LARGE-SCALE CRYSTAL PLASTICITY COMPUTATIONS OF MICROSTRUCTURAL FAILURE MODES

A computational scheme is introduced for the integration of rate-depen dent multiple-slip crystal plasticity constitutive relations. Fundamen tal issues of accuracy, stability, and stiffness that are intrinsicall y related to the evolution of microstructural failure modes in metalli c crystals are addressed. An adaptive finite-element methodology is in troduced to classify these characteristics. A nonlinear initial value system is derived to update the plastic deformation-rate tenser. An ex plicit method is used in non-stiff domains, where accuracy is required . If a time-step reduction is due to stability, a harbinger of numeric al stiffness, the algorithm is automatically switched to an A-stable m ethod. A stiffness ratio is defined to measure the eigenvalue dispersi on of the system. The adaptability of the proposed algorithm for the s olution of a class of inelastic constitutive relations is illustrated by investigating the influence of high angle grain boundary orientatio ns on failure in face-centered cubic (f.c.c.) bicrystals. The effects of grain boundary misorientation, dislocation densities, strain harden ing, and geometrical softening on failure evolution are investigated. This study underscores the importance of understanding the origin of n umerical instabilities, such that these instabilities are not mistaken for inherent material instabilities.