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

For the Al 5083 specimen, the same type of acoustic and optical measurement as 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. In addition, XRD analysis based on the 2*θ*- sin <sup>2</sup> Ψ plot and FEM analysis were 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

**Figure 13.** *Comparison of ESPI, XRD, FEM, and acoustic results.*

**4.1 Bead-on-plate welding on Al 5083**

**Figure 10.**

**Figure 11.**

**Figure 12.**

**24**

*on steel block for welding.*

*mode transducer head.*

A similar analysis was made for an aluminum alloy specimen [29]. The specimen used in this experiment was a bead-on-plate aluminum alloy 5083 [30] processed by gas tungsten arc (TIG) welding. **Figure 12** shows a photo of the specimen and the steel block used to place the specimen for welding. **Table 2** lists the welding condition. The specimen plate was placed on a steel block that held one end of the specimen without imposing any other constraint. The TIG welding torch applied

*(a) Al 5083 bead-on-plate specimen. Acoustic measurements were made along line a-c. (b) Specimen placed*

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

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

*New Challenges in Residual Stress Measurements and Evaluation*

the residual stress, and the acoustic result presents the relative acoustic velocity (normalized to the nominal velocity) of the *x*-shear wave.

causes the tensile residual stress on the top surface in the following sense. If the heat dissipation from the bottom surface is higher, the temperature gradient along the thickness of the specimen is lower in the cooling phase. This reduces the above-

The case when the bottom surface has higher heat dissipation rate appears to be closer to the experimental result with ESPI shown in **Figure 13**. This is not surprising because the specimen was placed on a steel block (**Figure 12**) that behaved as a heat sink through the bottom surface. Contrastively, the top surface was exposed to air. It is reasonable to assume that the steel block was a greater heat sink than the

The present FEM simulates the residual stress by making the strain exceed the yield strain permanent. As discussed above, during the heating and cooling phases, both tensile and compressive residual stresses are created. This indicates that both tensile and compressive permanent strain can create residual stress, and it is a good question which type has greater contribution to the creation of residual stress. A

**Figure 15** shows the *x*-component of residual stress on the top surface. Here the

Acoustoelastic method relies on the nonlinear elasticity (the third-order elastic constant). It is interesting to compare the acoustic velocity measured for all three

*Effect of permanent deformation setting. (a) Compressive yield strain only, (b) compressive and tensile yield*

*x*-axis is the axis parallel to the top surface and perpendicular to the weld line. **Figure 15a–c** shows the results from the three different conditions regarding the permanent deformation setting. (a) is the case when only the compressive yield strain is used for the permanent deformation setting, (b) is the case when both of the compressive and tensile yield strains are used, and (c) is the case when the tensile yield strain only is used. The heat dissipation setting for these cases is that the bottom surface has twice as high convection than the top surface. **Figure 15a, b** shows practically no difference. On the other hand, (c) is different from (a) and (b). These altogether indicate that the effect of compressive permanent deformation plays a more important role than the effect of tensile permanent deformation in

argued locking mechanism.

**5.2 Effect of permanent strain setting**

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

the formation of residual stresses.

*strain, and (c) tensile yield strain only is considered.*

**5.3 Effect of TOEC**

**Figure 15.**

**27**

numerical study was conducted to investigate this effect.

ambient air.

Although details are different, the results from all the four analyses show qualitative agreement in the following sense. (1) All data show the general tendency that the central (near weld) region tends to have tensile residual stresses and the boundary between the central and outside regions has more compressive residual stresses. (2) Along the weld line, all data indicate that the end point of welding has higher tensile stress than the start point of welding. These observations are consistent with the following widely accepted explanation. When the welding torch heats the work, the region near the weld (the central region) is thermally expanded pushing the sides of the weld line toward the ends of the specimen (sideways). The outside regions are cooler than the central region. Consequently, the outside regions experience less thermal expansion and constrain the thermal expansion of the central region. This causes a compressive residual stress at the boundary between the central and outside regions.

In the cooling phase, the higher heat dissipation on the bottom surface locks the abovementioned stress pattern on the top surface. As the temperature of the central region goes down, the material in this region tries to shrink. However, the region behind this central region (the region closer to the bottom surface) is relatively cooler from the beginning and, therefore, does not shrink as much as the top surface. This prevents the central region near the top surface from shrinking back to the initial length. In other words, it locks tensile residual stress near the top surface.

#### **5.1 Effect of heat dissipation**

According to the above arguments, the tensile residual stress of the central region is determined by the differential rate of heat dissipation between the top and bottom surface. It is possible that increases in heat dissipation from the bottom surface (the non-welded side) can reduce this tensile stress (because it takes the heat near the top surface more aggressively). A numerical study was made to test this scenario, and the result is presented in **Figure 14**. **Figure 14a** is the case when the same convection rate is used for the top and bottom surfaces. **Figure 14b** is the case when the convection on the bottom surface is increased by a factor of two. It is seen that when the heat dissipation from the bottom surface is higher, the tendency is that the central region along the weld line is reduced. This observation confirms that in the abovementioned scenario, the heat dissipation from the bottom surface

**Figure 14.**

*Effect of heat dissipation rates. (a) The same convection is used for top and bottom surfaces; (b) convection is doubled for bottom surface.*

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

the residual stress, and the acoustic result presents the relative acoustic velocity

Although details are different, the results from all the four analyses show qualitative agreement in the following sense. (1) All data show the general tendency that the central (near weld) region tends to have tensile residual stresses and the boundary between the central and outside regions has more compressive residual stresses. (2) Along the weld line, all data indicate that the end point of welding has higher tensile stress than the start point of welding. These observations are consistent with the following widely accepted explanation. When the welding torch heats the work, the region near the weld (the central region) is thermally expanded pushing the sides of the weld line toward the ends of the specimen (sideways). The outside regions are cooler than the central region. Consequently, the outside regions experience less thermal expansion and constrain the thermal expansion of the central region. This causes a compressive residual stress at the boundary between

In the cooling phase, the higher heat dissipation on the bottom surface locks the abovementioned stress pattern on the top surface. As the temperature of the central region goes down, the material in this region tries to shrink. However, the region behind this central region (the region closer to the bottom surface) is relatively cooler from the beginning and, therefore, does not shrink as much as the top surface. This prevents the central region near the top surface from shrinking back to the initial length. In other words, it locks tensile residual stress near the top surface.

According to the above arguments, the tensile residual stress of the central region is determined by the differential rate of heat dissipation between the top and bottom surface. It is possible that increases in heat dissipation from the bottom surface (the non-welded side) can reduce this tensile stress (because it takes the heat near the top surface more aggressively). A numerical study was made to test this scenario, and the result is presented in **Figure 14**. **Figure 14a** is the case when the same convection rate is used for the top and bottom surfaces. **Figure 14b** is the case when the convection on the bottom surface is increased by a factor of two. It is seen that when the heat dissipation from the bottom surface is higher, the tendency is that the central region along the weld line is reduced. This observation confirms that in the abovementioned scenario, the heat dissipation from the bottom surface

*Effect of heat dissipation rates. (a) The same convection is used for top and bottom surfaces; (b) convection is*

(normalized to the nominal velocity) of the *x*-shear wave.

*New Challenges in Residual Stress Measurements and Evaluation*

the central and outside regions.

**5.1 Effect of heat dissipation**

**Figure 14.**

**26**

*doubled for bottom surface.*

causes the tensile residual stress on the top surface in the following sense. If the heat dissipation from the bottom surface is higher, the temperature gradient along the thickness of the specimen is lower in the cooling phase. This reduces the aboveargued locking mechanism.

The case when the bottom surface has higher heat dissipation rate appears to be closer to the experimental result with ESPI shown in **Figure 13**. This is not surprising because the specimen was placed on a steel block (**Figure 12**) that behaved as a heat sink through the bottom surface. Contrastively, the top surface was exposed to air. It is reasonable to assume that the steel block was a greater heat sink than the ambient air.

#### **5.2 Effect of permanent strain setting**

The present FEM simulates the residual stress by making the strain exceed the yield strain permanent. As discussed above, during the heating and cooling phases, both tensile and compressive residual stresses are created. This indicates that both tensile and compressive permanent strain can create residual stress, and it is a good question which type has greater contribution to the creation of residual stress. A numerical study was conducted to investigate this effect.

**Figure 15** shows the *x*-component of residual stress on the top surface. Here the *x*-axis is the axis parallel to the top surface and perpendicular to the weld line. **Figure 15a–c** shows the results from the three different conditions regarding the permanent deformation setting. (a) is the case when only the compressive yield strain is used for the permanent deformation setting, (b) is the case when both of the compressive and tensile yield strains are used, and (c) is the case when the tensile yield strain only is used. The heat dissipation setting for these cases is that the bottom surface has twice as high convection than the top surface. **Figure 15a, b** shows practically no difference. On the other hand, (c) is different from (a) and (b). These altogether indicate that the effect of compressive permanent deformation plays a more important role than the effect of tensile permanent deformation in the formation of residual stresses.

#### **5.3 Effect of TOEC**

Acoustoelastic method relies on the nonlinear elasticity (the third-order elastic constant). It is interesting to compare the acoustic velocity measured for all three

#### **Figure 15.**

*Effect of permanent deformation setting. (a) Compressive yield strain only, (b) compressive and tensile yield strain, and (c) tensile yield strain only is considered.*

method. Previous experimental and numerical studies on welding-induced residual stresses are presented and discussed. These previous results show consistency among the different methods used. Further research is definitely necessary to confirm more quantitative agreement in the results obtained by the different methods. Some procedural proposals are presented as subjects of future research. It is our hope that the content of this article is helpful to engineers and researchers of the

The present research is in part supported by the Louisiana Board of Regents Pilot-funded grant LEQSF(2016-2017)-RD-C-13 and Southeastern Louisiana University STAR grant. The authors are grateful to Robert P. Waldron Jr. for his

related fields.

**Acknowledgements**

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

assistance in this project.

**Author details**

Sanichiro Yoshida<sup>1</sup>

Hammond, LA, USA

**29**

\* and Tomohiro Sasaki<sup>2</sup>

\*Address all correspondence to: syoshida@selu.edu

provided the original work is properly cited.

1 Department of Chemistry and Physics, Southeastern Louisiana University,

2 Department of Mechanical Engineering, Niigata University, Niigata, Japan

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

**Figure 16.**

*Effect of TOEC based on the comparison of experimental relative acoustic velocity data. (E1)–(E3): Experimental relative velocity in* x*,* y*, and* z*-directions. (N1)–(N3): Numerical data corresponding to (E1)–(E3).*

directions with numerical analysis conducted with the finite element model discussed above.

The top rows of **Figure 16** are the relative acoustic velocity (acoustic velocities normalized to the nominal value) measured with the contact acoustic transducer. The bottom graphs are numerical data corresponding to the three relative acoustic velocities, evaluated with the use of Eq. (22). For all three directions, the experimental and numerical results show qualitative agreement in the overall shape of the graphs. More importantly, **Figure 16** shows that the experimental and numerical changes in the acoustic velocity are in the same range, i.e., compressive/tensile residual stresses increase/decrease the acoustic velocity approximately by 1–2%. It should be noted that the root-mean-square error in the experimental acoustic velocity measured on a specimen with no residual stress is less than 0.05%.

The above agreement opens up a new way to use the conventional acoustoelastic technique. The general procedure is as follows. It is assumed that the second-order and third-order elastic coefficients (*cij*, *cijk*, etc.) are known:

Step 1: Measure the change in the acoustic velocity for all degrees of freedom, i.e., the longitudinal wave along the *x y*ð Þ , *z* axis and the shear wave along the *xy* ð Þ *yz*, *zx* surface.

Step 2: Use Eq. (22) backward to compute Δ*Cij*.

Step 3: Use Eq. (13), etc. to find the strain vector.

Step 4: Use Eq. (11) to find the residual stress.

This procedure has not been tested yet but is a subject of our future study.

### **6. Summary**

Applications of multiple methods to residual stress analyses are discussed. The idea behind the use of multiple methods is to compensate drawbacks of each *Opto-Acoustic Technique for Residual Stress Analysis DOI: http://dx.doi.org/10.5772/intechopen.90299*

method. Previous experimental and numerical studies on welding-induced residual stresses are presented and discussed. These previous results show consistency among the different methods used. Further research is definitely necessary to confirm more quantitative agreement in the results obtained by the different methods. Some procedural proposals are presented as subjects of future research. It is our hope that the content of this article is helpful to engineers and researchers of the related fields.
