Modeling the creep threshold stress due to climb of a dislocation in the stress field of a misfitting precipitate

A model for creep threshold stresses in alloys strengthened by coherent, misfitting precipitates is developed for the case where the precipitate is not sheared, and where there are elastic interactions between a dislocation and the precipitate over which it climbs. Calculations of the particle stress field due to a positive stiffness and lattice parameter mismatch between precipitate and matrix predict that the mismatch forces help the dislocation climb/glide process over the precipitates but that they trap it at the departure side of the particle. This results in a true threshold stress, rather than a slowing of the kinetics of dislocation climb as in previous models, which is given by the applied stress necessary to free the dislocation by a glide mechanism. Model predictions and experiment are compared for precipitation-strengthened aluminum alloys containing nanosize Al3Sc, Al3(Sc, Li) and Al3(Sc, Yb) precipitates with various sizes and mismatches. In agreement with experimental creep results, the model predicts that the threshold stress increases nearly linearly with precipitate radius, and also with the magnitude of the precipitate/matrix lattice mismatch.