Single crystal plasticity with bend–twist modes

• We propose single crystal plasticity with dislocation-based end-twist.
• We couple homogeneous and inhomogeneous modes through dislocation evolution.
• The burgers and Nye tensors are derived from a third-rank tensor Λp.
• A three-dimensional finite element scheme, without extra DOFs, is proposed.
• A single FCC crystal, with and without secondary θ phases, is modeled.

In this work a formulation is proposed and computationally implemented for rate dependent single crystal plasticity, which incorporates plastic bend–twist modes that arise from dislocation density based poly-slip mechanisms. The formulation makes use of higher order continuum theory and may be viewed as a generalized micromechanics model. The formulation is then linked to the burgers and Nye tensors, showing how their material rates are derivable from a newly proposed third-rank tensor Λp, which incorporates a crystallographic description of bend–twist plasticity through selectable slip-system level constitutive laws. A simple three-dimensional explicit finite element implementation is outlined and employed in three simulations: (a) bi-crystal bending; (b) tension on a notched single crystal; and (c) the large compression of a microstructure to induce the plastic buckling of secondary phases. All simulation are transient, for computational expediency. The results shed light on the physics resulting from dynamic inhomogeneous plastic deformation.