Analytical model for predicting induced-stress distributions in polycrystalline materials

TL;DR

This paper introduces a straightforward micromechanical model to predict stress distributions at grain boundaries in polycrystalline materials under elastic loading, aiding in understanding crack initiation risks.

Contribution

The model provides a quick method to estimate grain-boundary stresses, validated against finite element simulations for different conditions.

Findings

Model accurately predicts stress distributions in various scenarios.

Finite element results confirm the model's reliability.

Stress distributions are essential for assessing crack initiation probability.

Abstract

A simple micromechanical model of polycrystalline materials is proposed, which enables us to swiftly produce grain-boundary-stress distributions induced by the uniform external loading (in the elastic strain regime). Such statistical knowledge of local stresses is a necessary prerequisite to assess the probability for intergranular cracking initiation. Model predictions are verified through finite element calculations for various loading configurations, material properties, and grain-boundary types specified by the properties of a bicrystal pair of grains enclosing the grain boundary.