A discrete dislocation dynamics study of precipitate bypass mechanisms in nickel-based superalloys
Order strengthening in nickel-based superalloys is associated with the extra stress required for dislocations to bypass the $\gamma'$ precipitates distributed in the $\gamma$ matrix. Depending on the operating conditions and microstructure, a rich variety of bypass mechanism has been identified, with various shearing and Orowan looping processes gradually giving way to climb bypass as the operating conditions change from the low/intermediate temperatures and high stress regime, to the high temperature and low stress regime. When anti phase boundary (APB) shearing and Orowan looping mechanisms operate, the classical picture is that, at for a given volume fraction, the bypass mechanism changes from shearing to looping with increased particle size and within a broad coexistence size window. Another possibility, which is supported by indirect experimental evidence, is that a third “hybrid” transition mechanism may operate. Here, in this paper we use discrete dislocation dynamics (DDD) simulations to study dislocation bypass mechanisms in Ni-based superalloys. We develop a new method to compute generalized stacking fault forces in DDD simulations, based on a concept borrowed from complex analysis and known as the winding number of a closed curve about a point. We use this method to study the mechanisms of bypass of a square lattice of spherical $\gamma'$ precipitates by $a/2\langle110\rangle$ {111} edge dislocations, as a function of the precipitates volume fraction and size. We show that not only the hybrid mechanism is possible, but also that it operates as the transition mechanism between the shearing and looping regimes over a wide range of precipitates volume fraction and radii. Based on our simulation results, we propose a simple model for the strength of this mechanism. We also consider the effects of a $\gamma$/$\gamma'$ lattice misfit on the bypass mechanisms, which we approximate by an additional precipitate stress computed according to Eshelby’s inclusion theory. We show that in the shearing and hybrid looping-shearing regimes, a lattice misfit generally results in an increased bypass stress. For sufficiently high lattice misfit, the critical bypass configuration in attractive dislocation-precipitates interactions changes dramatically, and the bypass stress is controlled by the pinning of the trailing dislocation on the exit side of the precipitates, similar to what has been reported in the high-temperature creep literature.