Determination of sub-surface stresses at inclusions in single crystal superalloy using HR-EBSD, crystal plasticity and inverse eigenstrain analysis

The complementary techniques of high-resolution electron backscatter diffraction (HR-EBSD), crystal plasticity finite element modelling and the inverse method of eigenstrain are utilised for evaluating stresses resulting from the mismatch in thermal expansivities of a nickel single crystal containing a carbide particle. The EBSD method is employed to measure the complete residual elastic strain tensor on the free surface of the nickel matrix around a particular carbide particle. With these experimental results, the 3D inverse problem of eigenstrain is reconstructed to determine the complete residual stresses local to the particle at the sub-surface of the sample. A gradient-enhanced crystal plasticity finite element (CPFE) model has been developed for the same sample and loading conditions, and detailed comparisons of the eigenstrain and CPFE predicted stresses at the sub-surface of the sample are presented. In addition, free-surface residual elastic strains measured by HR-EBSD and predicted by the CPFE model are compared. Free-surface results show very good agreement, but some differences are apparent for sub-surface results. The eigenstrain technique relies on the assumption of uniform plastic strain in the direction normal to the free surface, and the CPFE approach provides an assessment of this assumption. The free-surface effects of 3D particle depth are also assessed.