A crystal plasticity study of cyclic constitutive behaviour, crack-tip deformation and crack-growth path for a polycrystalline nickel-based superalloy

Abstract

Crystal plasticity has been applied to model the cyclic constitutive behaviour of a polycrystalline nickel-based superalloy at elevated temperature using finite element analyses. A representative volume element, consisting of randomly oriented grains, was considered for the finite element analyses under periodic boundary constraints. Strain-controlled cyclic test data at 650 °C were used to determine the model parameters from a fitting process, where three loading rates were considered. Model simulations are in good agreement with the experimental results for stress–strain loops, cyclic hardening behaviour and stress relaxation behaviour. Stress and strain distributions within the representative volume element are of heterogeneous nature due to the orientation mismatch between neighbouring grains. Stress concentrations tend to occur within “hard” grains while strain concentrations tend to locate within “soft” grains, depending on the orientation of grains with respect to the loading direction. The model was further applied to study the near-tip deformation of a transgranular crack in a compact tension specimen using a submodelling technique. Grain microstructure is shown to have an influence on the von Mises stress distribution near the crack tip, and the gain texture heterogeneity disturbs the well-known butterfly shape obtained from the viscoplasticity analysis at continuum level. The stress–strain response near the crack tip, as well as the accumulated shear deformation along slip system, is influenced by the orientation of the grain at the crack tip, which might dictate the subsequent crack growth through grains. Individual slip systems near the crack tip tend to have different amounts of accumulated shear deformation, which was utilised as a criterion to predict the crack growth path.