A single crystal plasticity finite element formulation with embedded deformation twins

Abstract

Deformation twinning is an important plastic deformation mechanism in some polycrystalline metals such as titanium and magnesium. In this paper, we present a novel crystal plasticity finite element framework that accounts for deformation twinning explicitly, in addition to crystallographic slip. Within this computational framework, deformation twins are treated as weak discontinuities embedded within individual finite elements, such that a jump in the velocity gradient field is introduced (via the discretized gradient operator) between the twinned and untwinned crystalline regions, taking into account compatibility and traction continuity conditions at the interface between these two regions. The deformation gradient is multiplicatively split into elastic and plastic parts in the untwinned region, as is customary in finite-deformation crystal plasticity formulations. A different multiplicative decomposition of the deformation gradient into elastic, plastic (slip), and twinning parts is adopted in the twinned region, allowing deformation twinning to be accounted for as an additional mode of plastic deformation. A stochastic model is used to predict twin nucleation at grain boundaries, and the evolution of the length and thickness of the twinned region under subsequent deformation is taken into account. The linearization of the single-crystal plasticity model, required in order to enforce traction continuity at the interface between the twinned and untwinned regions using a Newton iterative scheme, is described in detail. Simulations of the initiation and propagation of {101¯2} tensile twins in hexagonal close packed (HCP) titanium are presented to demonstrate the capabilities of the proposed computational framework.