Assimilated model of work-hardening in FCC metals and its application to devolution of stored work

The new assimilated work-hardening model encompasses the imposed strain condition that creates slipped areas bounded by dislocations, and work hardening is due to operation of multiple slip systems forming forest dislocations. The minimum slip plane spacing is geometrically determinable and compared with the lattice spacing permitted for the passage of dislocations of opposite signs on parallel planes. This calculable spacing from the flow shear stress is larger than that imposed by the strain and is attributed to dynamic dislocation annihilation. The ratio of the expended work to that stored, defined as annihilation factor, A, can be related to the square of the ratio of the minimum spacing allowed by the flow stress to that imposed by the strain. The model predicts that 1/A relates to the stored fraction due to the total dislocation density of attractive and repulsive intersections, whereas the density determined from the flow stress is due to only the repulsive one, deduced to be the rate determining process. Because the predicted ratio of two (2) between total density and repulsive was experimentally validated, a model of parallel array of opposite sign dislocations showed that the flow stress due to the parallel array and that intersecting it are simultaneously satisfied. The conclusion is that the coordination of the strain and two stress criteria are self-organized by the evolving internal stress. The derived stored work is the sum of the fractions due to 1/A and the vacancy creation, CV, which is calculable from the constitutive relation. The model prediction validations were based on deforming systems without thermal recovery at 4.2 K and 78 K in super-pure aluminum.