Determination of material parameters and texture of a polycrystalline aggregate from ultrasonic measurements

Abstract

The propagation of ultrasonic waves in a polycrystalline aggregate is considered for a bulk sample with orthorhombic symmetry made of cubic crystals of the highest symmetry. The probability density function of the crystallite orientation and the stiffness moduli of a single grain (crystallite) of the polycrystalline aggregate are found from four ultrasonic velocities and the rules of orthorhombic symmetry. Moreover, Jaynes’ principle of maximum Shannon entropy and the averaging procedure proposed by Voigt are used. In this way, it is shown that on the basis of the measurements of four respectively chosen ultrasonic velocities it is possible to find simultaneously the maximum-entropy distribution function of the crystallite orientation and the crystallite stiffness moduli.