Wedge indentation into elastic-plastic single crystals. 2: Simulations for face-centered cubic crystals

The asymptotic stress and deformation fields associated with the contact point singularity of a nearly-flat wedge indenter impinging on a specially-oriented single face-centered cubic crystal are derived analytically in a companion paper. In order to investigate the extent of the asymptotic fields, the indentation process is simulated numerically using single crystal plasticity. The quasistatically translating asymptotic fields consist of four angular elastic sectors separated by plastically deforming sector boundaries, as predicted in the companion paper. The asymptotic stress distributions are in accord with the analytical predictions. In addition, simulations are performed for a wedge indenter with a 90° included angle in order to investigate the consequences of finite deformation and finite lattice rotation. Several salient features of the deformation field for the nearly-flat indenter persist in the deformation field for the 90° wedge indenter. The existence of the salient features is validated by comparison to experimental measurements of the lower bound on geometrically necessary dislocation (GND) densities.     

Wedge indentation into elastic-plastic single crystals, 1: Asymptotic fields for nearly-flat wedge

Asymptotic stress and deformation fields under the contact point singularities of a nearly-flat wedge indenter and of a flat punch are derived for elastic ideally-plastic single crystals with three effective in-plane slip systems that admit a plane strain deformation state. Face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal-close packed (HCP) crystals are considered. The asymptotic fields for the flat punch are analogous to those at the tip of a stationary crack, so a potential solution is that the deformation field consists entirely of angular constant stress plastic sectors separated by rays of plastic deformation across which stresses change discontinuously. The asymptotic fields for a nearly-flat wedge indenter are analogous to those of a quasistatically growing crack tip fields in that stress discontinuities can not exist across sector boundaries. Hence, the asymptotic fields under the contact point singularities of a nearly-flat wedge indenter are significantly different than those under a flat punch. A family of solutions is derived that consists entirely of elastically deforming angular sectors separated by rays of plastic deformation across which the stress state is continuous. Such a solution can be found for FCC and BCC crystals, but it is shown that the asymptotic fields for HCP crystals must include at least one angular constant stress plastic sector. The structure of such fields is important because they play a significant role in the establishment of the overall fields under a wedge indenter in a single crystal. Numerical simulations—discussed in detail in a companion paper—of the stress and deformation fields under the contact point singularity of a wedge indenter for a FCC crystal possess the salient features of the analytical solution.