**3. Technique for measurement of residual stresses**

Many different methods for measuring the residual stresses have been developed during the past several years. Techniques to measure residual stresses may be classified as either destructive or semi destructive or non-destructive. **Figure 2** below classifies the techniques in a detailed manner. The destructive and semi destructive techniques, called also the mechanical method, are dependent on inferring the original stress from the displacement incurred by completely or partially relieving the stress by removing material. Several destructive and semi destructive methods are available out of which the following are most common:


**Figure 2.**

*Various stress measurement methods.*

*Non-Destructive Evaluation of Residual Stresses in Welding DOI: http://dx.doi.org/10.5772/intechopen.101638*

iii. Ring core method;

iv. Deep hole method.

For the non-destructive evaluation of residual stresses, the following methods are most common:


#### **3.1 Destructive methods**

All destructive methods of residual stress measurement are dependent on the stress relaxation behavior of metals. When a small portion of material from the stressed part is removed, the locked-up stresses are relaxed and results in micro deformation (strain). By accurately measuring the relaxations, residual stresses can be calculated by one or more of the following techniques:

#### *3.1.1 Hole-drilling technique*

The hole drilling method is widely used and a very simple method. Generally, it is used to measure biaxial stresses. Residual stress is determined by measuring the relived radial strain by drilling a small hole in the welded plate. Measurement locations are outside the drilled holes. Measurement can be performed by measuring balls or by strain gauges. The primary requirement of the hole drilling method is that the material should be isotropic. It can be significant in the case of anisotropic materials. It is relatively reliable and accurate. Moreover, there is very little wastage or damage caused to the material due to the application of this technique. Generally, strain gauges are placed where the residual stresses are to be measured. Appropriate calibration standards are used for the measurement of stresses. Relaxation of stresses causes local strains which may be measured by the strain gauges and thus can be measured by comparing with the calibration standards.

There may be issues for accuracy of the results if the hole is drilled very near to the component edge or near to another hole. The calibration standard is generally based on infinite size or large plates. Moreover, there might be plastic deformation due to drilled holes which may affect the actual measurement of stress. If the residual stress is high (60% of yield stress or more) or if the drilling is not proper, this error may be as high as 15–16% depending on the hole diameter.

Generally, in most cases, the residual stresses are not uniform with the depth of the material from the surface. In such cases, the Incremental hole drilling method may be used. This method is based on the same principle as the basic hole drilling method stated above, but in this case, drilling is performed in a series of small steps. Drilling is performed by a high-speed pneumatic drill (more than 200,000 rpm). This highspeed drilling introduces very little stress into the material due to the drilling process, thus enabling the measurement more accurate.

### *3.1.2 Deep hole method*

The deep hole method is a hole trepanning method instead of direct drilling hole. At the first stage, the hole is drilled out. Then the diameter of the hole is measured accurately. After that, a trepanning tool is used to remove the metal from the inside surface of the hole. This process relaxes the residual stresses in the core. Again, the diameter of the hole is measured after trepanning out. The residual stress is calculated from the change in diameter of the hole. One of the great features of this technique is that it can measure the residual stresses in the interior of the material.

## **3.2 Non-destructive methods**

#### *3.2.1 X-ray diffraction method*

X-ray diffraction is one of the non-destructive techniques for the measurement of residual stresses on the surface of materials. Under the action of stress, either applied or residual, the resulting elastic strains cause the atomic planes in the metallic crystal structure to change their spacings. This change of the inter-planar atomic spacings can be detected and measured by X-ray diffraction. Thus, the total stress on the metal can then be obtained. ASTM E 2860 describes residual stress measurement technique by X ray diffraction for bearing steels.

Most metal components of practical concern consist of many tiny crystallites (grains), randomly oriented for their crystalline arrangement. This method applies to materials that are crystalline in nature. Most metallic components are crystalline and produce diffraction of definite pattern depending on X ray beam direction. Because of residual stresses present within the material, elastic strains are produced within the crystal lattice within the elastic limit of the material. By Hooke's law, this strain is proportional to the applied stress. Estimation of stress can be performed based on accurately measuring the distance between the crystallographic planes. Portable diffractometers that can be taken out into the field for measurements of structures such as pipelines, welds, and bridges are now available. Sometimes the layer-removal technique is used to remove a thin layer from the surface and stress profile again measured with X ray diffraction, but then the method becomes destructive and such cutting must be done with care to ensure the stress state is not unduly altered. The speed of measurement depends on several factors, including the type of material being examined, the X-ray source, and the degree of accuracy required [2].

Third-generation synchrotron sources provide access to high X-ray energies. They produce very high-energy X rays, which can penetrate greater depths within the material. Moreover, High energy X-ray beams are very collimated and X ray intensity is concentrated mainly in the central axis of the beam. They provide very high spatial resolution and very short data acquisition time. Because of these advantages, this technique is more useful to collect detailed data of strain fields in two dimensions as well as three dimensions. Even very minor phase transformation may be detected. There are also some serious drawbacks in the application of the synchrotron method. Mean that the sampling gauge is usually very elongated. The spatial variation is very different in different directions due to low scattering angles. Since the scattering angle is very short, it is good for simple geometries like plates, pipes, etc. but for large or geometrically complex samples it can be difficult to achieve short path lengths for all measurement directions [3].

#### *3.2.2 Neutron diffraction method*

The neutron diffractions method is also based on a similar principle of crystallographic planes spacing measurements as with X ray diffraction. Instead of X ray beam, a neutron beam is used. The advantage of the neutron diffraction methods in comparison with the X-ray technique is its larger penetration depth. X-ray diffraction technique has limits in measuring residual stresses through the thickness of a welded structure. Neutron beams can penetrate a few centimeters into the material. Hence, internal residual stresses can also be measured in some cases. Since X ray cannot penetrate deep into the high atomic number of materials because of high absorption coefficient, neutron diffraction can be used in such materials. Studies have revealed that the neutron beam can penetrate up to 30 mm in steel and up to 300 mm in light alloys like Aluminum. Because of high spatial resolution provided by neutron beams, this technique can be used to evaluate and measure stresses in three dimensions. Complete three-dimensional maps of the residual stresses in the material can be provided. However, compared to other diffraction techniques such as X-ray diffraction, the relative cost of application of neutron diffraction method, is much higher, mainly because of the equipment cost. It is too expensive to be used for routine process quality control in engineering applications [4].

#### *3.2.3 Magnetic Barkhausen noise method*

One of the recent developments of residual stress measurement by non-destructive methods is the magnetic Barkhausen Noise technique, popularly known as the MBN technique. The magnetic Barkhausen noise was discovered by Heinrich Barkhausen (1919). Ferromagnetic materials are composed of tiny magnetic zones called magnetic domains. In the non-magnetic state, all these magnetic domains are randomly oriented so that the resulting magnetic field is zero in and out of the material. When the ferromagnetic material is placed under a strong magnetic field, the tiny magnetic domains try to align themselves along the direction of the externally applied magnetic field. As discussed, the MBN technique is mostly applicable to ferromagnetic materials. Although, the MBN technique can be used to determine several other material parameters, the most common use to determine the residual stresses.

Magnetic domains are called as bloch walls also. During the magnetic hysteresis cycle, the bloch walls try to align themselves along the direction of externally applied magnetic fields and overall magnetization can be described in the form of hysteresis curves/cycles [5]. A close view of the hysteresis curve reveals that the curve is not smooth as can be seen from the cycle, rather it consists of small steps or jumps which can be seen in a zoomed view of the curve (**Figure 3**).

The MBN signals can only be seen in an enlarged cut-out of the hysteresis curve (indicated by a circle, see **Figure 3**). Barkhausen noise signal can have a range of frequencies. The effective depth of signal penetration is between 0.01 mm and 1 mm. The Barkhausen noise signal is damped due to the skin effect which is caused by the opposing eddy currents induced by the changing magnetic field. An estimation of the penetration depth of the BN signal can be calculated using the following formula- Eq. (2):

$$\mathfrak{G} = \mathbb{1} \sqrt{\mathfrak{n} \mathfrak{a} \mathfrak{f}} \tag{2}$$

where δ denotes the penetration depth, μ represents the magnetic permeability, σ means the electrical conductivity and ƒ denotes the frequency of the alternating magnetic field [5].

In general, microscopic Grain boundaries, lattice dislocations within and around the grains, second phase materials (e.g., carbides in iron) and impurities in the ferromagnetic material prevent the movement of domain walls. When a high amplitude magnetization force is applied, the above restraining resistance forces are overcome by the external magnetization forces and the domains try to align in the field direction. This movement is not continuous rather by small microscopic jumps. When an inductive coil is placed near the specimen being magnetized, the coil can sense the jumps and the magnitude because the change in magnetization induces an electrical pulse in the coil. When all electrical pulses produced by all domain movements are added together a noise-like signal called Barkhausen Noise is generated [6]. **Figure 4** shows the setup for the detection of MBN signals, where an electromagnet is placed on the object and produces an alternating magnetic field, which can be chosen between 0.1 and several 100 Hz depending on the testing problem. The inductive sensor is located between the magnetic poles along with a Hall probe to measure the tangential magnetic field strength (**Figure 4**). The voltage pulses induced in the sensor are amplified at various stages between 60 and 100 dB. They are then filtered and rectified and their envelope called the inductive Barkhausen noise amplitude, *M* is

**Figure 4.** *Barkhausen noise measurement set up.*

recorded and plotted against the tangential magnetic field strength *H*<sup>t</sup> (**Figure 5**). The inductive sensor may be pick up coil or ferrite core coil or any other device. The frequency content of the Barkhausen events extends from a few hundred Hz up to the MHz range. Barkhausen events excited at greater distances from the surface will result in voltage pulses with lower frequency content than near-surface events. By changing the analyzing frequency of a bandpass filter from low to high, a weighted characterization of the Barkhausen noise from near-surface regions can be obtained. **Figure 5** shows a typical Barkhausen noise profile curve [5]. Typical measuring quantities derived from the magnetic Barkhausen noise are the maximum of the profile curve *M*MAX, the *H*-field position of this, *H*CM, and the half widths Δ*H* by 75%, 50%, and 25% of the maximum value (**Figure 5**).

It was observed that as we move away from the weld, the MBN noise response depends on the stress state of the region of the material. Near the edge of the weld the amplitude of and the type of the MBN signals changes abruptly suggesting a high accumulation of stress at the weld toe. MBN is sensitive to changes in applied stress. The interaction of elastic strain with the magnetic domains is called "magneto-elastic

interaction". Accordingly, in ferromagnetic materials like iron, most steels and cobalt, compressive stresses will decrease the intensity of Barkhausen noise while tensile stresses increase it. This fact can be exploited so that by measuring the intensity of Barkhausen noise the amount of residual stresses can be determined. Barkhausen noise is also affected by the microstructural state of the material. Hence, the signal amplitude and the characteristics of MBN signals will not be the same for various materials. Therefore, for MBN to be effective in determining residual or applied stresses, different materials must be calibrated individually. Hence, the calibration procedure is very important for accurate and reliable results. Each zone having remarkably different microstructure should be separately considered for calibration.

For obvious reasons, it is known that the amplitude of the MBN signal decreases with the reduction in grain size. Also, the signal response increases with increasing misorientation angles at the grain boundary. Because of that, it is generally difficult to use the MBN to assess residual stresses in weldments containing heat-affected zones (HAZ), since HAZ has very rapid microstructural gradients. To reflect the microstructural variations in the heat-affected zone, calibration samples should be similar to the actual component to be tested. That means calibration should contain similar welding parameters, process, heat input, etc. the signals from the calibration samples (weld, HAZ and base metals) should be compared with the actual test object to validate the test results.

#### *3.2.4 Ultrasonic method*

Another promising non- destructive technique for residual stresses measurement is the Ultrasonic determination of residual stresses. The ultrasonic method, also called as critically refracted longitudinal (*L*CR) wave techniques can be utilized for residual stresses measurements on thick samples. Residual stress states can be determined by measuring LCR velocities in the material. Since the velocity of ultrasonic waves is dependent on the elastic constant and density of the material, the change in elastic stress state can be determined by this acoustic-elastic effect. The relationships between the changes of the velocities of longitudinal ultrasonic waves and shear waves with orthogonal polarization under the action of tensile and compressive loads in steel and aluminum alloys are established in several publications. The intensity and character of these changes can be different, depending on the material properties. Different configurations of ultrasonic equipment can be used for residual stresses measurements. A piezo electric transducer can be used as a transmitter of ultrasound and once the sound is passed through the material/zone of interest, it can be received by the same transducer or another dedicated transducer. The first one is called the pulse echo technique and the 2nd one is called the pitch catch or transmission technique. **Figure 6** shows a typical piezoelectric transducer that generate LCR waves at steel from a Perspex wedged transducer element. At an incident angle of 27.5°, the longitudinal mode of Ultrasonic sound refracted at 90° to the normal to the interface, producing a critically refracted LCR wave, sometimes called a creeping wave. **Figure 7** shows a typical pulse echo technique and **Figure 8** shows a typical pitch catch technique.

The ultrasonic method is effective for the analysis of residual stresses in the interior of the material. In this case, the trough- thickness average of the residual stresses is measured. Comparing to X-ray diffraction technique, the depth of measurement is higher and this technique is free from radiation hazard (X-ray technique uses X-ray radiation which is harmful to human body).

**Figure 6.**

*Typical piezoelectric transducer.*

**Figure 7.** *Pulse echo technique.*

**Figure 8.** *Pitch catch technique.*

In the above arrangements, velocities of longitudinal ultrasonic waves and shear waves with orthogonal polarization are measured at a considered point to determine the uniaxial and biaxial residual stresses. The bulk waves in this approach are used to determine the stresses averaged over the thickness of the investigated elements. In general, the change in the ultrasonic wave velocity in structural materials under mechanical stress amounts to only tenths of a percentage point. Therefore, the equipment for practical application of the ultrasonic technique for residual stress measurement should be of high resolution, reliable, and fully computerized. Currently, Aluminum alloys are widely used in the automotive, aerospace and other industries because of their high strength/weight ratio. The *L*CR technique offers greater advantages over other techniques in the case of Aluminum welded structures.

Using calibration specimens, the acoustic-elastic constants are measured and those constants are used to determine the stresses. The greatest sensitivity is obtained when the wave propagates in the same direction as the stress. The stress can be calculated according to:

$$(\mathbf{V\_{pp}} - \mathbf{V\_L}^0) / \mathbf{V\_L}^0 = \mathbf{k\_1}\sigma\_\mathbf{p} + \mathbf{k\_2}\left(\sigma\_\mathbf{q} + \sigma\_\mathbf{s}\right) \tag{3}$$

$$(\mathbf{V\_{pq}} - \mathbf{V\_T}^0) / \mathbf{V\_T}^0 = \mathbf{k\_3}\sigma\_\mathbf{p} + \mathbf{k\_4}\sigma\_\mathbf{q} + \mathbf{k\_5}\sigma\_\mathbf{s} \tag{4}$$

where *VL* <sup>0</sup> = Longitudinal Ultrasonic Velocity in the material. *VT* <sup>0</sup> = Transverse Ultrasonic Velocity in the material.

*V*ij is the velocity of a wave traveling in the direction *i* polarized in direction *j*, s = principal stress direction.

Vpp = Wave propagation direction parallel to the principal stress direction. Vpp = Wave propagation direction parallel to principal stress direction with polarized in direction q.

KI = coupling constants.

The ultrasonic stress measurement method provides a measure of the macro stresses over large volumes of material. Since, ultrasonic wave velocities also depend on microstructural inhomogeneities, it is sometimes difficult to differentiate the effect of stress from the microstructural inhomogeneities. Nevertheless, being portable and cheap to undertake, the method is well suited to routine inspection procedures and industrial studies of large components.
