| Nondestructive evaluation of residual stresses has long been desirable by engineers to be able to design structures and machines more efficiently regarding the strength to mass ratio. An ultrasonic immersion technique has been devised at the University of Oklahoma to determine residual stresses via oblique-incidence acoustoelasticity. In support of the experimental technique, an analysis is made to obtain the wave velocities in terms of the second-order and third-order elastic constants, texture parameters and applied or residual stresses. Based on the theory of finite deformation of elastic solids, the equations of motion in three orthogonal directions are derived and the resulting nonlinear partial differential equations are linearized to yield an eigenvalue problem. This is then solved to determine the wave velocities as functions of strains. Furthermore, assuming slight anisotropy the classical problem of wave propagation in an orthotropic aggregate of cubic crystallites is solved to obtain the wave velocities in terms of texture parameters. The results for both texture and stress are, then, linearized for the QSV wave mode propagating in an arbitrary direction as well as in two orthogonal symmetry planes. These are numerically evaluated to show very good approximation. The observed experimental results are compared to the evaluated analytical results to reveal excellent qualitative agreement. The quantitative discrepancies are also discussed and explained. Finally, two different solutions are presented to discriminate the texture parameters from the principal strains (or stresses), by velocity or time-delay measurements at different incident angles in the symmetry planes. |
