Crack nucleation at the surface of stressed fibers

A model is proposed for crack initiation on a pristine surface. In this model failure starts from a flat surface and the crack develops during the strength or lifetime experiment. Both energy and kinetic arguments are used. The model is applied to lifetime calculations of pristine optical fibers. Surface energy and bulk elastic energy are calculated for a fiber with a flat and a slightly distorted surface. When a small amount of elastic energy is removed locally from the fiber, e.g., by dissolution, the distorted state is more stable. Like cracks in brittle materials, the stable distortions for pristine optical fibers have local radii of curvature at atomic dimensions. In this model the lifetime of a pristine fiber is mainly determined by the time needed to pass from a flat surface to a relatively small surface distortion. From the derived expression for the lifetime, the exponent n in the empirical power law expression for subcritical crack growth can be interpreted. It is shown that n is stress dependent. The discrepancy in n value observed for silica glass fibers (n≂20) and bulk fused silica (n≂40) is removed.