Propagation of sound waves in stressed elasto-plastic material

Acoustoelasticity approach is a method of non-destructive testing and it is based upon the theory of propagation of ultrasonic longitudinal and transverse waves of different polarization in solids. This approach is able to uniquely determine the value of the principal stress in the case of no plastic deformation. An elastoplastic material with hardening is taken and the problem of propagation of a plane acoustic wave in a homogeneous prismatic elastic-plastic body that is uniaxially prestressed in the direction perpendicular to the wave propagation direction is solved. The sound velocities for the transverse and longitudinal waves are obtained for different approximations in terms of the first and second order of smallness. A strong dependence of the velocities from the hardening factor and component of the deviatoric stress tensor was detected. The study provides a number of closed-form expressions required for solving the practical problem of technical diagnostics of structures exposing plasticity.