A discrete slip plane model for simulating heterogeneous plastic deformation in single crystals

In small-scale mechanical tests, such as micropillar compression tests, plastic deformation is often localized in narrow slip traces. These slip traces result from a few dislocation sources with relatively low nucleation stresses that are present in the material. In order to accurately simulate such small-scale experiments, the stochastics of the underlying dislocation network must be taken into account, which is usually done by performing discrete dislocation dynamics simulations. However, their high computational cost generally restricts these simulations to small and simple geometries and small applied displacements. Furthermore, effects of geometrical changes are usually neglected in the small strain formulation adopted. In this study, a discrete slip plane model for simulating small-scale experiments on single crystals is proposed, which takes the most important characteristics of dislocation plasticity for geometries in the micrometer range into account, i.e.\ the stochastics and physics of dislocation sources. In the model, the properties of all lattice planes are sampled from a probability density function. This results in a heterogeneous flow stress within a single crystal, unlike the uniform properties assumed in conventional crystal plasticity formulations. Moreover, the slip planes can be grouped together in bands via a weakest-link principle. The resulting equations are implemented in a standard crystal plasticity finite element model, using a finite deformation formulation. Within this setting, only the collective dislocation motion on glide planes is modeled, resulting in a significantly lower computational cost compared to frameworks in which the dynamics of individual dislocations are considered. This allows for simulating multiple realizations in 3D, up to large deformations. A small case study on micropillar compression tests is presented to illustrate the capabilities of the model.