Statistical assessment of stress redistribution in loaded polycrystals

Abstract

This work deals with the analysis of stress redistribution in a polycrystal due to external loading, anisotropy of elastic properties, and microstructure characteristics. A statistical method that enables assessing relationships between stress fields and microstructure features of interest is suggested. The notion of generalised semivariogram is introduced and used to determine the extent of spatial dependence in multivariate random fields. Afterwards, it is allowed to perform the tests of independence based on the distance correlation coefficient. The detected non-spatial dependencies are further examined, focusing on the identification of the actual type of heteroscedasticity. The method is aimed at analysing large computational datasets resulting from numerical simulations of stress redistribution in polycrystals under external loads. It is demonstrated on datasets computed on a realistic microstructure of a NiTi wire subjected to tension while considering uniform and preferential lattice orientation distributions and various degrees of elastic anisotropy. The method shows for the considered microstructure and loading that the degree of elastic anisotropy does not affect the dependencies contrarily to the lattice orientation distribution.