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Plastic stresses at the tip of a crack impinging perpendicularly the interface of two different elastic-plastic materials

Espapragoza J. E.

International Journal of Applied Mechanics and Engineering

2005

Vol. 10, no. 2

207-216

The problem of stresses at the tip of a crack impinging the interface of two different elastic-perfectly plastic materials is considered. The mathematical model is based on the assumption that both solids are incompressible elastic-perfectly plastic materials obeying the Huber-Von Misses yielding criterion under conditions of plane strain. It is shown that the problem of local stresses near the crack tip has two possible solutions, one of which is continuous and the other discontinuous. For the inhomogeneous case it was found that the discontinuous solution is the only feasible. In the limiting case of a homogeneous elastic-perfectly plastic material, the continuous solution coincides with that of Prandtl (1920), and the discontinuous solution with that of Cherepanov (1997). Some reasons for preferring the discontinuous solutions are provided since it is evident that both solutions cannot exist simultaneously.