Comparison of physically based constitutive laws used for numerical simulations of plasticity of single crystals

Abstract
Various microstructural physical mechanisms involving mostly dislocation glides are responsible for plasticity of face centred cubic single crystals. These mechanisms have been pointed out experimentally using at least uniaxial tensile tests. Thus, many constitutive laws have been developed and integrated at the microstructural level to reproduce the experimental evolutions of various parameters (single glide, dislocation density...). More recently, general models have been written in a continuum mechanics framework for finite element simulations. Four main models of this kind are described and applied to the case of uniaxial tensile loading. The selected models present a similar formalism : a flow law plus a hardening law involving a hardening matrix describing the interaction between all the considered glide systems. Each model is integrated using a standard numerical procedure in order to simulate tensile tests. The simulation of a tensile test with a given orientation of the tensile axis is done for each model in order to compare them all together on the same basis. The suitability between the simulated results and experimental evidence is also commented. Finally, the evolution of the components of the hardening matrix is discussed.