Inclined pileup of screw dislocations at the crack tip without a dislocation-free zone

Abstract

A linear array of screw dislocations in front of a mode 3 crack lying on a plane inclined to the crack is studied. The problem is formulated in terms of an integral equation describing the equilibrium condition between the dislocations and the crack under an externally applied shear stress. The distribution function for dislocations is derived from a solution of the integral equation by applying the Wiener–Hopf technique. The condition of finite stress at the end of the pileup, or the Bilby, Cottrell, and Swindeman (BCS) condition and the crack opening displacement (COD) are obtained in simple analytical forms as a function of the angle of inclination. Numerical results show that, for a given applied stress, the distribution function, the length of the plastic zone, and the COD decrease only slightly as the angle of inclination increases from 0 to π/2. The quantity of σf COD , where σf is the friction stress, is shown to be equal to the radial component of the complex J integral and, hence, is the total force on the dislocations along the direction of the pileup. A method to estimate results under mode 1 condition involving an inclined pileup of edge dislocations is considered.