Evaluation of material parameters, texture and stress of a prestressed polycrystalline aggregate from ultrasonic measurements

Abstract

The propagation of ultrasonic plane waves in a polycrystalline aggregate (steel) is considered for a bulk sample of the material with plane initial (residual) stress, the material being made of cubic crystals of the highest symmetry. Some effective stiffness moduli of the bulk sample and the components of the initial stress are found as functions of the propagation velocities of the respective ultrasonic plane waves. Moreover, the use is made of Jaynes' principle of maximum Shannon entropy and the averaging procedure proposed by Voigt. In this way, the probability density function of the crystallite orientation (texture) and the effective stiffness moduli of a single crystallite of the polycrystalline aggregate are evaluated numerically for the initial plane stress increasing from zero up to about 300 MPa (in the range of elasticity). The numerical analysis shows that while the effect of the initial stress on the results of these calculations increases with increasing initial stress, the changes in the texture and effective stiffness moduli of a single crystallite are inconsiderable in the region of the values of the initial stress taken in to account.