FFT-based investigation of the shear stress distribution in face-centered cubic polycrystals

TL;DR

This study uses FFT-based methods to analyze shear stress distributions in face-centered cubic polycrystals, revealing how elastic anisotropy influences stress heterogeneity and identifying grain boundaries as critical regions for yielding.

Contribution

It introduces an FFT-based approach to quantify shear stress distributions in polycrystals, highlighting the impact of elastic anisotropy and comparing full-field simulations with the Maximum Entropy Method.

Findings

Elastic anisotropy significantly affects stress scatter.

Shear stresses deviate from normal distribution at high anisotropy.

Grain boundaries are key sites for stress fluctuations and yielding.

Abstract

The onset of nonlinear effects in metals, such as plasticity and damage, is strongly influenced by the heterogeneous stress distribution at the grain level. This work is devoted to studying the local stress distribution of shear stresses resolved in the slip systems as the critical driving force for plastic deformations. Specific grain orientations with respect to load direction are investigated in the linear elastic regime and at incipient plastic deformations based on a large ensemble of microstructures. The elastic anisotropy of the single crystal is found to have a crucial influence on the scatter of the stress distribution, whereas the Young's modulus in the respective crystal direction governs the mean stress in the grain. It is further demonstrated that, for higher anisotropy, the shear stresses deviate from the normal distribution and are better approximated by a log-normal fit. Comparing the full-field simulations to the Maximum Entropy Method (MEM), reveals that the MEM provides an excellent prediction up to the second statistical moment in the linear elastic range. In a study on the spatial distribution of shear stresses, the grain boundary is identified as a region of pronounced stress fluctuations and as the starting point of yielding during the elastic-plastic transition.