity of supply or cost it is not possible to break into the process vessel. However, the invasive transducers actually contact the flow inside the pipe, for obvious reasons it is not favoured by most

In Figure 3, the transmitter is modelled as a point source, which propagates within angle *a* in the image plane, and the receiver is modelled as a circular arc with radius of curvature *r*. The wavefronts are taken to be circular arcs of uniform ultrasonic energy. When ultrasound is propagating in the flow medium, areas occupied by the discontinuous component block the transmitted ultrasound. As a result, an effect analogous to the shadowing of visible light by an opaque object can be seen in Figure 4. An example of transmitting, and receiving

**3.1 Fan-shaped beam sensor array** 

the signal to the corresponding channels.

Fig. 3. Ultrasonic transceiver sensor array

industries (Sanderson & Yeung, 2002).

ultrasonic signals is shown in Figure 5.

Fig. 4. The discontinuous component viewed by the ultrasonic receiver

Fig. 5. An example of transmitting, and receiving an ultrasonic signal

In our work, a transmission-mode method emphasizing the receiver amplitude, and the arrival time analysis has been used. Arrival time analysis is based on the simple fact that it takes some finite time for an ultrasonic disturbance to move from one position to another inside the experimental pipe. In Figure 5, the *observation time* denoted by *ts* was the first peak after the time-of-flight corresponding to a straight path. By sampling amplitude of this observation time for every receiving sensor due to projection of transmitters, the information via transmission-mode method can be obtained. As the distance between the transmitting sensor, and the receiving sensor increases, the ultrasound will consume longer time-of flight to reach to the point of interest, and therefore, set out a longer observation time. This time-of-flight may then be assumed to be proportional to the distance that they had travelled (Moore *et al*. 2000).

Design and Development of Ultrasonic Process Tomography 219

The signal conditioning circuit consists of two components where the first component is the amplifier, and the second component is the signal processing circuit that is the sample and hold circuit. The amplifier was built using a dual-wide gain bandwidth op-amp to avoid signal distortion during amplification. The amplifier uses two stages inverting op-amp design. Both the first stage and the second stage amplifier gain were set with -150. The

When the components to be imaged are gases, there may be no directly transmitted signals from the transmitter to the receiver because of the obstacles. By reflecting at the gas component surfaces, the receiver may still detect some signals but at a later time though because direct transmission takes the shortest path, and hence the shortest time. Thus, if the *observation time* is monitored, it is possible to test whether there are any objects between the transmitter, and the receiver. By sampling the signals at this observation time for every receiving transceiver, the spatial information in the measurement area can be obtained. To discriminate the exact information (information by the observation time) the sample and

Fig. 8. The signal generator circuit

signal conditioning circuit is shown in Figure 9.

Fig. 9. The signal conditioning circuit

## **3.2 The system block diagram**

The system block diagram is shown in Figure 6. The microcontroller will generate a burst tone of a two-cycle ultrasonic pulses at 333kHz with duty-cycle of 50% at each cycle. The delay between each burst tone was 6.667ms which is for the reverberation effect delays of the receiver before the next transmitting transceiver excited. An illustration of the pulses is shown in Figure 7. The reverberation effect delays are needed to avoid overlapping echoes at the receiving transceiver due to two separate ultrasound excitation. To select the corresponding transmitting, and receiving transceivers, several analogue switches have been utilized.

Fig. 6. The ultrasonic system block diagram

Fig. 7. The burst tones generated by microcontroller

The signal generator was designed using a low-noise high-speed op-amp, TLE2141 that acts as comparator. The comparator will generate a 20Vp-p burst tone of 333 kHz. The burst tone excitation is designed so that it is long enough for transient effects but short enough for the burst to be received without multiple reflections as describe previously. The circuit is shown in Figure 8.

The system block diagram is shown in Figure 6. The microcontroller will generate a burst tone of a two-cycle ultrasonic pulses at 333kHz with duty-cycle of 50% at each cycle. The delay between each burst tone was 6.667ms which is for the reverberation effect delays of the receiver before the next transmitting transceiver excited. An illustration of the pulses is shown in Figure 7. The reverberation effect delays are needed to avoid overlapping echoes at the receiving transceiver due to two separate ultrasound excitation. To select the corresponding

transmitting, and receiving transceivers, several analogue switches have been utilized.

**3.2 The system block diagram** 

Fig. 6. The ultrasonic system block diagram

Fig. 7. The burst tones generated by microcontroller

in Figure 8.

The signal generator was designed using a low-noise high-speed op-amp, TLE2141 that acts as comparator. The comparator will generate a 20Vp-p burst tone of 333 kHz. The burst tone excitation is designed so that it is long enough for transient effects but short enough for the burst to be received without multiple reflections as describe previously. The circuit is shown

Fig. 8. The signal generator circuit

The signal conditioning circuit consists of two components where the first component is the amplifier, and the second component is the signal processing circuit that is the sample and hold circuit. The amplifier was built using a dual-wide gain bandwidth op-amp to avoid signal distortion during amplification. The amplifier uses two stages inverting op-amp design. Both the first stage and the second stage amplifier gain were set with -150. The signal conditioning circuit is shown in Figure 9.

Fig. 9. The signal conditioning circuit

When the components to be imaged are gases, there may be no directly transmitted signals from the transmitter to the receiver because of the obstacles. By reflecting at the gas component surfaces, the receiver may still detect some signals but at a later time though because direct transmission takes the shortest path, and hence the shortest time. Thus, if the *observation time* is monitored, it is possible to test whether there are any objects between the transmitter, and the receiver. By sampling the signals at this observation time for every receiving transceiver, the spatial information in the measurement area can be obtained. To discriminate the exact information (information by the observation time) the sample and

Design and Development of Ultrasonic Process Tomography 221

The inverse problem is to determine from the system response matrix (sensitivity matrices), a complex transformation matrix for converting the measured sensor values into pixel values. It is known as the tomogram. To reconstruct the tomogram requires an image reconstruction algorithm. The details for tomogram reconstruction are presented in the

To reconstruct the cross-section of an image plane from the projection data, the backprojection algorithm has been employed. Most of the work in process tomography has focused on the back-projection technique. It is originally developed for the X-ray tomography, and it also has the advantages of low computation cost (Garcia-Stewart et al., 2003). The measurements obtained at each projected data are the attenuated sensor values due to object space in the image plane. These sensor values are then back projected by multiply with the corresponding normalized sensitivity maps. The back projected data values are smeared back across the unknown density function (image), and overlapped to each other to increase the projection data density. The process of back-projection is shown in

The density of each point in the reconstructed image is obtained by summing up the densities of all rays which pass through that point. This process may be described by Equation 4. Equation 4 is the back-projection algorithm where the spoke pattern represents

( , ) ( cos sin )

  

(4)

*b jj j*

1

*j f xy g x y*

*m*

Fig. 12. The sensitivity map for projection TR25 to TR2

**4.2 The inverse problem** 

**4.3 Image reconstruction algorithm** 

following section.

Figure 13, and Figure 14.

blurring of the object in space.

hold method is used. A sample and hold circuit, also called a track-and-hold circuit is a circuit that captures, and holds an analogue voltage in a specific point in time under control of an external circuit (microcontroller). The operation of sample and hold is shown in Figure 10, and the circuit diagram for sample and hold is shown in Figure 11.

The holding signal is also known as the *sensor value* voltage will be sampled by the DAQ using the dsPIC30F6011A IC which served as the analogue-to-digital converter as well. The information captured by the DAQ will be processed, and send to the PC for generating the corresponding tomography images.

Fig. 10. The sample and hold operation

Fig. 11. The sample and hold circuit

## **4. Image reconstruction**

In this work, the tomographic images are derived by using a back projection algorithm. In order to derive this algorithm, which results in the solution to the inverse problem, the forward problem must be solved first.

## **4.1 The forward problem**

The forward problem determines the theoretical output of each of the sensors when the sensing area is considered to be two-dimensional. The cross-section of the pipe is mapped onto a 64 x 64 rectangular array consisting of 4096 pixels. The forward problem can be solved by using the analytical solution of sensitivity maps, which produces the sensitivity matrices. Each transmitting sensor is virtually excited, and the affected pixels are taken into account (as shown in Figure 12).

Fig. 12. The sensitivity map for projection TR25 to TR2

### **4.2 The inverse problem**

220 Ultrasonic Waves

hold method is used. A sample and hold circuit, also called a track-and-hold circuit is a circuit that captures, and holds an analogue voltage in a specific point in time under control of an external circuit (microcontroller). The operation of sample and hold is shown in Figure

The holding signal is also known as the *sensor value* voltage will be sampled by the DAQ using the dsPIC30F6011A IC which served as the analogue-to-digital converter as well. The information captured by the DAQ will be processed, and send to the PC for generating the

*t* 

*t* 

*t* 

In this work, the tomographic images are derived by using a back projection algorithm. In order to derive this algorithm, which results in the solution to the inverse problem, the

The forward problem determines the theoretical output of each of the sensors when the sensing area is considered to be two-dimensional. The cross-section of the pipe is mapped onto a 64 x 64 rectangular array consisting of 4096 pixels. The forward problem can be solved by using the analytical solution of sensitivity maps, which produces the sensitivity matrices. Each transmitting sensor is virtually excited, and the affected pixels are taken into

10, and the circuit diagram for sample and hold is shown in Figure 11.

*sample hold* 

*ts*

corresponding tomography images.

Receiver signal

*V*

S&H triggering

Fig. 10. The sample and hold operation

Sampled signal

Fig. 11. The sample and hold circuit

forward problem must be solved first.

**4. Image reconstruction** 

**4.1 The forward problem** 

account (as shown in Figure 12).

The inverse problem is to determine from the system response matrix (sensitivity matrices), a complex transformation matrix for converting the measured sensor values into pixel values. It is known as the tomogram. To reconstruct the tomogram requires an image reconstruction algorithm. The details for tomogram reconstruction are presented in the following section.

#### **4.3 Image reconstruction algorithm**

To reconstruct the cross-section of an image plane from the projection data, the backprojection algorithm has been employed. Most of the work in process tomography has focused on the back-projection technique. It is originally developed for the X-ray tomography, and it also has the advantages of low computation cost (Garcia-Stewart et al., 2003). The measurements obtained at each projected data are the attenuated sensor values due to object space in the image plane. These sensor values are then back projected by multiply with the corresponding normalized sensitivity maps. The back projected data values are smeared back across the unknown density function (image), and overlapped to each other to increase the projection data density. The process of back-projection is shown in Figure 13, and Figure 14.

The density of each point in the reconstructed image is obtained by summing up the densities of all rays which pass through that point. This process may be described by Equation 4. Equation 4 is the back-projection algorithm where the spoke pattern represents blurring of the object in space.

$$f\_b(\mathbf{x}, y) = \sum\_{j=1}^{m} g\_j(\mathbf{x}\cos\theta\_j + y\sin\theta\_j)\Delta\theta\tag{4}$$

Design and Development of Ultrasonic Process Tomography 223

The tomogram reconstruction on three phantoms of a small gas hold-up, a large gas holdup, and a dual gas hold-up are shown in Figure 15, 16, and 17 respectively. The results showed several tomograms reconstructed using; (a) LBP, and (b) LBP with a threshold ratio

(a) LBP (b) LBP (with threshold ratio 0.55)

(a) LBP (b) LBP (with threshold ratio 0.55)

**4.4 Image reconstruction results** 

Fig. 15. Small gas hold-up

Fig. 16. Large gas hold-up

of 0.55.

where *fb* (*x, y*) = the function of reconstructed image from the back-projection algorithm, *<sup>j</sup>* = the *j-*th projection angle, and Δ = the angular distance between projection, and the summation extends over all the *m-projection.* 

Fig. 13. The back-projection method

Fig. 14. The fan-shaped beam back-projection

(a) Fan-Shaped Beam Projection (b) Fan-Shaped Beam Back-Projection

### **4.3.1 Linear back projection algorithm**

The Linear Back Projection algorithm (LBP) is computationally straight forward to implement, and is a popular method for image reconstruction. Sensitivity maps, which were derived for the individual sensors are used by the LBP algorithm to calculate concentration profiles from measured sensor values. The process of obtaining concentration profile using LBP can be expressed mathematically as in Equation 5.

$$V\_{\rm LBP}(\mathbf{x}, y) = \sum\_{\mathbf{T} \mathbf{x} = \mathbf{0}}^{\mathbf{m}} \sum\_{\mathbf{R} \mathbf{x} = \mathbf{0}}^{\mathbf{m}} S\mathbf{r}\_{\mathbf{x}}, \mathbf{R} \mathbf{x} \times \overline{\mathbf{M}}\mathbf{T}\mathbf{x}, \mathbb{R}\mathbf{x}\{\mathbf{x}, y\} \tag{5}$$

where *VLBP(x,y)* is the voltage distribution on the concentration profile matrix, *STx,Rx* is the sensor loss value, and , *RxTx yxM* ),( is the normalized sensitivity matrices.

## **4.4 Image reconstruction results**

222 Ultrasonic Waves

*p*

(a) Fan-Shaped Beam Projection (b) Fan-Shaped Beam Back-Projection

The Linear Back Projection algorithm (LBP) is computationally straight forward to implement, and is a popular method for image reconstruction. Sensitivity maps, which were derived for the individual sensors are used by the LBP algorithm to calculate concentration profiles from measured sensor values. The process of obtaining concentration profile using

0 0

*V xy S M xy* 

where *VLBP(x,y)* is the voltage distribution on the concentration profile matrix, *STx,Rx* is the

*m n LBP Tx Rx Tx Rx Tx Rx*

sensor loss value, and , *RxTx yxM* ),( is the normalized sensitivity matrices.

(,) (,)

, ,

(5)

= the angular distance between projection, and the

**Back-Projection**

*y*

*<sup>j</sup>* =

*x*

where *fb* (*x, y*) = the function of reconstructed image from the back-projection algorithm,

*x*

the *j-*th projection angle, and Δ

*p*

summation extends over all the *m-projection.* 

**Projection**

Fig. 14. The fan-shaped beam back-projection

LBP can be expressed mathematically as in Equation 5.

**4.3.1 Linear back projection algorithm** 

Fig. 13. The back-projection method

*y*

The tomogram reconstruction on three phantoms of a small gas hold-up, a large gas holdup, and a dual gas hold-up are shown in Figure 15, 16, and 17 respectively. The results showed several tomograms reconstructed using; (a) LBP, and (b) LBP with a threshold ratio of 0.55.

Fig. 15. Small gas hold-up

(a) LBP (b) LBP (with threshold ratio 0.55)

Fig. 16. Large gas hold-up

(a) LBP (b) LBP (with threshold ratio 0.55)

Design and Development of Ultrasonic Process Tomography 225

Authors are grateful to the financial support by Ministry of Higher Education Malaysia, Research University Grant from Universiti Teknologi Malaysia (Grant No.

Asher, R. C. (1983). Ultrasonic Sensors in the Chemical, and Process Industries. *Journal* 

Broring, S., Fischer, J., Korte, T., Sollinger, S., & Lubbert, A. (1991). Flow Structure of The

Garcia-Stewart, C. A., Polydorides, N., Ozanyan, K. B. & McCann, H. (2003). Image

Kannath, A. & Dewhurst, R. J. (2004). Real-Time Measurement of Acoustic Field

Kytomaa, H. K. & Corrington, S. W. (1994). Ultrasonic Imaging Velocimetry of Transient

Moore, P. I., Brown, G. J. & Stimpson, B. P. (2000). Ultrasonic Transit-Time Flowmeters

Rahim, R. A., Rahiman, M. H. F., Zain, R. M., & Rahim, H. A. (2011). Image Fusion of Dual-

Rahiman, M. H. F., Rahim, R. A., & Ayob, N. M. N. (2010). The Front-End Hardware

Rahiman, M. H. F., Rahim, R. A., & Zakaria, Z. (2008). Design, and Modelling of Ultrasonic

Rashidi, M. (1997). Fluorescence Imaging Techniques: Application to Measuring Flow, and

Sanderson, M.L. & Yeung, H. (2002). Guidelines for the Use of Ultrasonic Non-invasive Metering Technique. *Flow Measurement, and Instrumentation*. Vol. 13, Pp. 125-142 Warsito, W., Ohkawa, M., Kawata, N., & Uchida, S. (1999). Cross-Sectional Distributions of

Computed Tomography. *Chemical Engineering Science*. Vol. 54, Pp. 4711-4728

*Actuators: A. Physical*. Vol. 147, Issue 2, Pp. 409-414

Dispersed Gas-phase in Real Multiphase Chemical Reactor-Investigated by A New Ultrasound-Doppler Technique. *Canadian Journal of Chemical Engineering*. Vol. 69,

Reconstruction Algorithms for High-Speed Chemical Species Tomography. *Proceedings 3rd World Congress on Industrial Process Tomography*. Banff, Canada. 80-

Displacements Using Ultrasonic Interferometry. *Measurement Science Technology*.

Liquefaction of Cohesionless Particulaled Media. *International Journal of Multiphase* 

Modelled With Theoretical Velocity Profiles: Methodology. *Measurement Science* 

Modal Tomography (Electrical Capacitance, and Optical) for Solid/Gas Flow. *International Journal of Innovative Computing, Information, and Control*. Vol. 7, No. 9,

Design Issue in Ultrasonic Tomography. *Sensors Journal*. Vol. 10, Issue 7, Pp. 1276-

Tomography for Two Component High Acoustic Impedance Mixture. *Sensors &* 

Transport in Refractive Index-Matched Porous Media. *Chemical Engineering* 

Gas, and Solid Holdups in Slurry Bubble Column Investigated by Ultrasonic

**6. Acknowledgment** 

Pp. 1247-1256

Vol. 15, Pp. 59–66

Pp. 5119- 5132

1281

*Flow*. Vol. 20, Pp. 915-926

*Technology*. Vol. 11, Pp. 1802–1811

*Technology*. Vol. 21, Pp. 7-18

**7. References** 

85

Q.J130000.7123.00J04), and Universiti Malaysia Perlis.

*Science Instrument Physics*. Vol. 16, Pp. 959-963

The tomogram in (a) showed that the LBP smears out, and introduces false images elsewhere. As seen in Figure 15(a), 16(a), and 17(a) the reconstructed images clearly contain qualitative information about the gas hold-up, but it is hard to distinguish the gas hold-up boundaries. However, the tomograms in Figure 15(a), 16(a), and 17(a) showed that the area of high gas concentration is clearly visible, and could be distinguished from the background image, and the shapes of the reconstructed images are reasonably accurate.

A thresholding technique has been used. To obtain the optimal threshold ratio, a further analysis has to be conducted by measuring the lowest error corresponds to the threshold ratio. By thresholding the image with a ratio of 0.55, the reconstructed images have tremendously improved. The smearing effects by back projection technique, which had caused non-uniformity of background image has been eliminated, and this is shown in Figure 15(b), 16(b), and 17(b). As a result, the information of liquid, and gas such as position, and shape could be easily obtained.

(a) LBP (b) LBP (with threshold ratio 0.55)

Fig. 17. Dual gas hold-up

## **5. Conclusions**

The ultrasonic process tomography has been designed, and developed. The results show that the system could be used to identify, and locate the size, and position of gas bubbles in the measurement column. Experiments showed that, the image reconstructed by LBP results in blurring the image. This blurry image is due to the nature of back projection technique. However, the blurry image can be reduced by applying a thresholding technique. Hence, a clearly visible gas hold-up can be identified. This information is useful, and could be used for measuring the liquid/gas concentrations.

## **6. Acknowledgment**

Authors are grateful to the financial support by Ministry of Higher Education Malaysia, Research University Grant from Universiti Teknologi Malaysia (Grant No. Q.J130000.7123.00J04), and Universiti Malaysia Perlis.

## **7. References**

224 Ultrasonic Waves

The tomogram in (a) showed that the LBP smears out, and introduces false images elsewhere. As seen in Figure 15(a), 16(a), and 17(a) the reconstructed images clearly contain qualitative information about the gas hold-up, but it is hard to distinguish the gas hold-up boundaries. However, the tomograms in Figure 15(a), 16(a), and 17(a) showed that the area of high gas concentration is clearly visible, and could be distinguished from the background

A thresholding technique has been used. To obtain the optimal threshold ratio, a further analysis has to be conducted by measuring the lowest error corresponds to the threshold ratio. By thresholding the image with a ratio of 0.55, the reconstructed images have tremendously improved. The smearing effects by back projection technique, which had caused non-uniformity of background image has been eliminated, and this is shown in Figure 15(b), 16(b), and 17(b). As a result, the information of liquid, and gas such as position,

(a) LBP (b) LBP (with threshold ratio 0.55)

The ultrasonic process tomography has been designed, and developed. The results show that the system could be used to identify, and locate the size, and position of gas bubbles in the measurement column. Experiments showed that, the image reconstructed by LBP results in blurring the image. This blurry image is due to the nature of back projection technique. However, the blurry image can be reduced by applying a thresholding technique. Hence, a clearly visible gas hold-up can be identified. This information is useful, and could be used

image, and the shapes of the reconstructed images are reasonably accurate.

and shape could be easily obtained.

Fig. 17. Dual gas hold-up

for measuring the liquid/gas concentrations.

**5. Conclusions** 


**Suppression of Corrosion Growth** 

*Department of Mechanical Systems Engineering, Faculty of Engineering,* 

Metals are smelted from natural minerals and they tend to return back to their original or stable states including oxides and hydroxides. One of the later processes is corrosion, which occurs from metal surfaces with surrounded air or electrolytes. With the propagation of corrosion, the metal becomes thin as well known as the uniform corrosion of carbon steels, holes appear from the surface such as pitting corrosion of stainless steels, or cracks initiate and propagate from or in the metal like stress corrosion cracking, hydrogen embrittlement or corrosion fatigue. In many cases, cracks initiate from pitting corrosion. Either of the above phenomena leads certainly to the strength loss of metals and accordingly largely shorten the structures' life. Before carrying out a maintenance of metallic structures, the ultrasound is frequently used to investigate the degradation level of the structures by comparing the emitted and the reflected waves. Many researches and applications have been carried out on

On the other hand, in comparison with the prediction of the residual life and the maintenance of structures, it is much more important to stop or retard the initiation of corrosion; at least the propagation of corrosion should be effectively suppressed to thoroughly prolong the structures' life. This is generally solved by increasing the thickness of the applied steels, using high grade steels containing expensive or rare elements of chromium, nickel and molybdeum, or changing the surroundings of air or electrolytes. In this topic, a new method of using

**2. Corrosion process of stainless steel with formation of corrosion products**  The high corrosion resistance of stainless steels originates from the formation of a passive film on the surface. In general, much oxide and hydroxide of chromium are contained in the passive film. However, the pitting corrosion or the crevice corrosion often occurs when the passive film is locally broken down by the chloride ions in solutions. The researches to retard the pitting initiation and growth have elapsed for near one century since the birth of stainless steel. In general, during the corrosion reaction, the metal surface will be separated into cathode zones and anode zones. On the cathode zones, the reduction reactions occur generally with the transformation of hydrogen ions to hydrogen gas or the transformation of oxygen gas to hydroxide ions, where the loss of metal does not occur. On the anode

ultrasound to suppress the corrosion of stainless steel was introduced.

**1. Introduction** 

this topic.

 **of Stainless Steel by Ultrasound** 

Rongguang Wang

 *Japan* 

*Hiroshima Institute of Technology,* 

Williams, R. A., & Beck, M. S. (1995). Process Tomography-Principles, Techniques, and Applications. Oxford, UK: Butterworth-Heinemann **12** 

## **Suppression of Corrosion Growth of Stainless Steel by Ultrasound**

Rongguang Wang

*Department of Mechanical Systems Engineering, Faculty of Engineering, Hiroshima Institute of Technology, Japan* 

## **1. Introduction**

226 Ultrasonic Waves

Williams, R. A., & Beck, M. S. (1995). Process Tomography-Principles, Techniques, and

Metals are smelted from natural minerals and they tend to return back to their original or stable states including oxides and hydroxides. One of the later processes is corrosion, which occurs from metal surfaces with surrounded air or electrolytes. With the propagation of corrosion, the metal becomes thin as well known as the uniform corrosion of carbon steels, holes appear from the surface such as pitting corrosion of stainless steels, or cracks initiate and propagate from or in the metal like stress corrosion cracking, hydrogen embrittlement or corrosion fatigue. In many cases, cracks initiate from pitting corrosion. Either of the above phenomena leads certainly to the strength loss of metals and accordingly largely shorten the structures' life. Before carrying out a maintenance of metallic structures, the ultrasound is frequently used to investigate the degradation level of the structures by comparing the emitted and the reflected waves. Many researches and applications have been carried out on this topic.

On the other hand, in comparison with the prediction of the residual life and the maintenance of structures, it is much more important to stop or retard the initiation of corrosion; at least the propagation of corrosion should be effectively suppressed to thoroughly prolong the structures' life. This is generally solved by increasing the thickness of the applied steels, using high grade steels containing expensive or rare elements of chromium, nickel and molybdeum, or changing the surroundings of air or electrolytes. In this topic, a new method of using ultrasound to suppress the corrosion of stainless steel was introduced.

## **2. Corrosion process of stainless steel with formation of corrosion products**

The high corrosion resistance of stainless steels originates from the formation of a passive film on the surface. In general, much oxide and hydroxide of chromium are contained in the passive film. However, the pitting corrosion or the crevice corrosion often occurs when the passive film is locally broken down by the chloride ions in solutions. The researches to retard the pitting initiation and growth have elapsed for near one century since the birth of stainless steel. In general, during the corrosion reaction, the metal surface will be separated into cathode zones and anode zones. On the cathode zones, the reduction reactions occur generally with the transformation of hydrogen ions to hydrogen gas or the transformation of oxygen gas to hydroxide ions, where the loss of metal does not occur. On the anode

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 229

concentration of chloride and hydrogen ions in the pit due to the destruction of the crust and the stirring of the solution in the pit by the probe. As a result, re-passivation on the

**3. Promotion or suppression of corrosion of steels by ultrasound (Wang &** 

If there is a simple method to remove the corrosion product covering pits, the growth of pits can be suppressed even for the cheap and low grade stainless steels. Here comes the idea of using ultrasound (US) to achieve this aim. The ultrasound in liquids always induces acoustic cavitation (Chouonpa Binran Henshu Iinkai(CBHI), 1999). In the acoustic cavitation, bubbles generate, grow and collapse due to the extremely increased internal tensile and compressive stress in the liquid. The cavitation power relates to the frequency and the amplitude of ultrasound as well as the type of liquid. It is widely used to clean solid surfaces, disperse powders and accelerate chemical reactions in liquids. The acceleration of chemical reactions is mainly caused by the high internal pressure and high temperature in the cavitation.

It is frequently reported that the erosion or corrosion rate on metal surfaces in specific liquids can be promoted by the acoustic cavitation. Alkire et al studied the passivity of iron in 2 N H2SO4 solution and found that iron became active when a focused ultrasound was applied in the solution (Alkire & Perusich, 1983). Al-Hashem et al investigated the acoustic cavitation corrosion behaviour of cast Ni-Al-Cu alloy in seawater. Both the cathodic and anodic current of the alloy increased by an order of magnitude and the rate of mass loss increased near 186 times under the application of a 20 kHz ultrasound (Al-Hashem et al., 1995). Whillock et al measured the corrosion behaviour of 304L stainless steel in 2 N HNO3

state and the breakdown of passive film was promoted when a 55 kHz and 380 kW/m2 ultrasound was applied with a vibrator-to-specimen distance of 1.1 mm (Whillock & Harvey, 1996). Kwok et al studied the cavitation erosion and corrosion characteristics on various engineering alloys including the grey cast iron, mild steels and stainless steels in 3.5% NaCl solution at 300 K when a 20 kHz ultrasound was applied. They found that corrosion mainly occurred on mild steel and grey cast iron but was negligible on stainless steel. The stainless steel only suffered pure mechanical erosion in the presence of cavitation (Kwok et al., 2000). Whillock et al also investigated the corrosion behaviour of 304L stainless steel in an ultrasonic field with different frequencies, acoustic powers and vibrator-tospecimen distances (Whillock & B.F. Harvey, 1997). At 20 kHz, the corrosion rate increased continuously with the increase in the power, while at the frequency of 40 to 60 kHz, the corrosion rate increased to the maximum and thereafter decreased with the increase in the power. The corrosion rate increased with the decrease in the vibrator-to-specimen distance, high corrosion rate in excess of 800 mm/year were obtained when the distance was 0.1 mm. On the other hand, several papers reported that the corrosion on stainless steel can also be suppressed by the application of ultrasound in chloride containing solutions (Nakayama & Sasa, 1976; Whillock & Harvey, 1996; Wang & Nakasa, 2007; Wang & Kido, 2008; Wang, 2008). Nakayama and Sasa measured the polarization curves of a 304 type stainless steel in 0.1 N NaCl solution when applying a 200 kHz and 38-46 kW/m2 ultrasound with a vibratorto-specimen distance of 60 mm (Nakayama & Sasa, 1976). They found that the critical pitting potential became noble in the applied ultrasound field. Whillock et al found that ultrasound

at 323 K. The corrosion rate increased in the active

inner surface of the pit easily occurred and the corrosion almost stopped.

**Kido, 2009)** 

solution containing a small amount of Cl-

zones, the oxidization reactions occur with the transformation of metals to metallic ions into the solution, which means the loss of metal. The total reaction on the anode zones is equal to that on the cathode ones. When either of the anode or the cathode reaction was suppressed, the corrosion propagation should be slowed down. In the pitting corrosion, the area of cathode zones is much larger than the anode ones, which results in that even small cathode reaction rate can induce deep pit formation.

The main characteristic of pitting corrosion is that the thickness of the steel almost does not verify, while in some places holes form from the surface and sometimes penetrate the whole steel. The formation of the holes (hereinafter called as pits) includes the initiation stage and the growth stage. It is very important to suppress both the initiation and the growth of stainless steels to prolong the life of machines and structures. The stainless steel generally contains chromium and nickel with the balance of iron. The widely used typical austenite stainless steel is the type 18-8 steel (also being called as SUS304 steel or Type 304 steel), where 18mass% Cr and 8% Ni were contained with a little of carbon less than 0.08%. In the initiation of pitting corrosion of stainless steel, the Cl ions generally concentrate to weak sites of the passive film, under which always impurities such as MnS, MnO, Al2O3, TiO2 and others exist (Ryan et al., 2002; Shimizu, 2010a, 2010b; Yashiro & Shimizu, 2010). In comparison to other zones with good state of passive film, the potential of such weak sites is somewhat lower, which promotes to form micro cells where the weak sites act as the anodes and other wide zones become the cathodes. This induces the acceleration of anode reaction at such weak sites, where pits initiate. The pit growth is always accompanied by the corrosion product of oxides and hydroxides of metals covering the pit, which accelerates the pit growth by promoting the accumulation of hydrogen and chloride ions into the pits, i.e., excessive hydrogen ions are produced in the pit with the hydrolysis reaction and the chloride ions migrate from outside to neutralize the excessive positive charges (Hisamatsu, 1981).

Fig. 1. Corrosion products on Type 304 stainless steel in 3.5% NaCl solution, in-situ observed by atomic force microscopy. Copyright 2005 Elsevier

The corrosion product on Type 304 steel in 3.5 mass% NaCl solution during the pitting corrosion was in-situ observed at room temperature by atomic force microscopy (AFM), as shown in Fig.1 (Zhang et al., 2005). A corrosion product crust covered perfectly a small pit at its initiation stage. Part of the corrosion product was then removed by the scanning probe of AFM (Fig.1 (a)). After the break of the corrosion product crust, the pit did not grow more. Fig.1 (b-d) shows several irregular pits formed near chromium carbides. With the increase in the corrosion time, a corrosion product and a small elliptical pit with corrosion product around it were observed (b, c). Almost all the corrosion products were removed by the probe of AFM and two small pits clearly appeared there (d). After then, their shapes did not change anymore. The retardation of pit growth is explained by the decrease in the

zones, the oxidization reactions occur with the transformation of metals to metallic ions into the solution, which means the loss of metal. The total reaction on the anode zones is equal to that on the cathode ones. When either of the anode or the cathode reaction was suppressed, the corrosion propagation should be slowed down. In the pitting corrosion, the area of cathode zones is much larger than the anode ones, which results in that even small cathode

The main characteristic of pitting corrosion is that the thickness of the steel almost does not verify, while in some places holes form from the surface and sometimes penetrate the whole steel. The formation of the holes (hereinafter called as pits) includes the initiation stage and the growth stage. It is very important to suppress both the initiation and the growth of stainless steels to prolong the life of machines and structures. The stainless steel generally contains chromium and nickel with the balance of iron. The widely used typical austenite stainless steel is the type 18-8 steel (also being called as SUS304 steel or Type 304 steel), where 18mass% Cr and 8% Ni were contained with a little of carbon less than 0.08%. In the initiation of pitting

under which always impurities such as MnS, MnO, Al2O3, TiO2 and others exist (Ryan et al., 2002; Shimizu, 2010a, 2010b; Yashiro & Shimizu, 2010). In comparison to other zones with good state of passive film, the potential of such weak sites is somewhat lower, which promotes to form micro cells where the weak sites act as the anodes and other wide zones become the cathodes. This induces the acceleration of anode reaction at such weak sites, where pits initiate. The pit growth is always accompanied by the corrosion product of oxides and hydroxides of metals covering the pit, which accelerates the pit growth by promoting the accumulation of hydrogen and chloride ions into the pits, i.e., excessive hydrogen ions are produced in the pit with the hydrolysis reaction and the chloride ions migrate from outside to neutralize the

Fig. 1. Corrosion products on Type 304 stainless steel in 3.5% NaCl solution, in-situ

The corrosion product on Type 304 steel in 3.5 mass% NaCl solution during the pitting corrosion was in-situ observed at room temperature by atomic force microscopy (AFM), as shown in Fig.1 (Zhang et al., 2005). A corrosion product crust covered perfectly a small pit at its initiation stage. Part of the corrosion product was then removed by the scanning probe of AFM (Fig.1 (a)). After the break of the corrosion product crust, the pit did not grow more. Fig.1 (b-d) shows several irregular pits formed near chromium carbides. With the increase in the corrosion time, a corrosion product and a small elliptical pit with corrosion product around it were observed (b, c). Almost all the corrosion products were removed by the probe of AFM and two small pits clearly appeared there (d). After then, their shapes did not change anymore. The retardation of pit growth is explained by the decrease in the

observed by atomic force microscopy. Copyright 2005 Elsevier

ions generally concentrate to weak sites of the passive film,

reaction rate can induce deep pit formation.

corrosion of stainless steel, the Cl-

excessive positive charges (Hisamatsu, 1981).

concentration of chloride and hydrogen ions in the pit due to the destruction of the crust and the stirring of the solution in the pit by the probe. As a result, re-passivation on the inner surface of the pit easily occurred and the corrosion almost stopped.

## **3. Promotion or suppression of corrosion of steels by ultrasound (Wang & Kido, 2009)**

If there is a simple method to remove the corrosion product covering pits, the growth of pits can be suppressed even for the cheap and low grade stainless steels. Here comes the idea of using ultrasound (US) to achieve this aim. The ultrasound in liquids always induces acoustic cavitation (Chouonpa Binran Henshu Iinkai(CBHI), 1999). In the acoustic cavitation, bubbles generate, grow and collapse due to the extremely increased internal tensile and compressive stress in the liquid. The cavitation power relates to the frequency and the amplitude of ultrasound as well as the type of liquid. It is widely used to clean solid surfaces, disperse powders and accelerate chemical reactions in liquids. The acceleration of chemical reactions is mainly caused by the high internal pressure and high temperature in the cavitation.

It is frequently reported that the erosion or corrosion rate on metal surfaces in specific liquids can be promoted by the acoustic cavitation. Alkire et al studied the passivity of iron in 2 N H2SO4 solution and found that iron became active when a focused ultrasound was applied in the solution (Alkire & Perusich, 1983). Al-Hashem et al investigated the acoustic cavitation corrosion behaviour of cast Ni-Al-Cu alloy in seawater. Both the cathodic and anodic current of the alloy increased by an order of magnitude and the rate of mass loss increased near 186 times under the application of a 20 kHz ultrasound (Al-Hashem et al., 1995). Whillock et al measured the corrosion behaviour of 304L stainless steel in 2 N HNO3 solution containing a small amount of Cl at 323 K. The corrosion rate increased in the active state and the breakdown of passive film was promoted when a 55 kHz and 380 kW/m2 ultrasound was applied with a vibrator-to-specimen distance of 1.1 mm (Whillock & Harvey, 1996). Kwok et al studied the cavitation erosion and corrosion characteristics on various engineering alloys including the grey cast iron, mild steels and stainless steels in 3.5% NaCl solution at 300 K when a 20 kHz ultrasound was applied. They found that corrosion mainly occurred on mild steel and grey cast iron but was negligible on stainless steel. The stainless steel only suffered pure mechanical erosion in the presence of cavitation (Kwok et al., 2000). Whillock et al also investigated the corrosion behaviour of 304L stainless steel in an ultrasonic field with different frequencies, acoustic powers and vibrator-tospecimen distances (Whillock & B.F. Harvey, 1997). At 20 kHz, the corrosion rate increased continuously with the increase in the power, while at the frequency of 40 to 60 kHz, the corrosion rate increased to the maximum and thereafter decreased with the increase in the power. The corrosion rate increased with the decrease in the vibrator-to-specimen distance, high corrosion rate in excess of 800 mm/year were obtained when the distance was 0.1 mm.

On the other hand, several papers reported that the corrosion on stainless steel can also be suppressed by the application of ultrasound in chloride containing solutions (Nakayama & Sasa, 1976; Whillock & Harvey, 1996; Wang & Nakasa, 2007; Wang & Kido, 2008; Wang, 2008). Nakayama and Sasa measured the polarization curves of a 304 type stainless steel in 0.1 N NaCl solution when applying a 200 kHz and 38-46 kW/m2 ultrasound with a vibratorto-specimen distance of 60 mm (Nakayama & Sasa, 1976). They found that the critical pitting potential became noble in the applied ultrasound field. Whillock et al found that ultrasound

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 231

Fig. 2. (a) Polarization apparatus and (b) timing of ultrasound. Copyright 2008 Elsevier

corresponding to the smaller electric charge.

The influence of ultrasound on the corrosion behaviour was observed mainly in the pitting zone. Fig.3 (a) shows parts of the polarization curves from *i*h = 20 A/m2, where the vertical axis is shown in a normal decimal scale. It is clear that the current density in condition A is much higher than those in conditions B and C. This means that the pitting growth can be largely suppressed by applying ultrasound in solution. On the other hand, no large difference can be found in conditions B and C, which means that ultrasound is only effective after corrosion has occurred. Fig.3 (b) shows the typical surface morphologies of specimens after polarization and the electric charge calculated by the integration of the current density during the 600 s holding of potential after the current density reached *i*h = 20 A/m2. The area of pits was measured from enlarged photos. The electric charge means the dissolution amount of metal ions into solution. Fewer pits were found on the surface with ultrasound,

Fig. 3. (a) Change of anodic current density from *i*h = 20 A/m2, and (b) electric charges for

The mechanism is schematically shown in Fig.4. When the ultrasound is not applied, pits grow on the specimen surface (a) and corrosion product covers the pit (b) (Wranglen, 1985; Zhang et al., 2005). The growth of pit is accelerated due to the hydrogen ions produced by hydrolysis reaction and the chloride ions attracted from solution (c) (Wranglen, 1985). When the ultrasound is applied to the specimen surface, the corrosion product is removed by the

the 600 s holding from *i*h = 20 A/m2. Copyright 2008 Elsevier

can encourage the passivation of 304L stainless steel in 2 N HNO3 containing small amounts of Cl- (Whillock & Harvey, 1996). Wang et al investigated the detail of the suppression effect of ultrasound on stainless steel in chloride solution (Wang & Nakasa, 2007; Wang & Kido, 2008; Wang, 2008; Wang & Kido, 2009; Wang, 2011).

The above conflicted influences of ultrasound on the corrosion behaviour of metals should be caused by (1) the type of metal, (2) the type of solution, (3) the acoustic power (frequency and amplitude) of ultrasound and (4) the ultrasound vibrator-metal distance. Especially, for stainless steels pitting corrosion and crevice corrosion usually occur when the passive film is locally broken down in chloride containing solutions. When the acoustic cavitation is strong enough, the passive film can be damaged and thus corrosion is activated. However, when the acoustic cavitation is not strong enough to damage the passive film the corrosion will not be accelerated. The suppression effect of acoustic cavitation on the pitting corrosion of stainless steel should be similar with that of the scanning of AFM probe in (a) the removal of the corrosion products (including the removal of the metallic cover under relatively larger power of ultrasound) and (b) the stirring of the solution in the pits. Of course, both of the removal and the stirring effects finally depend on a suitable power of the acoustic cavitation.

## **4. Suppression of pitting corrosion on stainless steel by ultrasound (Wang, 2008)**

A trial was carried out to use ultrasound to remove the corrosion products covering pits, and the growth of pitting corrosion on Type 304 stainless steel was investigated in 3.5% NaCl solutions at 308 K. Pitting corrosion tests were carried out by using a corrosion cell attached with potentiostat apparatus (Hokuto Denko. Co., HAB-151) and an ultrasound cleaner (Yamato Co., Branson 2510J-MTH, 100 W, 42 kHz) as shown in Fig.2 (a). The counter electrode was platinum and the reference electrode was saturated calomel electrode (S.C.E.). The polarization was started from the cathode side (*E* S.C.E.= –600 mV) to the anode side at a constant potential increasing rate of 50 mV/min under the control of the potentiostat. With the linear increase in potential, the current changes from the cathode and passive zone to the pitting zone where the current density largely increases with a small increase in potential (Fig.2 (b)). When the anodic current density reached a value of *i*h = 20 A/m2 in the pitting zone, the potential was immediately held constant for 600 s. In this way, the deviation of current density caused by different pitting potentials on different surfaces will be small. The ultrasound (nominate intensity: 3 kW/m2) was applied in 3 types of conditions, i.e., (i) without ultrasound (hereinafter called as condition A); (ii) applying ultrasound simultaneously with the holding of potential (condition B); (iii) applying ultrasound from the beginning to the end of the polarization (condition C). The potential corresponding to the above constant current density was kept for 600 s in all conditions.

For the polarization curves in conditions A, B and C, the current density changes from the cathode to the anode near the potential *E* = -150 mV irrespective of the application of ultrasound. No significant difference was found in the corrosion potential and in the current density in the cathode zone and the anodic passive zone. This indicates that the ultrasound is not strong enough to break the passive film down, or the partially broken passive film can be easily self-repaired.

can encourage the passivation of 304L stainless steel in 2 N HNO3 containing small amounts of Cl- (Whillock & Harvey, 1996). Wang et al investigated the detail of the suppression effect of ultrasound on stainless steel in chloride solution (Wang & Nakasa, 2007; Wang & Kido,

The above conflicted influences of ultrasound on the corrosion behaviour of metals should be caused by (1) the type of metal, (2) the type of solution, (3) the acoustic power (frequency and amplitude) of ultrasound and (4) the ultrasound vibrator-metal distance. Especially, for stainless steels pitting corrosion and crevice corrosion usually occur when the passive film is locally broken down in chloride containing solutions. When the acoustic cavitation is strong enough, the passive film can be damaged and thus corrosion is activated. However, when the acoustic cavitation is not strong enough to damage the passive film the corrosion will not be accelerated. The suppression effect of acoustic cavitation on the pitting corrosion of stainless steel should be similar with that of the scanning of AFM probe in (a) the removal of the corrosion products (including the removal of the metallic cover under relatively larger power of ultrasound) and (b) the stirring of the solution in the pits. Of course, both of the removal and the stirring effects finally depend on a suitable power of the acoustic cavitation.

**4. Suppression of pitting corrosion on stainless steel by ultrasound (Wang,** 

A trial was carried out to use ultrasound to remove the corrosion products covering pits, and the growth of pitting corrosion on Type 304 stainless steel was investigated in 3.5% NaCl solutions at 308 K. Pitting corrosion tests were carried out by using a corrosion cell attached with potentiostat apparatus (Hokuto Denko. Co., HAB-151) and an ultrasound cleaner (Yamato Co., Branson 2510J-MTH, 100 W, 42 kHz) as shown in Fig.2 (a). The counter electrode was platinum and the reference electrode was saturated calomel electrode (S.C.E.). The polarization was started from the cathode side (*E* S.C.E.= –600 mV) to the anode side at a constant potential increasing rate of 50 mV/min under the control of the potentiostat. With the linear increase in potential, the current changes from the cathode and passive zone to the pitting zone where the current density largely increases with a small increase in potential (Fig.2 (b)). When the anodic current density reached a value of *i*h = 20 A/m2 in the pitting zone, the potential was immediately held constant for 600 s. In this way, the deviation of current density caused by different pitting potentials on different surfaces will be small. The ultrasound (nominate intensity: 3 kW/m2) was applied in 3 types of conditions, i.e., (i) without ultrasound (hereinafter called as condition A); (ii) applying ultrasound simultaneously with the holding of potential (condition B); (iii) applying ultrasound from the beginning to the end of the polarization (condition C). The potential corresponding to

For the polarization curves in conditions A, B and C, the current density changes from the cathode to the anode near the potential *E* = -150 mV irrespective of the application of ultrasound. No significant difference was found in the corrosion potential and in the current density in the cathode zone and the anodic passive zone. This indicates that the ultrasound is not strong enough to break the passive film down, or the partially broken passive film can

the above constant current density was kept for 600 s in all conditions.

2008; Wang, 2008; Wang & Kido, 2009; Wang, 2011).

**2008)** 

be easily self-repaired.

Fig. 2. (a) Polarization apparatus and (b) timing of ultrasound. Copyright 2008 Elsevier

The influence of ultrasound on the corrosion behaviour was observed mainly in the pitting zone. Fig.3 (a) shows parts of the polarization curves from *i*h = 20 A/m2, where the vertical axis is shown in a normal decimal scale. It is clear that the current density in condition A is much higher than those in conditions B and C. This means that the pitting growth can be largely suppressed by applying ultrasound in solution. On the other hand, no large difference can be found in conditions B and C, which means that ultrasound is only effective after corrosion has occurred. Fig.3 (b) shows the typical surface morphologies of specimens after polarization and the electric charge calculated by the integration of the current density during the 600 s holding of potential after the current density reached *i*h = 20 A/m2. The area of pits was measured from enlarged photos. The electric charge means the dissolution amount of metal ions into solution. Fewer pits were found on the surface with ultrasound, corresponding to the smaller electric charge.

Fig. 3. (a) Change of anodic current density from *i*h = 20 A/m2, and (b) electric charges for the 600 s holding from *i*h = 20 A/m2. Copyright 2008 Elsevier

The mechanism is schematically shown in Fig.4. When the ultrasound is not applied, pits grow on the specimen surface (a) and corrosion product covers the pit (b) (Wranglen, 1985; Zhang et al., 2005). The growth of pit is accelerated due to the hydrogen ions produced by hydrolysis reaction and the chloride ions attracted from solution (c) (Wranglen, 1985). When the ultrasound is applied to the specimen surface, the corrosion product is removed by the

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 233

ultrasound, the broken line (b) shows the result when ultrasound was stopped after △*t*u = 0.6 ks but the potential was continuously kept constantly for further △*t*h = 0.3 ks, the dotted line (c) shows the result with ultrasound during the overall potential holding period (△*t*h = 1.2 ks). In the case of (a), the current density largely increased near *t* = 0.9~1.1 ks (*E* = 470~530 mV) after the passive zone. After the polarization, no pitting corrosion can be observed and only crevice corrosion appeared (see Fig.7), i.e., the increase in the current density means the happening of crevice corrosion. The potential was about *E*h = 488~570 mV at the moment of the crevice corrosion current density *i*h = 10 A/m2. During this period, the current density continued to rise slowly and finally kept almost stable at a value of about 200 A/m2. In the case of (b), the current density almost kept stable at the level of about 40 A/m2. This low and stable current density should be attributed to the dilution of the enriched Cl- and H+ in the crevice caused by the stirring effect of ultrasound. When the ultrasound was stopped after 0.6 ks, the current density increased. It will be due to the re-enrichment of Cl- and H+ because the disappearance of ultrasound. However, in the case of (c), the current density

Fig. 5. (a-c) Specimen with crevice and (d) apparatus for polarization test. Copyright 2008

Fig. 6. Polarization curves without ultrasound (a), with ultrasound (b) *i*h = *i*u = 10 A/m2 , △*t*<sup>h</sup> = 0.9 ks, △*t*u = 0.6 ks, and with ultrasound (c) *i*h = *i*u = 10 A/m2 , △*t*h = 1.2 ks, △*t*u = 1.2 ks.

Fig.7 shows the steel surface between crevices of (i) steel / steel and (ii) steel / washer (titanium) after the polarization. Crevice corrosion clearly appeared in any case. The difference between (a) and (b) is not remarkable probably because the applied period of

ultrasound was short in (b), however, the corrosion area in (c) is clearly small.

kept stable at a low level.

The Japan Institute of Metals

Copyright 2008 The Japan Institute of Metals

cavitation of ultrasound (b'). The concentration of corrosive hydrogen ions and chloride ions decreases due to the stirring effect of cavitation, and the growth rate of pits decreases (c').

Fig. 4. Decrease in growth of corrosion pits by ultrasound. Copyright 2007 The Japan Institute of Metals

## **5. Suppression of crevice corrosion on stainless steel by ultrasound (Wang & Kido, 2008)**

The mechanism of crevice corrosion is similar with pitting corrosion. In this section, the influence of ultrasound on the crevice corrosion will be introduced. Type 304 specimens were polished with the # 600 emery paper on both sides and then assembled by the following JIS G0592 standard (Japanese Industrial Standards Committee (JISC), 2002) to produce a crevice between the twice polished surfaces. The crevice was wetted by the 3.5% NaCl solution and tightened hardly by titanium nuts and washers to form the artificial crevices. Of course, there were also two small crevices between steel / washer. The corrosion test was carried out in a corrosion cell connected to a potentiostat (Hokuto Denko Co.; HAB-151) and an ultrasound cleaner (Yamato Co., Branson 2510J-MTH; 100 W, 42 kHz), as is shown in Fig.5. Hereinafter, *i*h and *i*u mean the current density when the potential was held constantly and the current density when the ultrasound was triggered, respectively. Δ*t*<sup>h</sup> and Δ*t*u mean the period for holding the potential constantly and the period for applying ultrasound, respectively.

Fig. 6 shows the change of the current density when the current density reached *i*h = 10 A/m2 and the potential at that moment was held for △*t*h = 0.9~1.2 ks. The arrow (⇒) shows the period for the application of ultrasound. The solid line (a) shows the result without

cavitation of ultrasound (b'). The concentration of corrosive hydrogen ions and chloride ions decreases due to the stirring effect of cavitation, and the growth rate of pits decreases (c').

Fig. 4. Decrease in growth of corrosion pits by ultrasound. Copyright 2007 The Japan

**5. Suppression of crevice corrosion on stainless steel by ultrasound (Wang &** 

The mechanism of crevice corrosion is similar with pitting corrosion. In this section, the influence of ultrasound on the crevice corrosion will be introduced. Type 304 specimens were polished with the # 600 emery paper on both sides and then assembled by the following JIS G0592 standard (Japanese Industrial Standards Committee (JISC), 2002) to produce a crevice between the twice polished surfaces. The crevice was wetted by the 3.5% NaCl solution and tightened hardly by titanium nuts and washers to form the artificial crevices. Of course, there were also two small crevices between steel / washer. The corrosion test was carried out in a corrosion cell connected to a potentiostat (Hokuto Denko Co.; HAB-151) and an ultrasound cleaner (Yamato Co., Branson 2510J-MTH; 100 W, 42 kHz), as is shown in Fig.5. Hereinafter, *i*h and *i*u mean the current density when the potential was held constantly and the current density when the ultrasound was triggered, respectively. Δ*t*<sup>h</sup> and Δ*t*u mean the period for holding the potential constantly and the period for applying

Fig. 6 shows the change of the current density when the current density reached *i*h = 10 A/m2 and the potential at that moment was held for △*t*h = 0.9~1.2 ks. The arrow (⇒) shows the period for the application of ultrasound. The solid line (a) shows the result without

Institute of Metals

ultrasound, respectively.

**Kido, 2008)** 

ultrasound, the broken line (b) shows the result when ultrasound was stopped after △*t*u = 0.6 ks but the potential was continuously kept constantly for further △*t*h = 0.3 ks, the dotted line (c) shows the result with ultrasound during the overall potential holding period (△*t*h = 1.2 ks). In the case of (a), the current density largely increased near *t* = 0.9~1.1 ks (*E* = 470~530 mV) after the passive zone. After the polarization, no pitting corrosion can be observed and only crevice corrosion appeared (see Fig.7), i.e., the increase in the current density means the happening of crevice corrosion. The potential was about *E*h = 488~570 mV at the moment of the crevice corrosion current density *i*h = 10 A/m2. During this period, the current density continued to rise slowly and finally kept almost stable at a value of about 200 A/m2. In the case of (b), the current density almost kept stable at the level of about 40 A/m2. This low and stable current density should be attributed to the dilution of the enriched Cl- and H+ in the crevice caused by the stirring effect of ultrasound. When the ultrasound was stopped after 0.6 ks, the current density increased. It will be due to the re-enrichment of Cl and H+ because the disappearance of ultrasound. However, in the case of (c), the current density kept stable at a low level.

Fig. 5. (a-c) Specimen with crevice and (d) apparatus for polarization test. Copyright 2008 The Japan Institute of Metals

Fig. 6. Polarization curves without ultrasound (a), with ultrasound (b) *i*h = *i*u = 10 A/m2 , △*t*<sup>h</sup> = 0.9 ks, △*t*u = 0.6 ks, and with ultrasound (c) *i*h = *i*u = 10 A/m2 , △*t*h = 1.2 ks, △*t*u = 1.2 ks. Copyright 2008 The Japan Institute of Metals

Fig.7 shows the steel surface between crevices of (i) steel / steel and (ii) steel / washer (titanium) after the polarization. Crevice corrosion clearly appeared in any case. The difference between (a) and (b) is not remarkable probably because the applied period of ultrasound was short in (b), however, the corrosion area in (c) is clearly small.

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 235

Fig. 9 (a) shows the change of current density for another type of crevice spcimen, where only one side of the specimen was polished when the potential was held constantly at *i*h = 10 A/m2. On this specimen, both pitting corrosion (on the not polished side) and crevice corrosion occurred. After the current density reached *i*u = 120 A/m2 the ultrasound was applied for 60 s and then stopped for 60 s. Such ultrasound application / stop repeated for 4 cycles. In the first application of ultrasound, the current density largely decreased to about 50 A/m2. It gradually recovered during the 60 s stop state of ultrasound to the previous level before the application of ultrasound. Such change almost synchronized with the cyclic application and stop of ultrasound. Fig.9 (b) shows the change of current density, after the current density reached *i*h = 50 A/m2 and the potential at that moment was kept constant. The ultrasound was applied for 60 s after the current density reached *i*u = 250 A/m2, and then stopped for 270 s. Such ultrasound application was twice cycled. The current density can be largely decreased to about 40 A/m2 during the 60 s application of ultrasound. During the stop of ultrasound for 270 s, the current density gradually increased to the previous level. Almost the same change occurred in the second ultrasound cycle. According to the change of electric charge *q* calculated from Fig.9, either of the happening of pitting corrosion or crevice corrosion, the decrease in the corrosion amount by ultrasound was about 44~55% in comparison with those without ultrasound. Therefore, even if the ultrasound was not continuously applied, an intermittently application for 60 s can bring about large

Fig. 9. Polarization curves of both pitting corrosion and crevice corrosion with ultrasound. (a): *i*h = 10 A/m2 , *i*u = 120 A/m2 , △*t*h = 1.2 ks, △*t*u = 60 s × 4 cycles; ( b): *i*h = 50 A/m2 , *i*u = 250 A/m2 , △*t*h = 1.2 ks, △*t*u = 60 sx2 cylces. Copyright 2008 The Japan Institute of Metals The schematic drawing of decrease in growth of crevice corrosion by application of ultrasound is shown in Fig.10. In the case of without ultrasound, the metallic ions (Mn+) in the crevice will be accumulated by the flow of the passive current before crevice corrosion is triggered, and

attracted from solution out of the crevice to neutralize the excessive plus charge. Thus, the

anodic crevice corrosion and the corrosion is accelerated ((b), (c)). On the one hand, when the

by the stirring effect of ultrasound, which results in the slowing down of the corrosion ((b'), (c')). In some cases, re-passivation of the crevice surface might occur (c). Of course, the promotion of the diffusion of oxygen into the crevice will also decrease the corrosion rate

ions were

ions enriched in the crevice with the

and H+ inside the crevice can be diluted

hydrogen ions increase due to the hydrolysis reaction of Mn+. Furthermore, Cl-

crevice corrosion is induced ((a)). That is, H+ and Cl-

ultrasound was applied, the concentration of Mn+, Cl-

suppression of corrosion.

Fig. 7. Specimen surfaces after polarization without and with ultrasound (*i*h = *i*u= 10 A/m2). Copyright 2008 The Japan Institute of Metals

Fig.8 shows the electric charge *q*, which is integrated with time during the period of potential holding for △*t*h = 0.6 ks, 0.9 ks or 1.2 ks. In the case of △*t*h = 0.6 ks, *q* without ultrasound was about 65 kC/m2, however, it decreased to about 15 kC/m2 when the ultrasound was applied for 0.6 ks. In the case of △*t*h = 1.2 ks, *q* without ultrasound was about 190 kC/m2, it decreased to about 45 kC/m2 when the ultrasound was applied for 1.2 ks. In addition, in the case of △*t*h = 0.9 ks and △*t*u = 0.6 ks, *q* was about 165 kC/m2. In any cases, about 77% of the electric charge decreased due to the application of ultrasound. Of course, the effect of ultrasound would be small if the ultrasound was midway stopped. The corrosion area of crevice corrosion is also shown in the right side of Fig.8 with hatching sticks. The corrosion area changed almost at the same ratio with the electric charge, although the depth of the corrosion zone would be different.

Fig. 8. Electric charge during the holding of potential without and with ultrasound (*i*h = *i*u = 10 A/m2). Copyright 2008 The Japan Institute of Metals

Fig. 7. Specimen surfaces after polarization without and with ultrasound (*i*h = *i*u= 10 A/m2).

Fig.8 shows the electric charge *q*, which is integrated with time during the period of potential holding for △*t*h = 0.6 ks, 0.9 ks or 1.2 ks. In the case of △*t*h = 0.6 ks, *q* without ultrasound was about 65 kC/m2, however, it decreased to about 15 kC/m2 when the ultrasound was applied for 0.6 ks. In the case of △*t*h = 1.2 ks, *q* without ultrasound was about 190 kC/m2, it decreased to about 45 kC/m2 when the ultrasound was applied for 1.2 ks. In addition, in the case of △*t*h = 0.9 ks and △*t*u = 0.6 ks, *q* was about 165 kC/m2. In any cases, about 77% of the electric charge decreased due to the application of ultrasound. Of course, the effect of ultrasound would be small if the ultrasound was midway stopped. The corrosion area of crevice corrosion is also shown in the right side of Fig.8 with hatching sticks. The corrosion area changed almost at the same ratio with the electric charge,

Fig. 8. Electric charge during the holding of potential without and with ultrasound (*i*h = *i*u =

Copyright 2008 The Japan Institute of Metals

although the depth of the corrosion zone would be different.

10 A/m2). Copyright 2008 The Japan Institute of Metals

Fig. 9 (a) shows the change of current density for another type of crevice spcimen, where only one side of the specimen was polished when the potential was held constantly at *i*h = 10 A/m2. On this specimen, both pitting corrosion (on the not polished side) and crevice corrosion occurred. After the current density reached *i*u = 120 A/m2 the ultrasound was applied for 60 s and then stopped for 60 s. Such ultrasound application / stop repeated for 4 cycles. In the first application of ultrasound, the current density largely decreased to about 50 A/m2. It gradually recovered during the 60 s stop state of ultrasound to the previous level before the application of ultrasound. Such change almost synchronized with the cyclic application and stop of ultrasound. Fig.9 (b) shows the change of current density, after the current density reached *i*h = 50 A/m2 and the potential at that moment was kept constant. The ultrasound was applied for 60 s after the current density reached *i*u = 250 A/m2, and then stopped for 270 s. Such ultrasound application was twice cycled. The current density can be largely decreased to about 40 A/m2 during the 60 s application of ultrasound. During the stop of ultrasound for 270 s, the current density gradually increased to the previous level. Almost the same change occurred in the second ultrasound cycle. According to the change of electric charge *q* calculated from Fig.9, either of the happening of pitting corrosion or crevice corrosion, the decrease in the corrosion amount by ultrasound was about 44~55% in comparison with those without ultrasound. Therefore, even if the ultrasound was not continuously applied, an intermittently application for 60 s can bring about large suppression of corrosion.

Fig. 9. Polarization curves of both pitting corrosion and crevice corrosion with ultrasound. (a): *i*h = 10 A/m2 , *i*u = 120 A/m2 , △*t*h = 1.2 ks, △*t*u = 60 s × 4 cycles; ( b): *i*h = 50 A/m2 , *i*u = 250 A/m2 , △*t*h = 1.2 ks, △*t*u = 60 sx2 cylces. Copyright 2008 The Japan Institute of Metals

The schematic drawing of decrease in growth of crevice corrosion by application of ultrasound is shown in Fig.10. In the case of without ultrasound, the metallic ions (Mn+) in the crevice will be accumulated by the flow of the passive current before crevice corrosion is triggered, and hydrogen ions increase due to the hydrolysis reaction of Mn+. Furthermore, Cl ions were attracted from solution out of the crevice to neutralize the excessive plus charge. Thus, the crevice corrosion is induced ((a)). That is, H+ and Cl ions enriched in the crevice with the anodic crevice corrosion and the corrosion is accelerated ((b), (c)). On the one hand, when the ultrasound was applied, the concentration of Mn+, Cl and H+ inside the crevice can be diluted by the stirring effect of ultrasound, which results in the slowing down of the corrosion ((b'), (c')). In some cases, re-passivation of the crevice surface might occur (c). Of course, the promotion of the diffusion of oxygen into the crevice will also decrease the corrosion rate

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 237

The ultrasound was applied in simultaneously with the holding of potential. The distance from the ultrasound vibrator to the specimen surface (*d*) and the input power to vibrator (*I*) were changed as *d* = 76 mm (*I* = 0, 2, 4, 6 and 8) and *I* = 8 (*d* = 19, 39, 76 and 95 mm). Note that the wavelength (*λ*) of the ultrasound in the frequency of 19 kHz is about 76 mm, which was calculated from the speed of sound of 1480 m/s. After the polarization tests, specimen surfaces were observed using an optical microscope and the corrosion areas were

Fig.12 (a) shows the typical change of the current density in the pitting corrosion zone from *i*h = 20 A/m2 during the period of simultaneously holding potential and applying ultrasound. The input power to ultrasound vibrator changed from *I* = 0 to *I* = 8 at a constant distance of *d* = 76 mm. The distance is just equal to the wavelength of ultrasound in the solution. In Fig.12 (a), the anodic current density increased gradually with time during the period of holding potential without the application of ultrasound (*I* = 0), however, the value largely decreased when the ultrasound was applied under each input power to vibrator. No large difference of the current density under *I* = 1, 2 and 4 can be seen, but the current density sharply decreased under *I* = 6. The largest decrease of the current density was obtained when applying ultrasound under *I* = 8 in this work. The smallest value of current density was near 1×10-3 A/m2, meaning the passivation of pits. Fig.12 (b) shows the electric charge obtained from the integrity of the current density during the potential holding. Each value of the electric charge is averaged from at least 3 tests. The value of electric charge was about 22 kC/m2 without ultrasound (*I* = 0), which is smaller than the value obtained in the previous report (Wang, 2008) perhaps because the chemical composition of the specimens in this work is different from those used in the previous work. The electric charge decreased to about 6 ~ 9 kC/m2 when applying ultrasound under *I* = 1, 2 or 4. Large decrease in the electric charge was obtained under *I* = 6 and *I* = 8, especially the electric charge under *I* = 8 was the smallest one in this work (1 kC/m2). Such results gave the detail of the corrosion rate and meaning that the pitting corrosion of Type 304 stainless steel can surely be suppressed by the application of ultrasound in the solution and the suppression effect

become remarkable with the increase in the input power to ultrasound vibrator.

Fig. 12. Pitting current density (a) and accumulated electric charge (b) during the period of simultaneously holding potential and applying ultrasound with different input powers at a

constant distance of 76 mm. Copyright 2009 Elsevier

accordingly measured.

Fig. 10. Schematic drawing of decrease in growth of crevice corrosion by application of ultrasound. Copyright 2008 The Japan Institute of Metals

## **6. Influence of power and distance of ultrasound on pitting corrosion of Type 304 steel (Wang & Kido, 2009)**

In this section, the influence of the transmitted acoustic power of ultrasound on the specimen and the vibrator-to-specimen distance on the pitting corrosion will be introduced. The corrosion tests were carried out in a corrosion cell connected to a potentiostat (Hokuto Denko. Co., HAB-151) and an ultrasound vibrator (Kaijo Co., 4292C; 19.5kHz; 130 mm x 150 mm) (Fig.11). The input power to the ultrasound vibrator can be adjusted by a controller (Kaijo Co., TA-4021) from *I* = 0 to *I* = 10, where the full input power of *I* = 10 to vibrator is 200 W corresponding to a mean input intensity of 10 kW/m2 from the vibrator. The specimen was immersed in 3.5% NaCl aqueous solution in the corrosion cell facing to the ultrasound vibrator and the temperature was tried to be kept stable at 305±2 K by an autoheater (thermostat without cooling function), but the increased temperature in the solution was not further adjusted when ultrasound was applied.

Fig. 11. Apparatus for polarization and applying ultrasound. Copyright 2009 Elsevier

Fig. 10. Schematic drawing of decrease in growth of crevice corrosion by application of

**6. Influence of power and distance of ultrasound on pitting corrosion of Type** 

In this section, the influence of the transmitted acoustic power of ultrasound on the specimen and the vibrator-to-specimen distance on the pitting corrosion will be introduced. The corrosion tests were carried out in a corrosion cell connected to a potentiostat (Hokuto Denko. Co., HAB-151) and an ultrasound vibrator (Kaijo Co., 4292C; 19.5kHz; 130 mm x 150 mm) (Fig.11). The input power to the ultrasound vibrator can be adjusted by a controller (Kaijo Co., TA-4021) from *I* = 0 to *I* = 10, where the full input power of *I* = 10 to vibrator is 200 W corresponding to a mean input intensity of 10 kW/m2 from the vibrator. The specimen was immersed in 3.5% NaCl aqueous solution in the corrosion cell facing to the ultrasound vibrator and the temperature was tried to be kept stable at 305±2 K by an autoheater (thermostat without cooling function), but the increased temperature in the solution

Fig. 11. Apparatus for polarization and applying ultrasound. Copyright 2009 Elsevier

ultrasound. Copyright 2008 The Japan Institute of Metals

was not further adjusted when ultrasound was applied.

**304 steel (Wang & Kido, 2009)** 

The ultrasound was applied in simultaneously with the holding of potential. The distance from the ultrasound vibrator to the specimen surface (*d*) and the input power to vibrator (*I*) were changed as *d* = 76 mm (*I* = 0, 2, 4, 6 and 8) and *I* = 8 (*d* = 19, 39, 76 and 95 mm). Note that the wavelength (*λ*) of the ultrasound in the frequency of 19 kHz is about 76 mm, which was calculated from the speed of sound of 1480 m/s. After the polarization tests, specimen surfaces were observed using an optical microscope and the corrosion areas were accordingly measured.

Fig.12 (a) shows the typical change of the current density in the pitting corrosion zone from *i*h = 20 A/m2 during the period of simultaneously holding potential and applying ultrasound. The input power to ultrasound vibrator changed from *I* = 0 to *I* = 8 at a constant distance of *d* = 76 mm. The distance is just equal to the wavelength of ultrasound in the solution. In Fig.12 (a), the anodic current density increased gradually with time during the period of holding potential without the application of ultrasound (*I* = 0), however, the value largely decreased when the ultrasound was applied under each input power to vibrator. No large difference of the current density under *I* = 1, 2 and 4 can be seen, but the current density sharply decreased under *I* = 6. The largest decrease of the current density was obtained when applying ultrasound under *I* = 8 in this work. The smallest value of current density was near 1×10-3 A/m2, meaning the passivation of pits. Fig.12 (b) shows the electric charge obtained from the integrity of the current density during the potential holding. Each value of the electric charge is averaged from at least 3 tests. The value of electric charge was about 22 kC/m2 without ultrasound (*I* = 0), which is smaller than the value obtained in the previous report (Wang, 2008) perhaps because the chemical composition of the specimens in this work is different from those used in the previous work. The electric charge decreased to about 6 ~ 9 kC/m2 when applying ultrasound under *I* = 1, 2 or 4. Large decrease in the electric charge was obtained under *I* = 6 and *I* = 8, especially the electric charge under *I* = 8 was the smallest one in this work (1 kC/m2). Such results gave the detail of the corrosion rate and meaning that the pitting corrosion of Type 304 stainless steel can surely be suppressed by the application of ultrasound in the solution and the suppression effect become remarkable with the increase in the input power to ultrasound vibrator.

Fig. 12. Pitting current density (a) and accumulated electric charge (b) during the period of simultaneously holding potential and applying ultrasound with different input powers at a constant distance of 76 mm. Copyright 2009 Elsevier

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 239

Fig. 14. Pitting current density (a) and accumulated electric charge (b) during the period of simultaneously holding potential and applying ultrasound with different distances at a

Fig. 15. Surface morphology (a), area ratio of pits (b) and mean depth of pits (c) on specimen surface after simultaneously holding potential and applying ultrasound with different

Although the input power to ultrasound vibrator can be exactly set from the ultrasound controller (see Fig.11), the transmitted power dissipated near the specimen surface was not known. Here, the transmitted acoustic power near the specimen surface was measured by a calorimetry method as follows (CBHI, 1999; Whillock & Harvey, 1996). The temperature of 5 mL pure water contained in a small glass tube (inner diameter φ = 12 mm) was inserted into the water bathe and measured at 10 s intervals by a digital thermometer during the sonication for a period of 120 s (before the application of ultrasound, the power of the auto-

where *m* is the mass of water (unit: kg), *C*p is the heat capacity of water (4180 J/(K・kg)) and d*T*/d*t* is the temperature rise per second during the initial 20 s (K/s), *A* is the cross-sectional area of the glass tube ( about 113 mm2). The result is shown in Fig.16. In Fig.16 (a), at the constant distance of *d* = 76 mm, almost no temperature increase can be detected under the input power of *I* = 1 and *I* = 2 to vibrator, meaning the transmitted power is weak. In the case of *I* = 4 the temperature slowly increased 0.4 K after 120 s, while the increased

<sup>p</sup> *p mC T t A* (d /d ) / (1)

constant input power of *I* = 8 or *I* = 2. Copyright 2009 Elsevier

distances at a constant input power of *I* = 8. Copyright 2009 Elsevier

heater was cut). The absorbed acoustic power density (*p*) was calculated using:

Fig.13 (a) shows the surface morphology of specimens after the polarization tests in Fig.12. The area ratio and the mean depth of pits are shown in Fig.13 (b) and (c). The depth of pits was obtained by focusing on the bottom of pits and the flat specimen surface by moving an optical lens. Pits appeared on each specimen surface after the polarization, but the sum, size and depth gradually decreased with the increase in the input power to ultrasound vibrator. Although the difference of current density under *I* = 1, 2 and 4 was indistinct, in Fig.13 it is known that the pitting corrosion can be suppressed more with the increase in the input power to ultrasound vibrator. The least and smallest pits were found when applying ultrasound under *I* = 8. It means that the initiation and growth of pits were suppressed both in the width and the depth by ultrasound.

Fig. 13. Surface morphology (a), area ratio of pits (b) and mean depth of pits (c) on specimen surface after simultaneously holding potential and applying ultrasound with different input powers at a constant distance of 76 mm ( = *λ)*. Copyright 2009 Elsevier

Fig. 14 (a) shows the pitting current density during the period of simultaneously holding potential and applying ultrasound at different distances under a constant input power of *I* = 8 to vibrator. For each case with the application of ultrasound, the current density decreased by comparing to that without ultrasound. No large difference of the current density can be seen at the distance of *d* = 19 and 38 mm, but the current density at *d* = 76 mm was the smallest one while the current at *d* = 95 mm was the largest one. Fig.14 (b) shows the electric charge during the potential holding under *I* = 2 and 8 at different distances. According to the left part of Fig.14 (b) (averaged results under *I* = 2), by comparing to that at *d* = 19 mm ( = *λ*/4) the current density increased at *d* = 38 mm ( = *λ*/2 ). However, it largely decreased at *d* = 76 mm ( = *λ*). The current is the largest at the distance of *d* = 95 mm ( = 5*λ*/4). In the right side of Fig.14 (b) (averaged results under *I* = 8), almost the same tendency was obtained with that under *I* = 2. Of course, the absolute value under *I* = 8 is much smaller than that under *I* = 2.

Fig. 15 (a) shows the specimen surface after the corrosion test with changing the distance under *I* = 8. Fig.15 (b) and (c) show the area ratio and the mean depth of pits in these cases. It is clear that both the area ratio and the mean depth decreased with the increase of distance from *d* = 19 mm to 76 mm, except the largest value appeared at the distance of *d* = 95 mm. It suggests that the suppression effect of acoustic cavitation on the pitting corrosion depends not only on the distance but also on the transmission phase of the ultrasound wave. Larger suppression effect appears at the vibrator-to-specimen distance equals to the transmission wavelength of ultrasound.

Fig.13 (a) shows the surface morphology of specimens after the polarization tests in Fig.12. The area ratio and the mean depth of pits are shown in Fig.13 (b) and (c). The depth of pits was obtained by focusing on the bottom of pits and the flat specimen surface by moving an optical lens. Pits appeared on each specimen surface after the polarization, but the sum, size and depth gradually decreased with the increase in the input power to ultrasound vibrator. Although the difference of current density under *I* = 1, 2 and 4 was indistinct, in Fig.13 it is known that the pitting corrosion can be suppressed more with the increase in the input power to ultrasound vibrator. The least and smallest pits were found when applying ultrasound under *I* = 8. It means that the initiation and growth of pits were suppressed both

Fig. 13. Surface morphology (a), area ratio of pits (b) and mean depth of pits (c) on specimen surface after simultaneously holding potential and applying ultrasound with different input

Fig. 14 (a) shows the pitting current density during the period of simultaneously holding potential and applying ultrasound at different distances under a constant input power of *I* = 8 to vibrator. For each case with the application of ultrasound, the current density decreased by comparing to that without ultrasound. No large difference of the current density can be seen at the distance of *d* = 19 and 38 mm, but the current density at *d* = 76 mm was the smallest one while the current at *d* = 95 mm was the largest one. Fig.14 (b) shows the electric charge during the potential holding under *I* = 2 and 8 at different distances. According to the left part of Fig.14 (b) (averaged results under *I* = 2), by comparing to that at *d* = 19 mm ( = *λ*/4) the current density increased at *d* = 38 mm ( = *λ*/2 ). However, it largely decreased at *d* = 76 mm ( = *λ*). The current is the largest at the distance of *d* = 95 mm ( = 5*λ*/4). In the right side of Fig.14 (b) (averaged results under *I* = 8), almost the same tendency was obtained with that under *I* = 2. Of course, the absolute value under *I* = 8 is much smaller than that

Fig. 15 (a) shows the specimen surface after the corrosion test with changing the distance under *I* = 8. Fig.15 (b) and (c) show the area ratio and the mean depth of pits in these cases. It is clear that both the area ratio and the mean depth decreased with the increase of distance from *d* = 19 mm to 76 mm, except the largest value appeared at the distance of *d* = 95 mm. It suggests that the suppression effect of acoustic cavitation on the pitting corrosion depends not only on the distance but also on the transmission phase of the ultrasound wave. Larger suppression effect appears at the vibrator-to-specimen distance equals to the transmission

powers at a constant distance of 76 mm ( = *λ)*. Copyright 2009 Elsevier

in the width and the depth by ultrasound.

under *I* = 2.

wavelength of ultrasound.

Fig. 14. Pitting current density (a) and accumulated electric charge (b) during the period of simultaneously holding potential and applying ultrasound with different distances at a constant input power of *I* = 8 or *I* = 2. Copyright 2009 Elsevier

Fig. 15. Surface morphology (a), area ratio of pits (b) and mean depth of pits (c) on specimen surface after simultaneously holding potential and applying ultrasound with different distances at a constant input power of *I* = 8. Copyright 2009 Elsevier

Although the input power to ultrasound vibrator can be exactly set from the ultrasound controller (see Fig.11), the transmitted power dissipated near the specimen surface was not known. Here, the transmitted acoustic power near the specimen surface was measured by a calorimetry method as follows (CBHI, 1999; Whillock & Harvey, 1996). The temperature of 5 mL pure water contained in a small glass tube (inner diameter φ = 12 mm) was inserted into the water bathe and measured at 10 s intervals by a digital thermometer during the sonication for a period of 120 s (before the application of ultrasound, the power of the autoheater was cut). The absorbed acoustic power density (*p*) was calculated using:

$$p = m\mathbb{C}\_p(\text{d}T \mid \text{d}t) / A \tag{1}$$

where *m* is the mass of water (unit: kg), *C*p is the heat capacity of water (4180 J/(K・kg)) and d*T*/d*t* is the temperature rise per second during the initial 20 s (K/s), *A* is the cross-sectional area of the glass tube ( about 113 mm2). The result is shown in Fig.16. In Fig.16 (a), at the constant distance of *d* = 76 mm, almost no temperature increase can be detected under the input power of *I* = 1 and *I* = 2 to vibrator, meaning the transmitted power is weak. In the case of *I* = 4 the temperature slowly increased 0.4 K after 120 s, while the increased

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 241

Table 1. Increased temperature and adsorbed acoustic power density in a 5 mL water when

Fig. 17. Pitting current density during the period of simultaneously holding potential and applying ultrasound with different input powers at distance of *d* = 76 mm and input power

When the acoustic cavitation is not strong enough to damage the passive film, the suppression effect of acoustic cavitation on pitting corrosion will increase with the increase in the stirring effect of solution in pits after removing the corrosion products (or the metallic cover). The suppression effect should be related to (1) the bubbles' size decided by the tensile stress and (2) the collapse power (shock wave power or cavitation power) decided by the compressive stress in the ultrasound field. Both of the stresses are determined by (i) the amplitude and (ii) the phase of the ultrasound wave. The collapse of larger bubbles brings

The removal of corrosion products or metallic covers can be promoted by larger collapse power of the cavitation under larger input power to vibrator and the solution in pits can be completely stirred. This is the reason that the suppression effect on corrosion can be enhanced when increasing the input power to vibrator from *I* = 1 to *I* = 8. However, the stirring of solution in pits after removing corrosion products or metallic covers should depend on both the bubbles' size as well as the collapse power. The schematic drawing is shown in Fig.18. Note that not all the pits are covered by metallic covers (a). Near the specimen, micro-jets to the specimen surface will appear from each collapsing bubble. When the input power to vibrator is small the bubbles' size and the collapse power are small. Part of corrosion products will be cleaned out but no damage occurs on the metallic cover. However, the collapse of bubbles smaller than pits perhaps gives relatively effective stirring effect of solution in pits (b). With the increase in the input power to vibrator (c), the removal

of *I* = 8 in 3.5% NaCl solution containing 0.5% ethanol . Copyright 2009 Elsevier

ultrasound is applied. Copyright 2009 Elsevier

about larger collapse power.

temperatures are respectively 0.8 K and 1.6 K in the case of *I* = 6 and *I* = 8. The above result shows the transmitted power of ultrasound to the specimen surface increases with the increase in the input power to vibrator. In each case of *I* = 4, 6 and 8, the temperature increased sharply at the initial 20 s but the increase became slow after then. This should be due to the happening of heat transfer in the solution during a relatively long period. Fig.16 (b) shows the temperature change under the constant input power of *I* = 8 to vibrator with changing the distance from *d* = 19 to 95 mm. In the case of *d* = 19 mm and *d* = 95 mm, the increase in temperature is almost the same after 120 s. This suggests that the transmitted power depends on the transmission phase of ultrasound wave. In the case of *d* = 38 mm ( = *λ*/2), the temperature almost did not change at the initial 40 s but after then largely increased more than 2.8 K. In the case of *d* = 76 mm, the largest increase of temperature obtained (more than 3.7 K). Note that two different curves of temperature are shown in Fig.16 (a) and (b) at the same condition of *I* = 8 and *d* = 76 mm.

Fig. 16. Temperature change of a 5 mL pure water during the application of ultrasound in different cases. Copyright 2009 Elsevier

Table 1 shows the transmitted power of ultrasound near the specimen surface using the increase in temperature during the initial 20 s by equation 1). Comparing to the results in Fig.12~15, it is clear that the suppression effect on the pitting corrosion increased with the increase in the transmitted power of ultrasound. During a long period measurement, the increased temperature in the solution will also largely influence the corrosion rate. However, this would not change the conclusion of the suppression effect of ultrasound in the input power to the vibrator and the distance. It is clear that the transmitted power depends on both the input power to the vibrator and the ultrasound phase.

Fig.17 shows the change of current density when applying ultrasound in solutions with and without the addition of 0.5% ethanol at the constant distance of *d* = 76 mm under the input power of *I* = 2 and *I* = 8 to vibrator. In the case of *I* = 2, the current density in the ethanoladded solution decreased comparing to that in the ethanol-not-added solution. This means that the enhanced cavitation in this solution enhanced the suppression effect on the pitting corrosion under a weak ultrasound. On the other hand, in the case of *I* = 8, the current in ethanol-added solution became larger and unstable comparing to that in the ethanol-notadded solution. (two curves in the ethanol-not-added solution were shown in Fig.17 (b), including the lowest and highest current in all measurements.) This means that the suppression effect of corrosion with the addition of ethanol decreased under higher input power to ultrasound vibrator.

temperatures are respectively 0.8 K and 1.6 K in the case of *I* = 6 and *I* = 8. The above result shows the transmitted power of ultrasound to the specimen surface increases with the increase in the input power to vibrator. In each case of *I* = 4, 6 and 8, the temperature increased sharply at the initial 20 s but the increase became slow after then. This should be due to the happening of heat transfer in the solution during a relatively long period. Fig.16 (b) shows the temperature change under the constant input power of *I* = 8 to vibrator with changing the distance from *d* = 19 to 95 mm. In the case of *d* = 19 mm and *d* = 95 mm, the increase in temperature is almost the same after 120 s. This suggests that the transmitted power depends on the transmission phase of ultrasound wave. In the case of *d* = 38 mm ( = *λ*/2), the temperature almost did not change at the initial 40 s but after then largely increased more than 2.8 K. In the case of *d* = 76 mm, the largest increase of temperature obtained (more than 3.7 K). Note that two different curves of temperature are shown in

Fig. 16. Temperature change of a 5 mL pure water during the application of ultrasound in

depends on both the input power to the vibrator and the ultrasound phase.

Table 1 shows the transmitted power of ultrasound near the specimen surface using the increase in temperature during the initial 20 s by equation 1). Comparing to the results in Fig.12~15, it is clear that the suppression effect on the pitting corrosion increased with the increase in the transmitted power of ultrasound. During a long period measurement, the increased temperature in the solution will also largely influence the corrosion rate. However, this would not change the conclusion of the suppression effect of ultrasound in the input power to the vibrator and the distance. It is clear that the transmitted power

Fig.17 shows the change of current density when applying ultrasound in solutions with and without the addition of 0.5% ethanol at the constant distance of *d* = 76 mm under the input power of *I* = 2 and *I* = 8 to vibrator. In the case of *I* = 2, the current density in the ethanoladded solution decreased comparing to that in the ethanol-not-added solution. This means that the enhanced cavitation in this solution enhanced the suppression effect on the pitting corrosion under a weak ultrasound. On the other hand, in the case of *I* = 8, the current in ethanol-added solution became larger and unstable comparing to that in the ethanol-notadded solution. (two curves in the ethanol-not-added solution were shown in Fig.17 (b), including the lowest and highest current in all measurements.) This means that the suppression effect of corrosion with the addition of ethanol decreased under higher input

Fig.16 (a) and (b) at the same condition of *I* = 8 and *d* = 76 mm.

different cases. Copyright 2009 Elsevier

power to ultrasound vibrator.


Table 1. Increased temperature and adsorbed acoustic power density in a 5 mL water when ultrasound is applied. Copyright 2009 Elsevier

Fig. 17. Pitting current density during the period of simultaneously holding potential and applying ultrasound with different input powers at distance of *d* = 76 mm and input power of *I* = 8 in 3.5% NaCl solution containing 0.5% ethanol . Copyright 2009 Elsevier

When the acoustic cavitation is not strong enough to damage the passive film, the suppression effect of acoustic cavitation on pitting corrosion will increase with the increase in the stirring effect of solution in pits after removing the corrosion products (or the metallic cover). The suppression effect should be related to (1) the bubbles' size decided by the tensile stress and (2) the collapse power (shock wave power or cavitation power) decided by the compressive stress in the ultrasound field. Both of the stresses are determined by (i) the amplitude and (ii) the phase of the ultrasound wave. The collapse of larger bubbles brings about larger collapse power.

The removal of corrosion products or metallic covers can be promoted by larger collapse power of the cavitation under larger input power to vibrator and the solution in pits can be completely stirred. This is the reason that the suppression effect on corrosion can be enhanced when increasing the input power to vibrator from *I* = 1 to *I* = 8. However, the stirring of solution in pits after removing corrosion products or metallic covers should depend on both the bubbles' size as well as the collapse power. The schematic drawing is shown in Fig.18. Note that not all the pits are covered by metallic covers (a). Near the specimen, micro-jets to the specimen surface will appear from each collapsing bubble. When the input power to vibrator is small the bubbles' size and the collapse power are small. Part of corrosion products will be cleaned out but no damage occurs on the metallic cover. However, the collapse of bubbles smaller than pits perhaps gives relatively effective stirring effect of solution in pits (b). With the increase in the input power to vibrator (c), the removal

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 243

Except the amplitude of ultrasound, the power of cavitation is also influenced by the evaporability of solution (CBHI, 1999). Ethanol is evaporable specie to improve the evaporability of the solution to result in the increase in stronger cavitation. Accordingly, the corrosion behaviour of stainless steel in the ethanol-added solution changed much with the application of ultrasound. In the case of *I* = 2, the current density is smaller in the ethanoladded solution than that in the ethanol-not-added solution. This means that the improved cavitation in ethanol-added solution gave fully stirring of the solution in the pits and suppressed the growth of pits. On the other hand, in the case of *I* = 8, the suppression of corrosion became weak after adding ethanol in the solution. This should be due to the activation of passive films on the surface by the excessively enhanced cavitation, which bring about promotion of pitting corrosion. This also means that strong acoustic cavitation can also promote corrosion, which corresponds well with other reports described before.

**7. Influence of frequency of ultrasound on the pitting corrosion of Type 304** 

The influence of the ultrasound frequency as well as the distance from vibrator to specimen on the growth of pitting corrosion will be introduced in this section. The vibrators were used with different frequencies of *f*1 = 19.5 kHz (Vibrator: Kaijo Co., 4292C), *f*2 = 50 kHz (4492H) or *f*3 = 420 kHz (4711C). The input power to the ultrasound vibrator was set at *I* = 8 by a controller (Kaijo Co., TA-4021). The distance from the vibrator to the specimen (d) was varied with the wavelength of each type of ultrasound (*λ*1 = 76 mm,*λ*2 = 29.6 mm,*λ*3 = 3.5 mm). In addition, the distance (*D*) from vibrator to the solution surface was set as several integral times of the half-wavelength of each ultrasound, i.e., 1.5 *λ*1 (*D*1 =114 mm), 3 *λ*2 (*D*2 = 89 mm) or 27.5 *λ*3 (*D*3 = 96 mm). Note that the distance of *D* from vibrator to the solution surface in the above sections was not precisely fixed; only in this section the *standing wave* from the solution surface can be discussed. When the anodic current density reached the value of *i*h = 20 A/m2 in the pitting growth zone, the potential was immediately held constant for 600 s. The ultrasound was applied simultaneously with the holding of potential

Fig.19 (a) shows the accumulated electric charge during the period of simultaneously holding potential and applying ultrasound at *I* = 8 with different frequencies (a: 19.5 kHz; b: 50 kHz; c: 420 kHz) and different vibrator-to-specimen distances. Although the input powers to the vibrators are the same, the suppression effects on the pitting corrosion showed large difference when changing either the frequency or the vibrator-to-specimen distance. At each frequency, there is an optimum distance where the largest suppression effect was obtained. The optimum vibrator-to-specimen distance is respectively 57 mm ( = 3*λ*1/4) in the case of *f*1 = 19.5 kHz, 29.6 mm ( = *λ*2) in the case of *f*2 = 50 kHz, and 17.6 mm ( = 5 *λ*3) in the case of *f*3 = 420 kHz. This difference should be attributed to the balance of the formation of standing wave and the energy attenuation of ultrasound in the solution. In addition, the suppression effect in the case of 19.5 kHz is much larger than (100 times of)

those in the cases of 50 kHz and 420 kHz. The latter two effects are almost the same.

From the observation of specimen surfaces after the polarization, the area ratio and the mean depth of pits are obtained (Fig.19 (b, c)). Note that the values were obtained from the surfaces after further ultrasonically cleaning with multi-vibrators (Fig.2). Pits appeared on each surface after the polarization and the pitting corrosion was surely suppressed by each type of ultrasound. However, the suppression of corrosion does not directly decrease the sum of pits. In several different distances of 19.5 kHz and 420 kHz the sum did not decrease, while in the

**steel (Wang, 2011)** 

for 600 s.

of corrosion products increases but the metallic covers still remains there because of the strong strength connecting with the substrate. This results in that the stirring effect does not remarkably increase and thus the suppression effect on pitting corrosion did not largely increase when the input power to vibrator increased from *I* = 1 to *I* = 2 and *I* = 4. With further increase in the input power to ultrasound vibrator (d), the extremely enhanced cavitation power on the removal of corrosion products and metallic covers, and the stirring effect will be significantly enlarged (with the neglect of the weakness in the enlarged size of bubbles). That is the reason that the corrosion was greatly suppressed under *I* = 6 and *I* = 8. Especially the current density decrease to a level of 1×10-3 A/m2 under *I* = 8, meaning the growth of the pit almost stopped.

On the other hand, the transmitted power to the specimen generally decreases with the increase in the vibrator-to-specimen distance because of the amplitude attenuation of ultrasound wave. It resulted in the decrease in the suppression effect when increasing the distance from *d* = 19 mm to *d* = 38 mm and *d* = 95 mm. On the other hand, the phase change of the wave should be also considered in the explanation of the result. In this section, the largest suppression effect of pitting corrosion was obtained at a distance of *d* = 76 mm, which is just equal to wavelength of ultrasound in the solution. In another word, the phase of the wave there is the same with that on the vibrator surface. This should be related to the formation of a "*standing wave field"* of ultrasound in the solution with overlapping the forward wave from the vibrator and the backward (reflected) wave from the liquid / air surface (CBHI, 1999; Mitome, 2008). In the standing wave field, anti-nodes with strong cavitation generally appears with an interval of *λ*/2 along the transmission direction. However, in this work only at a distance of *λ* (76 mm) the suppression effect of pitting corrosion is large while the suppression effect at a distance of *λ*/2 is much small (with good correspondence to the temperature measurement). The reason has not been clearly know, perhaps due to the unfixed distance from the vibrator to the solution surface in the above measurement.

Fig. 18. Schematic drawing of relation of effect of stirring solution in pits with change of bubble size and collapse power. (a) Pit is covered by metallic cover and corrosion product; (b) corrosion product is removed by smaller collapsing bubble; (c) (d) corrosion product and metallic cover is removed by larger collapsing bubble; (e) stirring effect and bubble size or collapse power. Copyright 2009 Elsevier

of corrosion products increases but the metallic covers still remains there because of the strong strength connecting with the substrate. This results in that the stirring effect does not remarkably increase and thus the suppression effect on pitting corrosion did not largely increase when the input power to vibrator increased from *I* = 1 to *I* = 2 and *I* = 4. With further increase in the input power to ultrasound vibrator (d), the extremely enhanced cavitation power on the removal of corrosion products and metallic covers, and the stirring effect will be significantly enlarged (with the neglect of the weakness in the enlarged size of bubbles). That is the reason that the corrosion was greatly suppressed under *I* = 6 and *I* = 8. Especially the current density decrease to a level of 1×10-3 A/m2 under *I* = 8, meaning the

On the other hand, the transmitted power to the specimen generally decreases with the increase in the vibrator-to-specimen distance because of the amplitude attenuation of ultrasound wave. It resulted in the decrease in the suppression effect when increasing the distance from *d* = 19 mm to *d* = 38 mm and *d* = 95 mm. On the other hand, the phase change of the wave should be also considered in the explanation of the result. In this section, the largest suppression effect of pitting corrosion was obtained at a distance of *d* = 76 mm, which is just equal to wavelength of ultrasound in the solution. In another word, the phase of the wave there is the same with that on the vibrator surface. This should be related to the formation of a "*standing wave field"* of ultrasound in the solution with overlapping the forward wave from the vibrator and the backward (reflected) wave from the liquid / air surface (CBHI, 1999; Mitome, 2008). In the standing wave field, anti-nodes with strong cavitation generally appears with an interval of *λ*/2 along the transmission direction. However, in this work only at a distance of *λ* (76 mm) the suppression effect of pitting corrosion is large while the suppression effect at a distance of *λ*/2 is much small (with good correspondence to the temperature measurement). The reason has not been clearly know, perhaps due to the unfixed distance from the vibrator to the solution surface in the above

Fig. 18. Schematic drawing of relation of effect of stirring solution in pits with change of bubble size and collapse power. (a) Pit is covered by metallic cover and corrosion product; (b) corrosion product is removed by smaller collapsing bubble; (c) (d) corrosion product and metallic cover is removed by larger collapsing bubble; (e) stirring effect and bubble size or

growth of the pit almost stopped.

measurement.

collapse power. Copyright 2009 Elsevier

Except the amplitude of ultrasound, the power of cavitation is also influenced by the evaporability of solution (CBHI, 1999). Ethanol is evaporable specie to improve the evaporability of the solution to result in the increase in stronger cavitation. Accordingly, the corrosion behaviour of stainless steel in the ethanol-added solution changed much with the application of ultrasound. In the case of *I* = 2, the current density is smaller in the ethanoladded solution than that in the ethanol-not-added solution. This means that the improved cavitation in ethanol-added solution gave fully stirring of the solution in the pits and suppressed the growth of pits. On the other hand, in the case of *I* = 8, the suppression of corrosion became weak after adding ethanol in the solution. This should be due to the activation of passive films on the surface by the excessively enhanced cavitation, which bring about promotion of pitting corrosion. This also means that strong acoustic cavitation can also promote corrosion, which corresponds well with other reports described before.

## **7. Influence of frequency of ultrasound on the pitting corrosion of Type 304 steel (Wang, 2011)**

The influence of the ultrasound frequency as well as the distance from vibrator to specimen on the growth of pitting corrosion will be introduced in this section. The vibrators were used with different frequencies of *f*1 = 19.5 kHz (Vibrator: Kaijo Co., 4292C), *f*2 = 50 kHz (4492H) or *f*3 = 420 kHz (4711C). The input power to the ultrasound vibrator was set at *I* = 8 by a controller (Kaijo Co., TA-4021). The distance from the vibrator to the specimen (d) was varied with the wavelength of each type of ultrasound (*λ*1 = 76 mm,*λ*2 = 29.6 mm,*λ*3 = 3.5 mm). In addition, the distance (*D*) from vibrator to the solution surface was set as several integral times of the half-wavelength of each ultrasound, i.e., 1.5 *λ*1 (*D*1 =114 mm), 3 *λ*2 (*D*2 = 89 mm) or 27.5 *λ*3 (*D*3 = 96 mm). Note that the distance of *D* from vibrator to the solution surface in the above sections was not precisely fixed; only in this section the *standing wave* from the solution surface can be discussed. When the anodic current density reached the value of *i*h = 20 A/m2 in the pitting growth zone, the potential was immediately held constant for 600 s. The ultrasound was applied simultaneously with the holding of potential for 600 s.

Fig.19 (a) shows the accumulated electric charge during the period of simultaneously holding potential and applying ultrasound at *I* = 8 with different frequencies (a: 19.5 kHz; b: 50 kHz; c: 420 kHz) and different vibrator-to-specimen distances. Although the input powers to the vibrators are the same, the suppression effects on the pitting corrosion showed large difference when changing either the frequency or the vibrator-to-specimen distance. At each frequency, there is an optimum distance where the largest suppression effect was obtained. The optimum vibrator-to-specimen distance is respectively 57 mm ( = 3*λ*1/4) in the case of *f*1 = 19.5 kHz, 29.6 mm ( = *λ*2) in the case of *f*2 = 50 kHz, and 17.6 mm ( = 5 *λ*3) in the case of *f*3 = 420 kHz. This difference should be attributed to the balance of the formation of standing wave and the energy attenuation of ultrasound in the solution. In addition, the suppression effect in the case of 19.5 kHz is much larger than (100 times of) those in the cases of 50 kHz and 420 kHz. The latter two effects are almost the same.

From the observation of specimen surfaces after the polarization, the area ratio and the mean depth of pits are obtained (Fig.19 (b, c)). Note that the values were obtained from the surfaces after further ultrasonically cleaning with multi-vibrators (Fig.2). Pits appeared on each surface after the polarization and the pitting corrosion was surely suppressed by each type of ultrasound. However, the suppression of corrosion does not directly decrease the sum of pits. In several different distances of 19.5 kHz and 420 kHz the sum did not decrease, while in the

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 245

It is known as above that the suppression effect on the pitting corrosion increased with the increase in the cavitation power when the power is less than 10 kJ/(m2・s) in the case of 19.5 kHz and 420 kHz. The optimum condition to suppress corrosion appeared at 19.5 kHz at the distance of 57 mm. However, when the cavitation power is larger than 50 kJ/(m2・s) in the case of 50 kHz, the much large cavitation power is not helpful to increase the suppression effect. This result should be attributed to the simultaneous damage of the passive film on the specimen surface. Of course, during a long period measurement, the increased temperature in the solution will also influence the corrosion rate to some extent. That is, the transmission

power depends on both the input power to vibrator and the ultrasound wave phase.

Fig. 20. Standing wave of ultrasonic pressure ultrasound from the vibrator to the solution

Fig.20 shows the simulated standing wave of ultrasonic pressure in the solution from the vibrator to the solution surface. Since the distance between the vibrator and the solution surface is set as several times of the half-wavelength of ultrasound, the large ultrasonic pressure generally appears at positions from either the solution surface or the vibrator surface with the interval of half-wavelength. Such positions of *λ*/4, 3*λ*/4, 5*λ*/4 and 7*λ*/4 from the vibrator are called as anti-nodes, where large cavitation theoretically occurs. This can be used to well explain the largest cavitation power and the largest suppression effect of corrosion at the 3λ1/4 in the case of 19.5 kHz. However, large cavitation power and suppression effect did not appear at other anti-nodes, which should also be influenced by

surface. The large ultrasonic pressure generally appears at anti-nodes.

case of 50 kHz the sum increased reversely in comparison with that without ultrasound. On the other hand, the total area of pits (Fig.19 (b)) changed, corresponding well with that of the accumulated electric charge for all ultrasound conditions. Large difference cannot be found in the depth of pits under different ultrasound conditions (Fig.19 (c)). The pits in the case of 50 kHz looked like a little shallower than others. This should be attributed to the low precision of the dial gauge (minimum value: 0.01 mm) and attribute to the residual metallic covers on pits (Laycock et al., 1998) (see description later in Fig.21 and 22). In general, the depth of pits with ultrasound is much shallower than those without ultrasound.

Fig.19 (d) shows the cavitation power during applying ultrasound with different frequencies and distances from the vibrator. According to the former report (Wang & Kido, 2009) , at the frequency of 19.5 kHz and at the distance of 76 mm, the cavitation power kept increasing with the increase in the input power from *I* = 0 to 8. In this work, at the frequency of 19.5 kHz and the input power of *I* = 8, the cavitation power kept increasing with the increase in the distance from 19 mm and reached the maximum value of about 9.5 kJ/(m2・s) at the distance of *d* = 57 mm. However, the power decreased with further increasing the distance and obtained the value of 2.2 kJ/(m2・s) at *d* = 95 mm. The largest cavitation power at *d* = 57 mm corresponds to the largest suppression effect on the growth of pitting at this frequency. On the other hand, the cavitation power at the frequency of 50 kHz did not show large change from the distance of 14.8 mm to 59.2 mm, which also corresponds well to the not largely changed suppression effect on pitting corrosion in this case. In the case of 420 kHz, the cavitation power at 17.6 mm and 35.2 mm was almost the same and that at 70.4 mm became a little small. This corresponds to the suppression effect on corrosion, where the largest effect was obtained at 17.6 mm in this case. On the other hand, the power at 50 kHz was the largest, with about 7~35 times of that of 19.5 kHz and 420 kHz. The power at 420 kHz was the smallest.

Fig. 19. Electric charge during potential holding and ultrasound applying (a), pit area ratio (b), pit depth (c) after polarization and cavitation power (d) during ultrasound applying. Copyright 2011 Japan Society of Corrosion Engineering

case of 50 kHz the sum increased reversely in comparison with that without ultrasound. On the other hand, the total area of pits (Fig.19 (b)) changed, corresponding well with that of the accumulated electric charge for all ultrasound conditions. Large difference cannot be found in the depth of pits under different ultrasound conditions (Fig.19 (c)). The pits in the case of 50 kHz looked like a little shallower than others. This should be attributed to the low precision of the dial gauge (minimum value: 0.01 mm) and attribute to the residual metallic covers on pits (Laycock et al., 1998) (see description later in Fig.21 and 22). In general, the depth of pits with

Fig.19 (d) shows the cavitation power during applying ultrasound with different frequencies and distances from the vibrator. According to the former report (Wang & Kido, 2009) , at the frequency of 19.5 kHz and at the distance of 76 mm, the cavitation power kept increasing with the increase in the input power from *I* = 0 to 8. In this work, at the frequency of 19.5 kHz and the input power of *I* = 8, the cavitation power kept increasing with the increase in the distance from 19 mm and reached the maximum value of about 9.5 kJ/(m2・s) at the distance of *d* = 57 mm. However, the power decreased with further increasing the distance and obtained the value of 2.2 kJ/(m2・s) at *d* = 95 mm. The largest cavitation power at *d* = 57 mm corresponds to the largest suppression effect on the growth of pitting at this frequency. On the other hand, the cavitation power at the frequency of 50 kHz did not show large change from the distance of 14.8 mm to 59.2 mm, which also corresponds well to the not largely changed suppression effect on pitting corrosion in this case. In the case of 420 kHz, the cavitation power at 17.6 mm and 35.2 mm was almost the same and that at 70.4 mm became a little small. This corresponds to the suppression effect on corrosion, where the largest effect was obtained at 17.6 mm in this case. On the other hand, the power at 50 kHz was the largest, with about 7~35 times of that of

Fig. 19. Electric charge during potential holding and ultrasound applying (a), pit area ratio (b), pit depth (c) after polarization and cavitation power (d) during ultrasound applying.

ultrasound is much shallower than those without ultrasound.

19.5 kHz and 420 kHz. The power at 420 kHz was the smallest.

Copyright 2011 Japan Society of Corrosion Engineering

It is known as above that the suppression effect on the pitting corrosion increased with the increase in the cavitation power when the power is less than 10 kJ/(m2・s) in the case of 19.5 kHz and 420 kHz. The optimum condition to suppress corrosion appeared at 19.5 kHz at the distance of 57 mm. However, when the cavitation power is larger than 50 kJ/(m2・s) in the case of 50 kHz, the much large cavitation power is not helpful to increase the suppression effect. This result should be attributed to the simultaneous damage of the passive film on the specimen surface. Of course, during a long period measurement, the increased temperature in the solution will also influence the corrosion rate to some extent. That is, the transmission power depends on both the input power to vibrator and the ultrasound wave phase.

Fig. 20. Standing wave of ultrasonic pressure ultrasound from the vibrator to the solution surface. The large ultrasonic pressure generally appears at anti-nodes.

Fig.20 shows the simulated standing wave of ultrasonic pressure in the solution from the vibrator to the solution surface. Since the distance between the vibrator and the solution surface is set as several times of the half-wavelength of ultrasound, the large ultrasonic pressure generally appears at positions from either the solution surface or the vibrator surface with the interval of half-wavelength. Such positions of *λ*/4, 3*λ*/4, 5*λ*/4 and 7*λ*/4 from the vibrator are called as anti-nodes, where large cavitation theoretically occurs. This can be used to well explain the largest cavitation power and the largest suppression effect of corrosion at the 3λ1/4 in the case of 19.5 kHz. However, large cavitation power and suppression effect did not appear at other anti-nodes, which should also be influenced by

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 247

the pits when ultrasound was applied at *I* = 0 and 4 (a, b), while it disappeared at *I* = 8. This means that the metallic cover forms during the corrosion and they can be removed when the applied ultrasound power is strong enough. Such removal of metallic cover and corrosion products is the reason of the suppression of the pitting corrosion. The depth of pit after further ultrasound cleaning was measured again and the results were shown in Fig.22. Of course the mean depth became larger than that before the ultrasound clean, which surely decreased with the increase in the input power from *I* = 0 to 8 but didn't verify much with

Fig. 22. Mean depth of pits before and after ultrasound cleaning on specimens, which were polarized by simultaneously holding potential and applying ultrasound with frequency of *f*<sup>1</sup>

Fig. 23 shows the re-passivation behaviour of the specimen when the potential was swift back from 500 mV at 19.5 kHz and *d* = 57 mm. In the case of without ultrasound (a), the repassive potential appeared at -93 mV with a necessary accumulated charge of 218 kC/m2, while the potential became 316 mV with only a much smaller charge of 1 kC/m2. This promoted re-passivation behaviour by ultrasound is attributed to the remove of corrosion

According to the above results, it is clear that the pitting corrosion can be suppressed by either type of ultrasound. However, the influence on the initiation of pits has not been known, which will be investigated in the near future. Except the above physical effect of ultrasound application in solution, a chemical effect should also be considered. When the ultrasound is applied to an aqueous solution, water can be decomposed to H・and OH・ radicals, and the solution becomes weak acidic (Jana & Chatterjee, 1995). According to the report of Jana, about 3×1021 /m3 radicals are produced by the ultrasound (frequency: 20 kHz, intensity: 190 k W/m2) and four OH・ transfer one Fe2+ ion to one Fe3+. The ultrasound

products and the metallic cover with the disturbing of the solution in pits.

the change of vibrator-to-specimen distance.

= 19.5 kHz.

**8. Future works** 

the energy attenuation of ultrasound in the solution. In the case of 50 kHz and 420 kHz, large cavitation power and suppression did not obtain at either of anti-nodes. In the case of 420 kHz, the wavelength is too small to precisely discuss the influence of position.

In the case of 19.5 kHz, the suppression effect of corrosion increased with the increase in the cavitation power when the power is less than 10 kJ/(m2・s). The effect should be attributed to the increased stirring effect of solution in pits after removing the corrosion products and the metallic covers. The cavitation power is generally related to the bubbles' size decided by the tensile stress and the sum of the collapsed bubbles. In general, the bubble size becomes smaller with the increase in the frequency of ultrasound and thus the happening of cavitation becomes difficult. This should be the reason to get the small cavitation power in the case of 420 kHz, which brought about weak suppression effect of corrosion. On the other hand, the much large cavitation power in the case of 50 kHz should be attributed to the increased sum of collapse of bubbles rather than the balance of the decreased bubbles' size.

Fig. 21. Surface morphology of specimens after simultaneously holding potential and applying ultrasound at *I* = 0 (a), *I* = 4 (b) and *I* = 8 (c) at frequency of 19.5 kHz. The surfaces a1, b1 and c1 are cleaned only by running distilled water; a2, b2, c2 and a3, b3, c3 are further cleaned in distilled water by an ultrasound cleaner for a total time of 600 s and 900 s.

Fig. 21 shows the specimen surfaces after the polarization with ultrasound at *I* = 0, 4 and 8 at the frequency of 19.5 kHz. The surfaces (a1, b1, c1) are rinsed only by running distilled water, while the surfaces (a2, b2, c2 and a3, b3, c3) are further cleaned in distilled water in an ultrasound cleaner with multi-vibrators (Fig.1) for 600 s or 900 s. Corrosion products were not found on the specimen without ultrasound (a), indicating that not all corrosion products reside on pits during the corrosion process. On the other hand, the metallic cover was left on

the energy attenuation of ultrasound in the solution. In the case of 50 kHz and 420 kHz, large cavitation power and suppression did not obtain at either of anti-nodes. In the case of

In the case of 19.5 kHz, the suppression effect of corrosion increased with the increase in the cavitation power when the power is less than 10 kJ/(m2・s). The effect should be attributed to the increased stirring effect of solution in pits after removing the corrosion products and the metallic covers. The cavitation power is generally related to the bubbles' size decided by the tensile stress and the sum of the collapsed bubbles. In general, the bubble size becomes smaller with the increase in the frequency of ultrasound and thus the happening of cavitation becomes difficult. This should be the reason to get the small cavitation power in the case of 420 kHz, which brought about weak suppression effect of corrosion. On the other hand, the much large cavitation power in the case of 50 kHz should be attributed to the increased sum of collapse of bubbles rather than the balance of the decreased bubbles' size.

420 kHz, the wavelength is too small to precisely discuss the influence of position.

Fig. 21. Surface morphology of specimens after simultaneously holding potential and applying ultrasound at *I* = 0 (a), *I* = 4 (b) and *I* = 8 (c) at frequency of 19.5 kHz. The surfaces a1, b1 and c1 are cleaned only by running distilled water; a2, b2, c2 and a3, b3, c3 are further cleaned in distilled water by an ultrasound cleaner for a total time of 600 s and 900 s.

Fig. 21 shows the specimen surfaces after the polarization with ultrasound at *I* = 0, 4 and 8 at the frequency of 19.5 kHz. The surfaces (a1, b1, c1) are rinsed only by running distilled water, while the surfaces (a2, b2, c2 and a3, b3, c3) are further cleaned in distilled water in an ultrasound cleaner with multi-vibrators (Fig.1) for 600 s or 900 s. Corrosion products were not found on the specimen without ultrasound (a), indicating that not all corrosion products reside on pits during the corrosion process. On the other hand, the metallic cover was left on the pits when ultrasound was applied at *I* = 0 and 4 (a, b), while it disappeared at *I* = 8. This means that the metallic cover forms during the corrosion and they can be removed when the applied ultrasound power is strong enough. Such removal of metallic cover and corrosion products is the reason of the suppression of the pitting corrosion. The depth of pit after further ultrasound cleaning was measured again and the results were shown in Fig.22. Of course the mean depth became larger than that before the ultrasound clean, which surely decreased with the increase in the input power from *I* = 0 to 8 but didn't verify much with the change of vibrator-to-specimen distance.

Fig. 22. Mean depth of pits before and after ultrasound cleaning on specimens, which were polarized by simultaneously holding potential and applying ultrasound with frequency of *f*<sup>1</sup> = 19.5 kHz.

Fig. 23 shows the re-passivation behaviour of the specimen when the potential was swift back from 500 mV at 19.5 kHz and *d* = 57 mm. In the case of without ultrasound (a), the repassive potential appeared at -93 mV with a necessary accumulated charge of 218 kC/m2, while the potential became 316 mV with only a much smaller charge of 1 kC/m2. This promoted re-passivation behaviour by ultrasound is attributed to the remove of corrosion products and the metallic cover with the disturbing of the solution in pits.

### **8. Future works**

According to the above results, it is clear that the pitting corrosion can be suppressed by either type of ultrasound. However, the influence on the initiation of pits has not been known, which will be investigated in the near future. Except the above physical effect of ultrasound application in solution, a chemical effect should also be considered. When the ultrasound is applied to an aqueous solution, water can be decomposed to H・and OH・ radicals, and the solution becomes weak acidic (Jana & Chatterjee, 1995). According to the report of Jana, about 3×1021 /m3 radicals are produced by the ultrasound (frequency: 20 kHz, intensity: 190 k W/m2) and four OH・ transfer one Fe2+ ion to one Fe3+. The ultrasound

Suppression of Corrosion Growth of Stainless Steel by Ultrasound 249

4. The suppression effect of the growth of pitting corrosion became large with the increase in the cavitation power when the power is less than 10 kJ/(m2・s). However, in the case of 50 kHz, the cavitation was strong enough to damage the passive film, which weakens the suppression effect on the corrosion. In the case of 420 kHz, the effect on the

5. The ultrasound promotes the re-passivation of pits by not only removing corrosion

This work is a summary of our recent researches on *suppression of corrosion of stainless steel by ultrasound*, which were carried out in Hiroshima University (2004.4~2005.3) and in Hiroshima Institute of Technology (2005.4~2011.7). Professor K.Nakasa gave important advices and discussion in this work. Dr. Q.Zhang helped the in-situ observation of pitting corrosion by atomic force microscope. The author is very grateful to Mr. T.Tamai, Mr. A.Yamamoto, Mr. T.Kangai, Mr. H.Morishita, Mr. S.Nagai, Mr.Y.Odagami, Mr. K.Etsuki, Mr. M.Kimura, Mr. H.Doi, Mr. G.Nishida, Mr. Y.Shibatani and Mr. S.Fujii for their assistance of experiments. Part of this work was supported by MEXT.HAITEKU, 2004~.

Ryan, M.P.; Williams, D.E.; Chater, R.J.; Hutton, B.M. & Mcphail, D.S. (2002). Why stainless

Shimizu, K. (2010). New Role of a Low-Voltage, Ultra-High Resolution FE-SEM for

*Engineering of Japan,* Vol.59, No.7, (July 2010), pp.245-250, ISSN 0917-0480 Shimizu, K. (2010). New Role of a Low-Voltage, Ultra-High Resolution FE-SEM for

Yashiro, H. & Shimizu, K. (2010). *Poc. 57th Japan Conf. Materials and Environments, JSCE*,

Hisamatsu, Y. (1981). Locallized Corrosion of Iron-Nickel-Chromium Alloys – Pitting,

Zhang, Q.; Wang, R.; Kato, M. & Nakasa, K. (2005). Observation by atomic force microscope

Chouonpa Binran Henshu Iinkai (1999). *Hand Book of Ultrasonic Wave*, Maruzen, ISBN 4-621-

*Materialla,* Vol.52, No.3, (February 2005), pp.227-230, ISSN 1359-6462 Wang, R. & Kido, M. (2009). Influence of input power to vibrator and vibrator-to-specimen

steel corrodes. *Nature*, Vol.415, No.6873, (February 2002), pp.770-774, ISSN 0028-

Corrosion Studies (2) – Application examples -. *Zairyo-to-Kankyo / Corrosion* 

Corrosion Studies (1) – Sample Surface Preparation for Ultra-High Resolution FE-SEM -. *Zairyo-to-Kankyo / Corrosion Engineering of Japan,* Vol.59, No.10, (October

Crevice Corrosion, and Stress Corrosion Cracking -. *Bulletin of the Japan Institute of* 

of corrosion product during pitting corrosion on SUS304 stainless steel. *Scripta* 

distance of ultrasound on pitting corrosion of SUS304 stainless steel in 3.5% chloride sodium aqueous solution. *Corrosion Science,* Vol.51, No.8, (August 2009),

suppression of corrosion was weak due to small cavitation power.

products but also removing the metallic cover.

2010), pp.360-365, ISSN 0917-0480

pp.1604-1610, ISSN 0010-938X

04663-0 C 3055

*Metals*, Vol.20, No.1, (1981), pp.3-11, ISSN 1340-2625

**10. Acknowledgment** 

**11. References** 

0836

pp.175-178

intensity in this research was about 3~10 kW/m2, and the application time is short. Therefore, the amount of radicals produced will be not large. However, it is possible that there is a contrary influence of radicals on the pitting corrosion behaviour considering the breakdown of passive film by lowered pH solution by H・radical and the re-passivation of the broken passive film by the OH・radical with strong oxidation ability.

Fig. 23. Polarization curves with reversely sweeping of the potential at 500 mV, simultaneously without or with ultrasound with *f*1 = 19.5 kHz at *d* = 57 mm and *I* = 8.

## **9. Conclusions**

The influence of ultrasound in solution on the corrosion behaviour of stainless steel was introduced basing on our results and other literatures. It has known that when the acoustic cavitation caused by ultrasound is strong enough, the passive film can be damaged and thus corrosion is activated. However, when the acoustic cavitation caused by ultrasound is not strong enough to damage the passive film the corrosion will not be accelerated. As for the suppression effect of ultrasound on the stainless steel of Type 304 stainless steel, the following conclusions were obtained.


## **10. Acknowledgment**

248 Ultrasonic Waves

intensity in this research was about 3~10 kW/m2, and the application time is short. Therefore, the amount of radicals produced will be not large. However, it is possible that there is a contrary influence of radicals on the pitting corrosion behaviour considering the breakdown of passive film by lowered pH solution by H・radical and the re-passivation of

the broken passive film by the OH・radical with strong oxidation ability.

Fig. 23. Polarization curves with reversely sweeping of the potential at 500 mV, simultaneously without or with ultrasound with *f*1 = 19.5 kHz at *d* = 57 mm and *I* = 8.

The influence of ultrasound in solution on the corrosion behaviour of stainless steel was introduced basing on our results and other literatures. It has known that when the acoustic cavitation caused by ultrasound is strong enough, the passive film can be damaged and thus corrosion is activated. However, when the acoustic cavitation caused by ultrasound is not strong enough to damage the passive film the corrosion will not be accelerated. As for the suppression effect of ultrasound on the stainless steel of Type 304 stainless steel, the

1. In case of pitting corrosion of Type 304 steel, the corrosion product was in-situ confirmed on the growing pits at the early stage. When the corrosion product was removed by the probe of AFM, the growth rate of pits largely decreased, which was explained by the decrease in the concentration of chloride and hydrogen ions in pits. 2. The cathode current, passive current and corrosion potential in the polarization curve were not almost changed by the application of ultrasound. However, the growth of pitting corrosion and crevice corrosion of Type 304 stainless steel can be suppressed by ultrasound with 19.5 kHz ultrasound. The change of the current density almost synchronized with the cyclic application and stop of ultrasound. In the case of 19.5 kHz at a constant vibrator-to-specimen distance of *d* = 76 mm, the suppression effect on

3. The suppression effect of the growth of pitting corrosion was different when changing either the frequency or the distance from ultrasound vibrator to the specimen with either of frequencies of 19.5, 50 and 420 kHz. The largest suppression effect in this work was obtained at 19.5 kHz at the vibrator-to-specimen distance of 57 mm at the input

pitting corrosion increased with the input power to vibrator.

**9. Conclusions** 

following conclusions were obtained.

power of *I* = 8 to vibrator.

This work is a summary of our recent researches on *suppression of corrosion of stainless steel by ultrasound*, which were carried out in Hiroshima University (2004.4~2005.3) and in Hiroshima Institute of Technology (2005.4~2011.7). Professor K.Nakasa gave important advices and discussion in this work. Dr. Q.Zhang helped the in-situ observation of pitting corrosion by atomic force microscope. The author is very grateful to Mr. T.Tamai, Mr. A.Yamamoto, Mr. T.Kangai, Mr. H.Morishita, Mr. S.Nagai, Mr.Y.Odagami, Mr. K.Etsuki, Mr. M.Kimura, Mr. H.Doi, Mr. G.Nishida, Mr. Y.Shibatani and Mr. S.Fujii for their assistance of experiments. Part of this work was supported by MEXT.HAITEKU, 2004~.

## **11. References**


**13** 

 *Greece* 

**New Trends in Materials** 

*Materials Science & Engineering Department,* 

T. E. Matikas and D. G. Aggelis

 *University of Ioannina, Ioannina,* 

 **Nondestructive Characterization Using Surface Acoustic Wave Methodologies** 

The surface of the materials is usually the most sensitive part due to exposure to environmental influence, as well as higher bending and torsional loads than the interior. Therefore, degradation is bound to initiate from the surface in most engineering components. Surface wave propagation in heterogeneous media is a topic concentrating many efforts in the engineering community. The main aim is quality characterization via nondestructive evaluation (NDE) methodologies by correlation of propagation characteristics with material properties. In the present chapter surface waves are examined in structural materials of outmost significance such as aerospace composites and concrete.

Concrete structures are exposed to deterioration factors like weathering, corrosive agents, thermal expansion and contraction or even freezing and thawing. Additionally, they support operation loads, own weight and possibly dynamic overloading by earthquakes. Most of the above factors affect primarily the surface of structures, which is directly exposed to the atmospheric conditions and sustain maximum flexural loads. Deterioration therefore, is bound to start from the surface in most cases. This deterioration may be manifested in the form of large surface breaking cracks and/or distributed micro-cracking in the surface layer of the material. Inspection techniques based on the propagation of elastic waves have been long used for the estimation of the quality and general condition of the material [1,2] either in through the thickness or in surface mode. Surface wave propagation is complicated in that different kinds of waves co-exist. Normally the Rayleigh waves occupy most of the energy, while the longitudinal are the fastest [3,4]. Therefore, measuring the transit time of the first detectable disturbance of the waveform, leads to the calculation of the longitudinal wave velocity. This is referred to as pulse velocity [1-3] and it is widely used for rough correlations with quality. Other forms of wave speed are the phase velocity, which is calculated either by some characteristic point in the middle of a tone-burst of a specific frequency [5,6], or by spectral analysis of a broadband pulse [7]. Additionally, group velocity is calculated by the maximum peak, the maximum of the wave envelope, or crosscorrelation between the "input" and "output" waveforms [8,9]. In homogeneous media all

**1. Introduction** 


## **New Trends in Materials Nondestructive Characterization Using Surface Acoustic Wave Methodologies**

T. E. Matikas and D. G. Aggelis *Materials Science & Engineering Department, University of Ioannina, Ioannina, Greece* 

## **1. Introduction**

250 Ultrasonic Waves

Alkire, R.C. & Perusich, S. (1983). The effect of focused ultrasound on the

Al-Hashem, A.; Caceres, P.G.; Riad, W.T. & Shalaby, H.M. (1995). Cavitation

Whillock, G.O.H. & Harvey, B.F. (1996). Preliminary investigation of the

*Ultrasonics Sonochemistry,* Vol.3, No.2, (1996), pp. S111-S118, ISSN 1350-4177 Kwok, C.T.; Cheng, F.T. & Man, H.C. (2000). Synergistic effect of cavitation erosion

*Engineering* A, Vol.290, No.1-2, (October 2000), pp.145-154, ISSN 0921-5093 Whillock, G.O.H. & Harvey, B.F. (1997). Ultrasonically enhanced corrosion of 304Lstainless

Wang, R. & Nakasa, K. (2007). Effect of ultrasonic wave on the growth of corrosion pits on

Wang, R. & Kido, M. (2008). Influence of application of ultrasound on corrosion behavior of

Wang, R. (2008). Influence of ultrasound on pitting corrosion and crevice corrosion of

Wang, R. (2011). Growth behavior of pitting corrosion of SUS304 stainless steel in NaCl

Wranglen, G. (1985). *An Introduction to Corrosion and Protection of Metals*. Chapman and Hall,

Japanese Industrial Standards Committee (2002). *JIS G0592:2002,* Method of determining the

Mitome, H. (2008). Generation of acoustic cavitation and its application. *Journal of the Japan* 

Laycock, N.J.; White, S.P.; Noh, J.S.; Wilson, P.T. & Newman, R.C. (1998). Perforated covers

Jana, A.K. & Chatterjee, S.N. (1995). *Ultrasonics Sonochemistry,* Vol.2, No.2, (1995), pp.s87–

Vol.50, No.2, (February 2008), pp.325-328, ISSN 0010-938X

repassivation potential for crevice corrosion of stainless steels

(October 1983), pp.1121-1132, ISSN 0010-938X

No.5, (May 1995), pp.331-342, ISSN 0010-9312

pp.283-285, ISSN 0010-9312

2008), pp.1806-1811, ISSN 1345-9678

1022, ISSN 1345-9678

0917-0480

4728

ISBN 0412260409

pp.1101-1108, ISSN 0013-4651

s91, ISSN 1350-4177

electrochemicalpassivity of iron in sulfuric acid. *Corrosion Science,* Vol.23, No.10,

corrosionbehavior of cast nickel–aluminum bronze in seawater. *Corrosion,* Vol.51,

ultrasonicallyenhanced corrosion of stainless steel in the nitric/chloride system.

andcorrosion of various engineering alloys in 3.5% NaCl solution. *Materials Science* 

steel II: the effect of frequency, acoustic power and vibrator-to specimen distance. *Ultrasonics Sonochemistry,* Vol.4, No.1, (January 1997), pp.33-38, ISSN 1350-4177 Nakayama, T. & Sasa, K. (1976). Effect of ultrasonic waves on the pitting potential of 18–8

stainless steel in sodium chloride solution. *Corrosion,* Vol.32, No.7, (July 1976),

SUS304 stainless steel. *Materials Transactions,* Vol.48, No.5, (May 2007), pp.1017-

SUS304 stainless steel with crevice. *Materials Transactions,* Vol.49, No.8, (August

SUS304 stainless steel in chloride sodium aqueous solution. *Corrosion Science,*

aqueous solution when applying ultrasound with different frequencies. *Zairyo-to-Kankyo / Corrosion Engineering of Japan*, Vol.60, No.2, (February 2011), pp.66-68, ISSN

*Society of Mechanical Engineering,* Vol.111, No.1074, (May 2008), pp.32-35, ISSN 0021-

for propagating pits. *Journal of the electrochemical society,* Vol.145, No.4, (April 1998),

The surface of the materials is usually the most sensitive part due to exposure to environmental influence, as well as higher bending and torsional loads than the interior. Therefore, degradation is bound to initiate from the surface in most engineering components. Surface wave propagation in heterogeneous media is a topic concentrating many efforts in the engineering community. The main aim is quality characterization via nondestructive evaluation (NDE) methodologies by correlation of propagation characteristics with material properties. In the present chapter surface waves are examined in structural materials of outmost significance such as aerospace composites and concrete.

Concrete structures are exposed to deterioration factors like weathering, corrosive agents, thermal expansion and contraction or even freezing and thawing. Additionally, they support operation loads, own weight and possibly dynamic overloading by earthquakes. Most of the above factors affect primarily the surface of structures, which is directly exposed to the atmospheric conditions and sustain maximum flexural loads. Deterioration therefore, is bound to start from the surface in most cases. This deterioration may be manifested in the form of large surface breaking cracks and/or distributed micro-cracking in the surface layer of the material. Inspection techniques based on the propagation of elastic waves have been long used for the estimation of the quality and general condition of the material [1,2] either in through the thickness or in surface mode. Surface wave propagation is complicated in that different kinds of waves co-exist. Normally the Rayleigh waves occupy most of the energy, while the longitudinal are the fastest [3,4]. Therefore, measuring the transit time of the first detectable disturbance of the waveform, leads to the calculation of the longitudinal wave velocity. This is referred to as pulse velocity [1-3] and it is widely used for rough correlations with quality. Other forms of wave speed are the phase velocity, which is calculated either by some characteristic point in the middle of a tone-burst of a specific frequency [5,6], or by spectral analysis of a broadband pulse [7]. Additionally, group velocity is calculated by the maximum peak, the maximum of the wave envelope, or crosscorrelation between the "input" and "output" waveforms [8,9]. In homogeneous media all

New Trends in Materials Nondestructive

damage characterization.

aerospace materials.

Characterization Using Surface Acoustic Wave Methodologies 253

for the case of actual cracks, which were simulated by thin, flakey, light inclusions, the random orientation and general shape complicates the anticipated results and increases experimental scatter. This study aims to supply more experimental data in the area of surface waves in media with random and randomly oriented inhomogenity, which has not been studied as widely as stratified media [11,25] and media with surface breaking cracks [26-29]. The results presented herein are realistic due to the shape of the light inclusions, while size and population of inclusions leave their fingerprint on the phase velocity and attenuation curves since large population of small inclusions impose stronger attenuation that small population of larger size. Additionally the application of other features from frequency domain, like the coherence function, is discussed as to their contribution in

Concerning aerospace materials, innovative NDE methods based on linear and nonlinear acoustics are of outmost importance for developing damage tolerance approaches by

High strength titanium alloys, as well as fiber reinforced metal matrix composite materials, are being considered for a number of applications because of their improved mechanical properties in high temperature applications. In applications where cyclic loading is expected and where life management is required, consideration must be given to the behavior of the material in the vicinity of stress risers such as notches and holes. It is in these regions that damage initiation and accumulations are expected. In the case of metal matrix composites for aircraft structural and engine components, several damage modes near stress risers have been identified [30]. One important damage mode under cyclic loading is the nucleation and growth of matrix cracks perpendicular to the fiber direction. In some composite systems, the matrix crack growth occurs without the corresponding failure of the fibers. This process results in the development of relatively large matrix cracks that are either fully or partially bridged by unbroken fibers. The presence of bridging fibers can significantly influence the fatigue crack growth behavior of the composite. To develop a life prediction methodology applicable to these composite systems, an understanding must be developed of both the matrix cracking behavior as well as the influence of the unbroken fibers on the crack driving force and the

effect of interfacial degradation and damage on the eventual failure of the composite.

Paramount to understanding the influence of unbroken fibers is to identify the mechanisms which transfer the load from the matrix to the fiber. The mechanics of matrix cracking and fiber bridging in brittle matrix composites has been addressed [31,32]. The analysis is based on the shear lag model to describe the transfer of load from the fiber to the matrix. In the shear lag model, the transfer of load occurs through the frictional shear force (τ) between the fiber and the matrix. The analyses indicate that size of the region on the fiber over which t acts can have a significant effect on the influence of unbroken fibers on crack growth rate behavior. However, although some indirect ultrasonic experimental techniques have been developed to determine the extent of influence of τ [33-35], no direct nondestructive experimental techniques currently exist. Another important interfacial phenomenon is the degradation, fracture and/or failure of the interface resulting from crack initiation and growth [36,37].

This chapter has an objective to discuss the utility and versatility of surface waves application in cementitious materials as well as two state-of-the-art surface acoustic wave techniques, ultrasonic microscopy and nonlinear acoustics, for material behavior research of

monitoring the accumulation of damage under cyclic loading.

these forms of velocity are expected to share the same value. However, for inhomogeneous media it has been shown that these velocities are not necessarily close [5,10].

From the above forms of velocity, the most common measurement in ultrasonics is the "pulse velocity". Considering that the material is homogeneous, pulse velocity is directly related to the elasticity modulus [11] and correlated to the strength of concrete through empirical relations [1,11-13]. Since it is measured by the first detectable disturbance of the waveform this measurement depends on the strength of the signal with respect to the noise, which could have environmental and equipment-induced components. In case the initial arrivals of the wave are weaker than or similar to the noise level, pulse velocity is underestimated. This could certainly be the case in actual structures, where propagation distances through damaged materials are usually long. Rayleigh waves are also excited in a concrete surface; they propagate within a penetration depth of approximately one wave length and carry more of the excitation energy [3,14]. Their velocity is also related to elasticity and Poisson's ratio. Measurement of Rayleigh velocity is usually conducted by a reference peak point, so it is not directly influenced by noise level [11]. However, for cases of severe damage or long propagation, the strong reference cycle used for the measurement is severely distorted making the selection of reference points troublesome [8,15], as will be seen later. Frequency domain techniques like phase difference calculation between signals recorded at specific distances may provide solution for velocity measurement revealing also the dependence of velocity on frequency [7,16].

In addition to wave velocity, attenuation has also been widely used for characterization of microstructural changes or damage existence [17,18]. It represents the reduction of the wave amplitude per unit of propagation length. Attenuation is more sensitive to damage or void content as has been revealed in several studies [5,8,18-20] and has been correlated to the size of the aggregates, as well as air void size and content in hardened and fresh cementitious materials [5,18]. The sensitivity of attenuation to the microstructure is such, that the content of "heterogeneity" is not the only dominating factor; the typical size and shape of the inclusions play an equivalently important role and therefore, Rayleigh wave attenuation has been related to parameters like aggregate size, and damage content [8,21-23]. This sensitivity to the microstructure may complicate assessment but on the other hand offers possibilities for more accurate characterization.

Accurate characterization would require determination of several damage parameters like the number (or equivalent damage content) of the cracks, their typical size, as well as their orientation. Though this is a nearly impossible task, especially in-situ, advanced features sensitive to the above damage parameters should be continuously sought for in order to improve the maintenance services in structures. The valuable but rough characterization based on pulse velocity can be improved by the addition of features from frequency domain as will be explained below.

Elastic waves are applied on the surface of mortar specimens with inhomogeneity. In order to simulate damage, small flakey inclusions were added in different contents and sizes, and parameters of the surface waves are calculated. The effect of "damage" content as well as the size of the inclusions on wave parameters is discussed showing that the typical size of inhomogeneity is equally important to the content. In similar studies, sphere is a first approximation for the damage shape, which produces quite reliable results [24]. However,

these forms of velocity are expected to share the same value. However, for inhomogeneous

From the above forms of velocity, the most common measurement in ultrasonics is the "pulse velocity". Considering that the material is homogeneous, pulse velocity is directly related to the elasticity modulus [11] and correlated to the strength of concrete through empirical relations [1,11-13]. Since it is measured by the first detectable disturbance of the waveform this measurement depends on the strength of the signal with respect to the noise, which could have environmental and equipment-induced components. In case the initial arrivals of the wave are weaker than or similar to the noise level, pulse velocity is underestimated. This could certainly be the case in actual structures, where propagation distances through damaged materials are usually long. Rayleigh waves are also excited in a concrete surface; they propagate within a penetration depth of approximately one wave length and carry more of the excitation energy [3,14]. Their velocity is also related to elasticity and Poisson's ratio. Measurement of Rayleigh velocity is usually conducted by a reference peak point, so it is not directly influenced by noise level [11]. However, for cases of severe damage or long propagation, the strong reference cycle used for the measurement is severely distorted making the selection of reference points troublesome [8,15], as will be seen later. Frequency domain techniques like phase difference calculation between signals recorded at specific distances may provide solution for velocity measurement revealing also

In addition to wave velocity, attenuation has also been widely used for characterization of microstructural changes or damage existence [17,18]. It represents the reduction of the wave amplitude per unit of propagation length. Attenuation is more sensitive to damage or void content as has been revealed in several studies [5,8,18-20] and has been correlated to the size of the aggregates, as well as air void size and content in hardened and fresh cementitious materials [5,18]. The sensitivity of attenuation to the microstructure is such, that the content of "heterogeneity" is not the only dominating factor; the typical size and shape of the inclusions play an equivalently important role and therefore, Rayleigh wave attenuation has been related to parameters like aggregate size, and damage content [8,21-23]. This sensitivity to the microstructure may complicate assessment but on the other hand offers possibilities

Accurate characterization would require determination of several damage parameters like the number (or equivalent damage content) of the cracks, their typical size, as well as their orientation. Though this is a nearly impossible task, especially in-situ, advanced features sensitive to the above damage parameters should be continuously sought for in order to improve the maintenance services in structures. The valuable but rough characterization based on pulse velocity can be improved by the addition of features from frequency domain

Elastic waves are applied on the surface of mortar specimens with inhomogeneity. In order to simulate damage, small flakey inclusions were added in different contents and sizes, and parameters of the surface waves are calculated. The effect of "damage" content as well as the size of the inclusions on wave parameters is discussed showing that the typical size of inhomogeneity is equally important to the content. In similar studies, sphere is a first approximation for the damage shape, which produces quite reliable results [24]. However,

media it has been shown that these velocities are not necessarily close [5,10].

the dependence of velocity on frequency [7,16].

for more accurate characterization.

as will be explained below.

for the case of actual cracks, which were simulated by thin, flakey, light inclusions, the random orientation and general shape complicates the anticipated results and increases experimental scatter. This study aims to supply more experimental data in the area of surface waves in media with random and randomly oriented inhomogenity, which has not been studied as widely as stratified media [11,25] and media with surface breaking cracks [26-29]. The results presented herein are realistic due to the shape of the light inclusions, while size and population of inclusions leave their fingerprint on the phase velocity and attenuation curves since large population of small inclusions impose stronger attenuation that small population of larger size. Additionally the application of other features from frequency domain, like the coherence function, is discussed as to their contribution in damage characterization.

Concerning aerospace materials, innovative NDE methods based on linear and nonlinear acoustics are of outmost importance for developing damage tolerance approaches by monitoring the accumulation of damage under cyclic loading.

High strength titanium alloys, as well as fiber reinforced metal matrix composite materials, are being considered for a number of applications because of their improved mechanical properties in high temperature applications. In applications where cyclic loading is expected and where life management is required, consideration must be given to the behavior of the material in the vicinity of stress risers such as notches and holes. It is in these regions that damage initiation and accumulations are expected. In the case of metal matrix composites for aircraft structural and engine components, several damage modes near stress risers have been identified [30]. One important damage mode under cyclic loading is the nucleation and growth of matrix cracks perpendicular to the fiber direction. In some composite systems, the matrix crack growth occurs without the corresponding failure of the fibers. This process results in the development of relatively large matrix cracks that are either fully or partially bridged by unbroken fibers. The presence of bridging fibers can significantly influence the fatigue crack growth behavior of the composite. To develop a life prediction methodology applicable to these composite systems, an understanding must be developed of both the matrix cracking behavior as well as the influence of the unbroken fibers on the crack driving force and the effect of interfacial degradation and damage on the eventual failure of the composite.

Paramount to understanding the influence of unbroken fibers is to identify the mechanisms which transfer the load from the matrix to the fiber. The mechanics of matrix cracking and fiber bridging in brittle matrix composites has been addressed [31,32]. The analysis is based on the shear lag model to describe the transfer of load from the fiber to the matrix. In the shear lag model, the transfer of load occurs through the frictional shear force (τ) between the fiber and the matrix. The analyses indicate that size of the region on the fiber over which t acts can have a significant effect on the influence of unbroken fibers on crack growth rate behavior. However, although some indirect ultrasonic experimental techniques have been developed to determine the extent of influence of τ [33-35], no direct nondestructive experimental techniques currently exist. Another important interfacial phenomenon is the degradation, fracture and/or failure of the interface resulting from crack initiation and growth [36,37].

This chapter has an objective to discuss the utility and versatility of surface waves application in cementitious materials as well as two state-of-the-art surface acoustic wave techniques, ultrasonic microscopy and nonlinear acoustics, for material behavior research of aerospace materials.

New Trends in Materials Nondestructive

sensors and the specimen.

Fig. 1. The experimental setup.

corresponding decrease of 8.5%.

the average of 20 individual measurements.

**2.2 Shape distortion and pulse velocity** 

Characterization Using Surface Acoustic Wave Methodologies 255

pencil lead break was excited (HB 0.5) producing frequencies in the bandwidth of 0–300 kHz, in front of the first receiver. The signals received by the three sensors were preamplified by 40 dB and digitized with a sampling rate of 10 MHz in a Mistras system of Physical Acoustics Corporation. Silicone grease was used as couplant between the

Figure 2a shows typical waveforms as captured by the first and last receivers on a plain mortar specimen. In both receivers the strong Rayleigh cycle is observed, preceded by the weaker longitudinal mode. Measuring the delay between the strong negative peaks (Fig. 2a), the Rayleigh velocity is calculated at 2116 m/s. When simulated damage is included in a content of 1%, the Rayleigh cycle is slightly distorted (Fig. 2b). The Rayleigh velocity in this case is measured at the value of 2062 m/s. It is mentioned that the pulse velocity, dictated by the first detectable disturbance of the waveforms, is essentially similar for both cases measured at around 4140 m/s, meaning that Rayleigh waves are more sensitive to the slight amount of simulated damage than longitudinal. When the content of damage is 10% (see Fig. 2c) the Rayleigh cycle is severely distorted and a reference point cannot be easily selected for the measurement. In case the minimum point of the 2nd cycle is chosen (marked by an arrow), the Rayleigh velocity is calculated at 1770 m/s, being reduced by 17% relatively to the sound material, while pulse velocity is measured at 3773 m/s, with a

Figure 3 depicts the average longitudinal wave velocity for different types of inclusions and constant content of 5% normalized to the velocity of plain mortar. As observed, the different size has considerable effect on the velocity since the inclusions of 15x15x0.5 mm size reduce the velocity to approximately 96.5% of plain mortar while inclusions of 30x30x0.2 mm reduce the velocity even to 83%. This shows that the material cannot be treated as homogeneous considering only the volume fraction of inclusions (or cracks in an actual situation), since their shape and size is also important. The velocities presented come from

Ultrasonic microscopy utilizes high focused ultrasonic transducers to induce surface acoustic waves in the material which can be successfully used for local elastic property measurement, crack-size determination, as well as for interfacial damage evaluation in high temperature materials, such as metal matrix composites [38]. Nonlinear acoustics enables real-time monitoring of material degradation in aerospace structures [39]. When a sinusoidal ultrasonic wave of a given frequency and of sufficient amplitude is introduced into a non-harmonic solid the fundamental wave distorts as it propagates, and therefore the second and higher harmonics of the fundamental frequency are generated. Measurements of the amplitude of these harmonics provide information on the coefficient of second and higher order terms of the stress-strain relation for a nonlinear solid. As it is shown here, the material bulk nonlinear parameter for metallic alloy samples at different fatigue levels exhibits large changes compared to linear ultrasonic parameters, such as velocity and attenuation [40].

## **2. Damage characterization in concrete using surface waves**

In order to characterize damage, several parameters are required. These include the quantification of: damage content, typical size of cracking or even distribution of sizes and possibly orientation preference. This task is nearly impossible in real structures or even in laboratory due to several variables that need to be determined. However, dealing with some of the aspects of characterization is extremely important bearing in mind that so far, the assessment of concrete condition is based on the rough and empirical correlations between pulse velocity and strength. In the next part, the simulated damage content and typical size of cracks in concrete are examined in terms of their influence on different parameters of the propagating wave studied complementary to the conventional pulse velocity.

#### **2.1 Experimental process**

Concerning the part of the study relevant to cementitious materials, the experimental specimens were made of cement mortar with water to cement ratio of 0.5 and sand to cement 2 by mass. The maximum sand grain size was 3 mm. Two minutes after the ingredients were mixed in a concrete mixer, vinyl inclusions were added and the mixing continued for two additional minutes. Then the mixture was cast in square metal forms of 150 mm side. The specimens were demolded one day later and cured in water for 28 days [41]. The vinyl inclusions were added in different volume contents (specifically 1%, 5% and 10%), while a mortar specimen was also cast without any inclusions. Vinyl inclusions were cut in small square coupons from sheets with thickness of 0.2 mm and 0.5 mm. The exact sizes of the vinyl coupons were 15x15x0.5 mm, 15x15x0.2, 30x30x0.5 and 30x30x0.2 mm. One specimen was cast for each inclusion size and content.

After fracturing one preliminary specimen, it was revealed that the dispersion of the fillers can be considered random, as would possibly be the case for actual cracks. Although the total volume content of the fillers was strictly measured to the specified value (i.e. 1%, 5% and 10%) in order to exclude local variations twenty measurements were taken on the surface and the results were averaged.

For the ultrasonic measurements, three broadband piezoelectric transducers, Fujiceramics 1045S, were placed on the specimens' surface with a distance of 20 mm, see Fig. 1. A pencil lead break was excited (HB 0.5) producing frequencies in the bandwidth of 0–300 kHz, in front of the first receiver. The signals received by the three sensors were preamplified by 40 dB and digitized with a sampling rate of 10 MHz in a Mistras system of Physical Acoustics Corporation. Silicone grease was used as couplant between the sensors and the specimen.

Fig. 1. The experimental setup.

254 Ultrasonic Waves

Ultrasonic microscopy utilizes high focused ultrasonic transducers to induce surface acoustic waves in the material which can be successfully used for local elastic property measurement, crack-size determination, as well as for interfacial damage evaluation in high temperature materials, such as metal matrix composites [38]. Nonlinear acoustics enables real-time monitoring of material degradation in aerospace structures [39]. When a sinusoidal ultrasonic wave of a given frequency and of sufficient amplitude is introduced into a non-harmonic solid the fundamental wave distorts as it propagates, and therefore the second and higher harmonics of the fundamental frequency are generated. Measurements of the amplitude of these harmonics provide information on the coefficient of second and higher order terms of the stress-strain relation for a nonlinear solid. As it is shown here, the material bulk nonlinear parameter for metallic alloy samples at different fatigue levels exhibits large changes

In order to characterize damage, several parameters are required. These include the quantification of: damage content, typical size of cracking or even distribution of sizes and possibly orientation preference. This task is nearly impossible in real structures or even in laboratory due to several variables that need to be determined. However, dealing with some of the aspects of characterization is extremely important bearing in mind that so far, the assessment of concrete condition is based on the rough and empirical correlations between pulse velocity and strength. In the next part, the simulated damage content and typical size of cracks in concrete are examined in terms of their influence on different parameters of the

Concerning the part of the study relevant to cementitious materials, the experimental specimens were made of cement mortar with water to cement ratio of 0.5 and sand to cement 2 by mass. The maximum sand grain size was 3 mm. Two minutes after the ingredients were mixed in a concrete mixer, vinyl inclusions were added and the mixing continued for two additional minutes. Then the mixture was cast in square metal forms of 150 mm side. The specimens were demolded one day later and cured in water for 28 days [41]. The vinyl inclusions were added in different volume contents (specifically 1%, 5% and 10%), while a mortar specimen was also cast without any inclusions. Vinyl inclusions were cut in small square coupons from sheets with thickness of 0.2 mm and 0.5 mm. The exact sizes of the vinyl coupons were 15x15x0.5 mm, 15x15x0.2, 30x30x0.5 and 30x30x0.2 mm. One

After fracturing one preliminary specimen, it was revealed that the dispersion of the fillers can be considered random, as would possibly be the case for actual cracks. Although the total volume content of the fillers was strictly measured to the specified value (i.e. 1%, 5% and 10%) in order to exclude local variations twenty measurements were taken on the

For the ultrasonic measurements, three broadband piezoelectric transducers, Fujiceramics 1045S, were placed on the specimens' surface with a distance of 20 mm, see Fig. 1. A

compared to linear ultrasonic parameters, such as velocity and attenuation [40].

propagating wave studied complementary to the conventional pulse velocity.

specimen was cast for each inclusion size and content.

surface and the results were averaged.

**2.1 Experimental process** 

**2. Damage characterization in concrete using surface waves** 

## **2.2 Shape distortion and pulse velocity**

Figure 2a shows typical waveforms as captured by the first and last receivers on a plain mortar specimen. In both receivers the strong Rayleigh cycle is observed, preceded by the weaker longitudinal mode. Measuring the delay between the strong negative peaks (Fig. 2a), the Rayleigh velocity is calculated at 2116 m/s. When simulated damage is included in a content of 1%, the Rayleigh cycle is slightly distorted (Fig. 2b). The Rayleigh velocity in this case is measured at the value of 2062 m/s. It is mentioned that the pulse velocity, dictated by the first detectable disturbance of the waveforms, is essentially similar for both cases measured at around 4140 m/s, meaning that Rayleigh waves are more sensitive to the slight amount of simulated damage than longitudinal. When the content of damage is 10% (see Fig. 2c) the Rayleigh cycle is severely distorted and a reference point cannot be easily selected for the measurement. In case the minimum point of the 2nd cycle is chosen (marked by an arrow), the Rayleigh velocity is calculated at 1770 m/s, being reduced by 17% relatively to the sound material, while pulse velocity is measured at 3773 m/s, with a corresponding decrease of 8.5%.

Figure 3 depicts the average longitudinal wave velocity for different types of inclusions and constant content of 5% normalized to the velocity of plain mortar. As observed, the different size has considerable effect on the velocity since the inclusions of 15x15x0.5 mm size reduce the velocity to approximately 96.5% of plain mortar while inclusions of 30x30x0.2 mm reduce the velocity even to 83%. This shows that the material cannot be treated as homogeneous considering only the volume fraction of inclusions (or cracks in an actual situation), since their shape and size is also important. The velocities presented come from the average of 20 individual measurements.

New Trends in Materials Nondestructive

**2.3 Phase velocity** 

Characterization Using Surface Acoustic Wave Methodologies 257

Fig. 3. Wave velocities for different inclusion sizes and constant content (5%).

As to the Rayleigh wave propagation, if a reference point can be identified, e.g. the strong negative peaks in Fig. 2(a), the Rayleigh velocity can be calculated easily. However, in case of strong distortion, case of Fig. 2(c) selection of a single point would not be safe. Therefore, an approach with cross-correlation was followed. The time lag resulting after cross correlation between the signals, over the separation distance between the first and third transducer (40 mm), gives a measure of the velocity with which the energy propagates [8]. For this task the first 100 μs of the waveforms were used where the Rayleigh contribution is certain to exist.

The results are shown again in Fig. 3 normalized to the plain mortar Rayleigh velocity of 2116m/s. The Rayleigh velocity follows similar diminishing trend with the longitudinal, being however more strongly reduced, to even 66% of the plain mortar, for the case of 30x30x0.2 inclusions. This again shows the importance of the scatterer size. Additionally, the differential influence of inclusion shape on longitudinal and Rayleigh wave velocities should be highlighted. This is another indication of the inhomogeneous nature of the material. The addition of lower elasticity inclusions reduces the "effective" modulus of elasticity of mortar. In case the material could be regarded as homogeneous, the influence on longitudinal and Rayleigh velocities should be the same, since they are both firmly connected to the elastic properties. However, for the material at hand, the Rayleigh is obstructed much more intensively, especially by the thin inclusions, showing that a traditional homogenized approach used for concrete is not adequate for cementitious material with inclusions. This should also be related to the propagation mechanism of Rayleigh waves, which includes displacement components in two directions (parallel and vertical to the direction of propagation) being therefore more sensitive to inhomogeneity.

The above mentioned approach yields a measure of the velocity of the whole pulse. In a heterogeneous medium like the one studied herein, the velocity is expected to be strongly dependent on the frequency. Therefore, it is significant to calculate the dispersion curve (phase velocity vs. frequency). In the case of Rayleigh waves this is not trivial since there are

Fig. 2. Sample waveforms of 1st and 3rd receiver for mortar with inclusions contents 0% (a), 1% (b) and 10% (c) and inclusion size 30x30x0.5 mm.

dt

(a)

(b)

(c)

Fig. 2. Sample waveforms of 1st and 3rd receiver for mortar with inclusions contents 0% (a),

1% (b) and 10% (c) and inclusion size 30x30x0.5 mm.

Fig. 3. Wave velocities for different inclusion sizes and constant content (5%).

As to the Rayleigh wave propagation, if a reference point can be identified, e.g. the strong negative peaks in Fig. 2(a), the Rayleigh velocity can be calculated easily. However, in case of strong distortion, case of Fig. 2(c) selection of a single point would not be safe. Therefore, an approach with cross-correlation was followed. The time lag resulting after cross correlation between the signals, over the separation distance between the first and third transducer (40 mm), gives a measure of the velocity with which the energy propagates [8]. For this task the first 100 μs of the waveforms were used where the Rayleigh contribution is certain to exist.

The results are shown again in Fig. 3 normalized to the plain mortar Rayleigh velocity of 2116m/s. The Rayleigh velocity follows similar diminishing trend with the longitudinal, being however more strongly reduced, to even 66% of the plain mortar, for the case of 30x30x0.2 inclusions. This again shows the importance of the scatterer size. Additionally, the differential influence of inclusion shape on longitudinal and Rayleigh wave velocities should be highlighted. This is another indication of the inhomogeneous nature of the material. The addition of lower elasticity inclusions reduces the "effective" modulus of elasticity of mortar. In case the material could be regarded as homogeneous, the influence on longitudinal and Rayleigh velocities should be the same, since they are both firmly connected to the elastic properties. However, for the material at hand, the Rayleigh is obstructed much more intensively, especially by the thin inclusions, showing that a traditional homogenized approach used for concrete is not adequate for cementitious material with inclusions. This should also be related to the propagation mechanism of Rayleigh waves, which includes displacement components in two directions (parallel and vertical to the direction of propagation) being therefore more sensitive to inhomogeneity.

## **2.3 Phase velocity**

The above mentioned approach yields a measure of the velocity of the whole pulse. In a heterogeneous medium like the one studied herein, the velocity is expected to be strongly dependent on the frequency. Therefore, it is significant to calculate the dispersion curve (phase velocity vs. frequency). In the case of Rayleigh waves this is not trivial since there are

New Trends in Materials Nondestructive

**2.4 Spectral distortion** 

Characterization Using Surface Acoustic Wave Methodologies 259

2116 m/s measured by cross-correlation. However, as the inhomogeneity increases, considerable discrepancies arise. Indicatively, for the inclusions of 30x30x0.2 mm the phase velocity curve of Fig. 4 averages at 1217 m/s, while the cross-correlation leads to a velocity of 1426 m/s, see Fig. 3. This discrepancy has been observed in other cases of cementitious materials and increases with the level of inhomogeneity, i.e. from cement paste to mortar with sand grains or concrete with large aggregates [5], as well as other strongly scattering systems [10]. This trend is reasonable because in heterogeneous, dispersive materials the pulse shape changes during propagation and the expressions of velocity may well differ as

Apart from the velocity decrease, which is approximately of the order of 35% for Rayleigh waves, the signal suffers strong distortion which is evident from the shape of the time domain waveform. The distortion of the spectral content can be evaluated by the coherence function [45]. The frequency dependent coherence γxy(f) between two time domain waveforms x(t) and y(t) is a measure of the similarity of their spectral content and can be described as the corresponding of cross-correlation in the frequency domain. It is given by:

*xx yy G f <sup>f</sup> G fG f*

2

, <sup>2</sup> 0 1 *xy*

where Gxy(f) is the cross-spectral density function between time domain waveforms x(t) and

*f* (1)

they depend on the reference points selected for the calculation.

y(t), while Gxx and Gyy are the auto-spectral density functions of x(t) and y(t).

Fig. 5. Coherence function for different size of inclusions and content 5% by vol.

2 *xy*

*xy*

always contributions from longitudinal and shear waves that are faster. Therefore, the Rayleigh cannot be isolated. However, since they generally carry more energy than the other types, concentrating on a time window where the Rayleigh are expected, can yield information about this wave with little influence from other types. In this case a window of 30 μs located around the major Rayleigh arrivals was isolated and the rest of the waveform was zero-padded as presented in similar cases [42]. Using Fast Fourier Transform, the phase of the waveform is calculated and unwrapped. Therefore, the difference of phase between waveforms collected at different distances from the excitation (i.e. the first and third receiver) leads to the calculation of phase velocity vs. frequency curve [7]. The results are depicted in Fig. 4 for materials with different inclusion type and volume content 5%. Each curve is the average of 20 individual curves in order to diminish variation effects.

Fig. 4. Phase velocity vs. frequency curves for different size of inclusions and content 5% by vol.

It is seen that even plain mortar exhibits dispersive behavior with velocity increasing throughout the first 200 kHz. The dispersion curve for inclusions with dimensions 15x15x0.5 is translated to lower levels by about 400 m/s. However, other inclusion sizes seem to have much stronger influence, with the large and thin inclusions (30x30x0.2) lowering the curve by more than 800 m/s in average. Additionally, all the curves exhibit strong velocity increase for the band up to 50 kHz or 60 kHz. For higher frequencies each curve seems to converge. This is a behavior generally observed in composite systems. For low frequencies, the velocity may exhibit strong variations or resonance peaks but, as the frequency increases, the variations seem to diminish [43-44] as is the case for this study.

It is mentioned that the level of the dispersion curve is not necessarily close to the value of Rayleigh velocity measured by cross-correlation. For plain mortar, the Rayleigh phase velocity curve seen in Fig. 4, averages at 2073 m/s being close to the Rayleigh velocity of 2116 m/s measured by cross-correlation. However, as the inhomogeneity increases, considerable discrepancies arise. Indicatively, for the inclusions of 30x30x0.2 mm the phase velocity curve of Fig. 4 averages at 1217 m/s, while the cross-correlation leads to a velocity of 1426 m/s, see Fig. 3. This discrepancy has been observed in other cases of cementitious materials and increases with the level of inhomogeneity, i.e. from cement paste to mortar with sand grains or concrete with large aggregates [5], as well as other strongly scattering systems [10]. This trend is reasonable because in heterogeneous, dispersive materials the pulse shape changes during propagation and the expressions of velocity may well differ as they depend on the reference points selected for the calculation.

## **2.4 Spectral distortion**

258 Ultrasonic Waves

always contributions from longitudinal and shear waves that are faster. Therefore, the Rayleigh cannot be isolated. However, since they generally carry more energy than the other types, concentrating on a time window where the Rayleigh are expected, can yield information about this wave with little influence from other types. In this case a window of 30 μs located around the major Rayleigh arrivals was isolated and the rest of the waveform was zero-padded as presented in similar cases [42]. Using Fast Fourier Transform, the phase of the waveform is calculated and unwrapped. Therefore, the difference of phase between waveforms collected at different distances from the excitation (i.e. the first and third receiver) leads to the calculation of phase velocity vs. frequency curve [7]. The results are depicted in Fig. 4 for materials with different inclusion type and volume content 5%. Each

curve is the average of 20 individual curves in order to diminish variation effects.

Fig. 4. Phase velocity vs. frequency curves for different size of inclusions and content 5% by

It is seen that even plain mortar exhibits dispersive behavior with velocity increasing throughout the first 200 kHz. The dispersion curve for inclusions with dimensions 15x15x0.5 is translated to lower levels by about 400 m/s. However, other inclusion sizes seem to have much stronger influence, with the large and thin inclusions (30x30x0.2) lowering the curve by more than 800 m/s in average. Additionally, all the curves exhibit strong velocity increase for the band up to 50 kHz or 60 kHz. For higher frequencies each curve seems to converge. This is a behavior generally observed in composite systems. For low frequencies, the velocity may exhibit strong variations or resonance peaks but, as the frequency

It is mentioned that the level of the dispersion curve is not necessarily close to the value of Rayleigh velocity measured by cross-correlation. For plain mortar, the Rayleigh phase velocity curve seen in Fig. 4, averages at 2073 m/s being close to the Rayleigh velocity of

increases, the variations seem to diminish [43-44] as is the case for this study.

vol.

Apart from the velocity decrease, which is approximately of the order of 35% for Rayleigh waves, the signal suffers strong distortion which is evident from the shape of the time domain waveform. The distortion of the spectral content can be evaluated by the coherence function [45]. The frequency dependent coherence γxy(f) between two time domain waveforms x(t) and y(t) is a measure of the similarity of their spectral content and can be described as the corresponding of cross-correlation in the frequency domain. It is given by:

$$\left|\boldsymbol{\gamma}\_{\rm xy}^{2}\left(\boldsymbol{f}\right)\right| = \frac{\left|\boldsymbol{G}\_{\rm xy}\left(\boldsymbol{f}\right)\right|^{2}}{\boldsymbol{G}\_{\rm xy}\left(\boldsymbol{f}\right)\boldsymbol{G}\_{\rm yy}\left(\boldsymbol{f}\right)}, \; 0 \le \boldsymbol{\gamma}\_{\rm xy}^{2}\left(\boldsymbol{f}\right) \le 1 \tag{1}$$

where Gxy(f) is the cross-spectral density function between time domain waveforms x(t) and y(t), while Gxx and Gyy are the auto-spectral density functions of x(t) and y(t).

Fig. 5. Coherence function for different size of inclusions and content 5% by vol.

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recorded.

size 30x30x0.5 mm.

Characterization Using Surface Acoustic Wave Methodologies 261

curve of sound material is much lower (average at 0.005 dB/mm). This attenuation behavior is a result of the combined effect of geometric spreading, damping and scattering. Geometric spreading has exactly the same effect on all curves, due to the same experimental conditions. Damping depends on the viscosity parameters of the constituents and therefore, for material with the same content of inclusions should not lead to strong changes. Therefore, the strong discrepancies between the curves within the graph, are attributed directly to scattering on the flakey inclusions. The different size of them imposes different scattering conditions and crucially affects the scattered wave field. For certain frequency bands differences of the order of 100% may arise depending on the size of the inclusions alone, even though the inclusion content is constant. This trend once again shows the complexity of wave propagation in damaged concrete and the need of multi-parameter approach for structural condition characterization. In general, it can be mentioned that 30x30x0.5 mm inclusion size exhibits the lowest attenuation curve. This is reasonable since for this shape, the volume of each particle is larger, and therefore, less individual inclusions are necessary to build the specified content. This leads to less scattering incidences as the wave propagates from the excitation point to the receivers, only moderately reducing the amplitude of the wave

Fig. 6. Attenuation vs. frequency for mortar with different inclusion contents and inclusion

Figure 5 shows the coherence between signals collected at separation distance of 40 mm in mortar with different typical sizes of inhomogeneity. For no inclusions, the coherence is almost maximum (value close to 1), showing little distortion. Addition of inclusions in the content of 5% certainly diminishes the level of coherence but the result strongly depends on the size of the heterogeneity as well. Specifically for the size of 15x15x0.5 mm the average coherence is 0.92, while for 30x30x0.5 mm is 0.66. The lowest coherence is exhibited between signals recorded in specimens with 30x30x0.2 mm inclusions with an average value of 0.54. This shows the importance of the dominant size of inhomogeneity in spectral similarity and makes coherence a descriptor with strong characterizing power over the typical size of damage. It has also been used for characterization of concrete composition through ultrasonic signals and classification of acoustic emission signals [13,46].

#### **2.5 Attenuation curves**

The comparison of the peak amplitude of waveforms captured at different positions is a measure of attenuation. If the time domain signals are transformed into the frequency domain by fast Fourier transform (FFT) their response leads to the frequency dependent attenuation coefficient through the next equation:

$$a(f) = -\frac{20}{\pi} \log \left( \frac{A(f)}{B(f)} \right) \tag{2}$$

where a(f) is the attenuation coefficient with respect to frequency, A(f) and B(f) are the FFTs of the responses of the two sensors and x is the distance between the sensors (in this case 40 mm).

*α(f)* reveals the attenuative characteristics for specific frequency bands improving the characterization capacity, especially in controlled laboratory conditions, since the typical size of inhomogeneity affects specific wavelengths. Attenuation curves were calculated according to Eq. 2 for different inclusion contents and are seen in Fig. 6 for material with inclusion size of 30x30x0.5 mm. The curves exhibit strong fluctuations throughout the frequency band of 0 to 300 kHz. These fluctuations are difficult to be accurately evaluated and therefore, the curves are indicatively fitted by exponential functions, which although do not map the fluctuations, follow the general increasing trend. It is seen that plain mortar exhibits the lowest attenuation, while the attenuation curve of the 10% inclusions is the highest. The inclusions force an attenuation increase of approximately 200% - 300% compared to the attenuation of the plain material, while at the same time they were responsible only for a slight decrease of 35% in Rayleigh velocity, as was seen earlier. Additionally, the curve of 1% damage content is distinctly higher than plain material, showing the strong sensitivity of attenuation even to slight damage content.

As mentioned earlier, apart from the content, the size of the inhomogeneity plays an important role in the wave behavior and especially the attenuation. This is demonstrated in Fig. 7 where the attenuation curves for different sizes of inclusions are shown for the content of 5%. In general all "damaged" material curves exhibit an increase with frequency, as is expected for scattering media in a moderate frequency regime. The inclusions size 30x30x0.2 mm exhibits the highest attenuation in average (approximately 0.016 dB/mm), while 30x30x0.5 mm the lowest of all "damaged" specimens (0.013 dB/mm). The attenuation

Figure 5 shows the coherence between signals collected at separation distance of 40 mm in mortar with different typical sizes of inhomogeneity. For no inclusions, the coherence is almost maximum (value close to 1), showing little distortion. Addition of inclusions in the content of 5% certainly diminishes the level of coherence but the result strongly depends on the size of the heterogeneity as well. Specifically for the size of 15x15x0.5 mm the average coherence is 0.92, while for 30x30x0.5 mm is 0.66. The lowest coherence is exhibited between signals recorded in specimens with 30x30x0.2 mm inclusions with an average value of 0.54. This shows the importance of the dominant size of inhomogeneity in spectral similarity and makes coherence a descriptor with strong characterizing power over the typical size of damage. It has also been used for characterization of concrete composition through

The comparison of the peak amplitude of waveforms captured at different positions is a measure of attenuation. If the time domain signals are transformed into the frequency domain by fast Fourier transform (FFT) their response leads to the frequency dependent

> <sup>20</sup> ( ) ( ) log ( ) *A f a f x Bf*

where a(f) is the attenuation coefficient with respect to frequency, A(f) and B(f) are the FFTs of the responses of the two sensors and x is the distance between the sensors (in this case 40 mm). *α(f)* reveals the attenuative characteristics for specific frequency bands improving the characterization capacity, especially in controlled laboratory conditions, since the typical size of inhomogeneity affects specific wavelengths. Attenuation curves were calculated according to Eq. 2 for different inclusion contents and are seen in Fig. 6 for material with inclusion size of 30x30x0.5 mm. The curves exhibit strong fluctuations throughout the frequency band of 0 to 300 kHz. These fluctuations are difficult to be accurately evaluated and therefore, the curves are indicatively fitted by exponential functions, which although do not map the fluctuations, follow the general increasing trend. It is seen that plain mortar exhibits the lowest attenuation, while the attenuation curve of the 10% inclusions is the highest. The inclusions force an attenuation increase of approximately 200% - 300% compared to the attenuation of the plain material, while at the same time they were responsible only for a slight decrease of 35% in Rayleigh velocity, as was seen earlier. Additionally, the curve of 1% damage content is distinctly higher than plain material,

showing the strong sensitivity of attenuation even to slight damage content.

As mentioned earlier, apart from the content, the size of the inhomogeneity plays an important role in the wave behavior and especially the attenuation. This is demonstrated in Fig. 7 where the attenuation curves for different sizes of inclusions are shown for the content of 5%. In general all "damaged" material curves exhibit an increase with frequency, as is expected for scattering media in a moderate frequency regime. The inclusions size 30x30x0.2 mm exhibits the highest attenuation in average (approximately 0.016 dB/mm), while 30x30x0.5 mm the lowest of all "damaged" specimens (0.013 dB/mm). The attenuation

(2)

ultrasonic signals and classification of acoustic emission signals [13,46].

attenuation coefficient through the next equation:

**2.5 Attenuation curves** 

curve of sound material is much lower (average at 0.005 dB/mm). This attenuation behavior is a result of the combined effect of geometric spreading, damping and scattering. Geometric spreading has exactly the same effect on all curves, due to the same experimental conditions. Damping depends on the viscosity parameters of the constituents and therefore, for material with the same content of inclusions should not lead to strong changes. Therefore, the strong discrepancies between the curves within the graph, are attributed directly to scattering on the flakey inclusions. The different size of them imposes different scattering conditions and crucially affects the scattered wave field. For certain frequency bands differences of the order of 100% may arise depending on the size of the inclusions alone, even though the inclusion content is constant. This trend once again shows the complexity of wave propagation in damaged concrete and the need of multi-parameter approach for structural condition characterization. In general, it can be mentioned that 30x30x0.5 mm inclusion size exhibits the lowest attenuation curve. This is reasonable since for this shape, the volume of each particle is larger, and therefore, less individual inclusions are necessary to build the specified content. This leads to less scattering incidences as the wave propagates from the excitation point to the receivers, only moderately reducing the amplitude of the wave recorded.

Fig. 6. Attenuation vs. frequency for mortar with different inclusion contents and inclusion size 30x30x0.5 mm.

New Trends in Materials Nondestructive

and Δz is the periodicity of the V(z) curve.

the surface and subsurface features in the sample.

relationship:

imaged.

Characterization Using Surface Acoustic Wave Methodologies 263

attenuation of Rayleigh waves which are leaking toward the transducer and are very sensitive to local mechanical properties of the materials being evaluated [36]. The generation and propagation of a leaky Rayleigh wave is modulated by the material's properties, thereby making it feasible to image even very subtle changes of the mechanical properties. The sensitivity of the SAW signals to surface and subsurface features depends on the degree of defocus and has been documented in the literature as the V(z) curves [49]. A V(z) curve is obtained when the transducer, kept over a single point, is moved toward the specimen. Then, the signal, rather than simply decreasing monotonically, can undergo a series of oscillations. The series of oscillations at a defocus distance can be associated with Rayleigh wave excitation and interaction of a SAW with the specular reflection received directly by the transducer. The Rayleigh wave velocity, vR, can then be calculated using a simple

> 1 2

where, vo is the sound velocity in the coupling medium, ω is the frequency of ultrasound,

The defocus distance also has another important effect on the SAW signal obtained by the SAM transducer and dictates whether the SAW signal is separated in time from the specular reflection or interferes with it. Thus, depending on the defocus, the technique can be used either to map the interference phenomenon in the first layer of subsurface fibers, or to map

The conventional technique for measuring SAW velocity is based on a V(z) curve acquisition and analysis procedure utilizing a tone-burst system to interrogate the sample at a specific frequency using specially designed acoustic lenses. This technique requires calibration of the specific lens as well as of the response of the electronic circuit using a V(z) curve obtained from a lead sample, a material for which the Rayleigh wave has too low a velocity to be excited. This procedure requires specialized instrumentation, is timeconsuming, and cannot be used for on-line measurements in interrupted testing mode. However, a novel ultrasonic microscopy method [37] overcomes the limitations of the conventional technique because it is based on automated SAW velocity determination via V(z) curve measurements using short-pulse ultrasound. The principle of ultrasonic microscopy is presented in Figure 8. A SAM transducer is schematically shown in Figure 1. The transducer used in ultrasonic microscopy has a piezoelectric-active element situated behind a delay line made of fused silica. The thickness of the active element is chosen to excite ultrasonic signals with a desired nominal frequency when an electrical spike voltage is delivered to the piezoelectric element. The silica delay has a highly focused spherical acoustical concave lens that is ground to an optical finish. A numerical aperture (NA; ratio of the diameter of the lens to the focal distance) of >1 (or F number focal distance/diameter—of the lens <1) is essential for the ultrasonic microscopy technique to effectively generate and receive surface waves [50] in the sample being

*v*

*o*

(3)

*v z*

*<sup>o</sup> <sup>R</sup>*

*v*

Fig. 7. Attenuation vs. frequency for mortar with different inclusion size and content 5%.

As a conclusion to the study on concrete it is worth to mention that surface wave propagation has not been previously studied for media with randomly distributed inhomogeneity. In this case surface wave features are used for accurate material characterization. Wave velocity of both longitudinal and Rayleigh waves exhibit close connection to the damage content as well as typical size. However, phase velocity vs. frequency curves prove more sensitive since they exhibit stronger decrease for the same damage content. Additionally spectral distortion can also be exploited by means of the coherence function and supply another descriptor sensitive to damage content and size. Finally, attenuation coefficient seems to be the strongest parameter since it suffers an increase of even 300 % compared to sound material. The merit from such a work would be the application of these parameters in real structures, since the complementary use of a combination of parameters will certainly enhance the characterization accomplished by pulse velocity alone.

## **3. Ultrasonic microscopy for characterization of damage in fiber-reinforced composites**

The principle of operation of ultrasonic microscopy is based on the production and propagation of surface acoustic waves (SAW) as a direct result of a combination of the high curvature of the focusing lens of the transducer and the defocus of the transducer into the sample [47, 48]. The most important contrast phenomenon in this technique is based on the

Fig. 7. Attenuation vs. frequency for mortar with different inclusion size and content 5%.

**3. Ultrasonic microscopy for characterization of damage in fiber-reinforced** 

The principle of operation of ultrasonic microscopy is based on the production and propagation of surface acoustic waves (SAW) as a direct result of a combination of the high curvature of the focusing lens of the transducer and the defocus of the transducer into the sample [47, 48]. The most important contrast phenomenon in this technique is based on the

pulse velocity alone.

**composites** 

As a conclusion to the study on concrete it is worth to mention that surface wave propagation has not been previously studied for media with randomly distributed inhomogeneity. In this case surface wave features are used for accurate material characterization. Wave velocity of both longitudinal and Rayleigh waves exhibit close connection to the damage content as well as typical size. However, phase velocity vs. frequency curves prove more sensitive since they exhibit stronger decrease for the same damage content. Additionally spectral distortion can also be exploited by means of the coherence function and supply another descriptor sensitive to damage content and size. Finally, attenuation coefficient seems to be the strongest parameter since it suffers an increase of even 300 % compared to sound material. The merit from such a work would be the application of these parameters in real structures, since the complementary use of a combination of parameters will certainly enhance the characterization accomplished by

attenuation of Rayleigh waves which are leaking toward the transducer and are very sensitive to local mechanical properties of the materials being evaluated [36]. The generation and propagation of a leaky Rayleigh wave is modulated by the material's properties, thereby making it feasible to image even very subtle changes of the mechanical properties. The sensitivity of the SAW signals to surface and subsurface features depends on the degree of defocus and has been documented in the literature as the V(z) curves [49]. A V(z) curve is obtained when the transducer, kept over a single point, is moved toward the specimen. Then, the signal, rather than simply decreasing monotonically, can undergo a series of oscillations. The series of oscillations at a defocus distance can be associated with Rayleigh wave excitation and interaction of a SAW with the specular reflection received directly by the transducer. The Rayleigh wave velocity, vR, can then be calculated using a simple relationship:

$$
\upsilon\_R = \frac{\upsilon\_o}{\sqrt{1 - \frac{\upsilon\_o}{2\alpha\alpha\Delta z}}} \tag{3}
$$

where, vo is the sound velocity in the coupling medium, ω is the frequency of ultrasound, and Δz is the periodicity of the V(z) curve.

The defocus distance also has another important effect on the SAW signal obtained by the SAM transducer and dictates whether the SAW signal is separated in time from the specular reflection or interferes with it. Thus, depending on the defocus, the technique can be used either to map the interference phenomenon in the first layer of subsurface fibers, or to map the surface and subsurface features in the sample.

The conventional technique for measuring SAW velocity is based on a V(z) curve acquisition and analysis procedure utilizing a tone-burst system to interrogate the sample at a specific frequency using specially designed acoustic lenses. This technique requires calibration of the specific lens as well as of the response of the electronic circuit using a V(z) curve obtained from a lead sample, a material for which the Rayleigh wave has too low a velocity to be excited. This procedure requires specialized instrumentation, is timeconsuming, and cannot be used for on-line measurements in interrupted testing mode. However, a novel ultrasonic microscopy method [37] overcomes the limitations of the conventional technique because it is based on automated SAW velocity determination via V(z) curve measurements using short-pulse ultrasound. The principle of ultrasonic microscopy is presented in Figure 8. A SAM transducer is schematically shown in Figure 1. The transducer used in ultrasonic microscopy has a piezoelectric-active element situated behind a delay line made of fused silica. The thickness of the active element is chosen to excite ultrasonic signals with a desired nominal frequency when an electrical spike voltage is delivered to the piezoelectric element. The silica delay has a highly focused spherical acoustical concave lens that is ground to an optical finish. A numerical aperture (NA; ratio of the diameter of the lens to the focal distance) of >1 (or F number focal distance/diameter—of the lens <1) is essential for the ultrasonic microscopy technique to effectively generate and receive surface waves [50] in the sample being imaged.

New Trends in Materials Nondestructive

Characterization Using Surface Acoustic Wave Methodologies 265

(a) (b) Fig. 9. The role of coupling medium in ultrasonic microscopy; using (a) water as coupling medium for imaging damage in Ti-24Al-11Nb/SCS-6 composite subjected to TMF, (b)

The capability of ultrasonic microscopy to determine cracks size and evaluate interfacial damage is depicted in Figure 10. This figure shows the first ply of titanium matrix composites with [0/90]S cross-ply and unidirectional lay-up of fibers subjected to isothermal mechanical fatigue [51, 52]. Matrix cracks and interfacial debonding are clearly observed in the figure. Crack bridging by unbroken fibers resulting to interface debonding dominate the fatigue crack growth life as evidenced by the characteristic decrease in crack growth rates as

(a) (b) Fig. 10. Ultrasonic microscopy micrographs of (a) Ti-15Mo-3Nb-3Al-0.2Si/SCS-6 composite with [0/90]S cross-ply lay-up of fibers subjected to 70 hours of isothermal (650oC) fatigue; (b) Ti-15Mo-3Nb-3Al-0.2Si/SCS-6 composite with unidirectional lay-up of fibers after 1.8x105 cycles of isothermal (650o C) fatigue: A. Point of accelerated crack growth to failure. B. Interfacial degradation due to compressive stresses. C. Interfacial degradation due to

methanol as coupling medium for imaging the same specimen.

the crack length increased during fatigue cycling.

tensile stresses.

Fig. 8. Principle of ultrasonic microscopy.

The sensor used is a highly focused ultrasonic transducer with a central frequency of 50 MHz. The method employed here is self-calibrated, and is used to obtain Rayleigh velocity maps of the specimen through automated V(z) curve acquisition and analysis [37]. The resolution of the technique for characterizing individual fibers and determining interfacial properties strongly depends on the lens defocus from the surface of the sample. In addition, it should be underlined that the choice of the coupling medium is essential for resolving individual fibers in the composite, since, for a specific ultrasonic transducer with a fixed lens curvature, the generation of Rayleigh waves on the surface of the composite only depends on the sound velocities of the coupling medium and of the material under interrogation. Based on Snell's law, the curvature of a transducer's lens required to generate SAW in a material is given by the relationship,

$$\theta = \sin^{-1}\left(\frac{c\_{coupling}}{c\_{material}}\right) \tag{4}$$

where, θ is the half-arc of the lens, and ccoupling and cmaterial are the ultrasonic velocities of the coupling medium and the material, respectively.

Figure 9 shows ultrasonic microscopy imaging of a Ti-24Al-11Nb/SCS-6 composite subjected to thermo-mechanical fatigue (TMF) using a highly focused 50 MHz transducer, designed to generate SAW in metals such as titanium and steel with water as a coupling medium.

Due to environmental exposure, oxides were formed on the material's surface. This altered the sound velocity of the surface of the composite and, therefore, SAW could not be generated (Fig. 9a). The use of methanol as a coupling medium alleviated this difficulty (Fig. 9b).

 **R**

The sensor used is a highly focused ultrasonic transducer with a central frequency of 50 MHz. The method employed here is self-calibrated, and is used to obtain Rayleigh velocity maps of the specimen through automated V(z) curve acquisition and analysis [37]. The resolution of the technique for characterizing individual fibers and determining interfacial properties strongly depends on the lens defocus from the surface of the sample. In addition, it should be underlined that the choice of the coupling medium is essential for resolving individual fibers in the composite, since, for a specific ultrasonic transducer with a fixed lens curvature, the generation of Rayleigh waves on the surface of the composite only depends on the sound velocities of the coupling medium and of the material under interrogation. Based on Snell's law, the curvature of a transducer's lens required to generate SAW in a

<sup>1</sup> sin *coupling*

where, θ is the half-arc of the lens, and ccoupling and cmaterial are the ultrasonic velocities of the

Figure 9 shows ultrasonic microscopy imaging of a Ti-24Al-11Nb/SCS-6 composite subjected to thermo-mechanical fatigue (TMF) using a highly focused 50 MHz transducer, designed to

Due to environmental exposure, oxides were formed on the material's surface. This altered the sound velocity of the surface of the composite and, therefore, SAW could not be generated

generate SAW in metals such as titanium and steel with water as a coupling medium.

(Fig. 9a). The use of methanol as a coupling medium alleviated this difficulty (Fig. 9b).

*c c*

*material*

**Solid Material**

**Rayleigh Wave Longitudinal Wave Shear Wave**

**Coupling Medium (water)**

**Highly Focused Transducer**

Fig. 8. Principle of ultrasonic microscopy.

material is given by the relationship,

coupling medium and the material, respectively.

**Active Piezoelectric Element**

**Water Leaky** 

**Virtual Focal Point**

**Axial Rays**

**Transducer and Lens**

**Defocus**

(4)

**Waves**

Fig. 9. The role of coupling medium in ultrasonic microscopy; using (a) water as coupling medium for imaging damage in Ti-24Al-11Nb/SCS-6 composite subjected to TMF, (b) methanol as coupling medium for imaging the same specimen.

The capability of ultrasonic microscopy to determine cracks size and evaluate interfacial damage is depicted in Figure 10. This figure shows the first ply of titanium matrix composites with [0/90]S cross-ply and unidirectional lay-up of fibers subjected to isothermal mechanical fatigue [51, 52]. Matrix cracks and interfacial debonding are clearly observed in the figure. Crack bridging by unbroken fibers resulting to interface debonding dominate the fatigue crack growth life as evidenced by the characteristic decrease in crack growth rates as the crack length increased during fatigue cycling.

Fig. 10. Ultrasonic microscopy micrographs of (a) Ti-15Mo-3Nb-3Al-0.2Si/SCS-6 composite with [0/90]S cross-ply lay-up of fibers subjected to 70 hours of isothermal (650oC) fatigue; (b) Ti-15Mo-3Nb-3Al-0.2Si/SCS-6 composite with unidirectional lay-up of fibers after 1.8x105 cycles of isothermal (650o C) fatigue: A. Point of accelerated crack growth to failure. B. Interfacial degradation due to compressive stresses. C. Interfacial degradation due to tensile stresses.

New Trends in Materials Nondestructive

constants.

**4.2 Theoretical analysis** 

engineering materials.

**4.2.1 Nonlinear bulk-wave propagation** 

**Nonlinear medium**

**Linear medium**

**sin ωt A1 sin ωt sin ωt**

Fig. 11. Linear and nonlinear wave propagation in solid materials.

material. This parameter is a measure of the degree of material nonlinearity.

Characterization Using Surface Acoustic Wave Methodologies 267

it is necessary to understand the physics of propagation of acoustic or elastic waves in solids and also the physics involved in the process of fatigue damage in materials. In this direction, the "vibrating string model of dislocation damping" developed in the 1950's [54] is the

It is well known that linearized relation between stress and strain "linearized Hooke's law" is sufficient to describe the mechanical properties of solids. The Hooke's law provides a way to relate stress to strain through the second order elastic constants or moduli of the solid. The linear approximation allows the properties of the material that can be measured experimentally to two properties namely, the velocity of sound (elastic modulus) and attenuation (damping) in the material. However, it has been shown [53] that these parameters are not robust enough to describe the fatigue mechanism. Generally a solid possesses nonlinear elastic behavior, but for practical engineering applications and for the purpose of simplification it is ignored and treated as a linear material. Thus it is necessary to understand acoustic wave propagation in nonlinear elastic material. Introduction of nonlinear terms into stress-strain relationship leads to inclusion of higher-order elastic

Derivation of analytical expressions for the nonlinear parameter enables using nonlinear acoustics techniques for real-time monitoring of fatigue damage accumulation in

In conventional wave propagation analysis the solid medium is considered as linear. Figure 11 depicts the difference in wave propagation between a linear and nonlinear medium.

Engineering materials are nonlinear media. The fundamental wave (sin ωt) that propagates in such material will distort as it propagates, therefore the second-order (sin 2ωt) and higher-order (sin nωt) harmonics will be generated. The anharmonicity of the lattice and dislocation structures contribute in particular to the nonlinearity parameter, β, of the

A longitudinal stress, σ, associated with an ultrasonic wave propagating in the material produces a longitudinal strain, ε, which is a combination of elastic, εel, and plastic, εpl, strains: ε = εel + εpl. The plastic strain component is associated with the motion of

**Nonlinear medium**

**Nonlinear medium**

**A1 sin ωt**

**A2 sin 2ωt**

**An sin nωt**

starting point for all the theories on acoustic wave interaction with dislocations.

## **4. Real-time assessment of damage in aerospace materials based on nonlinear surface acoustic waves**

This section presents an innovative NDE technique based on nonlinear surface-wave acoustics, which is sensitive to early stages of the fatigue process. A nonlinear parameter is derived and monitored to quantify the state of damage during cyclic loading of the material.

## **4.1 Background**

A reliable inspection methodology for quantifying damage in space structures and for relating the level of damage to the remaining life of the material is essential for preventing catastrophic failures in aerospace systems. Many researchers have tried to develop techniques for fatigue damage characterization of aerospace materials based on linear acoustics, i.e. measurements of ultrasonic velocity and attenuation.

Studies of sound velocity as a function of number of fatigue cycles do not show appreciable changes. On the other hand, ultrasonic attenuation exhibits large changes however, relating these changes to the level of material damage is almost impossible since many other factors (experimental parameters, grain size, etc.) can affect the attenuation in a similar way. Studies [53] on nonlinear property of aluminium alloy and stainless steel have shown dramatic changes in the nonlinearity parameter by the time the material undergoes 30-40% of total fatigue life. However, this technique could not be applied, in real time, in test specimens during fatigue. Several dog-bone fatigue specimens were prepared, then fatigued to different number of cycles and the middle section of each one was cut off. This process is reliable as long as the test coupons are assumed to have the same microstructural characteristics before fatigue. However, due to normal statistical variability of test coupons this methodology may not provide meaningful information about the fatigue process. Moreover, the method is not applicable in real structures for health monitoring purposes. Other studies were carried out [38, 39], where two piezoelectric crystals were placed on the two opposite ends of a dog-bone titanium alloy specimen, and nonlinear measurements were performed in real time on the same specimen while undergoing cyclic loading. These studies utilized bulk acoustic waves and was a first step in the direction of developing a methodology for continuing monitoring of fatigue damage in the laboratory. The main drawback of the method for evaluating damage evolution in real aerospace structures is that it is based on bulk acoustic waves and requires access on the two sides of the structure that must also be perfectly parallel to each other, which is not the usual case. Based on the excellent results that the bulk-wave nonlinear method showed for evaluating the level of damage in aerospace materials, a whole new approach has been developed by performing second harmonic nonlinear measurements of surface acoustic waves, which enabled true health monitoring of damage evolution in space structures since the use of SAW overpasses the limitations of existing methods and do not require access to both sides of the structure.

In order to enhance the understanding and predict fatigue failure in critical components used in aerospace applications an innovative NDE technique based on nonlinear acoustics has been developed. This method is sensitive to early stages of fatigue damage accumulation. Failures of engine components, which often occur much earlier than predictions by initial design, increase the need for reliable NDE methods for early fatigue damage characterization. In order to characterize fatigue mechanisms using acoustic waves it is necessary to understand the physics of propagation of acoustic or elastic waves in solids and also the physics involved in the process of fatigue damage in materials. In this direction, the "vibrating string model of dislocation damping" developed in the 1950's [54] is the starting point for all the theories on acoustic wave interaction with dislocations.

It is well known that linearized relation between stress and strain "linearized Hooke's law" is sufficient to describe the mechanical properties of solids. The Hooke's law provides a way to relate stress to strain through the second order elastic constants or moduli of the solid. The linear approximation allows the properties of the material that can be measured experimentally to two properties namely, the velocity of sound (elastic modulus) and attenuation (damping) in the material. However, it has been shown [53] that these parameters are not robust enough to describe the fatigue mechanism. Generally a solid possesses nonlinear elastic behavior, but for practical engineering applications and for the purpose of simplification it is ignored and treated as a linear material. Thus it is necessary to understand acoustic wave propagation in nonlinear elastic material. Introduction of nonlinear terms into stress-strain relationship leads to inclusion of higher-order elastic constants.

## **4.2 Theoretical analysis**

266 Ultrasonic Waves

This section presents an innovative NDE technique based on nonlinear surface-wave acoustics, which is sensitive to early stages of the fatigue process. A nonlinear parameter is derived and monitored to quantify the state of damage during cyclic loading of the material.

A reliable inspection methodology for quantifying damage in space structures and for relating the level of damage to the remaining life of the material is essential for preventing catastrophic failures in aerospace systems. Many researchers have tried to develop techniques for fatigue damage characterization of aerospace materials based on linear

Studies of sound velocity as a function of number of fatigue cycles do not show appreciable changes. On the other hand, ultrasonic attenuation exhibits large changes however, relating these changes to the level of material damage is almost impossible since many other factors (experimental parameters, grain size, etc.) can affect the attenuation in a similar way. Studies [53] on nonlinear property of aluminium alloy and stainless steel have shown dramatic changes in the nonlinearity parameter by the time the material undergoes 30-40% of total fatigue life. However, this technique could not be applied, in real time, in test specimens during fatigue. Several dog-bone fatigue specimens were prepared, then fatigued to different number of cycles and the middle section of each one was cut off. This process is reliable as long as the test coupons are assumed to have the same microstructural characteristics before fatigue. However, due to normal statistical variability of test coupons this methodology may not provide meaningful information about the fatigue process. Moreover, the method is not applicable in real structures for health monitoring purposes. Other studies were carried out [38, 39], where two piezoelectric crystals were placed on the two opposite ends of a dog-bone titanium alloy specimen, and nonlinear measurements were performed in real time on the same specimen while undergoing cyclic loading. These studies utilized bulk acoustic waves and was a first step in the direction of developing a methodology for continuing monitoring of fatigue damage in the laboratory. The main drawback of the method for evaluating damage evolution in real aerospace structures is that it is based on bulk acoustic waves and requires access on the two sides of the structure that must also be perfectly parallel to each other, which is not the usual case. Based on the excellent results that the bulk-wave nonlinear method showed for evaluating the level of damage in aerospace materials, a whole new approach has been developed by performing second harmonic nonlinear measurements of surface acoustic waves, which enabled true health monitoring of damage evolution in space structures since the use of SAW overpasses the limitations of existing methods and do not require access to both sides of the structure. In order to enhance the understanding and predict fatigue failure in critical components used in aerospace applications an innovative NDE technique based on nonlinear acoustics has been developed. This method is sensitive to early stages of fatigue damage accumulation. Failures of engine components, which often occur much earlier than predictions by initial design, increase the need for reliable NDE methods for early fatigue damage characterization. In order to characterize fatigue mechanisms using acoustic waves

**4. Real-time assessment of damage in aerospace materials based on** 

acoustics, i.e. measurements of ultrasonic velocity and attenuation.

**nonlinear surface acoustic waves** 

**4.1 Background** 

Derivation of analytical expressions for the nonlinear parameter enables using nonlinear acoustics techniques for real-time monitoring of fatigue damage accumulation in engineering materials.

## **4.2.1 Nonlinear bulk-wave propagation**

In conventional wave propagation analysis the solid medium is considered as linear. Figure 11 depicts the difference in wave propagation between a linear and nonlinear medium.

Fig. 11. Linear and nonlinear wave propagation in solid materials.

Engineering materials are nonlinear media. The fundamental wave (sin ωt) that propagates in such material will distort as it propagates, therefore the second-order (sin 2ωt) and higher-order (sin nωt) harmonics will be generated. The anharmonicity of the lattice and dislocation structures contribute in particular to the nonlinearity parameter, β, of the material. This parameter is a measure of the degree of material nonlinearity.

A longitudinal stress, σ, associated with an ultrasonic wave propagating in the material produces a longitudinal strain, ε, which is a combination of elastic, εel, and plastic, εpl, strains: ε = εel + εpl. The plastic strain component is associated with the motion of

New Trends in Materials Nondestructive

*<sup>e</sup> C* (C1 equals the initial stress)

the lattice can be written in the form, <sup>111</sup>

 

**4.2.2 Nonlinear Rayleigh wave propagation** 

fundamental frequency and the second order harmonic.

ultrasonic waves,

fundamental wave, A1, and the second harmonic, A2,

1 1

2 1 11 *<sup>e</sup> C C* 3 11 111 3 *<sup>e</sup> C C*

Characterization Using Surface Acoustic Wave Methodologies 269

Assuming C1 = 0, the portion of β describing the nonlinear contribution from the elasticity of

 

3 *<sup>e</sup>*

 

Assuming a purely sinusoidal input wave, εο sin (ωt - kX), a solution to Eq. (9) is:

11

.

 

*t kX k X t kX* (10)

(11)

*C C*

 <sup>1</sup> <sup>2</sup> sin sin 2 4

 

> 2 2 1

 

Therefore β can be described by the following expression containing the amplitudes of the

4*k A X A*

Eq. (11) permits the experimental determination of the nonlinear parameter β. This parameter depends on the amplitudes of the fundamental as well as the second harmonic, the frequency, wave velocity and propagation distance. To obtain experimentally the nonlinear parameter β of a material, the amplitude of the second harmonic needs to be determined experimentally using a specific frequency and propagation distance (38-40,53).

The analysis for obtaining β as described in Section 4.1.1 is only valid for longitudinal ultrasonic waves. The derivation of the nonlinear parameter β for the propagation of 2-D Rayleigh waves is more challenging. Surface acoustic waves are in general a superposition of bulk waves. Longitudinal waves are sensitive as it concerns the generation of higher harmonics, contrary to shear waves which are not considered prone to higher harmonic generation. In this respect, Rayleigh waves are expected to have a similar nonlinear wave propagation behavior as the longitudinal waves. In practice, it is essential to derive the nonlinear parameter β for surface acoustic waves as a function of the amplitudes of the

If one considers a Rayleigh wave propagating in the positive x direction, assuming the z axis into the material, the displacement potentials describing the longitudinal and shear

1

*Ae e*

2

*<sup>L</sup>* ( ) *<sup>c</sup> k z <sup>c</sup> ik x ct*

(12)

The Huang coefficients can be expressed in terms of higher elastic constants. Specifically,

dislocation in the dipole configuration [53-55]. The relation between the stress and elastic strain can be written in the nonlinear form of Hooke's law (quadratic nonlinear approach),

$$
\sigma = \mathbf{A}\_2^{\epsilon} \boldsymbol{\varepsilon}\_{\epsilon} + \frac{1}{2} \mathbf{A}\_3^{\epsilon} \boldsymbol{\varepsilon}\_{\epsilon}^2 + \dots \text{ or } \boldsymbol{\varepsilon} = \frac{1}{\mathbf{A}\_2^{\epsilon}} \boldsymbol{\sigma} - \frac{1}{2} \frac{\mathbf{A}\_3^{\epsilon}}{\left(\mathbf{A}\_2^{\epsilon}\right)^3} \boldsymbol{\sigma}^2 + \dots \tag{5}
$$

where 2 *<sup>e</sup>* and 3 *<sup>e</sup>* are the Huang coefficients.

By considering the dipolar forces one can easily obtain the relation between the stress and the plastic strain [53]. For edge dislocation pairs with opposite polarity, for example, these forces can be written in the following form:

$$F\_x = -\frac{Gb^2}{2\pi(1-\nu)} \frac{\varkappa\left(\chi^2 - \chi^2\right)}{\left(\chi^2 + \chi^2\right)^2} \tag{6}$$

where, b is the Burgers vector, ν the Poisson's ratio, G the shear modulus, and x and y the Cartesian coordinates of one dislocation in the pair in respect to the other. At equilibrium state, y equals the dipole height, h.

The relation between the plastic strain and the relative dislocation displacement ξ=x−h is given by the expression *pl dp b* , where Ω is a conversion factor and Λdp is the dipole density [53].

Using these relationships and an expansion of Eq. (6) in a power series in x with respect to h leads to the following equation

$$
\sigma = \mathbf{A}\_2^{\varepsilon} \left[ \varepsilon - \frac{1}{2} \left( \frac{\mathbf{A}\_3^{\varepsilon}}{\left( \mathbf{A}\_2^{\varepsilon} \right)^3} + \frac{\mathbf{A}\_3^{dp}}{\left( \mathbf{A}\_2^{4p} \right)^3} \right) \right] \varepsilon^2 + \dots \tag{7}
$$

The wave equation with respect to the Lagrangian coordinate X is given by

$$
\rho \frac{\partial^2 \mathcal{E}}{\partial t^2} = \frac{\partial^2 \sigma}{\partial \mathbf{X}^2} \tag{8}
$$

Replacing σ, given by Eq. (7), in Eq. (8) the following equation can be obtained:

$$\frac{\partial^2 \mathcal{E}}{\partial t^2} - c^2 \frac{\partial^2 \mathcal{E}}{\partial \mathbf{X}^2} = -c^2 \mathcal{J} \left[ \varepsilon \frac{\partial^2 \mathcal{E}}{\partial \mathbf{X}^2} + \left( \frac{\partial \mathcal{E}}{\partial \mathbf{X}} \right)^2 \right] \tag{9}$$

$$\text{where } c = \sqrt{\frac{A\_2^{\varepsilon}}{\rho}} \text{ and } \beta = \beta\_\varepsilon + \beta\_{dp} \text{ with } \beta\_\varepsilon = -\frac{A\_3^{\varepsilon}}{A\_2^{\varepsilon}} \text{ and } \beta\_{dp} = \frac{16\pi\Omega R^2 \Lambda\_{d\eta} h^3 (1-\nu)^2 \left(\Lambda\_2^{\varepsilon}\right)^2}{G^2 b}$$

The Huang coefficients can be expressed in terms of higher elastic constants. Specifically,

1 1 *<sup>e</sup> C* (C1 equals the initial stress)

$$\begin{aligned} \mathbf{A}\_2^\varepsilon &= \mathbf{C}\_1 + \mathbf{C}\_{11} \\ \mathbf{A}\_3^\varepsilon &= \mathbf{\mathcal{B}} \mathbf{C}\_{11} + \mathbf{C}\_{111} \end{aligned}$$

268 Ultrasonic Waves

dislocation in the dipole configuration [53-55]. The relation between the stress and elastic strain can be written in the nonlinear form of Hooke's law (quadratic nonlinear

By considering the dipolar forces one can easily obtain the relation between the stress and the plastic strain [53]. For edge dislocation pairs with opposite polarity, for example, these

> <sup>2</sup> 2 (1 ) 2 2 *<sup>x</sup> Gb x x <sup>y</sup> <sup>F</sup>*

where, b is the Burgers vector, ν the Poisson's ratio, G the shear modulus, and x and y the Cartesian coordinates of one dislocation in the pair in respect to the other. At equilibrium

The relation between the plastic strain and the relative dislocation displacement ξ=x−h is

Using these relationships and an expansion of Eq. (6) in a power series in x with respect to h

2 2 <sup>1</sup> ... <sup>2</sup>

*e dp*

 

*dp*

2 3 3

2 2 2 2 *t* 

22 2 2

 

2

*e e e A A*

*<sup>e</sup> dp <sup>e</sup>*

3 3 2

 

1 1 ... <sup>2</sup> *e*

<sup>2</sup> <sup>2</sup>

*x y*

2 2 <sup>2</sup>

*<sup>e</sup> <sup>e</sup>*

 

3 2 3

 

, where Ω is a conversion factor and Λdp is the

(8)

and <sup>2</sup> 23 2

(5)

(6)

(7)

(9)

 

2 16 (1 ) *<sup>e</sup> dp*

*G b*

*R h*

2

2

<sup>1</sup> ... <sup>2</sup>

 *e e* or

2 3

*<sup>e</sup>* are the Huang coefficients.

*e e*

forces can be written in the following form:

state, y equals the dipole height, h.

given by the expression *pl dp*

leads to the following equation

dipole density [53].

where <sup>2</sup>

*c*

*e A*

and  

 

The wave equation with respect to the Lagrangian coordinate X is given by

Replacing σ, given by Eq. (7), in Eq. (8) the following equation can be obtained:

2 2 22 2 *c c t X*

 

*e d <sup>p</sup>* with <sup>3</sup>

*b*

approach),

where 2

*<sup>e</sup>* and 3

Assuming C1 = 0, the portion of β describing the nonlinear contribution from the elasticity of the lattice can be written in the form, <sup>111</sup> 11 3 *<sup>e</sup> C C* .

Assuming a purely sinusoidal input wave, εο sin (ωt - kX), a solution to Eq. (9) is:

$$\varepsilon = \varepsilon\_o \sin\left(\alpha t - kX\right) - \frac{1}{4}\beta k \varepsilon\_o^2 X \sin\left[2\left(\alpha t - kX\right)\right] \tag{10}$$

Therefore β can be described by the following expression containing the amplitudes of the fundamental wave, A1, and the second harmonic, A2,

$$
\beta = \frac{4k}{X} \frac{A\_2}{A\_1^2} \tag{11}
$$

Eq. (11) permits the experimental determination of the nonlinear parameter β. This parameter depends on the amplitudes of the fundamental as well as the second harmonic, the frequency, wave velocity and propagation distance. To obtain experimentally the nonlinear parameter β of a material, the amplitude of the second harmonic needs to be determined experimentally using a specific frequency and propagation distance (38-40,53).

### **4.2.2 Nonlinear Rayleigh wave propagation**

The analysis for obtaining β as described in Section 4.1.1 is only valid for longitudinal ultrasonic waves. The derivation of the nonlinear parameter β for the propagation of 2-D Rayleigh waves is more challenging. Surface acoustic waves are in general a superposition of bulk waves. Longitudinal waves are sensitive as it concerns the generation of higher harmonics, contrary to shear waves which are not considered prone to higher harmonic generation. In this respect, Rayleigh waves are expected to have a similar nonlinear wave propagation behavior as the longitudinal waves. In practice, it is essential to derive the nonlinear parameter β for surface acoustic waves as a function of the amplitudes of the fundamental frequency and the second order harmonic.

If one considers a Rayleigh wave propagating in the positive x direction, assuming the z axis into the material, the displacement potentials describing the longitudinal and shear ultrasonic waves,

$$\varphi = A e^{-k \sqrt{1 - \left(\frac{c}{c\_L}\right)^2} z} e^{ik \left(x - ct\right)}\tag{12}$$

New Trends in Materials Nondestructive

particle velocity, *<sup>z</sup> u* or displacement, *<sup>z</sup> u* , is detected.

(2 )

*z*

2 2 1

(2 ) ( ) *z z*

*u A u A* 

propagation distance.

fundamental is given by:

where ( ) ( ; , 0) *u u xz z z* 

parenthesis of Eq. (19).

The harmonic ratio <sup>2</sup>

dependent on the amplitude ratio <sup>2</sup>

required for a quadratic nonlinearity [56].

waves [56],

 

Characterization Using Surface Acoustic Wave Methodologies 271

harmonic generation in the case of the propagation of surface acoustic waves. Hence, the amplitudes of the in-plane displacement, ux, of the fundamental and second harmonic of a near-surface Rayleigh wave can be related as those in the case of bulk longitudinal waves [56]:

> <sup>2</sup> 8 *k xB <sup>B</sup>*

where β is the acoustic nonlinear parameter for the bulk longitudinal waves, and x is the

In case of experimental determination of β for Rayleigh waves using contact ultrasonic transducers of interferometry, the out-of-plane component on the surface (z=0) of the

From Eqs. (15b), (16b), and (17), the ratio of the amplitudes of the second harmonic to the

<sup>2</sup> 2 2 <sup>2</sup>

*<sup>z</sup> R l <sup>R</sup>*

components are related to the acoustic nonlinear parameter β for the bulk longitudinal

2 2 2 2 8 (2 ) <sup>2</sup> <sup>1</sup> ( ) 2 *z R l R lz R R R S i u k k k kxu k k k k*

While the shear wave alone does not generate higher harmonics, shear wave components interact with longitudinal ones, as it becomes evident from the second term in the

assess the state of damage in materials with different levels of fatigue. The dimensionless nonlinear parameter β in case of propagating Rayleigh surface waves in the material is also

Although the nonlinear parameter β remains constant for different propagation distances, the amplitude of the second harmonic changes linearly with the propagation distance, as

In the measurement of nonlinearity parameter β under cyclic loading the change in β is more important than its absolute values. Hence, measurements of relative changes in the

(2 ) <sup>2</sup> 8 1

*<sup>u</sup> k k <sup>k</sup> <sup>i</sup>*

*u k x*

2 1 *A*

**4.3 Real time measurement of material nonlinearity during fatigue** 

2 1

2 2

can be used to determine material nonlinearity and to

*A* as in case of bulk longitudinal waves.

2

*R R S*

2 2 2

*k k k*

. Therefore, the measured out-of-plane displacement

2 2 1 1

(17)

(18)

(19)

2 1 *<sup>S</sup>* ( ) *<sup>c</sup> k z <sup>c</sup> ik x ct Be e* can be re-written in the form:

$$
\phi = -i \frac{B\_1}{k\_R} e^{-\sqrt{k\_R^2 - k\_I^2}z} e^{i(k\_R x - \alpha t)}\tag{13}
$$

$$
\phi = -i \frac{C\_1}{k\_R} e^{-\sqrt{k\_R^2 - k\_S^2}z} e^{i(k\_R x - \alpha t)}
$$

where, kR, kl, ks are the wave-numbers for Rayleigh, longitudinal, and shear ultrasonic waves, respectively [56].

Considering the boundary conditions for a stress-free surface in Eq. (13), a relation between the constants B1 and C1 can be obtained:

$$B\_1 = -i\frac{2k\_R\sqrt{k\_R^2 - k\_1^2}}{2k\_R^2 - k\_S^2}C\_1\tag{14}$$

Taking into account that the surface acoustic waves are a superposition of longitudinal and shear waves propagating along a stress-free surface that have the same velocity, the displacement components can be decomposed into their longitudinal and shear components [56-60]:

$$u\_x = B\_1 \left( e^{-\sqrt{k\_R^2 - k\_I^2}z} - \frac{2\sqrt{\left(k\_R^2 - k\_I^2\right)\left(k\_R^2 - k\_S^2\right)}}{2k\_R^2 - k\_S^2} e^{-\sqrt{k\_R^2 - k\_S^2}z} \right) e^{i\left(k\_R x - \alpha t\right)}\tag{15}$$

$$u\_z = iB\_1 \frac{\sqrt{k\_R^2 - k\_I^2}}{k\_R} \left( e^{-\sqrt{k\_R^2 - k\_I^2}z} - \frac{2k\_R^2}{2k\_R^2 - k\_S^2} e^{-\sqrt{k\_R^2 - k\_S^2}z} \right) e^{i\left(k\_R x - \alpha t\right)}$$

The first term in Eq. (15a) presents the pure longitudinal wave motion. Considering a material with a weak nonlinearity, the second order harmonic Rayleigh waves that propagate a large enough distance can be expressed in the form [56-60]:

$$u\_x \approx B\_2 \left( e^{-2\sqrt{k\_R^2 - k\_l^2}z} - \frac{2\sqrt{\left(k\_R^2 - k\_l^2\right)\left(k\_R^2 - k\_S^2\right)}}{2k\_R^2 - k\_S^2} e^{-2\sqrt{k\_R^2 - k\_S^2}z} \right) e^{i2\left(k\_R x - \alpha t\right)}\tag{16}$$

$$u\_z \approx iB\_2 \frac{\sqrt{k\_R^2 - k\_l^2}}{k\_R} \left( e^{-2\sqrt{k\_R^2 - k\_l^2}z} - \frac{2k\_R^2}{2k\_R^2 - k\_S^2} e^{-2\sqrt{k\_R^2 - k\_S^2}z} \right) e^{i2\left(k\_R x - \alpha t\right)}$$

Taking into account the fact that the acoustic nonlinear behavior of the shear waves in an isotropic medium ceases to exist due to the symmetry of the third order elastic constants, it can be inferred that the longitudinal wave component is only one contributing to the higher

2 2 <sup>1</sup> *R l* ( ) *<sup>R</sup> k kz ikx t*

2 2 <sup>1</sup> *R S* ( ) *<sup>R</sup> k kz ikx t*

2 2 1 (13)

(14)

( )

( )

(15)

(16)

*R B*

*R C*

*k*

*k*

*ie e*

*ie e*

where, kR, kl, ks are the wave-numbers for Rayleigh, longitudinal, and shear ultrasonic

Considering the boundary conditions for a stress-free surface in Eq. (13), a relation between

1 1 2 2

Taking into account that the surface acoustic waves are a superposition of longitudinal and shear waves propagating along a stress-free surface that have the same velocity, the displacement components can be decomposed into their longitudinal and shear components

> 2 2 2 2 2 22 2

*k kk k*

*R S*

2 2 2 2 2 2 <sup>2</sup>

The first term in Eq. (15a) presents the pure longitudinal wave motion. Considering a material with a weak nonlinearity, the second order harmonic Rayleigh waves that

> 2 2 2 2 2 22 2 2 2 2( )

*k kk k*

*R S*

2 2 2 2 2 2 <sup>2</sup>

Taking into account the fact that the acoustic nonlinear behavior of the shear waves in an isotropic medium ceases to exist due to the symmetry of the third order elastic constants, it can be inferred that the longitudinal wave component is only one contributing to the higher

2 2 *R l R S <sup>R</sup> R l k kz R k kz i kx t*

*R l R S <sup>R</sup> Rl RS k kz k kz i kx t*

2 2 2( )

*R l R S <sup>R</sup> Rl RS k kz k kz ikx t*

2 2 *R l R S <sup>R</sup> R l k kz R k kz ikx t*

2

*R R S k k <sup>k</sup> u iB e e e k k k*

2

*u Be e e k k* 

2 2 2

*R R S k k <sup>k</sup> u iB <sup>e</sup> e e k k k*

*u Be e e k k* 

1 2 2

1 2 2 2

propagate a large enough distance can be expressed in the form [56-60]:

2 2 2 2

*kk k Bi C k k*

2 2 *R R R S*

2

waves, respectively [56].

the constants B1 and C1 can be obtained:

*x*

*z*

*x*

*z*

*<sup>S</sup>* ( ) *<sup>c</sup> k z <sup>c</sup> ik x ct*

can be re-written in the form:

1

 *Be e* 

[56-60]:

harmonic generation in the case of the propagation of surface acoustic waves. Hence, the amplitudes of the in-plane displacement, ux, of the fundamental and second harmonic of a near-surface Rayleigh wave can be related as those in the case of bulk longitudinal waves [56]:

$$B\_2 = \frac{\beta k\_1^2 x B\_1^2}{8} \tag{17}$$

where β is the acoustic nonlinear parameter for the bulk longitudinal waves, and x is the propagation distance.

In case of experimental determination of β for Rayleigh waves using contact ultrasonic transducers of interferometry, the out-of-plane component on the surface (z=0) of the particle velocity, *<sup>z</sup> u* or displacement, *<sup>z</sup> u* , is detected.

From Eqs. (15b), (16b), and (17), the ratio of the amplitudes of the second harmonic to the fundamental is given by:

$$\frac{\overline{\mu}\_z(2\alpha o)}{\overline{\mu}\_z^2(2\alpha o)} = \frac{\beta k\_1^2 \alpha}{8i \left(\frac{\sqrt{k\_R^2 - k\_l^2}}{k\_R}\right) \left(1 - \frac{2k\_R^2}{2k\_R^2 - k\_S^2}\right)}\tag{18}$$

where ( ) ( ; , 0) *u u xz z z* . Therefore, the measured out-of-plane displacement components are related to the acoustic nonlinear parameter β for the bulk longitudinal waves [56],

$$\beta = \frac{8i \ \overline{u}\_z(2o)}{k\_l^2 \ge \overline{u}\_z^2(o)k\_R} \frac{\sqrt{k\_R^2 - k\_l^2}}{k\_R} \left(1 - \frac{2k\_R^2}{2k\_R^2 - k\_S^2}\right) \tag{19}$$

While the shear wave alone does not generate higher harmonics, shear wave components interact with longitudinal ones, as it becomes evident from the second term in the parenthesis of Eq. (19).

The harmonic ratio <sup>2</sup> 2 2 1 (2 ) ( ) *z z u A u A* can be used to determine material nonlinearity and to

assess the state of damage in materials with different levels of fatigue. The dimensionless nonlinear parameter β in case of propagating Rayleigh surface waves in the material is also

dependent on the amplitude ratio <sup>2</sup> 2 1 *A A* as in case of bulk longitudinal waves.

Although the nonlinear parameter β remains constant for different propagation distances, the amplitude of the second harmonic changes linearly with the propagation distance, as required for a quadratic nonlinearity [56].

#### **4.3 Real time measurement of material nonlinearity during fatigue**

In the measurement of nonlinearity parameter β under cyclic loading the change in β is more important than its absolute values. Hence, measurements of relative changes in the

New Trends in Materials Nondestructive

Characterization Using Surface Acoustic Wave Methodologies 273

(a)

(b)

Since the nonlinear property of the specimen was measured, it was necessary to verify that the measurement setup itself was linear indeed. For checking the system's linearity a simple experiment was performed with an unfatigued Ti-6Al-4V sample at room temperature by changing the input voltage to the transmitting transducer. It was thus demonstrated that the slope of the curve of the amplitude of second harmonic vs. the fundamental using the linear

Fig. 12. Performance data of the (a) 5 MHz and (b) 10 MHz 100 W band-pass filters.

filters was linear.

nonlinearity of the material from the virgin state to a fatigued state are discussed here. Therefore, the β parameter defined in Eq. (19) and normalized by the value βo (nonlinear parameter of the material at the virgin state) is experimentally measured. In this sense, in order to assess the level of fatigue damage using nonlinear acoustics measurements a determination of the absolute value of the material's nonlinearity is not required, enabling real-time experiments [38-39].

Below it is shown an example of assessing in real-time the state of fatigue damage in titanium alloys undergone cyclic loading. The piezoelectric detection of second harmonic ultrasonic amplitude is based on propagating a pure single frequency f ultrasonic wave through the sample. As the elastic wave propagates through the medium, it is distorted as the result of the anharmonicity of the crystalline lattice and other microstructural disturbances, such as the grain boundaries and dislocations. During the fatigue process of Ti-6Al-4V, the lattice anharmonicity remains constant since the stress level applied to the specimen is far below the yield strength i.e., in the elastic region. However, the other factors like grain boundaries, dislocations, and other impurities change as a function of fatigue level. The distorted signal is composed of the combination of the harmonics and grows as it propagates until the attenuation factor stops its growth. The harmonic portion of the distorted ultrasonic signal is very sensitive to the changes in the strain energy density due to the changes of these factors. The second harmonic wave, of frequency 2f, is detected by a second piezoelectric transducer. The transducer was manufactured using 36o Y-cut LiNbO3 crystals placed inside specially designed brass housing and plexiglass tubing. Lithium niobate single-crystals were used since they are linear materials and also exhibit higher electromechanical coupling compared to quartz crystals.

An important issue for correctly measuring material nonlinearity is to use linear instrumentation. The experimental data shown below are obtained using amplifiers and filters of linear response. For example, the fundamental and second harmonic signals were detected using high quality linear band-pass filters with a rejection ratio better than 60 dB. Two such low power (up to 100 W) filters were designed, one with a central frequency of 5 MHz, the other 10 MHz. Figures 12(a) and 12(b) show the 5 MHz and 10MHz low power filters' characteristics and simulation performance data, respectively.

Transducer holder and the grips for the fatigue load frame were designed to enable on-line monitoring of the material's nonlinearity parameter during the fatigue process, since the conventional grips are inadequate for attaching transducers to the specimen.

The experimental configuration for on-line piezoelectric detection of second harmonic signal during mechanical fatigue is based on a tone-burst generator and a power amplifier to launch longitudinal sound waves into the specimen at a frequency of 5 MHz. A linear highpower band-pass filter was placed between the power amplifier and the transducer to make sure that unwanted harmonic signals are filtered out. The same transducer was used to detect the fundamental signal reflected from the other end of the specimen. A 10 MHz transducer bonded to the other end of the specimen was used to receive the second harmonic signal. After the second harmonic signal is detected, it was fed to a linear narrow band amplifier through the 10 MHz band-pass filter. Both fundamental V1 (mV) and second harmonic V2 (mV) signals were sent to the A/D converter for digitization and the nonlinear parameter β was finally determined from the sampled signals.

nonlinearity of the material from the virgin state to a fatigued state are discussed here. Therefore, the β parameter defined in Eq. (19) and normalized by the value βo (nonlinear parameter of the material at the virgin state) is experimentally measured. In this sense, in order to assess the level of fatigue damage using nonlinear acoustics measurements a determination of the absolute value of the material's nonlinearity is not required, enabling

Below it is shown an example of assessing in real-time the state of fatigue damage in titanium alloys undergone cyclic loading. The piezoelectric detection of second harmonic ultrasonic amplitude is based on propagating a pure single frequency f ultrasonic wave through the sample. As the elastic wave propagates through the medium, it is distorted as the result of the anharmonicity of the crystalline lattice and other microstructural disturbances, such as the grain boundaries and dislocations. During the fatigue process of Ti-6Al-4V, the lattice anharmonicity remains constant since the stress level applied to the specimen is far below the yield strength i.e., in the elastic region. However, the other factors like grain boundaries, dislocations, and other impurities change as a function of fatigue level. The distorted signal is composed of the combination of the harmonics and grows as it propagates until the attenuation factor stops its growth. The harmonic portion of the distorted ultrasonic signal is very sensitive to the changes in the strain energy density due to the changes of these factors. The second harmonic wave, of frequency 2f, is detected by a second piezoelectric transducer. The transducer was manufactured using 36o Y-cut LiNbO3 crystals placed inside specially designed brass housing and plexiglass tubing. Lithium niobate single-crystals were used since they are linear materials and also exhibit higher

An important issue for correctly measuring material nonlinearity is to use linear instrumentation. The experimental data shown below are obtained using amplifiers and filters of linear response. For example, the fundamental and second harmonic signals were detected using high quality linear band-pass filters with a rejection ratio better than 60 dB. Two such low power (up to 100 W) filters were designed, one with a central frequency of 5 MHz, the other 10 MHz. Figures 12(a) and 12(b) show the 5 MHz and 10MHz low power

Transducer holder and the grips for the fatigue load frame were designed to enable on-line monitoring of the material's nonlinearity parameter during the fatigue process, since the

The experimental configuration for on-line piezoelectric detection of second harmonic signal during mechanical fatigue is based on a tone-burst generator and a power amplifier to launch longitudinal sound waves into the specimen at a frequency of 5 MHz. A linear highpower band-pass filter was placed between the power amplifier and the transducer to make sure that unwanted harmonic signals are filtered out. The same transducer was used to detect the fundamental signal reflected from the other end of the specimen. A 10 MHz transducer bonded to the other end of the specimen was used to receive the second harmonic signal. After the second harmonic signal is detected, it was fed to a linear narrow band amplifier through the 10 MHz band-pass filter. Both fundamental V1 (mV) and second harmonic V2 (mV) signals were sent to the A/D converter for digitization and the nonlinear

real-time experiments [38-39].

electromechanical coupling compared to quartz crystals.

filters' characteristics and simulation performance data, respectively.

parameter β was finally determined from the sampled signals.

conventional grips are inadequate for attaching transducers to the specimen.

Fig. 12. Performance data of the (a) 5 MHz and (b) 10 MHz 100 W band-pass filters.

Since the nonlinear property of the specimen was measured, it was necessary to verify that the measurement setup itself was linear indeed. For checking the system's linearity a simple experiment was performed with an unfatigued Ti-6Al-4V sample at room temperature by changing the input voltage to the transmitting transducer. It was thus demonstrated that the slope of the curve of the amplitude of second harmonic vs. the fundamental using the linear filters was linear.

New Trends in Materials Nondestructive

fatigue.

incorporate the changes in the specimen length.

Fig. 15. Variation of longitudinal wave velocity with fatigue life

6000

6050 6100

6150

**Ultrasonic velocity (m/s)**

6200 6250

6300

Characterization Using Surface Acoustic Wave Methodologies 275

Fig. 14. Long term stability test of the measurement system at room temperature.

The experimental technique described above was used to measure the nonlinear acoustic properties of Ti-6Al-4V alloys and characterize in real-time their fatigue behavior. During the fatigue tests, the samples were subjected to cyclic loading at the frequency of 1 Hz under low cycle fatigue conditions (σmax = 850 MPa, and R ratio = 0.1). The ultrasonic velocity and nonlinear property were measured at zero-load on the sample, at an interval of 100 cycles of

Attenuation and velocity of longitudinal wave measurements were performed at a frequency of 5 MHz at various stages of fatigue. It was observed that the longitudinal sound velocity had a minute measurable change in the beginning of the fatigue process (Fig. 15). This can be explained by the small increase of the specimen's length that occurs during the fatigue process. For an accurate determination of the velocity of sound it is necessary to

> 0 500 1000 1500 2000 **Number of cycle (X 10)**

Fig. 13. Linearity check of the measurement setup; (a) without the linear band-pass filter for the second harmonic signal, and (b) with the linear band-pass filter for the second harmonic signal.

As it is demonstrated by comparing Figs. 13(a) and 13(b), using linear band-pass filters leads to a totally linear experimental setup. Thus, any determination of nonlinear behavior can be attributed to material nonlinearity and not to the measurement system.

Since the measurements require a relatively long time for experiments performed at a cyclic frequency of 1 Hz, it is necessary to check the stability of the measuring system over a period time. The amplitudes of the fundamental and second harmonic signals were monitored over a period of 24 hours in the laboratory and only small, almost negligible fluctuations, compared to the size of the measured values during the fatigue test, were observed. Figure 14 shows the amplitudes of the fundamental, A1, and second harmonic, A2, signals as a function of time for period of 24 hours in laboratory conditions.

Fig. 13. Linearity check of the measurement setup; (a) without the linear band-pass filter for the second harmonic signal, and (b) with the linear band-pass filter for the second harmonic

As it is demonstrated by comparing Figs. 13(a) and 13(b), using linear band-pass filters leads to a totally linear experimental setup. Thus, any determination of nonlinear behavior can be

Since the measurements require a relatively long time for experiments performed at a cyclic frequency of 1 Hz, it is necessary to check the stability of the measuring system over a period time. The amplitudes of the fundamental and second harmonic signals were monitored over a period of 24 hours in the laboratory and only small, almost negligible fluctuations, compared to the size of the measured values during the fatigue test, were observed. Figure 14 shows the amplitudes of the fundamental, A1, and second harmonic, A2,

attributed to material nonlinearity and not to the measurement system.

signals as a function of time for period of 24 hours in laboratory conditions.

signal.

Fig. 14. Long term stability test of the measurement system at room temperature.

The experimental technique described above was used to measure the nonlinear acoustic properties of Ti-6Al-4V alloys and characterize in real-time their fatigue behavior. During the fatigue tests, the samples were subjected to cyclic loading at the frequency of 1 Hz under low cycle fatigue conditions (σmax = 850 MPa, and R ratio = 0.1). The ultrasonic velocity and nonlinear property were measured at zero-load on the sample, at an interval of 100 cycles of fatigue.

Attenuation and velocity of longitudinal wave measurements were performed at a frequency of 5 MHz at various stages of fatigue. It was observed that the longitudinal sound velocity had a minute measurable change in the beginning of the fatigue process (Fig. 15). This can be explained by the small increase of the specimen's length that occurs during the fatigue process. For an accurate determination of the velocity of sound it is necessary to incorporate the changes in the specimen length.

Fig. 15. Variation of longitudinal wave velocity with fatigue life

New Trends in Materials Nondestructive

experimental work [38-40, 53].

nonlinearity as a function of fatigue level.

**5. Conclusion** 

Characterization Using Surface Acoustic Wave Methodologies 277

As the material was undergoing fatigue the amplitude of the second harmonic signal increases to give a steeper slope. Figure 17 shows measurements of β as a function of fatigue cycles for three different Ti-6Al-4V samples. The trend of the variation of relative β as a function of fatigue life is similar for the three samples; however, the level of nonlinearity is different due to the fact that different samples are fatigue damaged in a dissimilar way.

Figure 18 depicts the normalized nonlinearity (shown with line plot) of Ti-6Al-4V samples as a function of the number of cycles and correlation with transmission electron microscopy (TEM) analysis of the dislocation density (shown with data points). It can be observed in Fig. 18 that acoustic nonlinearity of the material exhibits large changes during the fatigue process. This finding is in contrast with the measurements of attenuation and elastic behavior, where the majority of variation occurred before the 20% of fatigue lifetime. The second harmonic signal generated during the fatigue process is not only sensitive to the early stage of the process, but also to later stages of damage. This implies that the harmonic signal is very sensitive to the microstructural changes in the material. The variation of nonlinearity continues due to the generation of additional dislocation dipoles by the fatigue process and their interaction with the acoustic waves, as predicted by relevant models and

Fig. 18. Correlation of TEM imaging and dislocation density in Ti-6Al-4V with normalized

The present chapter gives an overview of contemporary techniques to assess the quality of materials using surface elastic waves. It is highlighted that different instrumentation and methodology facilitates non destructive evaluation in quite distinct material groups, like concrete and aerospace composites. In both kinds of material, damage is primarily initiated on the surface. Therefore, early assessment by surface waves is crucial for the estimation of

Additionally, it was observed that the attenuation increased significantly in the initial stages of fatigue (Fig. 16). The initial increase of attenuation of 50 % is quite significant; however, it is less sensitive to fatigue process beyond 20% of the fatigue life. The higher attenuation at the higher fatigue cycles may indicate an increase in the scattering of sound waves due to the increased dislocation dipole density from fatigue. As the increase in dislocation density saturates, the level of scattering of sound wave within the material become stable. It should be pointed out, however, that the general tendency of dislocation movement is known to migrate to the surface of the material. This could mean that the attenuation measurement in the bulk is less meaningful throughout the entire lifetime of the material.

Fig. 16. Variation of ultrasonic attenuation with fatigue life

Fig. 17. Variation of the nonlinear parameter β with fatigue life in Ti-6Al-4V

Variation in amplitude of the second harmonic signal, as the amplitude of the fundamental signal is changed, was used for measurement of nonlinear acoustic behavior of the material.

Additionally, it was observed that the attenuation increased significantly in the initial stages of fatigue (Fig. 16). The initial increase of attenuation of 50 % is quite significant; however, it is less sensitive to fatigue process beyond 20% of the fatigue life. The higher attenuation at the higher fatigue cycles may indicate an increase in the scattering of sound waves due to the increased dislocation dipole density from fatigue. As the increase in dislocation density saturates, the level of scattering of sound wave within the material become stable. It should be pointed out, however, that the general tendency of dislocation movement is known to migrate to the surface of the material. This could mean that the attenuation measurement in

0 200 400 600 800 1000 1200 1400 1600 1800 2000 **Number of cycle (X 10)**

0 5000 10000 15000 20000 25000 30000 35000 40000

Number of cycles

Variation in amplitude of the second harmonic signal, as the amplitude of the fundamental signal is changed, was used for measurement of nonlinear acoustic behavior of the material.

Fig. 17. Variation of the nonlinear parameter β with fatigue life in Ti-6Al-4V

sample #1 sample #2 sample #3

the bulk is less meaningful throughout the entire lifetime of the material.

Fig. 16. Variation of ultrasonic attenuation with fatigue life

0

0

0.5

1

1.5

 

Nonlinearity 0

2

2.5

0.5

1

1.5

**Attenuation (dB/cm)**

2

2.5

3

As the material was undergoing fatigue the amplitude of the second harmonic signal increases to give a steeper slope. Figure 17 shows measurements of β as a function of fatigue cycles for three different Ti-6Al-4V samples. The trend of the variation of relative β as a function of fatigue life is similar for the three samples; however, the level of nonlinearity is different due to the fact that different samples are fatigue damaged in a dissimilar way.

Figure 18 depicts the normalized nonlinearity (shown with line plot) of Ti-6Al-4V samples as a function of the number of cycles and correlation with transmission electron microscopy (TEM) analysis of the dislocation density (shown with data points). It can be observed in Fig. 18 that acoustic nonlinearity of the material exhibits large changes during the fatigue process. This finding is in contrast with the measurements of attenuation and elastic behavior, where the majority of variation occurred before the 20% of fatigue lifetime. The second harmonic signal generated during the fatigue process is not only sensitive to the early stage of the process, but also to later stages of damage. This implies that the harmonic signal is very sensitive to the microstructural changes in the material. The variation of nonlinearity continues due to the generation of additional dislocation dipoles by the fatigue process and their interaction with the acoustic waves, as predicted by relevant models and experimental work [38-40, 53].

Fig. 18. Correlation of TEM imaging and dislocation density in Ti-6Al-4V with normalized nonlinearity as a function of fatigue level.

## **5. Conclusion**

The present chapter gives an overview of contemporary techniques to assess the quality of materials using surface elastic waves. It is highlighted that different instrumentation and methodology facilitates non destructive evaluation in quite distinct material groups, like concrete and aerospace composites. In both kinds of material, damage is primarily initiated on the surface. Therefore, early assessment by surface waves is crucial for the estimation of

New Trends in Materials Nondestructive

*Press, Boca Raton FL,* pp. 275-304

*concrete. Boca Raton: CRC Press*

Surface Waves. *NDT&E INT,* Vol. 33, pp. 1-6

*and Building Materials,* Vol. 25, pp. 3089-3097

*International,* Vol. 39, pp. 514–524

*Journal* Vol. 95, No. 1, pp. 27-36

(10.1111/j.1475-1305.2009.00721.x)

*Ultrasonics,* Vol. 44, pp. 200-210

*Composites,* Vol. 31, No. 1, pp. 77-83

754-760

1124-1130

4, pp. 289–297

Vol. 33, No. 4, pp. 525-538

Characterization Using Surface Acoustic Wave Methodologies 279

[11] Sansalone, M. and Carino, N. J. (2004). Stress Wave Propagation Methods. *CRC* 

[12] Naik, T. R., Malhotra, V. M. and Popovics, J. S. (2004). The Ultrasonic Pulse Velocity

[13] Philippidis, T. P. and Aggelis, D. G. (2003). An Acousto-Ultrasonic Approach for the

[14] Gudra, T. and Stawinski, B. (2000). Non-Destructive Characterization of Concrete Using

[15] Aggelis, D. G., Kordatos, E. Z., Strantza, M., Soulioti, D. V. and Matikas, T. E. (2011).

[16] Aggelis, D. G. and Shiotani, T. (2008). Surface Wave Dispersion in Cement-Based

[17] Landis, E. N. and Shah, S. P. (1995). Frequency-Dependent Stress Wave Attenuation in Cement-Based Materials. *J. Eng. Mech.-ASCE,* Vol. 121, No. 6, pp. 737-743 [18] Punurai, W., Jarzynski, J., Qu, J., Kurtis, K. E. and Jacobs, L. J. (2006). Characterization

[19] Shah, S. P., Popovics, J. S., Subramanian, K. V. and Aldea, C. M. (2000). New Directions

[20] Selleck, S. F., Landis, E. N., Peterson, M. L., Shah, S. P. and Achenbach, J. D. (1998).

[21] Jacobs, L. J. and Owino, J. O. (2000). Effect of Aggregate Size on Attenuation of Rayleigh

[22] Owino, J. O. and Jacobs, L. J. (1999). Attenuation Measurements in Cement-Based Materials Using Laser Ultrasonics. *J. Eng. Mech.-ASCE,* Vol. 125, No. 6, pp. 637-647 [23] Aggelis, D. G. (2010). Damage Characterization of Inhomogeneous Materials:

[24] Chaix, J. F., Garnie, r. V. and Corneloup, G. (2006). Ultrasonic Wave Propagation in

[25] Kim, D. S., Seo, W. S. and Lee, K. M. (2006). IE–SASW Method for Nondestructive Evaluation of Concrete Structure. *NDT&E International,* Vol. 39, pp. 143-154 [26] Hevin, G., Abraham, O., Pedersen, H. A. and Campillo, M. (1998). Characterisation of

[27] Aggelis, D. G., Shiotani, T. and Polyzos, D. (2009). Characterization of Surface Crack

Media: Inclusion Size Effect. *NDT&E INT,* Vol. 41, pp. 319-325

*Handbook on Nondestructive Testing of Concrete, Malhotra V. M., Carino N. J., eds. CRC* 

Method. *Malhotra VM, Carino NJ. editors. CRC Handbook on nondestructive testing of* 

Determination of Water-to-Cement Ratio in Concrete. *Cement and Concrete Research,*

NDT Approach for Characterization of Subsurface Cracks in Concrete. *Construction* 

of Entrained Air Voids in Cement Paste with Scattered Ultrasound. *NDT&E* 

in Concrete Health Monitoring Technology. *J. Eng. Mech.-ASCE,* Vol. 126, No. 7, pp.

Ultrasonic Investigation of Concrete with Distributed Damage. *ACI Materials* 

Surface Waves in Cement-Based Materials. *J. Eng. Mech.-ASCE,* Vol. 126, No. 11, pp.

Experiments and Numerical Simulatios of Wave Propagation. *Strain,* in press

Hetero- Geneous Solid Media: Theoretical Analysis and Experimental Validation.

Surface Cracks with Rayleigh Waves: A Numerical Model. *NDT&E Int* Vol. 31, No.

Depth and Repair Evaluation Using Rayleigh Waves. *Cement and Concrete* 

remaining life or repair method. Concrete, including large scale of inhomogeneity is typically examined by comparatively long wavelengths by means of pulse velocity correlation with strength or damage. The present study complements the information of pulse velocity using features like the dispersion curve, the attenuation coefficient as a function of frequency, as well as the spectral distortion between pulses recorded at different points of the surface. It is seen that combined wave features can act complementary, while their acquisition does not require further upgrade on the equipment used for conventional pulse velocity measurements. Concerning alloys and metal matrix composites used in aerospace applications, due to their much shorter typical size of inhomogeneity, delicate equipment should be employed enabling the evaluation on a microscopic scale. In these components fatigue loading is of primary concern, which may result in different damage modes. Acoustic microscopy enables the scanning of the material for surface or subsurface defects providing a detailed point by point assessment on the elastic properties. Additionally, nonlinear surface waves are extremely sensitive to the evolution of microdamage, including dislocation motion and micro-cracking. This is due to the development of higher harmonics and, therefore, is an excellent way to monitor in real time the damage as evolved during cyclic loading from early stages of fatigue to final failure of the structure. The derived nonlinear parameter enables the prediction of remaining life in critical components.

#### **6. References**


remaining life or repair method. Concrete, including large scale of inhomogeneity is typically examined by comparatively long wavelengths by means of pulse velocity correlation with strength or damage. The present study complements the information of pulse velocity using features like the dispersion curve, the attenuation coefficient as a function of frequency, as well as the spectral distortion between pulses recorded at different points of the surface. It is seen that combined wave features can act complementary, while their acquisition does not require further upgrade on the equipment used for conventional pulse velocity measurements. Concerning alloys and metal matrix composites used in aerospace applications, due to their much shorter typical size of inhomogeneity, delicate equipment should be employed enabling the evaluation on a microscopic scale. In these components fatigue loading is of primary concern, which may result in different damage modes. Acoustic microscopy enables the scanning of the material for surface or subsurface defects providing a detailed point by point assessment on the elastic properties. Additionally, nonlinear surface waves are extremely sensitive to the evolution of microdamage, including dislocation motion and micro-cracking. This is due to the development of higher harmonics and, therefore, is an excellent way to monitor in real time the damage as evolved during cyclic loading from early stages of fatigue to final failure of the structure. The derived nonlinear parameter enables the prediction of remaining life in critical

[1] Kaplan, M. F. (1959). The Effects of Age and Water/Cement Ratio Upon the Relation

[2] Popovics, S., Rose, J. L. and Popovics, J. S. (1990). The Behavior of Ultrasonic Pulses in

[3] Qixian, L. and Bungey, J. H. (1996). Using Compression Wave Ultrasonic Transducers to

[4] Graff, K. F. (1975). Wave Motion in Elastic Solids. *New York: Dover Publications,* Vol., No. [5] Philippidis, T. P. and Aggelis, D. G. (2005). Experimental Study of Wave Dispersion and

[6] Kinra, V. K. and Rousseau, C. (1987). Acoustical and Optical Branches of Wave

[7] Sachse, W. and Pao, Y.-H. (1978). On the Determination of Phase and Group Velocities of Dispersive Waves in Solids. *J. Appl. Phys.,* Vol. 49, No. 8, pp. 4320–4327 [8] Aggelis, D. G. and Shiotani, T. (2007). Experimental Study of Surface Wave Propagation

[9] Washer, G. A., Green, R. E. and Jr, R. B. P. (2002). Velocity Constants for Ultrasonic Stress Measurement in Prestressing Tendons. *Res. Nondestr. Eval.,* Vol. 14, pp. 81-94 [10] Cowan, M. L., Beaty, K., Page, J. H., Zhengyou, L. and Sheng, P. (1998). Group Velocity

Concrete. *Cement Concrete Res.,* Vol. 20, pp. 259–270

Elasticity for Concrete. *Constr Build Mater,* Vol. 4, pp. 237–242

Attenuation in Concrete. Ultrasonics. 43, No. 7, pp. 584-595

Propagation. *J.Wave-Mater. Interact.,* Vol. 2, pp. 141–152

Fraction of Scatterers. *Phys. Rev. E,* Vol. 58, pp. 6626–6636

between Ultrasonic Pulse Velocity and Compressive Strength. *Mag. Concrete Res.,*

Measure the Velocity of Surface Waves and Hence Determine Dynamic Modulus of

in Strongly Heterogeneous Media. *Journal of the Acoustical Society of America,* Vol.

of Acoustic Waves in Strongly Scattering Media: Dependence on the Volume

components.

**6. References** 

Vol. 11, No. 32, pp. 85-92

122, No. 5, pp. EL 151-157


New Trends in Materials Nondestructive

Vol. 106, pp. 652-659

2, pp. 274-290

Vol. 39, No. 6, pp. 737-744

52, No. 2, pp. 261-266

*Journal of Applied Physics,* Vol. 27, pp. 583

*Acoust Soc Am,* Vol. 120, No. 3, pp. 1266-1273

*International,* Vol. 41, pp. 326-329

213-224

851-856

Spectral Analysis. *2nd ed., Wiley, New York*

Techniques. *NDT&E INT,* Vol. 30, No. 4, pp. 223-230

Characterization Using Surface Acoustic Wave Methodologies 281

[44] Mobley, J., Waters, K. R., Hall, C. H., Marsh, J. N., Hughes, M. S., Brandenburger, G. H.

[45] Bendat, J. S. and Piersol, A. G. (1993). Engineering Applications of Correlation and

[46] Grosse, C., Reinhardt, H. and Dahm, T. (1997). Localization and Classification of

[47] Quate, C. F., Atalar, A. and Wickramasinghe, H. K. (1979). Acoustic Microscopy with Mechanical Scanning - a Review. *Proceedings of the IEEE,* Vol. 67, pp. 1092-1114 [48] Bertoni, H. L. (1985). Rayleigh Waves in Scanning Acoustic Microscopy. *Ash EA, Paige* 

[49] Liang, K. K., Kino, G. S. and Khuri-Yakub, B. T. (1985). Material Characterization by the

[50] Matikas, T. E., Rousseau, M. and Gatignol, P. (1992). Experimental Study of Focused

[51] Blatt, D., Karpur, P., Matikas, T. E., Blodgett, M. P. and Stubbs, D. A. (1993). Elevated

[52] Waterbury, M. C., Karpur, P., Matikas, T. E., Krishnamurthy, S. and Miracle, D. B.

[53] Cantrell, J. H. and Yost, W. T. (1994). Acoustic Harmonic Generation from Fatigue-Induced Dislocation Dipoles. *Philosophical magazine A,* Vol. 69, No. 2, pp. 315-326 [54] Granato, A. and Lücke, K. (1956). Theory of Mechanical Damping Due to Dislocations.

[55] Planat, M. (1985). Multiple Scale Analysis of the Nonlinear Surface Acoustic Wave Propagation in Anisotropic Crystals. *J. Appl. Phys.,* Vol. 57, pp. 4911–4915 [56] Herrmann, J., Kim, J. Y., Jacobs, L. J., Qu, J., Littles, J. W. and Savage, M. F. (2006).

[58] Shui, G., Kim, J. Y., Qu, J., Wang, Y.-S. and Jacobs, L. J. (2008). A New Technique for

and Miller, J. G. (1999). Measurements and Predictions of Phase Velocity and Attenuation Coefficient in Suspensions of Elastic Microspheres. *J. Acoust. Soc. Am.,*

Fracture Types in Concrete with Quantitative Acoustic Emission Measurement

*EGS, editors. Rayleigh-Wave Theory and Application. The Royal Institution, London,* Vol.

Inversion of V(Z). *IEEE Transactions on Sonics and Ultrasonics,* Vol. SU-32, No. 2, pp.

Ultrasonic Beams Reflected at a Fluid-Solid Interface in the Neighborhood of the Rayleigh Angle. *IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control,*

Temperature Degradation and Damage Mechanisms of Titanium Based Metal Matrix Composites with SCS-6 Fibers. *Scipta Metallurgica et Materialia,* Vol. 29, pp.

(1994). In Situ Observation of the Single-Fiber Fragmentation Process in Metal-Matrix Composites by Ultrasonic Imaging. *Composites Science and Technology,* Vol.

Assessment of Material Damage in a Nickel-Base Superalloy Using Nonlinear Rayleigh Surface Waves, *Journal of Applied Physics,* Vol. 99, No. 12, pp. 124913 [57] Kim, J.-Y., Jacobs, L. J., Qu, J. and Littles, J. W. (2006). Experimental Characterization of

Fatigue Damage in a Nickel-Base Superalloy Using Nonlinear Ultrasonic Waves. *J* 

Measuring the Acoustic Nonlinearity of Materials Using Rayleigh Waves. *NDT&E* 


[28] vanWijk, K., Komatitsch, D., Scales, J. A. and Tromp, J. (2004). Analysis of Strong Scattering at the Micro-Scale. *J. Acoust. Soc. Am.,* Vol. 115, pp. 1006–1011 [29] Pecorari, C. (1998). Rayleigh Wave Dispersion Due to a Distribution of Semi-Elliptical Surface-Breaking Cracks. *J Acoust Soc Am,* Vol. 103, No. 3, pp. 1383-1387 [30] Harmon, D. and Saff, C. (1988). Metal Matrix Composites: Testing, Analysis, and Failure

*Matrix Composites. Philadelphia, PA,* Vol. ASTM STP 1032, pp. 237-250 [31] Marshall, D. B., Cox, B. N. and Evans, A. G. (1985). The Mechanics of Matrix Cracking

Reinforced Composites. *Proc. R. Soc. Lond.,* pp. A409:329-350

17, No. 1, pp. 75-87

4, pp. 1295-1298

*NDE. La Jolla CA,* Vol. 12B, pp. 1515-1522

*Research Society,* Vol. 591, pp. 79-84

Vol. 105, No. 2, pp. 187-193

*of America,* Vol. 116, pp. 3443-3452

*and Performance,* Vol. 19, No. 5, pp. 751-760

*Acoustical Society of America,* Vol. 93, No. 3, pp. 1407-1416

Materials Characterization. *Microsc. Microanal.,* Vol. 6, pp. 59–67

[32] McCartney, L. N. (1987). Mechanics of Matrix Cracking in Brittle-Matrix Fibre-

[33] Karpur, P., Matikas, T. E., Krishnamurthy, S. and Ashbaugh, N. (1992). Ultrasound for

[35] Matikas, T. E. and Karpur, P. (1992). Matrix-Fiber Interface Characterization in Metal

[36] Matikas, T. E., Rousseau, M. and Gatignol, P. (1993). Theoretical Analysis for the

[37] Matikas, T. E. (2000). Quantitative Short-Pulse Acoustic Microscopy and Application to

[38] Frouin, J., Sathish, S., Matikas, T. E. and Na, J. K. (1999). Ultrasonic Linear and

[39] Frouin, J., Maurer, J., Sathish, S., Eylon, D., Na, J. K. and Matikas, T. E. (2000). Real-Time

[40] Matikas, T. E. (2010). Damage Characterization and Real-Time Health Monitoring of

[41] Aggelis, D. G. and Shiotani, T. (2008). Effect of Inhomogeneity Parameters on the Wave

[42] Dokun, O. D., Jacobs, L. J. and Haj-Ali, R. M. (2000). Ultrasonic Monitoring of Material Degradation in FRP Composites. *J. Eng. Mech.,* Vol. 126, pp. 704–710 [43] Aggelis, D. G., Tsinopoulos, S. V. and Polyzos, D. (2004). An Iterative Effective Medium

Modes. *Johnson EWS, editor. Damage Initiation and Growth in Fiber Reinforced Metal* 

in Brittle-Matrix Fiber Composites. *Acta Metallurgica,* Vol. 33, No. 11, pp. 2013-2021

Fiber Fragmentation Size Determination to Characterize Load Transfer Behavior of Matrix-Fiber Interface in Metal Matrix Composites. *Thompson DO, Chimenti DE, editors. Review of Progress in Quantitative NDE. La Jolla CA,* Vol. 12B, pp. 1507-1513 [34] Matikas, T. E. (2008). High Temperature Fiber Fragmentation Characteristics of SiC

Single-Fiber Composite with Titanium Matrices. *Advanced Composite Materials,* Vol.

Matrix Composites Using Ultrasonic Shear-Wave Back-Reflection Coefficient Technique. *Thompson DO, Chimenti DE, editors. Review of Progress in Quantitative* 

Reflection of a Focused Ultrasonic Beam from a Fluid-Solid Interface. *Journal of the* 

Nonlinear Behavior of Fatigued Ti-6Al-4V. *Journal of Materials Research,* Vol. 14, No.

Monitoring of Acoustic Linear and Nonlinear Behavior of Titanium Alloys During Cyclic Loading. *Nondestructive Methods for Materials Characterization, Materials* 

Aerospace Materials Using Innovative NDE Tools. *Journal of Materials Engineering* 

Propagation in Cementitious Materials. *American Concrete Institute Materials Journal,*

Approximation (Iema) for Wave Dispersion and Attenuation Predictions in Particulate Composites, Suspensions and Emulsions *Journal of the Acoustical Society* 


[59] Shull, D. J., Hamilton, M. F., Ilinsky, Y. A. and Zabolotskaya, E. A. (1993). Harmonic

[60] Zabolotskaya, E. A. (1992). Nonlinear Propagation of Plane and Circular Rayleigh Waves in Isotropic Solids. *J. Acoust. Soc. Am.,* Vol. 91, No. 5, pp. 2569-2575

Vol. 94, pp. 418-427

Generation in Plane and Cylindrical Nonlinear Rayleigh Waves. *J. Acoust. Soc. Am.,*

## *Edited by Auteliano Antunes dos Santos Júnior*

Ultrasonic waves are well-known for their broad range of applications. They can be employed in various fields of knowledge such as medicine, engineering, physics, biology, materials etc. A characteristic presented in all applications is the simplicity of the instrumentation involved, even knowing that the methods are mostly very complex, sometimes requiring analytical and numerical developments. This book presents a number of state-of-the-art applications of ultrasonic waves, developed by the main researchers in their scientific fields from all around the world. Phased array modelling, ultrasonic thrusters, positioning systems, tomography, projection, gas hydrate bearing sediments and Doppler Velocimetry are some of the topics discussed, which, together with materials characterization, mining, corrosion, and gas removal by ultrasonic techniques, form an exciting set of updated knowledge. Theoretical advances on ultrasonic waves analysis are presented in every chapter, especially in those about modelling the generation and propagation of waves, and the influence of Goldberg's number on approximation for finite amplitude acoustic waves. Readers will find this book ta valuable source of information where authors describe their works in a clear way, basing them on relevant bibliographic references and actual challenges of their field of study.

Ultrasonic Waves

Ultrasonic Waves

*Edited by Auteliano Antunes dos Santos Júnior*

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