Modelling the elastic-plastic transition of polycrystalline metals with a distribution of grain sizes

A number of recent studies have indicated that the extent of the elastoplastic stage in nanocrystalline polycrystals, with grain sizes smaller than several hundred nanometres, is appreciably larger than that for coarse-grained polycrystals (i.e. grain sizes larger than approximate to 1 mu m). The so-called tangent modulus approach has, accordingly, been used in order to identify the extent of this stage and to define the stress at which all the grains of a polycrystal become plastic. In this work, the applicability of this methodology to single-phase polycrystals, where deformation is accommodated by dislocation slip, is examined in the context of a grain size dependent elastoplastic self-consistent model. Assuming the size distribution is the primary cause of inhomogeneous yielding among the grains of a polycrystal, the stress-strain behaviour of a number of lognormal, fcc polycrystals with varying mean grain sizes and standard deviations is simulated. The true yield strength of the polycrystals is determined by monitoring the evolution of the volume fraction of yielded grains as a function of imposed deformation. It is found that yielding is essentially complete when the tangent modulus (i.e. the work hardening rate) of the polycrystal drops below similar to E/20, with E being Young's modulus. A simple statistical model for the simulation of the elastoplastic response of polycrystals is introduced. Using this model, the offset strain corresponding to the onset of macro-plasticity in copper polycrystals having different grain size distributions is determined.