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

Abstract

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.

Effects of the grain size and shape on the flow stress: A dislocation dynamics study

“…In Eq. 6, ab is the interaction matrix known from previous DD simulations investigations (Hansen et al, 2010), accounting for the interaction strength between slip system i and s. Since dislocation density evolution on every slip system is recorded in the simulations, Eq. 6 gives a precise evaluation of the flow stress all along the stress strain curves.…”

“…The heterogeneity in grain size basically reduces the sensitivity to grain size. On the other hand, although grain shape is suspected to have strong effect on the flow stress (Van Houtte, 1982), little is known about the influence of grain shape on the HP Law (Delannay and Barnett, 2012;Hansen et al, 2010). Using DD simulations, only Yellakara and Wang (Yellakara and Wang, 2014) investigated the response of polycrystalline thin films and reported a variation of the HP exponent with the simulated volume shape.…”

A hybrid variationally consistent homogenization approach based on Ritz's method

“…For that purpose, a generalized principle of maximum dissipation related to generalized standard materials was considered in [21,30]; see also [31,32]. Other examples for constitutive models based on energy minimization include, among others, those for deformation-induced twinning [33,34], 628 N. BLEIER AND J. MOSLER thermomechanically coupled phenomena [35,36], the evolution of microstructures [37][38][39], or gradient-enhanced continua [40,41].…”

Thermodynamic theory of crystal plasticity: Formulation and application to polycrystal fcc copper

“…The work of Hansen et al (2013) in particular includes non-mobile populations of dislocations which are sources of internal stored energy. In fact, some work suggests that dislocation sub-cell development is a result of lowering overall system energy (e.g., Hansen et al, 2010) and these continuum formulations have been used to study dislocation structural development during deformation at high resolutions (Dequiedt et al, 2015;Grilli et al, 2018;Arora and Acharya, 2019).…”