Dislocation behaviours ahead of crack tip

Abstract

In this paper, a unified mechanics model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations within the plastic zone in the form of an inverse pile up are treated as discrete elastic edge dislocations. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear governing equations are obtained which take into account for the interaction between the emitted dislocations and cohesive zone and the nonlinear interaction between sliding displacement and the opening displacement. After discretization, the governing equations are transformed into a set nonlinear algebraic equations which are solved with Newton-Raphson Method. The results of calculation for pure shearing and combined tension and shear loading after dislocation emission are given in detail. Finally, the process of dislocation nucleation and emission on a pair of symmetric slip planes of angle α with respect to the crack plane under pure mode I load is analysed. The equilibrium positions and the number of emitted dislocation are determined. Several possible competition behaviors of dislocation emission vs cleavage are revealed.