The Analysis of the Stress and Displacement Field near the Surface Crack Tip Terminating Perpendicular to the Interface between Two Orthotropic Materials

Abstract

The evaluation of the generalized stress intensity factor (GSIF) and T-stress for the case of the surface crack terminating perpendicular to the interface between two orthotropic materials is considered. The combination of the discretization, numerical and analytic methods is used. The discretization method, such as common finite element method (FEM), is served to include the boundary condition to the GSIF solution and to describe the remote stress and displacement field region with the low influence of the singularity of the crack tip. The Lekhnickii-Eshelby-Stroh (LES) formalism is used to derive the approach solution for the near stress field of the crack tip and the singularity problem in an orthotropic 'trimaterial' using the Schwartz-Neumann's alternating technique. The problem of the stress singularity is treated as a non-linear eigenvalue problem, which leads to the characteristic equation for the stress singularities of the form rδ −1 , 0 <δ <1. Two ways of the evaluation of the GSIF are presented, using the reciprocal theorem ψ -integral) and the crack model by means of continuous distribution of dislocations. Both results are compared for a specific material. The continuous distribution of dislocations technique is also used for determination of the T-stress.