Modelling of Ultrasonic Waves in Layered Elastic Heterogeneous Materials

This article considers the propagation of high frequency elastic waves in a polycrystalline material. In this high frequency regime, we assume that the wave ’sees’ the complex media as a series of locally anisotropic layers with varying
thicknesses, where the distribution of layer thicknesses and orientations follow a stochastic (Markovian) process. This leads to a set of stochastic differential equations which describe the statistics of the energy in the system. The material properties are captured by the correlation integral which encapsulates the coupling of length-scales between the random media and the probing wave. Using experimentally obtained EBSD (electron backscatter diffraction) data for an austenitic steel weld, and subsequent processing of the data via a ray based probing technique, this paper reports on how to calculate the correlation integral.