The development of physically based micro-mechanics — Based on the characteristic tip field of dislocation pileup

Abstract

Based on the analytical solution by Eshelby, Frank, and Nabarro and the numerical calculations by Chou and Li and Armstrong et al., it is shown that the force, F, on the locked leading dislocation of a discrete dislocation pileup is capable of characterizing uniquely the stress, strain, and displacement fields at the tip of the pileup, including the positions of the discrete mobile dislocations next to the leading dislocation. Conversely, the positions of the mobile dislocations can be used to measure F. The F thus measured can be used to study micro-plastic deformation and micro-fractures at grain boundaries or any other dislocation barriers. Both the resolved shear stress intensity coefficient, ReSIC, and the resolved cleavage stress intensity coefficient, ReCIC, are defined. Both are related to the positions of the mobile dislocations near the tip of a pileup. The applications of ReSIC and ReCIC to the studies of micro-yielding and micro-cleavage are discussed. Macro-yielding and macro-fracture are analyzed in terms of the tip stress field of a pileup.