# Strain distribution in polycrystals: Theory and Application for Diffraction Experiments

## TL;DR

This paper develops a theory to accurately average tensor properties in polycrystals, enabling precise prediction of elastic behavior and internal stress states, validated by diffraction experiments and applicable to textured materials.

## Contribution

It introduces a unified averaging method for tensor coefficients in polycrystals, improving predictions of elastic moduli and internal stresses, validated against experimental data.

## Key findings

- High-precision elastic moduli for cubic polycrystals recovered
- Analytical prediction of stress and strain states matches neutron diffraction data
- Method applicable to textured materials with potential for further generalizations

## Abstract

Randomly textured polycrystalline materials of constituents with highly anisotropic nature of grains can be considered globally isotropic. In order to determine the isotropic properties, like elasticity or conductivity, we propose a theory for averaging the coefficients of the corresponding tensors unifying Voigt's, Reuss' or other self-consistent homogenization theories. We apply the method to determine elastic moduli of untextured polycrystals with arbitrary crystal structures, recovering experimental data with high precision for cubic materials. We show that the average moduli can be used to predict analytically stress and strain states inside individual grains as proven by the comparison with neutron diffraction measurements. Finally, we discuss a few possible generalizations for textured materials for further applications.