Surface morphology evolution in stressed solids: Surface diffusion controlled crack initiation

We present a nonlinear analysis of the temporal evolution of the surface morphology of a stressed solid based on a general parametric description of the surface shape. We find that surfaces of elastic, defect-free solids are unstable against the nucleation and growth of cracks. The rate at which this surface instability occurs depends on the material transport kinetic mechanism. The surface instability creates a groove that sharpens as it grows deeper. The groove growth rate accelerates until the groove reaches a critical length (or time) where the growth rate diverges. Comparison of these results with predictions of linear elastic fracture mechanics shows that the critical length is in excellent agreement with the classical Griffith fracture criterion, with no adjustable parameters. The stress field ahead of the growing groove becomes increasingly singular as the groove grows. Once the critical groove length is achieved, the stress field ahead of the groove approaches the inverse square root dependence on distance from the tip, which is characteristic of a sharp crack. Therefore, the sub-critical groove is not simply a short crack.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31315/1/0000224.pd