The determination of a continuum mechanics equivalent elastic strain from the analysis of multiple diffraction peaks

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Abstract
Stress measurement by neutron or synchrotron x-ray diffraction is a nondestructive technique that provides insights into strain and/or stress fields deep within engineering components and structures. The technique is seeing increased use for the validation of finite element process models, however, present FE models predict a continuum elastic strain rather than diffraction strains. An expression is therefore derived for a physically realistic weighting of strains obtained from multiple single peak diffraction measurements of internal elastic strain in order to determine a macroscopic equivalent elastic strain, and hence stress. A practical approach to the use of the expression is suggested. A similar expression is derived for the equivalent weighting used in Rietveld refinements, for both polychromatic and monochromatic sources, which is applicable to both neutron and x-ray diffraction. The use of these expressions is illustrated for both textured and untextured, cubic (steel) and hexagonal (titanium) symmetry polycrystals. The physically realistic weighting is different from that used in the Rietveld refinement however both provide good estimates of the macroscopic equivalent elastic strain.