Discrete dislocation simulations of precipitation hardening in superalloys

Abstract

The low-temperature yield stress of a nickel-based superalloy, containing up to 40% Ni3A1 precipitates (γ′), is calculated by discrete dislocation simulations. A pair of screw or 60°(a/2) ⟨110⟩ dislocation glides under external stress across a {111} plane of γ phase, intersected by a random distribution of either spherical or cubic γ′ precipitates. The stress is raised until the dislocations can cut or bow round all the obstacles. In this paper the emphasis is on the cutting regime which is prevalent when the precipitates are small and/or have low antiphase-boundary (APB) energies. From a large number of simulations in the cutting regime, the effects of size, shape, volume fraction and APB energy are found to be as follows: The yield stress is proportional to the square root of the volume fraction of γ′. The yield stress depends weakly on the precipitate size in the size range 20–400 nm, for APB energies of 150, 250 and 320 mJ m−2. The yield stress depends linearly on the APB energy for APB energies up to 320 mJ m−2 in the size range 50–200 nm. At a precipitate size of 100 nm, cubes are weaker obstacles than equivalent spheres by about 25% for an APB energy of 320 mJ m−2; however, the shape effect on strengthening decreases with decreasing APB energy and decreasing precipitate size. When a coherency stress (from a lattice parameter mismatch of 0.3%) is added, the yield stress increases by about 10%. When solid-solution strenthening is added, it is potent when the solute is in the γ matrix, but much less potent when the solute is in γ′. When the γ′ precipitates are larger than 400 nm across and the APB energy greater than 250 mJ m−2, significant Orowan looping occurs. The yield stress drops inversely as the precipitate size and becomes insensitive to the APB energy but sensitive to the shear modulus. Many of these results from the full simulations differ from the analytical models of strengthening in superalloys but they can be rationalized from the results of simulations on simple homogenized precipitate structures.