An energetic criterion for a micro-crack of finite length initiated in orthotropic bi-material notches

The singular stress field at the tip of a bi-material orthotropic notch may cause the initiation of micro-cracks into one of its material part. Assuming the plane elasticity of the anisotropic media, the Lekhnitskii–Eshelby–Stroh formalism is used to express the characteristics of the singular stress field at the notch tip, the auxiliary solution necessary for the calculation of the contour-independent integrals and consequently generalized stress intensity factors. The matched asymptotic expansion analysis is used to evaluate the fracture energy release rate which allows one to assess the potential direction of a crack and establish the fracture criterion based on the theory of the finite fracture mechanics.