Estimation of local material and structure parameters of a polycrystalline aggregate from ultrasonic measurements

The propagation velocities of four ultrasonic waves in a
steel plate are measured in twelve equally spaced observation points lying in a
rolling plane on a straight line perpendicular to the rolling direction. The
plate material was rolled plastically and uniaxially in the situation where the
edges parallel to the rolling direction were free. The plate is considered to be
a bulk sample with orthorhombic symmetry of bulk mechanical properties made of
cubic crystals of the highest symmetry. The local probability density function
of the crystallite orientation and the local effective stiffness moduli of a
single grain (crystallite) are found from four ultrasonic velocities and the
rules of orthorhombic symmetry and Jaynes' principle of maximum Shannon entropy.
These results, which have been obtained for twelve mesodomains centered at each
of the twelve observation points, show the effect of the distance between an
observation point and a free plate edge on the local effective stiffness moduli
and on the local probability density function of the crystallite orientation.