Gradient crystal plasticity including dislocation-based work-hardening and dislocation transport

• A gradient crystal plasticity model using continuum dislocation dynamics is proposed.
• The model is well-suited for a three-dimensional numerical implementation.
• Dislocation density and curvature field variables evolve according to PDEs.
• A composite microstructure is simulated.
• Strain gradient effects are modeled by an equivalent plastic strain gradient.

This work aims at the formulation of a gradient crystal plasticity model which incorporates some of the latest developments in continuum dislocation theory and is, at the same time, well-suited for a three-dimensional numerical implementation. Specifically, a classical continuum crystal plasticity framework is extended by taking into account continuous dislocation density and curvature field variables which evolve according to partial differential equations (Hochrainer et al., 2014; Ebrahimi et al., 2014). These account for dislocation transport and curvature-induced line-length production and have been derived from a higher-dimensional continuum dislocation theory. The dislocation density information is used to model work hardening as a consequence of dislocation entanglement.A composite microstructure is simulated consisting of a soft elasto-plastic matrix and hard elastic inclusions. The particles are assumed to act as obstacles to dislocation motion, leading to pile-ups forming at the matrix–inclusion interface. This effect is modeled using gradient plasticity with a simplified equivalent plastic strain gradient approach (Wulfinghoff et al., 2013) which is used here in order to allow for an efficient numerical treatment of the three-dimensional numerical model. A regularized logarithmic energy is applied which is intended to approximate the higher order gradient stress of the statistical theory of Groma et al. (2003).