Further development of the hybrid model for polycrystal deformation

Abstract

The Kocks-Mecking hybrid model for polycrystal deformation has been developed further, in order to obtain an easy definition of polycrystalline behaviour, from knowledge of the single crystal stress-strain curves. The hybrid model is a one-parameter theory that considers the flow stress governed by total dislocation density. This is the addition of the statistically stored dislocations, independent of the grain size, and the geometrical dislocations, necessary to accommodate the deformation, and thus dependent on the grain size (as proposed by Ashby). The condition for the onset of necking is used to determine the parameters of the equation of the model. The analytical description of the resulting flow law was used to analyse the tensile behaviour of copper sheets, with five different grain sizes, which were deformed at three different strain rates.