Finite element analysis of a crack tip in silicate glass:: No evidence for a plastic zone

Recently, the claim was made that cracks in silicate glasses propagate by the nucleation, growth, and coalescence of cavities at crack tips, which is the same way as in metals but at a much smaller scale. This hypothesis for crack growth is based in part on the measurement of surface displacements near the tip of an emerging crack, which is the point at which a crack front intersects the side surface of the specimen. Surface displacements measured by atomic force microscopy were less than theoretically predicted. The difference between the theoretical and experimental displacements was attributed to a plastic zone surrounding the tip of the moving crack. In this paper, we show that the theoretical analysis used earlier was based on an incorrect assumption about the functional dependence of the displacement with distance from the crack tip. We use a full three-dimensional finite element analysis combined with an asymptotic solution of the crack geometry to obtain a solution to the surface displacement problem. We show that the calculated displacements are fully consistent with those experimentally measured by using an atomic force microscope. No divergence from elastic behavior is observed. Our results support the view that crack propagation in glass is entirely brittle. No evidence for plasticity at the crack tips is obtained.