Characterization of the tip field of a discrete dislocation pileup for the development of physically based micromechanics

It is shown, on the basis of calculations by Eshelby et al. (1951), Armstrong et al. (1966), and Chou and Li (1969), that a single parameter, such as the force on the leading dislocation (F), the crack extension force, or the stress intensity factor, is capable of characterizing uniquely the entire tip field of a discrete dislocation pileup, including the positions of mobile dislocations behind the locked leading dislocation at the tip. Conversely, the position of the i-th mobile dislocation X(i) is related to the value of F and is capable of characterizing the entire stress, strain, and displacement fields at the tip of a discrete dislocation pileup. If the interactions between dislocations are linear elastic, the measured positions of the mobile dislocations can be used to determine the value of F, which can then be used as a quantitative measure of the strength of a dislocation barrier resisting the propagation of a microslip or the nucleation of a microfracture.