Comparisons of Representative Volume Elements for Mechanical and Diffraction Stress Measurements

An open question in the measurement of residual stress is the definition of the probe volume (or representative volume elements, RVEs) necessary to measure the continuum stress state. The answer to this question will not only be material microstructure and property dependent, but also dependent on the level of deformation as microscale stress and strain states evolve to simultaneously satisfy equilibrium and compatibility, respectively. The use of diffraction-based techniques further complicates the probe volume size question due to the discontinuous sampling of material volumes by Bragg selection rules. Here we utilize micromechanical crystal plasticity simulation data to begin to quantify the necessary probe volumes to recover the continuum stress state using both spatial (direct space) averaging and diffraction simulations. Comparisons are made between necessary probe volume sizes for Cu, W, and CuW polycrystals loaded in the elastic regime, through yield, and upon unloading.