Strain-rate dependent crystal plasticity model and aluminum softening/hardening transition

Abstract

Hardening or softening associated with the increase of dislocation density is correlated with strain rate and dislocation density. Taking aluminum as a model material, we investigate the strain rate and dislocation density dependence of the strength and the accompanying hardening or softening effect upon a dislocation increase. This investigation is enabled by employing a newly developed crystal plasticity model, which is validated against the mechanical behaviors in an extremely wide strain rate range, and featured by a parameter-free mobile dislocation fraction law based on the exponential distribution of dislocation link lengths and an averaged dislocation velocity model that considers both thermally-activated waiting mechanism and drag-dominated running mechanism. Results show that at different strain rates, the material strength varies with a universal feature that it first softens as the dislocation density increases from a sufficiently low initial value, and then hardens after reaching the minimum strength, where the critical dislocation density separating the softening from hardening regimes increases with the strain rate. Microscopically, the strength dependence on dislocation density and strain rate originates from their influence on the two competing effects of a dislocation increase, where the hardening effect comes from the higher resistance to dislocation slip by increased forest dislocations while the softening effect comes from the larger quantity of mobile dislocations. These two competing effects are quantitatively evaluated by the crystal plasticity model and are further cast into the competition between the partial derivatives of normalized dislocation velocity and of normalized mobile dislocation density, and the governing equation for the critical dislocation density is thus furnished by balancing these two competing effects. Further, a complete map in the entire space of strain rate and dislocation density (ε̇,ρ) is constructed for the zones of dislocation hardening or softening, where the zone-boundary curve for critical dislocation density exhibits a two-stage character and it agrees well with the available experimental data. Such a map is expected to help predict the trend for strength evolution under different serving conditions and also guide the material design according to the requirements for strength variation in service.