Dislocation subgrain structures and modeling the plastic hardening of metallic single crystals

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 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 is accomplished by an evolution of the subgrain structure length scale. The substructure length scale is computed by minimizing the nonlocal energy. The minimization of the nonlocal energy is a competition between the dislocation wall energy and the boundary layer energies. The nonlocal terms are also directly minimized within the subgrain model as they affect deformation response. The geometrical relationship between the dislocation walls and slip planes affecting the dislocation mean free path is taken into account, giving a firstorder approximation to shape effects. A coplanar slip model is developed due to requirements while 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 dependence due to the formation of the subgrain structures. Validation is accomplished by comparison with single crystal tension test results. (Some figures in this article are in colour only in the electronic version) 0965-0393/10/055001+42$30.00 © 2010 IOP Publishing Ltd Printed in the UK & the USA 1 Modelling Simul. Mater. Sci. Eng. 18 (2010) 055001 B L Hansen et al