Constrained molecular dynamics for quantifying intrinsic ductility versus brittleness

International audienceEvaluating the critical load levels for intrinsic ductility and brittle propagation is a first, but necessary, step for modeling semibrittle crack propagation. In the most general case, the calculations have to be fully atomistic because the details of the crack tip structure cannot be captured by continuum mechanics. In this paper, we present a method to explore ductile and brittle configurations, within the same force field, giving a quantitative estimate of the proximity of a transition from intrinsic ductility to brittleness. The shear localization is characterized by a centrosymmetry criterion evaluated on each atom in the vicinity of the crack tip. This provides an efficient order parameter to track the nucleation and propagation of dislocations. We show that it can be used as a holonomic constraint within molecular dynamics simulations, giving a precise control over plasticity during crack propagation. The equations of motion are derived and applied to crack propagation in the [112̅ ] direction of an fcc crystal loaded in mode I along [111]. The critical loads for dislocation emission and for brittle propagation are computed. The key point is that the generalized forces of constraint are not dissipative. Therefore, they do not spoil the critical elastic energy release rates (the Griffith criterion is preserved). As an example of the possibilities of the method, the response of blunted tips is investigated for three configurations: a slab of vacancies, an elliptical hole, and a circular hole. Brittle propagation by an alternative mechanism to cleavage, called “vacancy injection,” is reported