The influence of the first non-singular stress terms on crack initiation direction in an orthotropic bi-material plate

A bi-material plate composed of two orthotropic parts leads to free edge stress singularity. This is considered as a bi-material notch with ω1 = ω2 = 90° under general loading. Besides the singular term the first non-singular term is also included in the stress distribution at the notch tip. The Stroh–Eshelby–Lekhnitskii formalism for plane elasticity is used to express stress and displacement fields and the strain energy density factor. The exponents of the singular and non-singular stress terms and corresponding eigenvectors are the solution of the eigenvalue problem resulting from the prescribed boundary and compatibility conditions at the notch tip. The potential direction of crack initiation is determined from the local minimum of the mean value of the strain energy density factor in both materials. The necessary knowledge of the generalized stress intensity factor and generalized T-stress is realized by means of the employment of the two state conservation integrals. Following the assumption of the same mechanism of rupture in the case of a crack and a notch, an expression for the critical values of the generalized stress intensity factor is obtained.