A Dislocation-Crystal Plasticity Simulation on Large Deformation Considering Geometrically Necessary Dislocation Density and Incompatibility (1st Report, Definitions of GN Crystal Defects and Multiscale Modeling)

Plastic deformation and work-hardening of a crystal are caused by dislocation motions and dislocation accumulations, respectively. Recently, studies of crystal plasticity with the dislocation information have actively been done by many researchers. In this paper, both densities of isolated dislocation and dislocation pair corresponding respectively to the conventional GN and SS dislocation densities are uniformly defined as geometrical quantities, i.e., GN dislocation density and GN incompatibility tensors by extending Kröner's dislocation density and incompatibility tensors so that they are suitable for a crystal plasticity framework. Furthermore, we newly introduce a term of dynamic recovery that occurs in stage III of work-hardening of a single crystal into the expression of dislocation density. A new model of dislocation-crystal plasticity coupling deformation field with dislocation field is developed by introducing these dislocation densities into a hardening modulus matrix of crystal plasticity through the Bailey-Hirsch relation.