We describe here a computational method to study γ-precipitate strengthening in nickel-based superalloys, and to specifically investigate the relative importance of stacking-fault energy and coherency strains. The method is a combination of the Parametric Dislocation Dynamics (PDD), an analytical solution to the spherical inclusion problem and the generalized Peierls-Nabarro (P-N) model. Earlier analytical solutions to stacking-fault strengthening predict a lower critical resolved shear stress (CRSS) in comparison with the results of the present model. This is attributed to shape changes of super-dislocations during their interaction with γ-precipitates. However, existing analytical solutions to coherency strengthening provide considerably larger values of the CRSS compared with the results of present simulations. The dislocation core is found to spread widely as it interacts with γ-precipitates, and is thus much softer than what has been considered in previous analytical solutions. This remarkable effect is a direct result of the core structure of dislocations interacting with precipitates. When this effect is accounted for, a new analytical solution is shown to give excellent agreement with present simulation results. We finally discuss the combined effects of the two strengthening mechanisms, when they operate simultaneously.
- Ni-based superalloys
- dislocation dynamics
- generalized Peierls-Nabarro model