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

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.