Elastic strain and stress determination by Rietveld refinement: generalized treatment for textured polycrystals for all Laue classes

Abstract

A novel approach to model diffraction line shifts caused by elastic residual or applied stresses in textured polycrystals is proposed. The model yields the complete strain and stress tensors as a function of crystallite orientation, as well as the average values of the macroscopic strain and stress tensors. It is particularly suitable for implementation in Rietveld refinement programs. The requirements on refinable parameters for all crystal Laue classes are given. The effects of sample symmetry are also included and the conditions for strain invariance to both the sample symmetries (texture and stress/strain) are discussed.

Temperature-dependent elastic anisotropy and mesoscale deformation in a nanostructured ferritic alloy

“…The second approach has been developed as a tool for residual stress determination in deformed specimens after the external load is released. The macroscopic stress components are not known in this case; it is thus necessary to define a mesoscopic average stress field depending on the grain orientations, known as the stress orientation distribution function [25][26][27][28] . In this case, the proportionality factors between the strain and stress components are fully determined by the single-crystal elastic constants, although additional restrictive conditions or grain interaction models are often needed to obtain physically consistent solutions for the stress field.…”

Crystallite Size and Microstrain Measurement of Cathode Material after Mechanical Milling using Neutron Diffraction Technique

“…Rietveld refinement is becoming more popular for nonstructural applications, such as texture [6] and residual-stress [7] determination. It is practice to estimate domain size and strain values from the refined profile width parameters.…”

Rietveld texture analysis from synchrotron diffraction images. II. Complex multiphase materials and diamond anvil cell experiments

“…One should then only fit either stress or strain values (depending on the model of choice). The four models in MAUD to fit stress-strain are: (1) a triaxial elastic stress, isotropic elastic material, sin 2 ψ method (Noyan and Cohen, 1987); (2) the moment pole stress (Matthies, 1996 andMatthies et al, 2001); (3) WSODF (Popa and Balzar, 2001); and (4) the radial diffraction in the DAC (Singh, 1993 andSingh et al, 1998). Of these four models only the second and the fourth are appropriate for the type of analysis we want to do in this case.…”