A unified model was presented, for dislocation nucleation, emission and dislocation-free zone, which was based upon the Peierls framework. Three regions were identified ahead of the crack tip. The emitted dislocations, which were situated away from the crack tip in the form of an inverse pile-up, defined the plastic zone. Between that zone, and the cohesive zone which was immediately ahead of the crack tip, there was a dislocation-free zone. The stress field and the dislocation density field in the cohesive zone and the plastic zone were described by the first and second Chebyshev polynomials, respectively. The opening and slip displacements were described by trigonometric series. By combining all of these, a set of non-linear algebraic equations could be obtained and solved using the Newton-Raphson Method. Detailed results of calculations for pure shear and combined tension and shear loading, after dislocation emission, were given. The calculated results were found to be in good agreement with the results of molecular dynamics simulations.

T.C.Wang, K.R.Wang, Y.W.Zhang: International Journal of Fracture, 1996, 78[3-4], 227-39