Triangular dislocation loop model for indented material

Abstract

We present triangular dislocation loop (TDL) model to describe the pile-up and the residual stress field caused by Berkovich indent according to Mura’s method. Various regular polygonal loops are derived from analytical solution of angular dislocation, and correction terms necessary for the exact displacement are provided. The elastic field by different numbers of TDLs is similar, but influenced by the plastic zone shape when the slope of indenter is ideally constant. The size dependent hardening behavior among the similar internal stress field is discussed from the view points of the dislocation density and the geometry of plastic zone. Prediction of pileup displacement shows good agreement with reported values when hemi-spherical type dislocation arrangement is assumed for plastic zone.