A Hybrid Multi-Scale Model of Crystal Plasticity for Handling Stress Concentrations

Microstructural effects become important at regions of stress concentrators such as notches,
cracks and contact surfaces. A multiscale model is presented that efficiently captures microstructural
details at such critical regions. The approach is based on a multiresolution mesh that includes an
explicit microstructure representation at critical regions where stresses are localized. At regions farther
away from the stress concentration, a reduced order model that statistically captures the effect of the
microstructure is employed. The statistical model is based on a finite element representation of the
orientation distribution function (ODF). As an illustrative example, we have applied the multiscaling
method to compute the stress intensity factor KI around the crack tip in a wedge-opening load
specimen. The approach is verified with an analytical solution within linear elasticity approximation
and is then extended to allow modeling of microstructural effects on crack tip plasticity.