Statistical effects in X-ray diffraction lattice strain measurements of ferritic steel using crystal plasticity

The influence of statistics on calculated lattice strains has been studied by comparing crystal plasticity finite element (CPFE) calculations with strains measured experimentally. Experimentally, when Bragg's law is obeyed, a plane normal must lie within a narrow orientation range (∼ 0.02° for synchrotron diffraction), or Bragg tolerance. However, CPFE models consider only a small number of grains compared to experiments, necessitating a justification of the statistically representative volume. It also becomes necessary to assess the threshold of Bragg tolerance allowable for the determined statistically representative volume. In this study, an 8 × 8 × 8 model was deemed as statistically representative such that only small benefits are obtained in terms of lattice strain calculations by adopting larger models such as 10 × 10 × 10. Based on the selected model, an allowable Bragg tolerance of approximately 5° was calculated. Also highlighted was the coupling between lattice strain, texture, hardening and applied boundary condition which are discriminators that will affect the choice of model size and Bragg tolerance threshold.