MODELING OF WORK-HARDENING AND STRESS SATURATION IN FCC METALS

A work hardening theory has been developed based on a microstructural concept comprising three elements; the cell/subgrain size, delta, the dislocation density inside the cells, rho(i), and the cell boundary di slocation density or the sub boundary misorientation, rho(b) or phi. T he theory is based on a statistical approach to the storage of disloca tions. This approach predicts that the slip length, L, scales with the inverse square root of the stored dislocation density, rho(-1/2), and also, predicts a substructure evolution which is consistent with the concept of microstructural scaling (similitude) at zero degree Kelvin, at stress tau < tau(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 (ii i) the creation of new cell boundaries. By combining such a solution f or the dislocation storage problem with models for the dynamic recover y of network dislocations and sub-boundary structures, the result beco mes a general internal slate 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 dislocat ion density rho(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 ref inement of the cell/subgrain structure. The characteristic features of Stages III and IV are well accounted for by the model. The present wo rk hardening model also provides the necessary basis for the construct ion of constitutive laws for the saturation stresses; tau(III), tau(II Is) and tau(s) and steady-state creep. Beyond Stage II breakdown only two rate controlling dynamic recovery mechanisms are involved, relatin g to dislocation network growth and subgrain growth. The activation en ergy of both growth reactions is that of self diffusion. Steady-state creep laws are presented covering the entire range From low temperatur e creep to Harper-Dorn creep. (C) 1998 Elsevier Science Ltd. All right s reserved.