Gradient effects in inhomogeneous plastic flow and fracture behavior of single crystals

Gradient effects in inhomogeneous plastic flow in elastic-plastic layers under simple shear deformation are studied in two cases. A simplification of an incompatibility-enhanced hardening model is used in the calculations for an infinitely long layer of rate-independent material within a small strain framework. Gradient effects are induced via initial nonuniformity of plastic strain. In the rate-dependent case of a finite layer, the material is assumed to be an FCC crystal. The calculations are conducted in the context of a viscoplastic theory within a finite deformation framework. Gradient effects are triggered by constraining the plastic strains on the boundaries or traction free ends. Both cases exhibit stable and convergent solutions. In particular, gradients display a strong propensity to remove the nouniformity of plastic strain in the case with initially inhomogeneous plastic strain.; Plane-strain mode-I cracks in a ductile single crystal are studied under conditions of small scale yielding. The specific case of a (010) crack growing in the [101] direction for FCC crystals is considered. Crack initiation and its subsequent growth are computed by specifying a traction-separation relation in the crack plane ahead of the crack tip. The crystal is characterized by a hardening model that incorporates physically motivated gradient effects. Significant traction elevation ahead of the crack tip is obtained by incorporating gradient effects, allowing a better basis for the prediction of cleavage in the presence of substantial plastic flow. Resistance curves based on parameters characterizing the fracture process and the continuum properties of the crystal are computed. Both the work of separation and the peak separation stress play an important role in determining the fracture resistance of the crystal.; The directional dependence of crack growth along the interface of a bicrystal with symmetric tilt boundary is investigated. Both crack tip fields and resistance curves are studied to rationalize the mechanisms of the direction dependence on the basis of a crystal plasticity theory. Gradient effects are incorporated in the incompatibility-enhanced Voce-law hardening model as in the study of traction elevation and fracture resistance. It is found that conventional crystal plasticity theories fail to predict the experimentally observed directional dependence as represented by the computed resistance curves, regardless of the larger plastic zone corresponding to the ductile cracking direction for a stationary crack. The inclusion of gradient effects enables such prediction to be in better agreement with experimental observations.