Elastic Deformation of Polycrystals

TL;DR

This paper introduces a comprehensive model for the elastic behavior of polycrystals, incorporating grain orientation, elastic strains, and long-range interactions, enabling simulation of deformation under various loading conditions.

Contribution

It presents a novel framework coupling crystal orientations with elastic strains, explicitly accounting for symmetry and long-range interactions in polycrystals.

Findings

The model successfully simulates uniaxial tensile loading of 2D polycrystals.

It captures the effects of grain rotation under external loads.

The response of polycrystals differs from single crystals with similar orientations.

Abstract

We propose a framework to model elastic properties of polycrystals by coupling crystal orientational degrees of freedom with elastic strains. Our model encodes crystal symmetries and takes into account explicitly the strain compatibility induced long-range interaction between grains. The coupling of crystal orientation and elastic interactions allows for the rotation of individual grains by an external load. We apply the model to simulate uniaxial tensile loading of a 2D polycrystal within linear elasticity and a system with elastic anharmonicities that describe structural phase transformations. We investigate the constitutive response of the polycrystal and compare it to that of single crystals with crystallographic orientations that form the polycrystal.