Numerical study of the flow responses and the geometric constraint effects in Ni-base two-phase single crystals using strain gradient plasticity

The [0 0 1] tensile flow of a single-crystal superalloy (CMSX-4) having a high volume fraction of regularly-arrayed cuboidal γ′ precipitates was simulated using a gradient-dependent plasticity model for the constitutive description of the γ-matrix. The simulated flow curves showed flow softening in the early stage of straining. Flow softening was accompanied by the organized catastrophic plastic flow of the γ-matrix, which resulted from the breakdown of the geometric (or kinematic) constraints imposed by the γ/γ′ microstructure. The flow-softening behavior was influenced by the thickness of γ-matrix channels (a volume fraction of the γ′ precipitates), the flow property of the γ-matrix and the geometry of the γ′-precipitate edge. In particular, changing the radius of the γ′-precipitate edge resulted in a dramatic variations in the flow curves. The present unit-cell simulations exhibited good predictions for the γ′-precipitate size dependence of the flow stress at moderate strains.