Contact model of cracks in orthotropic materials

We consider a plane strain problem for an orthotropic half plane loaded at infinity and containing a crack along its fixed edge. To remove a singularity near the right crack tip, we introduce an artificial contact zone. The problem under consideration is reduced to the mixed Dirichlet-Riemann boundaryvalue problem. We present the exact solution of this problem and deduce formulas for stresses in the contact zone and on the continuation of the crack and for the stress intensity factors. By using both analytic and numerical methods, we prove that the energy-release rate is quasiinvariant in the process of crack propagation relative to the size of the contact zone. On the basis of these results, we propose an algorithm for the evaluation of the paramenters of fracture of composites of finite dimensions with interface cracks. As a special case, we develop a model of interface cracks with actual contact zone and establish the dependences of the length of this zone on the external load and elasticity moduli of the material. Dnepropetrovsk State University, Dnepropetrovsk. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 5, pp. 59–66, September–October, 1999