From 2D to 3D: Exploring the validity of two-point correlation functions to study polycrystalline media

Abstract

Acoustic attenuation in polycrystalline materials is generally formulated using statistical representations of the material in the form of two-point correlation functions. Common formulations assume decoupling of the spatial and tensorial components and invoke analytical forms to represent the spatial correlation function (W(r)). A widely accepted form of W(r) is an exponential expression that employs a single characteristic length to describe the microstructure. More recently, this approach has been extended to include grain size distributions and different grain morphologies. To date, experimental approaches have relied on using 2D micrographs of material sections to obtain the necessary material parameters. However, the accuracy of the 2D statistical parameters relative to the three-dimensional two-point statistics is yet to be validated. In this presentation, we propose an analytical approach to transform 2D image data to 3D volumetric data by extending Wicksell's corpuscle problem to the case of equiaxed grains in polycrystalline materials. We use digital microstructures to evaluate the validity of the transformation for a broad scope of grain size distribution parameters and evaluate the accuracy of the analytical forms of the spatial correlation function. Finally, we study the impact of these approximations on acoustic attenuation.