**4. Depth of residual stress**

Another important factor in residual stress analysis in general is the information regarding the depth of residual stresses. The capability to detect the depth of

residual stresses is important not only to identify the depth of a given residual stress accurately but also to prevent the possibility to overlook residual stresses. The X-ray diffractometry (XRD) is one of the most developed methods of residual stress analysis. However, the XRD is applicable to the identification of residual stresses within the penetration depth of the X-ray, which is typically a few hundreds of *μ*m from the surface.

modulus averaged over the entire thickness. The acoustic velocity data with 400 MHz SAM shows much greater deviation in the acoustic velocity from the nominal value than the 200 MHz SAM or the contact transducer. On the other hand, the data with (ii) the 200 MHz SAM and (iv) the contact transducer with the longitudinal mode are similar to each other. **Figure 9** shows the similarity between (ii) and (iv) more clearly by expressing the signal and the relative velocity to the nominal value. These indicate that the residual stress in this specimen is localized

While the longitudinal wave data taken with the contact acoustic transducer is similar to the SAM data with 200 MHz, the shear wave data obtained with (v) the contact acoustic transducer shows considerable difference from the data taken with (iii) the 200 MHz SAM with the cylindrical lens of the same focal length (310 *μ*m focal length) as the spherical lens. **Figure 10** compares the data between the contact acoustic transducer and SAM for the oscillation direction of *x* and *y*, respectively. In both directions, the signal from the SAM shows considerable difference from the bulk shear wave from the contact acoustic transducer on the V30 side, while no difference is seen on the skh51 side. This indicates that on the V30 side, the material undergoes significant in-plane tensile deformation at the region twice as deep as the out-of-plane expansion (the wavelength at 200 MHz is twice of that at

Comparison was also made between the optical interferometric data and acoustic data. **Figure 11** compares the acceleration map obtained by the ESPI and relative acoustic velocity (shear wave with oscillation along *x*). Qualitative agreement is seen indicating the consistency between the stress evaluation based on the acceler-

within approximately 20 *μ*m from the surface.

*Opto-Acoustic Technique for Residual Stress Analysis DOI: http://dx.doi.org/10.5772/intechopen.90299*

ation algorithm and the acoustoelasticity.

*Comparison of SAM with 200 MHz head data and contact acoustic transducer.*

400 MHz).

**Figure 9.**

**23**

One way to evaluate the depth of residual stresses is to apply a contact acoustic transducer and SAM to the same specimen. In the experiment discussed here [27], the following configurations are used for the acoustic devices: (i) the SAM (Olympus UH3) with a 400 MHz transducer head and a spherical lens (310 *μ*m focal length); (ii) the SAM with a 200 MHz transducer head and the same spherical lens as (ii); (iii) the SAM with a 200 MHz transducer head and a cylindrical lens of the same focal length (310 *μ*m) as the spherical lens; (iv) the contact acoustic transducer with a longitudinal wave sensor head (M110-RM); and (iv) the contact acoustic transducer with a shear wave sensor head (V156-RM). These configurations work differently as follows. The SAM generates a Rayleigh wave [28] on the surface of the specimen [23]. The Rayleigh wave is mostly out of plane (normal to the specimen surface) but contains in-plane components (the component whose acoustic oscillation is parallel to the surface). When the incident acoustic wave is focused with a spherical lens, a surface acoustic wave is generated in random directions parallel to the specimen surface. Consequently, the in-plane components are averaged out, and the resultant (superposed) acoustic oscillation is out of plane. So, signals with configurations (i), (ii), and (iv) are sensitive to the elastic modulus in the *z*-direction. When the same incident wave from the SAM is line-focused with a cylindrical lens, on the other hand, the in-plane components whose acoustic oscillation is perpendicular to the axis of the cylindrical lens are not averaged out. Thus, the resultant acoustic wave is sensitive to the elastic modulus in the direction perpendicular to the lens's axis. So, signals with configurations (ii) and (v) are sensitive to the elastic modulus in the *x* or *y* direction (depending on the orientation of the cylindrical lens and the shear wave sensor head).

**Figure 8** compares the measurement conducted with configurations (i) SAM 400 MHz spherical lens, (ii) SAM 200 MHz spherical lens, and (iv) contact acoustic transducer with the longitudinal wave mode. The 400 MHz SAM and 200 MHz SAM used the same acoustic spherical lens (310 *μ*m focal length). Hence, the angle of incidence of the acoustic wave to the specimen surface was the same. The penetration depth of the acoustic wave is of the order of the acoustic wave length, i.e., approximately 15 *μ*m for skh51 and 17 *μ*m for V30. The longitudinal bulk acoustic wave from the contact transducer passes through the specimen and reflects off the rear surface. Therefore, the acoustic velocity data represents the elastic

#### **Figure 8.**

*Comparison of acoustic velocity data obtained with (a) SAM with 400 MHz head, (b) SAM with 200 MHz head, and (c) contact acoustic transducer.*

#### *Opto-Acoustic Technique for Residual Stress Analysis DOI: http://dx.doi.org/10.5772/intechopen.90299*

residual stresses is important not only to identify the depth of a given residual stress accurately but also to prevent the possibility to overlook residual stresses. The X-ray diffractometry (XRD) is one of the most developed methods of residual stress analysis. However, the XRD is applicable to the identification of residual stresses within the penetration depth of the X-ray, which is typically a few hundreds of *μ*m

One way to evaluate the depth of residual stresses is to apply a contact acoustic transducer and SAM to the same specimen. In the experiment discussed here [27],

**Figure 8** compares the measurement conducted with configurations (i) SAM 400 MHz spherical lens, (ii) SAM 200 MHz spherical lens, and (iv) contact acoustic transducer with the longitudinal wave mode. The 400 MHz SAM and 200 MHz SAM used the same acoustic spherical lens (310 *μ*m focal length). Hence, the angle of incidence of the acoustic wave to the specimen surface was the same. The penetration depth of the acoustic wave is of the order of the acoustic wave length, i.e., approximately 15 *μ*m for skh51 and 17 *μ*m for V30. The longitudinal bulk acoustic wave from the contact transducer passes through the specimen and reflects off the rear surface. Therefore, the acoustic velocity data represents the elastic

*Comparison of acoustic velocity data obtained with (a) SAM with 400 MHz head, (b) SAM with 200 MHz*

the following configurations are used for the acoustic devices: (i) the SAM (Olympus UH3) with a 400 MHz transducer head and a spherical lens (310 *μ*m focal length); (ii) the SAM with a 200 MHz transducer head and the same spherical lens as (ii); (iii) the SAM with a 200 MHz transducer head and a cylindrical lens of the same focal length (310 *μ*m) as the spherical lens; (iv) the contact acoustic transducer with a longitudinal wave sensor head (M110-RM); and (iv) the contact acoustic transducer with a shear wave sensor head (V156-RM). These configurations work differently as follows. The SAM generates a Rayleigh wave [28] on the surface of the specimen [23]. The Rayleigh wave is mostly out of plane (normal to the specimen surface) but contains in-plane components (the component whose acoustic oscillation is parallel to the surface). When the incident acoustic wave is focused with a spherical lens, a surface acoustic wave is generated in random directions parallel to the specimen surface. Consequently, the in-plane components are averaged out, and the resultant (superposed) acoustic oscillation is out of plane. So, signals with configurations (i), (ii), and (iv) are sensitive to the elastic modulus in the *z*-direction. When the same incident wave from the SAM is line-focused with a cylindrical lens, on the other hand, the in-plane components whose acoustic oscillation is perpendicular to the axis of the cylindrical lens are not averaged out. Thus, the resultant acoustic wave is sensitive to the elastic modulus in the direction perpendicular to the lens's axis. So, signals with configurations (ii) and (v) are sensitive to the elastic modulus in the *x* or *y* direction (depending on the orientation

*New Challenges in Residual Stress Measurements and Evaluation*

of the cylindrical lens and the shear wave sensor head).

from the surface.

**Figure 8.**

**22**

*head, and (c) contact acoustic transducer.*

modulus averaged over the entire thickness. The acoustic velocity data with 400 MHz SAM shows much greater deviation in the acoustic velocity from the nominal value than the 200 MHz SAM or the contact transducer. On the other hand, the data with (ii) the 200 MHz SAM and (iv) the contact transducer with the longitudinal mode are similar to each other. **Figure 9** shows the similarity between (ii) and (iv) more clearly by expressing the signal and the relative velocity to the nominal value. These indicate that the residual stress in this specimen is localized within approximately 20 *μ*m from the surface.

While the longitudinal wave data taken with the contact acoustic transducer is similar to the SAM data with 200 MHz, the shear wave data obtained with (v) the contact acoustic transducer shows considerable difference from the data taken with (iii) the 200 MHz SAM with the cylindrical lens of the same focal length (310 *μ*m focal length) as the spherical lens. **Figure 10** compares the data between the contact acoustic transducer and SAM for the oscillation direction of *x* and *y*, respectively. In both directions, the signal from the SAM shows considerable difference from the bulk shear wave from the contact acoustic transducer on the V30 side, while no difference is seen on the skh51 side. This indicates that on the V30 side, the material undergoes significant in-plane tensile deformation at the region twice as deep as the out-of-plane expansion (the wavelength at 200 MHz is twice of that at 400 MHz).

Comparison was also made between the optical interferometric data and acoustic data. **Figure 11** compares the acceleration map obtained by the ESPI and relative acoustic velocity (shear wave with oscillation along *x*). Qualitative agreement is seen indicating the consistency between the stress evaluation based on the acceleration algorithm and the acoustoelasticity.

**Figure 9.** *Comparison of SAM with 200 MHz head data and contact acoustic transducer.*

the heat on the top surface of the specimen from the bottom end (the side close to reference line a in **Figure 12**) toward the top end (the side close to line c). During the heating process and the postheating phase, the specimen was air-cooled.

**Welding speed Welding current Welding voltage Shielding gas Cooling** 5.0 mm/s 100 A 200 V Ar (10 l/min) Ambient air

For the Al 5083 specimen, the same type of acoustic and optical measurement as

Ψ plot and FEM analysis were

the skh51-V30 dissimilar weld specimen was made. The same contact acoustic transducer was used at the same coordinate points for the acoustic wave velocity measurement, and the same ESPI setup was used for the acceleration measurement.

conducted. The FEM model simulated the TIG welding by a Gaussian profiled heat input (1.2 cm full width at half maximum) moving at the speed of the welding torch with an electric power of 20 kW and a coupling coefficient to the specimen of 0.9%. The cooling phase (500 s) was simulated with natural convection at all the surfaces. The deformation was made permanent when the strain exceeded a preset yield strain. More about this modeling can be found in [29]. **Figure 13** compares the results from the above four types of analyses. The data is presented in the form of two-dimensional mapping where the vertical axis represents a physical quantity associated with the residual stress in the *x*-direction. The ESPI analysis presents the acceleration in the *x*-direction, the XRD and FEM analyses present *x*-component of

**5. Acoustic, optical, and XRD measurements**

*Opto-Acoustic Technique for Residual Stress Analysis DOI: http://dx.doi.org/10.5772/intechopen.90299*

**Table 2.**

**Figure 13.**

**25**

*Comparison of ESPI, XRD, FEM, and acoustic results.*

*Bead-on-plate welding condition.*

In addition, XRD analysis based on the 2*θ*- sin <sup>2</sup>

**Figure 10.**

*Comparison of shear wave velocity obtained with contact acoustic transducer and SAM with 200 MHz shear mode transducer head.*

**Figure 11.**

*Comparison of ESPI acceleration (x) and acoustic velocity (x). (a) ESPI, and (b) Acoustic transducer x.*
