A minimum parameter approach to crystal plasticity modelling

Plastic deformation processes in hexagonal metals are complex and are best analyzed using procedures such as visco-plastic self-consistent crystal plasticity modelling. These involve a large number of adjustable parameters and make limited use of independent input data. Using physical arguments, the authors show that several of the parameters can be replaced by experimentally measured values of critical resolved shear stresses from the literature. A further simplification derives from the argument that all deformation modes interact with the same substructure, and so a common work-hardening behaviour can be assumed as a reasonable first approximation. Furthermore, many microstructural contributions to the strength can be introduced through a single constant term. In these ways, the twelve or more adjustable parameters in the model are reduced to only three. This new approach is tested critically by applying it to a sheet magnesium alloy for which the plastic strain ratio varies markedly during the test. Its complex plastic behaviour, which arises from changes among the active deformation modes, is successfully predicted. A benefit of the present approach is that the effect of metallurgical variables such as grain size or precipitation strengthening can be readily investigated. Although tested here for a magnesium alloy, the same principles should be applicable to other hexagonal close-packed materials.