Interfacial dislocation network in precipitation strengthened alloys during creep: a discrete dislocation dynamics (DDD) study in three dimensions

Abstract

Ni-base superalloys show an intricate network of dislocations around γ′ precipitates during high-temperature low-to-intermediate stress creep. With an aim to understand the formation of this interfacial dislocation network on the surfaces of unsheared, cuboidal γ′ precipitates, we perform three-dimensional discrete dislocation dynamics simulations at constant stress in a model system containing superellipsoidal inclusions. The exponents of the superellipsoid are adjusted to fit the cuboidal shape of γ′. We use a fault-energy-based back-force model to describe interactions between dislocations and structurally inhomogeneous inclusions. The model incorporates climb of edge dislocation segments on non-glissile planes through a modified dislocation mobility law for face-centred cubic crystals. Athermal repulsive intersection cross-slip is considered for the screw segments. We systematically show the evolution of dislocation network as a function of applied stress, inter-particle spacing, and ratio of glide-to-climb mobility. We scale the simulation box and the inclusions by the same factor in order to keep the volume fraction of inclusions constant in all cases. Although the dislocation density increases with the increase in applied stress as well as inter-particle spacing, the onset of steady-state in all cases is marked by a constant mobile-to-immobile dislocation density (ρ m/ρ im) ratio. For the range of stresses and inter-particle spacings considered in this study, the steady-state ρ m/ρ im remains nearly the same. Our simulations indicate a power-law behaviour where the stress exponent n ≈ 4 suggests dislocation climb to be the rate-controlling mechanism. The simulated morphological features of the dislocation network formed on the surfaces of the inclusions at steady-state (e.g., hexagonal nets due to dislocation reactions) are similar to those observed experimentally in single-crystalline superalloys crept at high temperatures and low stresses. Moreover, we obtain a relationship between length scale associated with dislocation density and applied stress.