Measuring and modeling distributions of stress state in deforming polycrystals

Crystal stress distributions from synchrotron X-ray diffraction experiments and crystal-based finite element simulations conducted on copper specimens loaded through yielding and the elastic-plastic transition are presented. In the experiments, the lattice strain tensor, ε{lunate} (R), and ultimately the stress tensor, σ (R), for every crystal orientation, R, within the aggregate were determined at discrete load levels during a tension test by inverting measured lattice strain pole figures. The simulation conditions exactly mimicked the experiment and the underlying model employed single-crystal elasticity and restricted-slip plasticity. In the simulation, ε{lunate} (R) and σ (R) are the average values from all elements at a particular orientation. Significant dependence in the components of σ (R) with orientation were found and the σ (R) determined from the experiment compared well with the simulation results. In addition we employed a spherical harmonic expansion of each component of stress over orientation space. The coefficients from the experiments compared well with those obtained from the simulation.