Disorder strengthening of ordered L12 alloys by face centered cubic (A1) precipitates

Abstract

We present a new theory of strengthening (disorder strengthening) of a crystallographically ordered L12 matrix by spherical, coherent crystallographically disordered fcc (A1) precipitates. There are two versions of the theory, each involving different approximations for the length of the chord, inside the precipitate, subtended by the trailing dislocation in the super-dislocation pair. Each of these versions incorporates two other assumptions involving the statistics of dislocation-precipitate interactions, which determine the average spacing of the precipitates along the super-dislocation. All versions of the theory predict a peak-strength condition at small particle sizes, followed by an extended period of overaging in which the strength decreases slowly with increasing particle size. We compare the quantitative predictions of the theory with both computer-simulated and experimentally generated data on inverse Ni-base γ′-type superalloy matrices strengthened by γ precipitates. In all cases at least one version of the theory is in excellent agreement with the data. The predicted strengthening is significant, the order of 85–110 MPa in the computer simulated results and 40–80 MPa in model precipitation strengthened inverse superalloys containing small volume fractions (≤0.04) of γ precipitates. The results are discussed in light of the statistics of dislocation-precipitate interactions and the resistance of individual γ particles to shearing by the super-dislocation pair; this resistance depends on the ratio of maximum force required to break free of the precipitate and the line tension of the dislocation pair.