Biaxial extension of a plane single crystal

This paper concerns the rigid-plastic modelisation of a f.c.c. single crystal, deforming by crystallographic slip, under large strain. Adopting the plane single crystal model, which corresponds to a true two-dimensional evolution of a real three-dimensional crystal, the activity of slip systems and the plastic indetermination, due to multiplicity of solutions, are studied according to the rate-independent Schmid law or the rate-dependent Bingham law. To promote a more general situation of potential multiple slip and therefore of potential indeterminacy, the biaxial loading is investigated. Based on this model and the Bingham slip law, the indeterminacy problem is surmounted, by adopting the geometrical analysis in the strain rate space and it is proved that the linear viscoplastic analysis is a new way of solving the indeterminacy problem.