An anisotropic distribution dislocation loop model for simulation of nanoindentation of single crystals

Abstract

An anisotropic distribution dislocation loop model is proposed for simulation of nanoindentation of single crystals based on the recently available solution of the elastic displacement and stress fields due to a polygonal dislocation within an anisotropic homogeneous half-space (Chu et al., 2012). The present investigation is a direct extension of the approach established by Mura et al. (1989), and its recent application to triangular dislocation loop model (Muraishi, 2013), which is only capable of describing the indentation processes of isotropic materials, thus ruling out the possibility of characterizing the nanoindentation of elastically anisotropic single crystals. By following the procedure of Mura et al. (1989), we adopt square and triangular prismatic dislocation loops (PDLs) as building blocks with Burgers vectors normal to the free surface to simulate the Vickers and Berkovich indentation, respectively. However, we place all the prismatic dislocation loops within a semi-ellipsoidal volume rather than a semi-spherical region as adopted by Mura et al. (1989) after analyzing the existing simulation results based on dislocation density formulation (Huang et al., 2000). The nanoindentation is performed in [001] and [111] crystallographic directions employing Vickers and Berkovich indenters, respectively, and different magnitude of pile-up, sink-in and spring-back is observed in different directions, clearly demonstrating the effects of elastic anisotropy of the indented single crystals on nanoindentation, hence a further improvement of the original model of Mura et al. (1989).