Von Kármán spatial correlation function to describe wave propagation in polycrystalline media

Analytical functions that describe the spatial heterogeneity in polycrystalline media are highly desirable. These mathematically tractable descriptors can be readily implemented in physical models of static and dynamic material behavior, including wave propagation. This paper explores the suitability of von Kármán spatial correlation functions (SCFs) to describe polycrystalline media with a distribution of grain sizes. The empirical two-point statistics are compared to the von Kármán and other commonly reported SCFs. The von Kármán function is shown to be more accurate than the exponential function and more tractable than the sum of exponentials form. The impact of the SCF on wave propagation and scattering is studied by employing a well-defined analytical model for attenuation. The attenuation varies by over a factor of two for the aluminum case considered. These results provide preliminary insights into the suitability of a closed-form von Kármán SCF to describe polycrystalline media with increasingly complex microstructures.