Single-parameter characterization of discrete-dislocation pileup tipfield and its application to physically based micro-mechanics

The equivalence between continuous dislocation pileups and cracks is reviewed. The force on the leading dislocation is defined and a general method of calculation of the force is proposed. The equivalence relations are given. Based on the analysis by Eshelby, Frank, and Nabarro and the numerical calculations by Chou and Li and Armstrong et al, it will be shown that the force, F, on the locked leading dislocation of a discrete 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 behind the leading dislocation. Conversely, the positions of the mobile dislocations can be used to measure F. If the propagation of micro-slips and the initiation of micro-fractures at the tip of a pileup are controlled by resolved shear stress and normal cleavage stress respectively, the resolved shear stress intensity coefficient, ReSIC, and the resolved cleavage stress intensity coefficient, ReCIC, must be constant.