**2.2 Acoustic emission method**

264 Recent Trends in Processing and Degradation of Aluminium Alloys

crystals. Secondly, in the contemporary materials science, one of the basic problems of plastic deformation of metals are questions of strain localization due to the formation and development of slip lines and slip bands as well as shear banding and twinning processes. In the last decade the methods of intensive strain have become more and more widely used to obtain microstructure refinement and finally ultra fine-grained (UFG), nanocrystalline materials which have the excellent mechanical properties, such as great strength and plasticity or even superplasticity occurring in the conditions of relatively not too high temperatures (Vinogradov, 1998). They allow obtaining massive samples of metals ready for a further treatment. This refers in particular to the packet rolling with bonding, so called ARB (Accumulative Roll-Bonding) method (Saito et al., 1999; Pawełek et al., 2007). There are also known products obtained on industrial scale by the method of channel compression ECAP (Equal Channel Angular Pressing), (Kuśnierz, 2001). The method of torsion under high pressure HPT (High Pressure Torsion), (Valiev et al., 2000) has been the least known

The subject concerns the Al alloys of AA6060, AA2014 and AA5182 type as well as AA5754 and AA5251 ones. The examinations of Al alloys of AA6060 and AA2014 types were carried out applying the HPT method as well as ECAP technique with circular cross section of the channel. The anisotropy of Portevin-Le Châtelier (PL) and AE effects was described and the relation between the PL and AE effects in UFG (nanocrystalline) Al alloy after intensive

On the other hand the results of the examinations of Mg-Li and Mg-Li-Al alloys, presented here for comparison, were carried out applying HPT method (Kúdela et al., 2011) as well as

The aim of this chapter has been also an attempt to present the correlations between the mechanisms of plastic deformation and the AE phenomenon and the discussion of the connection of AE with the possible phenomenon of superplasticity in UFG (nanocrystalline)

The Al crystals of several different crystallographic orientations were obtained using a standard Bridgman method, while the Al bi-crystals of crystallite orientations {100}<011>/{110}<001> (Goss/shear) were produced applying a modified Bridgman

The samples of Al single- and bi-crystals, of dimensions 10x10x10mm of various orientations were cut out and subjected to tests of channel-die compression at room and liquid nitrogen temperature (77K) using an INSTRON testing machine equipped with channel-die (Fig. 1), which ensured plastic flow merely in the normal direction (ND) and in the elongation direction (ED), parallel to the channel axis, since the deformation in the transverse direction

The samples were deformed in a multi-stage way in order to obtain appropriate values of intermediate and final degrees of deformation. After each deformation stage they were trimmed to satisfy the slenderness ratio. In each case the traverse speed of the testing

An apparatus recording the AE descriptors was coupled with the testing machine. Both systems are unique, fully computerized set for a simultaneous measurement of external

ECAP technique (Kuśnierz et al., 2008) with squared cross section of the channel.

since obtaining the high pressure itself is a difficult problem.

strain processing was reported here for the first time.

aluminium alloys.

**2. Materials and methods** 

**2.1 Production of single and bi-crystals** 

technique of horizontal crystallization.

(TD) was held back by the channel walls.

machine was 0.05 mm/min.

The AE phenomenon takes place during a rapid release of elastic energy, accumulated in the material as a result of acting external or internal conversions, which can be emitted in the form of elastic waves which the frequency is contained between several kilohertz and a few megahertz. In metals and alloys, in general, they are generated as the effect of plastic deformation and particular dislocation strain mechanisms. The AE method enables sensitive monitoring effects in real time, even in considerable volume of investigated elements.

Considering simplifying assumptions, that the function of amplitude of strain field changes in the AE source has a form of elementary shock, the point of observation is in a distant area, and the elastic wave propagates in a homogeneous medium, the elementary equation of the signal propagation distance given in literature (Resnikoff & Wells, 1998) takes the form:

$$\begin{split} G \left( \mathbf{x}\_{i} \; t^{\prime} - t \right) &= \frac{1}{4 \pi \rho \left. \upsilon\_{p}^{2} \right|\_{p}} \left. \gamma\_{i} \right|\_{p} \frac{1}{r} \left. \delta \left( \left. t^{\prime} - t - r \right/ \upsilon\_{p} \right) \right|\_{p} \\ &- \frac{1}{4 \pi \rho \left. \upsilon\_{s}^{2} \right|\_{s}} \left( \gamma\_{i} \left. \gamma\_{j} - \delta\_{ij} \right) \frac{1}{r} \left. \delta \left( \left. t^{\prime} - t - r / \upsilon\_{s} \right) \right|\_{s} \right) \end{split} \tag{1}$$

where: *G*ij *(r',t'-t;r)* is Green function for the displacement in directions xi ' , yi ' , zi ' in point *r*', in time *t*', in the case, when a local disturbance of strain field in point *r* in time *t* becomes the source of the displacement, ρ *–* medium density, *v*p *–* velocity of dilatation wave, *v*s *–*  velocity of shear wave, γi, γj - for i=1, 2, 3 and j=1, 2, 3 are directional cosines source-receiver and receiver-source, *r* – distance between AE source and sensor, δij – Kronecker delta, δ(*x*) – delta function equal +∞, for *x*=0 and equal 0 for the remaining values *x.*

Apart from the AE signal the apparatus registers also a noise of acoustic background and that generated during the processing of the recorded signal. In the course of its processing from the analogue form into digital one, so called *quantization noise* occurs, resulting from

Mechanical Behavior and Plastic Instabilities of Compressed Al Metals

is a frequency pulsation *f,* defined as

ω

the distribution of events number versus their energy.

*n*

function *ν(t)* is linearly transformed into the function of spectral density *A(*

0

In consequence, the procedure of spectral density function determination *A(*

∞

π

1

*c vm e*

Fig. 3. Acoustogram of AE event set, previously presented in Fig. 2 in the form of

*N*

*m*

in which *j* denotes −1 and mod is the module of complex expression.

*N*

0

=

where

ω

the Fourier transformation:

coefficients *cn* : *v(m)* ⇒ *cn (*

the form of color code.

Level re [1 mV pp]

dependence of signal amplitude on time

and Alloys Investigated with Intensive Strain and Acoustic Emission Methods 267

The AE signals generated by different sources in the examined object can be analyzed inspecting the changes of its *spectral characteristic*. A continuous AE signal *ν(t)* in a selected finite range of time can be demonstrated as a function of its spectral characteristic *A(*

> <sup>1</sup> *vt A* ( ) ( )exp( ) . ω*j*

consecutive segments of discrete set of AE signal samples was elaborated together with a corresponding graphic presentation of results in the form of acoustic maps i.e*. acoustograms* or *spectrograms*. A numerical method of Windowed Fourier Transformation (WFT) is applied here. Next, the discrete form of spectral density function is determined using several thousands of signal samples adjacent to the central sample of the recorded AE event. The algorithm, which transforms the set of signal samples into a set of spectral density

ω*=2*π

> ω ω*d*

*)* is similar to the approximate formula (Scott, 1991):

<sup>1</sup> ( ) mod( ),

<sup>−</sup>

The acoustogram of AE event set presented earlier in dependence of signal amplitude on time in Fig. 2 has now been shown in Fig. 3. The spectral characteristic of signal is illustrated every 0.5ms. The discrete equivalent of the *A*(ω), spectral density function is presented in

The AE analyzer is equipped with an additional measurement channel enabling simultaneous recording of sample load by the computer as well as the registration of AE parameters in the form of AE event rate together with their duration, amplitude and effective value connected with conventional value of the event energy and in consequence,

2 /

≈ ⋅ ∑ (5)

*jn m N*

π

<sup>=</sup> ∫ (4)

ω*)*,

*)* according to

ω*)* for

t [ms]

*f.* Assuming absolute integrality,

ω

the process of rounding the instantaneous value of the signal to the levels, which are the components of a binary form of the record. The decrease of quantization noise was attained through the use of modern analogue-numerical processors of high linearity of processing and resolution of 12 bytes in an optimal range of input voltages of about ±5V.

Fig. 2. The principles of AE event detection

The line determining the maximum level of noise voltage of surrounding background is shown in Fig. 2. The level is taken as a discrimination voltage. The occurrence of AE is defined as a moment of increase of instantaneous signal value above the discrimination voltage. The duration of the AE event is determined to the moment of the decrease of instantaneous signal value below the discrimination voltage. The method takes into account the detection of events with the possibility of software increase/decrease of the discrimination level voltage (Paupolis, 1980). The applied algorithm of AE event detection enables a program implementation of numerical records of signals containing even a few hundred of megabites. By means of such an algorithm, it is possible to detect the events lasting at least three times the sampling period of the applied analogue-numerical processor. For example, for the frequency of sampling used at present in long-lasting examinations, which is 88.2kHz, the minimum duration time of an event is 34 microseconds. A 9812 ADLINK fast card of analogue-numerical processor was used for the analysis of AE signals. Such a device enables the increase of instrument sensitivity and detection of AE events differing by an order of magnitude. The indexes of start and end of AE event recorded in the program table can serve to the determination of its duration. The *E* energy of AE event can be derived from the approximate formula:

$$E = 0.5 \text{ ( $\nu\_{\text{max}}$ )} \,\text{\textdegree } \Delta t,\tag{2}$$

where *νmax* denotes maximum value of AE signal during the event, *Δt* – time of AE event. To characterize the material subjected to the examinations, values of arithmetic means of all measured values *E*, *νmax* and *Δt* are needed. The AE instrument is also equipped with an analogue system, which allows obtaining an effective value of the signal.

The transformation of the set of instantaneous values of the measured *v*(*t*) signal into effective value *VRMS* for time *T* is realized according to formula:

$$V\_{RMS} = \sqrt{\frac{1}{T} \int\_0^T \nu^2(t)dt}. \tag{3}$$

the process of rounding the instantaneous value of the signal to the levels, which are the components of a binary form of the record. The decrease of quantization noise was attained through the use of modern analogue-numerical processors of high linearity of processing

> **programmed discrimination threshold**

The line determining the maximum level of noise voltage of surrounding background is shown in Fig. 2. The level is taken as a discrimination voltage. The occurrence of AE is defined as a moment of increase of instantaneous signal value above the discrimination voltage. The duration of the AE event is determined to the moment of the decrease of instantaneous signal value below the discrimination voltage. The method takes into account the detection of events with the possibility of software increase/decrease of the discrimination level voltage (Paupolis, 1980). The applied algorithm of AE event detection enables a program implementation of numerical records of signals containing even a few hundred of megabites. By means of such an algorithm, it is possible to detect the events lasting at least three times the sampling period of the applied analogue-numerical processor. For example, for the frequency of sampling used at present in long-lasting examinations, which is 88.2kHz, the minimum duration time of an event is 34 microseconds. A 9812 ADLINK fast card of analogue-numerical processor was used for the analysis of AE signals. Such a device enables the increase of instrument sensitivity and detection of AE events differing by an order of magnitude. The indexes of start and end of AE event recorded in the program table can serve to the determination of its duration. The *E* energy of AE event can

 *E =* 0.5 (*νmax*)*<sup>2</sup> Δt*, (2)

The transformation of the set of instantaneous values of the measured *v*(*t*) signal into

2 0 <sup>1</sup> () . *T V t RMS dt <sup>T</sup>* <sup>=</sup> ν

∫ (3)

where *νmax* denotes maximum value of AE signal during the event, *Δt* – time of AE event. To characterize the material subjected to the examinations, values of arithmetic means of all measured values *E*, *νmax* and *Δt* are needed. The AE instrument is also equipped with an

analogue system, which allows obtaining an effective value of the signal.

effective value *VRMS* for time *T* is realized according to formula:

and resolution of 12 bytes in an optimal range of input voltages of about ±5V.

**AE event end** 

Fig. 2. The principles of AE event detection

**AE event start** 

be derived from the approximate formula:

The AE signals generated by different sources in the examined object can be analyzed inspecting the changes of its *spectral characteristic*. A continuous AE signal *ν(t)* in a selected finite range of time can be demonstrated as a function of its spectral characteristic *A(*ω*)*, where ω is a frequency pulsation *f,* defined as ω*=2*π*f.* Assuming absolute integrality, function *ν(t)* is linearly transformed into the function of spectral density *A(*ω*)* according to the Fourier transformation:

$$v(t) = \frac{1}{\pi} \int\_0^\wp A(o\rho) \exp(j\, o\rho) \, doo. \tag{4}$$

In consequence, the procedure of spectral density function determination *A(*ω*)* for consecutive segments of discrete set of AE signal samples was elaborated together with a corresponding graphic presentation of results in the form of acoustic maps i.e*. acoustograms* or *spectrograms*. A numerical method of Windowed Fourier Transformation (WFT) is applied here. Next, the discrete form of spectral density function is determined using several thousands of signal samples adjacent to the central sample of the recorded AE event. The algorithm, which transforms the set of signal samples into a set of spectral density coefficients *cn* : *v(m)* ⇒ *cn (*ω*)* is similar to the approximate formula (Scott, 1991):

$$c\_n \approx \frac{1}{N} \sum\_{m=0}^{N-1} v(m) \cdot \text{mod}(\, e^{j n \, 2 \, \pi m/N} \rangle\_{\prime} \tag{5}$$

in which *j* denotes −1 and mod is the module of complex expression.

The acoustogram of AE event set presented earlier in dependence of signal amplitude on time in Fig. 2 has now been shown in Fig. 3. The spectral characteristic of signal is illustrated every 0.5ms. The discrete equivalent of the *A*(ω), spectral density function is presented in the form of color code.

The AE analyzer is equipped with an additional measurement channel enabling simultaneous recording of sample load by the computer as well as the registration of AE parameters in the form of AE event rate together with their duration, amplitude and effective value connected with conventional value of the event energy and in consequence, the distribution of events number versus their energy.

Fig. 3. Acoustogram of AE event set, previously presented in Fig. 2 in the form of dependence of signal amplitude on time

Mechanical Behavior and Plastic Instabilities of Compressed Al Metals

Fig. 5. Scheme of the ARB process

of the registered AE signal were measured.

and Alloys Investigated with Intensive Strain and Acoustic Emission Methods 269

Fig. 5 presents the scheme of the ARB technique. Purified and degreased surfaces of two sheet plates are folded and fastened, next heated and rolled to reduction *z* = 50%. The sheet obtained after rolling is cut into halves and subjected to the same procedure as before. The procedure may be repeated several times. For example, a sheet plate with thickness *go*, subjected to rolling in succession *n* time to the reduction of *z=*50%, i.e. after n passes, has thickness *gn=go/2n*, and the total reduction is equal to zn=1– gn/go=1–1/2*n*. The tensile tests were carried out with ten-fold plane specimens using the standard INSTRON machine. The rate of the traverse of the testing machine was 2mm/min. Each specimen was of gauge

The samples for ECAP tests (for circular cross-section) had the shape of rolls with diameter 20mm and height 30÷40mm while that for the ECAP processing in the channel of square cross section was in the shape of rectangular prisms of dimensions 10x10x40mm. The samples to be used in HPT tests had the shape of discs of diameter 10mm and thickness 3÷5mm. The samples intended for compression had the shape of cubes with the edge not greater than 10mm in the case of ECAP or the shape of square plates with side 10mm and thickness 1mm, cut in the case of ARB from the samples prepared earlier for the tensile tests. The discs after HPT, intended for the compression, had the thickness of the order of 1÷2mm.

Simultaneously with the registration of the external force F and the sample elongation, the basic AE parameters in the form of AE event rates, or as RMS – the effective value of voltage

The aim of the research has been the documentation and interpretation of correlation of the AE descriptors during compression tests of Al alloys before and after pre-deformation by intensive strain methods. The evolution of micro- and/or nanostructure in dependence on dislocation mechanisms of deformation as well as slip processes occurring along grain

boundaries, responsible for possible superplastic flow, is also considered.

length l0=90mm (overall length lc=105mm), b0=20mm wide and a0=3.50mm thick.

The effective value of noises at the inlet of the preamplifier is about 20÷30mV, depending on the selected frequency band. During the signal processing the value undergoes about fourfold decrease due to the application of a band-pass filtration. An active upper-pass filter of 8th order of cut off frequency 5kHz is joined to the preamplifier. Another filter of 4th order of 20kHz frequency can be additionally switched on. Thanks to that, the signals of a vibroacoustic background, which do not originate from the processes occurring because of sample loading, are eliminated from the further processing. The signal is next passed to a lower-pass filter of cut-off frequency 1MHz. The total amplification of AE signal at the outlet of instrument is 70dB and the threshold voltage is 0.5V. The effective voltage value of the AE signal recorded is derived through the second exit. The analysis of energy and duration of individual AE events is possible with an appropriate program, which determines time of the AE event occurrence, its maximum amplitude, sum of recorded amplitudes and duration time of the event up to significant decrease of its amplitude.

### **2.3 Methods of microstructure observations**

After each stage of a compressive test, microstructure observations were carried out using a standard technique of optical microscopy at NEOPHOT instrument. The further observations were performed using transmission (TEM) and scanning (SEM) electron microscopes. The techniques of *convergent beam electron diffraction* (CBED) and *electron back scattered diffraction* (EBSD) as well as SEM with *field emission gun* (FEG) were applied in the examinations of bi-crystals.

### **2.4 Methods of intensive deformation**

Fig. 4a shows the scheme of the ECAP method. The parameters of the installation have the following values: *b*=10mm, *a*=30mm, angle α=31.3° or α=90°. Equivalent strain (for square cross-section) is equal to εn=0.5922*n*, where *n* – number of passes. For angle Φ= 90° and α=0 it amounts to εn=0.9069*n*.

Fig. 4b shows the scheme of the HPT method of torsion under high pressure. The sample is in the form of a roll with *R* radius and the height *l*. Dilatation strain *γ* after *N* rotations is equal to *γ=(2πRN)/l*, and the equivalent strain *εN=γ*/1.73.

Fig. 4. Scheme of ECAP (a) angular extrusion: ED – direction of outflow, PP – direction of punch pressure and the scheme of the HPT process (b)

The effective value of noises at the inlet of the preamplifier is about 20÷30mV, depending on the selected frequency band. During the signal processing the value undergoes about fourfold decrease due to the application of a band-pass filtration. An active upper-pass filter of 8th order of cut off frequency 5kHz is joined to the preamplifier. Another filter of 4th order of 20kHz frequency can be additionally switched on. Thanks to that, the signals of a vibroacoustic background, which do not originate from the processes occurring because of sample loading, are eliminated from the further processing. The signal is next passed to a lower-pass filter of cut-off frequency 1MHz. The total amplification of AE signal at the outlet of instrument is 70dB and the threshold voltage is 0.5V. The effective voltage value of the AE signal recorded is derived through the second exit. The analysis of energy and duration of individual AE events is possible with an appropriate program, which determines time of the AE event occurrence, its maximum amplitude, sum of recorded amplitudes and

After each stage of a compressive test, microstructure observations were carried out using a standard technique of optical microscopy at NEOPHOT instrument. The further observations were performed using transmission (TEM) and scanning (SEM) electron microscopes. The techniques of *convergent beam electron diffraction* (CBED) and *electron back scattered diffraction* (EBSD) as well as SEM with *field emission gun* (FEG) were applied in the

Fig. 4a shows the scheme of the ECAP method. The parameters of the installation have the following values: *b*=10mm, *a*=30mm, angle α=31.3° or α=90°. Equivalent strain (for square cross-section) is equal to εn=0.5922*n*, where *n* – number of passes. For angle Φ= 90° and α=0

Fig. 4b shows the scheme of the HPT method of torsion under high pressure. The sample is in the form of a roll with *R* radius and the height *l*. Dilatation strain *γ* after *N* rotations is

P

 **punch** 

**base**

duration time of the event up to significant decrease of its amplitude.

**2.3 Methods of microstructure observations** 

examinations of bi-crystals.

it amounts to εn=0.9069*n*.

**2.4 Methods of intensive deformation** 

equal to *γ=(2πRN)/l*, and the equivalent strain *εN=γ*/1.73.

(a) (b)

punch pressure and the scheme of the HPT process (b)

Fig. 4. Scheme of ECAP (a) angular extrusion: ED – direction of outflow, PP – direction of

Fig. 5 presents the scheme of the ARB technique. Purified and degreased surfaces of two sheet plates are folded and fastened, next heated and rolled to reduction *z* = 50%. The sheet obtained after rolling is cut into halves and subjected to the same procedure as before. The procedure may be repeated several times. For example, a sheet plate with thickness *go*, subjected to rolling in succession *n* time to the reduction of *z=*50%, i.e. after n passes, has thickness *gn=go/2n*, and the total reduction is equal to zn=1– gn/go=1–1/2*n*. The tensile tests were carried out with ten-fold plane specimens using the standard INSTRON machine. The rate of the traverse of the testing machine was 2mm/min. Each specimen was of gauge length l0=90mm (overall length lc=105mm), b0=20mm wide and a0=3.50mm thick.

The samples for ECAP tests (for circular cross-section) had the shape of rolls with diameter 20mm and height 30÷40mm while that for the ECAP processing in the channel of square cross section was in the shape of rectangular prisms of dimensions 10x10x40mm. The samples to be used in HPT tests had the shape of discs of diameter 10mm and thickness 3÷5mm. The samples intended for compression had the shape of cubes with the edge not greater than 10mm in the case of ECAP or the shape of square plates with side 10mm and thickness 1mm, cut in the case of ARB from the samples prepared earlier for the tensile tests. The discs after HPT, intended for the compression, had the thickness of the order of 1÷2mm.

Fig. 5. Scheme of the ARB process

Simultaneously with the registration of the external force F and the sample elongation, the basic AE parameters in the form of AE event rates, or as RMS – the effective value of voltage of the registered AE signal were measured.

The aim of the research has been the documentation and interpretation of correlation of the AE descriptors during compression tests of Al alloys before and after pre-deformation by intensive strain methods. The evolution of micro- and/or nanostructure in dependence on dislocation mechanisms of deformation as well as slip processes occurring along grain boundaries, responsible for possible superplastic flow, is also considered.

Mechanical Behavior and Plastic Instabilities of Compressed Al Metals

characteristic features of the recorded courses.

**AE Events [1/s]**

and Alloys Investigated with Intensive Strain and Acoustic Emission Methods 271

When analyzing Fig. 6, it can be stated, that evident correlation exists between the course of force and behavior of AE. All the local decreases of the force curve are accompanied by more or less distinct areas of elevated AE activity. It seems that these strong plastic instabilities on the compression curve correspond to the occurrence of shear bands. Vertical areas in the acoustogram containing a broad range of frequency spectrum visible in Fig. 6b. On the other hand, low temperature courses of AE impulses together with external compressive force in dependence on time are presented in Figs. 8 and 9a and 10a for the Al single crystals of two selected orientations: {112}<111> (Fig. 8) and {531}<231> (Fig. 9a for reduction z≅27.1% and Fig. 10a for reduction z≅51.4%). Attention should be drawn to some

Moreover, the experimental {111} pole figures (EXP) presented in Figs.9b and 10b, as well as the calculated orientation distribution functions (ODF) referred to in Figs.9c and 10c, illustrate explicitly the existence of twin orientation after compression to z≅51.4% (Fig. 10b and 10c), and suggest strongly the possibility of deformation twinning also in the Al single crystals channel-die compressed at the liquid nitrogen temperature. In {111} pole figure (Fig. 10c), the component of twin orientation ( 4 4 1) [ 1 3 8], appearing after reduction z≅51.4% (initial matrix orientation ( 1 3 5)[ 1 3 2 ], Figs. 9b and 9c) is now given by orientation ( 2 2 5)[ 3 7 4 ] (Fig. 10c) – corresponds to the twinning on the active co-planar slip system.

0 500 1000 1500 2000 2500 3000 time [s]

Based on the dislocation dynamics and the AE model (Jasieński et al., 2010; Pawełek, 1988a; Pawełek et al., 2001; Ranachowski et al., 2006) a number of AE impulses, which were generated due to the appearance of an individual twin lamella can be estimated. It was assumed, that the twins formed as a result of the pole mechanism action. It was also accepted, that an individual AE impulse occurred, when a partial twinning dislocation, which moved in the area of a single atomic plane, approached the surface. This suggestion is in agreement with the results and concepts reported by Boiko et al. (1973, 1974, 1975) for the

Fig. 7. Acoustic emission and compressive force in Al single crystal of orientation type C≡{112}<111>. The arrows indicate the correlations between AE and drops of force

**Force [N] x 50**
