Modelling of work hardening and stress saturation in FCC metals

Abstract

A work hardening theory has been developed based on a microstructural concept comprising three elements; the cell/subgrain size, δ, the dislocation density inside the cells, ρ i , and the cell boundary dislocation density or the sub boundary misorientation, ρ b or ϕ. The theory is based on a statistical approach to the storage of dislocations. This approach predicts that the slip length, L, scales with the inverse square root of the stored dislocation density, ρ −1/2, and also, predicts a substructure evolution which is consistent with the concept of microstructural scaling (similitude) at zero degree Kelvin, at stress τ< τ III . The model provides a solution to the basic `dislocation–book-keeping-problem' by defining a differential equation which regulates the storage of dislocations into (i) a cell interior dislocation network, (ii) increases in boundary misorientation and (iii) the creation of new cell boundaries. By combining such a solution for the dislocation storage problem with models for the dynamic recovery of network dislocations and sub-boundary structures, the result becomes a general internal state variable solution which has the potential of giving the flow stress as a function of strain for any combination of strain-rate and temperature. The theory predicts that the dislocation density ρ i inside the cells saturates at the end of the Stage II–III transition, a saturation effect which regulates the subsequent stress–strain behaviour which is then controlled by the continuous refinement of the cell/subgrain structure. The characteristic features of Stages III and IV are well accounted for by the model. The present work hardening model also provides the necessary basis for the construction of constitutive laws for the saturation stresses; τ III , τ IIIs and τ s and steady-state creep. Beyond Stage II breakdown only two rate controlling dynamic recovery mechanisms are involved, relating to dislocation network growth and subgrain growth. The activation energy of both growth reactions is that of self diffusion. Steady-state creep laws are presented covering the entire range from low temperature creep to Harper–Dorn creep.