Stress concentration and unsteady propagation of longitudinal shear cracks

Unsteady propagation of a longitudinal shear crack is studied through numerical calculation for better understanding of fracture and earthquakes. The relation that formulates rupture velocity as a function of stress intensity is used to describe the fracture process at the crack tip. The effects of creep and frictional slidings are taken into account by assuming a suitable form of the slip velocity dependent boundary condition. In this model stress accumulation takes place through creep, and then the crack begins to grow, controlled by the dynamic friction across the crack surface. It is shown that the motion of the crack tip is either smooth or bumpy, depending on the parameters of the boundary condition. The brittleness and ductility of material are interpreted by these two types of crack propagation, and this interpretation is qualitatively consistent with the experimental results on brittle-ductile transition induced by the temperature, the confining pressure, and the pore pressure. It is shown that the presence of smooth and bumpy crack propagations might give a possible explanation on the dissimilarity between large and small earthquakes, pointed out by Aki. This model also suggests a method of estimating the recurrence period of earthquakes, based on the crustal deformation across the fault.