Modeling Metallic Single Crystal Plastic Hardening through the Evolution of Dislocation Subgrain Structures

A single crystal plasticity theory for insertion into finite element simulation is formulated using sequential laminates to model subgrain dislocation structures. It is known that local models do not adequately account for latent hardening, as latent hardening is not only a material property, but a nonlocal property (e.g., grain size and shape). The addition of the nonlocal energy from the formation of subgrain structure dislocation walls and the boundary layer misfits provide both latent and self hardening of crystal slip. Latent hardening occurs as the formation of new dislocation walls limit motion of new mobile dislocations, thus hardening future slip systems. Self hardening is accomplished by evolution of the subgrain structure length scale. No multiple slip hardening terms are included.;The substructure length scale is computed by minimizing the nonlocal energy. The minimization of the nonlocal energy is a competition between the dislocation wall and boundary layer energy. The nonlocal terms are also directly minimized within the subgrain model as they impact deformation response. The geometrical relationship between the dislocation walls and slip planes affecting dislocation mean free path is accounted for giving a first-order approximation to shape effects. A coplanar slip model is developed due to requirements when modeling the subgrain structure. This subgrain structure plasticity model is noteworthy as all material parameters are experimentally determined rather than fit. The model also has an inherit path dependency due to the formation of the subgrain structures. Validation is accomplished by comparison to single crystal tension test results.