The low-temperature yield stress of a Ni-based superalloy, which contained up to 40% of Ni3Al precipitates (γ′), was calculated by means of discrete dislocation simulations. A pair of screw or 60° (a/2)<110> dislocation glided, under external stress, across a {111} plane of the γ-phase; intersected by a random distribution of spherical or cubic γ′ precipitates. The stress increased until the dislocations could, cut or bow around, all of the obstacles. The emphasis here was on the cutting process which prevailed when the precipitates were small, and/or had low antiphase-boundary energies. A large number of simulations, in the cutting regime, showed that the yield stress was proportional to the square root of the volume fraction of γ′. The yield stress depended weakly upon precipitates with sizes of 20 to 400nm, for antiphase-boundary energies of 150, 250 and 320mJ/m2. The yield stress depended linearly upon the antiphase-boundary energy, for energies of up to 320mJ/m2, at sizes ranging from 50 to 200nm. At a precipitate size of 100nm, cubes were weaker obstacles, than were the equivalent spheres, by about 25% for an antiphase-boundary energy of 320mJ/m2. The shape effect upon strengthening decreased with decreasing antiphase-boundary energy and decreasing precipitate size. When a coherency stress (from a lattice parameter mismatch of 0.3%) was added, the yield stress increased by about 10%. When solid-solution strengthening was added, it was effective when the solute was in the γ matrix, but much less effective when the solute was in γ′. When the γ′ precipitates were larger than 400nm across, and the antiphase-boundary energy was greater than 250mJ/m2, significant Orowan looping occurred. The yield stress decreased inversely as the precipitate size, and became insensitive to the antiphase-boundary energy; but sensitive to the shear modulus.

Discrete Dislocation Simulations of Precipitation Hardening in Superalloys. S.I.Rao, T.A.Parthasarathy, D.M.Dimiduk, P.M.Hazzledine: Philosophical Magazine, 2004, 84[30], 3195-215