Large-scale crystal plasticity computations of microstructural failure modes

A computational scheme is introduced for the integration of rate-dependent multiple-slip crystal plasticity constitutive relations. Fundamental issues of accuracy, stability, and stiffness that are intrinsically related to the evolution of microstructural failure modes in metallic crystals are addressed. An adaptive finite-element methodology is introduced to classify these characteristics. A nonlinear initial value system is derived to update the plastic deformation-rate tensor. An explicit method is used in non-stiff domains, where accuracy is required. If a time-step reduction is due to stability, a harbinger of numerical stiffness, the algorithm is automatically switched to an A-stable method. A stiffness ratio is defined to measure the eigenvalue dispersion of the system. The adaptability of the proposed algorithm for the solution of a class of inelastic constitutive relations is illustrated by investigating the influence of high angle grain boundary orientations on failure in face-centered cubic (f.c.c.) bicrystals. The effects of grain boundary misorientation, dislocation densities, strain hardening, and geometrical softening on failure evolution are investigated. This study underscores the importance of understanding the origin of numerical instabilities, such that these instabilities are not mistaken for inherent material instabilities.