A monolithically implicit time-integration approach for a dislocation-density-based b.c.c. single crystal plasticity model

This paper presents a novel time-integration algorithm for dislocation-densitybased crystal plasticity models specific to body-centered cubic (b.c.c.) single crystals. The approach effectively integrates salient features of b.c.c. single crystals, including orientation- and temperature-dependent yield strength and notable non-Schmid effects, into the constitutive model. The algorithm incorporates the Newton-Raphson method in a unified iterative loop with a new convergence criterion that effectively addresses the computational complexities associated with the exponential increase in dislocation densities. Furthermore, a consistent tangent modulus has been derived, ensuring compatibility with the balance of linear momentum for displacement correction. This algorithm has been implemented as a user-subroutine UMAT within the finite element software Abaqus. Validation of the computational approach was conducted through comparisons with experimental data on α-iron single crystals. Moreover, the impact of active slip systems on the texture development of b.c.c. polycrystalline materials has been investigated using the proposed computational framework.