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(R)ϵ(R), and ultimately the stress tensor, σ(R)σ(R), for every crystal orientation, RR, 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(R)ϵ(R) and σ(R)σ(R) are the average values from all elements at a particular orientation. Significant dependence in the components of σ(R)σ(R) with orientation were found and the σ(R)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.