Ensemble averaging stress–strain fields in polycrystalline aggregates with a constrained surface microstructure – Part 1: anisotropic elastic behaviour

The effect of three-dimensional (3D) grain morphology on the deformation at a free surface in polycrystalline aggregates is investigated by means of a large-scale finite element and statistical approach. For a given two-dimensional surface at z = 0 containing 39 grains with given crystal orientations, 17 random 3D polycrystalline aggregates are constructed having different 3D grain shapes and orientations except at z = 0, based on an original 3D image analysis procedure. They are subjected to overall tensile loading conditions. The resulting stress–strain fields at the free surface z = 0 are analyzed. Ensemble average and variance maps of the stress field at the observed surface are computed. In the case of an anisotropic elastic behaviour of the grains, fluctuations ranging between 5% and 60% are found in the equivalent stress level at a given material point of the observed surface from one realization of the microstructure to another. These results have important implications in the way of comparing finite element simulations and surface strain field measurements in metal polycrystals.