Effects of atoms on brittle fracture

This article aims to answer two related sets of questions. First: in principle, how large an effect can structure at the atomic scale have upon the fracture of two macroscopically identical samples? The answer to this question is that the effects can be very large. Perfectly sharp cracks can be pinned and stationary under loading conditions that put them far beyond the Griffith point. Crack paths need not obey the rule KII = 0. Crack speeds can vary from zero to the Rayleigh wave speed under identical loading conditions but depending upon microscopic rules. These conclusions are obtained from simple solvable models, and from techniques that make it possible to extrapolate reliably from small numerical calculations to the macroscopic limit. These techniques are described in some detail. Second: in practice, should any of these effects be visible in real laboratory samples? The answer to this second question is less clear. The qualitative phenomena exhibited by simple models are observed routinely in the fracture of brittle crystals. However, the correspondence between computations in perfect two-dimensional numerical samples at zero temperature and imperfect three-dimensional laboratory specimens at nonzero temperature is not simple. This paper reports on computations involving nonzero temperature, and irregular crack motion that indicate both strengths and weaknesses of two-dimensional microscopic modeling.