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~.

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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<PHONE_NUMBER>

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.

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**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

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**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.

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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.