Constitutive relation based on Taylor slip analysis to replicate work-hardening evolution

A constitutive relation based on crystal plasticity was derived by equating the energy of dislocations required to generate the imposed incremental strain with that which was stored as determined from the flow stress. The dynamic annihilation of created dislocations was accounted for by using a factor to balance the equation. The specific case of Taylor’s parabolic relation was reproduced and microstructure-based parameters were explicitly formulated in the proportionality constant usually attributed as empirical in the Hollomon relation. The nearly precise replication of the stress–strain relation using at least two curve-fits for aluminum and its alloys validates the quantitative determination of the mean slip distance. The intersection of the two fits appears to be analogous to Stage II to III transition, which was confirmed by analysis of [1 1 1] and [1 0 0] single-crystal studies taken from the literature. The correlation of the flow stress with inverse mean slip distance and deformation cell size, together with the measured stored work, permitted an insight into this Stage II to III transition. The analysis suggests that dynamic-recovery effect in Stage III may be attributed to the change in mean slip distance pattern due to the evolution of cells.