A continuum approach to combined γ/γ′ evolution and dislocation plasticity in Nickel-based superalloys

In single crystal Nickel-based superalloys subject to creep loading, the γ/γ′ phase microstructure co-evolves with the system of dislocations under load. Computational modeling thus requires multiphysics approaches capable of describing and simulating both phase and defect microstructures within a common conceptual framework. To do so, we formulate a coupled continuum model of the evolution of phase and dislocation microstructures. The simulated γ/γ′ phase microstructure accounts for concentration as well as crystallographic order parameters. Dislocation microstructure evolution is described in terms of dislocation densities and associated stress-driven dislocation fluxes. The creep strain curve is obtained as a natural by-product of the microstructure evolution equations. We perform simulations of γ/γ′ evolution for different dislocation densities and establish the driving forces for microstructure evolution by analyzing in detail the changes in different contributions to the elastic energy and chemical free energy density, as well as the evolution of stress concentrations that may trigger the transition from dislocation flow in the γ channels towards shearing of the γ′ precipitates. Our investigation reveals the mechanisms controlling the process of directional coarsening (rafting) and demonstrates that the kinetics of rafting significantly depends on characteristics of the dislocation microstructure. In addition to rafting under constant load, we investigate the effect of changes in loading conditions and explore the possibility of improving creep properties by pre-rafting along a different loading path.