Multiscale simulation of crack tip shielding by a dislocation

Crack tip shielding by dislocations is an essential feature of the modeling of semi-brittle crack propagation and the brittle to ductile transition. The stress field, in the elementary configuration where a single dislocation interacts with a crack, is obtained by two independent methods, at two different scales. Analytical formulas, by Lin and Thomson, are used in the case of a semi-infinite crack in an isotropic linear elastic medium. Atomistic simulations are used to simulate the emission of a perfect dislocation from the tip of a nano-scale flaw. Constrained molecular dynamics enables the dislocation to be pinned during the relaxation of the system. With this method, it is possible to obtain the static stress field which can be compared to the elastic solution. Semi-infinite and nano-scale cracks produce the same stress field in the vicinity of the tip, as predicted by continuum fracture mechanics. This property is the basis of the multiscale approach proposed here, where critical stress intensity factors are computed at the atomic scale, on the nano-scale crack, and transfered to the meso-scale simulation, based on the elastic theory of discrete dislocations.