**Author details**

directions with numerical analysis conducted with the finite element model

*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*

*New Challenges in Residual Stress Measurements and Evaluation*

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

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*

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

Applications of multiple methods to residual stress analyses are discussed. The idea behind the use of multiple methods is to compensate drawbacks of each

and third-order elastic coefficients (*cij*, *cijk*, etc.) are known:

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.

discussed above.

**Figure 16.**

*(E1)–(E3).*

ð Þ *yz*, *zx* surface.

**6. Summary**

**28**

Sanichiro Yoshida<sup>1</sup> \* and Tomohiro Sasaki<sup>2</sup>

1 Department of Chemistry and Physics, Southeastern Louisiana University, Hammond, LA, USA

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

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

© 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, provided the original work is properly cited.
