Efficient and robust constitutive integrators for single-crystal plasticity modeling

Abstract

Small-scale deformation phenomena such as subgrain formation, development of texture, and grain boundary sliding require simulations with a high degree of spatial resolution. When we consider finite-element simulation of metal deformation, this equates to thousands or hundreds of thousands of finite elements. Simulations of the dynamic deformations of metal samples require elastic–plastic constitutive updates of the material behavior to be performed over a small time step between updates, as dictated by the Courant condition. Further, numerical integration of physically-based equations is inherently sensitive to the step in time taken; they return different predictions as the time step is reduced, eventually approaching a stationary solution. Depending on the deformation conditions, this converged time step becomes short (10 −9 s or less). If an implicit constitutive update is applied to this class of simulation, the benefit of the implicit update (i.e., the ability to evaluate over a relatively large time step) is negated, and the integration is prohibitively slow. The present work recasts an implicit update algorithm into an explicit form, for which each update step is five to six times faster, and the compute time required for a plastic update approaches that needed for a fully-elastic update. For dynamic loading conditions, the explicit model is found to perform an entire simulation up to 50 times faster than the implicit model. The performance of the explicit model is enhanced by adding a subcycling algorithm to the explicit model, by which the maximum time step between constitutive updates is increased an order of magnitude. These model improvements do not significantly change the predictions of the model from the implicit form, and provide overall computation times significantly faster than the implicit form over finite-element meshes. These modifications are also applied to polycrystals via Taylor averaging, where we also see improved model performance.