The grain size effect on strain hardening and necking instability revisited from the dislocation density evolution approach

Abstract

Revisiting the classical topic of the strain hardening behaviour from a perspective of the analytical model based on the evolution of dislocation density with strain, we extended the capacity of the single internal variable model towards predicting necking instability and re-examined the grain size dependence of the flow stress. An excellent agreement is observed between the model predictions of the necking strain and stress and the results of tensile testing of nickel polycrystals with grain sizes varied from sub-micrometres to hundred micrometres. The pivotal significance of the dynamic recovery in the occurrence of necking has been analysed and emphasised in the context of the discussion on the effect of grain size on flow stress. The most interesting corollary of the analysis made is that not only the simple modelling of the dislocation density evolution, which can be traced back from the very early stage of plastic flow in materials with different grain sizes, can be used for realistic approximation of the stress-strain behaviour during homogeneous deformation under constant plastic strain rate, but also for predicting the onset of necking instability with high confidence.