A perturbation analysis of the unstable plastic flow pattern evolution in an aluminum alloy

In the tensile loading of sheet metals made from some polycrystalline aluminum alloys, a single deformation band appears inclined to the elongation axis in the early stage of deformation, and symmetric double bands are observed in the later stage. This evolution of spatial characteristics of such an unstable plastic flow pattern in a polycrystalline aluminum alloy has been analyzed by a perturbation method. A small number of slip modes are taken to describe the tensile strain. A rate-dependent constitutive equation is used for each slip mode to account for the interaction between dislocations and solute atoms in dynamic strain aging. Unconstrained and constrained models are used to impose appropriate loading conditions at the early and later deformation stages, respectively. Both plane-strain and plane-stress cases are considered. It is found out that the change of boundary conditions and material inhomogeneity during the course of plastic deformation are closely related to the evolution of spatial characteristics of shear band (the Portevin–Le Chatelier band) patterns observed in experiments.