Diffraction Stress Factors Calculated Using a Maximum Entropy Method

TL;DR

This paper introduces the application of the Maximum Entropy Method (MEM) for diffraction stress analysis in textured materials, demonstrating its accuracy and efficiency in modeling local strains in cold-rolled metals.

Contribution

It is the first to apply MEM to textured materials, providing a new, efficient way to calculate stress factors based on effective stiffness.

Findings

MEM yields accurate local strains in highly textured copper.

The approach compares favorably with established methods in accuracy.

It is numerically efficient for practical stress analysis.

Abstract

Diffraction-based stress analysis of textured materials depends on understanding their elastic heterogeneity and its influence on microscopic strain distributions, which is generally done by using simplifying assumptions for crystallite interactions to calculate tensorial stress factors or in the case of very strong textures, by considering the material phase as a single crystal (crystallite group method). In this paper, we apply the micromechanical Maximum Entropy Method (MEM) to this purpose, which marks its first use for materials with texture. The special feature of this approach is a native parametrization by the effective stiffness of the material, which allows the approach to be tailored to a macroscopically measurable sample property. We perform example stress analyses of cold-rolled copper, finding through validation with full-field simulations that the MEM yields accurate local strains even for materials with extremely sharp textures. In an example stress analysis of mildly textured cold-rolled ferritic steel, the accuracy of the approach compares favorably to the established Voigt, Reuss and self-consistent Eshelby-Kr\"oner approaches. Compared to the latter, the method is also numerically efficient to calculate.