A dislocation model for the stress-strain behaviour of polycrystalline α-Fe with special emphasis on the variation of the densities of mobile and immobile dislocations

Abstract A dislocation model for the stress-strain behaviour of polycrystalline α-Fe at around 20° C and beyond the Luder's strain is presented. In the model a relationship between total dislocation density (ϱ) and strain (ϵ) is deduced. From the ϱ-ϵ relationship and the general relationship between stress (σ) and ϱ, σ=σ0Gb√ϱ, the σ-ϵ relationship is obtained. The model is based on the average behaviour of large numbers of dislocations (mobile and immobile) and it is assumed that the variation of total dislocation density with strain is determined by four dislocation processes, namely the creation, the immobilization, the re-mobilization and the annihilation of dislocations. Three main parameters are introduced and these are discussed and given physical interpretation. It is shown the ϱ-e relationships obtained experimentally can be very well accounted for by the present dislocation model.