Effect of boundary conditions in mode I fracture in brittle materials

We present results on the effect of geometrical boundary conditions on the stress distribution at the tip of cracks in mode I fracture. We have made molecular dynamics simulations on a 2-D triangular lattice of point masses connected by brittle Hookean springs. We study the configuration of the stress field in rectangular shape lattices of different aspect ratios and with initial notches of varying lengths subjected to constant strain. We show that the stress of the most stretched spring at the tip of the notch presents a saturation as a function of notch length. The detailed form of this saturation depends on the aspect ratio of the lattice. Simulation on the dynamics of propagating cracks suggest that the selection of the tip velocity is strongly dependent on the initial notch length. The saturation of the stress intensity factor provides an appealing explanation for some of the experimental observations by Boudet et al. (1995) and Marder et al. (1995).