Characterization of random stress fields obtained from polycrystalline aggregate calculations using multi-scale stochastic finite elements

TL;DR

This paper investigates the spatial variability of stress fields in polycrystalline materials using a novel periodogram-based method to characterize the properties of Gaussian random fields derived from finite element simulations.

Contribution

It introduces a new method for identifying the properties of stress fields in polycrystalline aggregates, accounting for random grain geometries and orientations.

Findings

The method effectively characterizes the stress field properties.

It remains stable across different sample sizes and load levels.

The approach applies to both fixed and random grain geometries.

Abstract

The spatial variability of stress fields resulting from polycrystalline aggregate calculations involving random grain geometry and crystal orientations is investigated. A periodogram-based method is proposed to identify the properties of homogeneous Gaussian random fields (power spectral density and related covariance structure). Based on a set of finite element polycrystalline aggregate calculations the properties of the maximal principal stress field are identified. Two cases are considered, using either a fixed or random grain geometry. The stability of the method w.r.t the number of samples and the load level (up to 3.5 % macroscopic deformation) is investigated.