Diffraction-based residual stress measurements in low symmetry materials

The underlying assumption for diffraction based residual stress techniques

is that the strain measured in a subset of grains within the gauge volume is

representative of the macroscopic stress state in that volume. The literature

has many examples where the lattice parameter strain determined from

Rietveld refinements for materials with cubic crystal structure are successful

in representing the bulk average strain, and even for simple weighted lattice

parameter strains, e.g. (2a+c)/3 for materials with hexagonal crystal

structure. However, the situation is more complicated for materials with

lower symmetry, e.g. monoclinic, where the angles of the lattice are also

variable. Here, one must consider in detail what the lattice parameters, e.g.

a, b, c, and γ, determined by Rietveld analysis of a diffraction pattern where

each peak is comprised of contributions from distinct, mutually exclusive,

grain sets represent. We present an approach based upon Rietveld

refinement that determines a bulk representative lattice strain along a single

material direction, defined by the scattering vector, employing recalculated

strains for all peaks in the measured pattern, as well as the texture

information provided by the measurement. The results are validated for

measurements where the macroscopic stress state is known, i.e. in-situ

uniaxial loading tests.