A single crystal plasticity theory for insertion into finite element simulation was formulated using sequential laminates to model sub-grain dislocation structures. It was known that local models did not adequately account for latent hardening, as latent hardening was 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 sub-grain structure dislocation walls and the boundary layer misfits provide both latent and self-hardening of a crystal slip. Latent hardening occurs as the formation of new dislocation walls limits motion of new mobile dislocations, thus hardening future slip systems. Self-hardening was accomplished by an evolution of the sub-grain structure length scale. The substructure length scale was computed by minimizing the nonlocal energy. The minimization of the nonlocal energy was a competition between the dislocation wall energy and the boundary layer energies. The nonlocal terms were also directly minimized within the sub-grain model as they affect deformation response. The geometrical relationship between the dislocation walls and slip planes affecting the dislocation mean free path was taken into account, giving a first-order approximation to shape effects. A coplanar slip model was developed due to requirements while modelling the sub-grain structure. This sub-grain structure plasticity model was noteworthy as all material parameters were experimentally determined rather than fit. The model also has an inherit path dependence due to the formation of the sub-grain structures. Validation was accomplished by comparison with single crystal tension test results.

Dislocation Subgrain Structures and Modeling the Plastic Hardening of Metallic Single Crystals. B.L.Hansen, C.A.Bronkhorst, M.Ortiz: Modelling and Simulation in Materials Science and Engineering, 2010, 18[5], 055001