Solutions for moving glide dislocations, of intersonic speed, were derived on the basis of Weertman’s fundamental equation for a moving dislocation; together with a proposed generalized Bilby-Cottrell-Swinden-Dugdale model. In this model, a straight weak path within an infinite elastic plate was assumed. Two length scales (thickness of the weak path, material intrinsic length) which reflected strain-gradient induced hardening and energy dissipation were taken into account by applying the traction-separation law to decohesion of the weak path. Dislocations propagated along this weak path with a speed that was higher than the shear-wave speed. Accumulation of the moving dislocations led to macroscopic-scale crack growth, with a cohesive zone ahead of the crack tip. As in the Bilby-Cottrell-Swinden-Dugdale model, the remote applied stress and/or stress-rate boundary conditions were represented by an equivalent crack-surface traction which was associated with the dislocation distribution. The associated Cauchy integral and corresponding eigenvalue problem were solved by using the Muskhelishvili-Weertman algorithms. The problems which were associated with 3 types of decohesion law were constant traction, traction which was linearly dependent upon separation, and separation-dependent and separation-rate dependent traction. The problems were solved by using 3 different solution strategies. These were the direct integration method, the iteration method and the Jacobi polynomial expansion, respectively. The solutions furnished explicit relationships between the remote-load propagation speed, the material intrinsic length, the weak-path thickness and the strain-rate hardening parameter. The solutions demonstrated that the intersonic speed region could be divided into 2 sub-domains. Steady-state propagation occurred within the sub-domain, where the propagation speeds were equal to, or greater than, the Eshelby speed, 21/2c; where c was the shear-wave speed. For a weak path with a finite width, and a corresponding decohesion law scaled by the material intrinsic length, intersonic crack propagation would not take place if only a constant remote stress was imposed. A steady-state crack surface load and/or a remote stress-rate boundary condition (representing a point force, or a distributed force with a constant distance to the moving crack tip) was required in order to maintain steady-state intersonic crack propagation.

Cohesive Solutions of Intersonic Moving Dislocations. S.Hao, W.K.Liu, J.Weertman: Philosophical Magazine, 2004, 84[11], 1067-104