Creep of metals containing high volume fractions of unshearable dispersoids - Part I. Modeling the effect of dislocation pile-ups upon the detachment threshold stress

The high creep resistance of dispersion-strengthened metals is the result of a threshold stress, which is determined in existing models by considering the interaction of a single dislocation with dispersoids. This paper presents a new model which takes into account the effect of dislocation pile-ups upon the detachment threshold stress of dispersion-strengthened metals. First, it is shown that dislocation pile-ups are expected to form at dispersoids when the volume fraction and/or size of the dispersoids is large. Then, the equilibrium dislocation positions within the pile-ups are calculated and the resulting shear stress exerted upon the detaching dislocations pinned at the dispersoids is determined. Finally, this pile-up stress is added to the athermal detachment threshold stress determined with existing models to find a total threshold stress. Calculations for aluminum containing 25 vol.% alumina dispersoids show that the magnitude of the pile-up stress is comparable to the athermal threshold stress, and thus contributes significantly to the total threshold stress. The model also predicts a creep activation energy much higher than that of the unreinforced metal as a result of the temperature dependence of the number of dislocations in the pile-ups.