Dislocation behaviours ahead of crack tip (Q1282685)

We propose a unified model for dislocation nucleation, emission and dislocation free zone 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, expressed through Chebyshev polynomial series, and the opening and slip displacements expressed through trigonometric series, we derive nonlinear governing equations which take into account the interaction between 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 of nonlinear algebraic equations which are then solved with Newton-Raphson method.