Simulation on crack propagation vs. crack-tip dislocation emission by XFEM-based DDD scheme

An XFEM-based DDD scheme is developed to study multiple-dislocation emission from the crack tip and crack propagation in the ductile fracture of a single crystal. A dislocation emission model based on Rice-Thomson theory is incorporated to capture the dynamic dislocation emission from the crack-tip and a normal traction-separation distance model to depict the propagation of mode I cohesive crack. The boundary value problem containing complex surfaces/interfaces and discrete dislocations can be solved by the present XFEM-based DDD scheme directly in a unified framework with satisfactory accuracy. A careful examination shows that the local stress field at the crack tip induced by emitted dislocations can be exactly depicted by this XFEM-based DDD scheme. This local stress field can not only shield the crack from the applied load but also inhibit the emission of subsequent dislocations from the crack-tip; therefore, it plays a crucial role in the ductile-to-brittle competition during crack propagation. After careful verification, this XFEM-based DDD scheme is used to simulate dynamic propagation of mode I cohesive crack. The ductile-to-brittle competition in the crack-tip process zone is investigated with a special attention. Both the dislocation emission-crack propagation process within the crack-tip zone and the discrete dislocation dynamics details behind it are captured and show good agreements with the previous MD simulations conducted by other researchers.