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 ., 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.