Single-crystal plasticity at finite strains: a computational investigation of hardening relations

This dissertation has two main objectives. The first is to develop and implement a numerical algorithm to solve the system of equations that describe single-crystal viscoplasticity under finite strains. The second objective is to use the computer code that is developed to examine three hardening laws that have been proposed. The first is an isotropic hardening law. The second is a hardening law that is expressed implicitly. The third is a novel hardening law in which the slip resistance is expressed explicitly in terms of the accumulated slip on each slip-system. The numerical method uses a predictor-corrector type algorithm and is coupled with a finite element method. The numerical method is validated by comparing with results from the literature. After calibrating the hardening rules, two different model problems are examined: A spherical indentation problem and a three dimensional shear problem. For both problems, the numerical code is run with the three hardening rules. For each hardening rule three types of crystal are examined: A crystal with only one slip system, a crystal with two slip systems and a front centered cubic (FCC) crystal. All three hardening rules show very similar results