Von Karman spatial correlation functions for modeling ultrasonic scattering in metallic media

Abstract

In recent years, ultrasonic scattering has been studied as a potential method for nondestructive microstructure characterization in polycrystalline media. In order to invert microstructural data from ultrasonic data, analytical models of wave propagation and material statistics are generally employed. The microstructure statistics are frequently represented by spatial correlation functions (SCFs), which describe how microscopic variables at random positions are correlated (e.g., elastic stiffness). In polycrystalline media with statistically isometric crystallites, SCFs are defined as the probability that two randomly chosen points lie within a single crystallite (or grain). This work reviews common forms of the SCF in the context of ultrasonic scattering measurements. In addition, we introduce the von Karman SCF, frequently used in seismic wave propagation studies, as a potential alternative for metallic components with increased microstructural complexity. In the macroscale, the material systems are assumed to be statistically isotropic, and the microstructural differences focus on the morphology of the grain structure.