A DISLOCATION DENSITY APPROXIMATION FOR THE FLOW STRESS-GRAIN SIZE RELATION OF POLYCRYSTALS

Based on the dislocation pile-up theory and the Ashby model of polycrystalline deformation, an expression for flow stress was derived, which shows that the flow stress depends on the densities of statistically stored dislocation rho(s) and geometrically necessary dislocation rho(g). The contribution of rho(g) to the flow stress is related to the grain boundary region fraction 1 - x which was derived to be the functions of rho(s) and rho(g). This expression does not predict a precise Hall-Fetch relation. If rho(s) dominates, the expression reduces to a linear sigma-d(-1) relation; if rho(g) dominates, the expression reduces to a linear sigma-d(-1/2) relation, i.e. the Hall-Fetch relation. The expression was applied to calculate the sigma-d(-1/2) curves of three typical polycrystalline materials, aluminium, copper and brass in the literatures and very good agreements between the calculations and experiments were obtained. By incorporating the experimental data, the contributions of rho(s) and rho(g) to flow stress was analysed and the Hall-Fetch parameters were discussed in terms of rho(s) and rho(g).