Hybrid Center Penetrate Interface Crack Stress Field Analysis

Composite materials have been the focus of attention from it appears. With the increasing composite materials are widely applied to real life, the interface mechanical behavior of different types of materials gets more and more concern and attention. The interface is a combination of two different materials or two same materials. Because the binding materials are easy to cause stress concentration at the interface, especially at the mutations of interface geometric shapes, stress concentration will become very serious and the stress tends to infinity at the mutation. The feature that stress tends to infinity at some point is called stress singularity, and we take the precise and comprehensive analysis of stress singularity and singularity stress field of the central-penetrated interface crack as the foundation for evaluation of the strength of the interface edge. It has a decisive significance.Using the method of composite material complex and the theory of partial differential equations and constructing new stress functions with complex singularity exponents, the problems of singularities near orthotropic bi-material interface crack tip for mode Ⅰ,mode Ⅱ and mixed mode are studied in this paper. We study and solve the boundary value problems of a class of generalized bi-harmonic equations with the help of boundary conditions. When the discriminations of the characteristic equations of the governing equations are△1<0and△2<0, the relationship between the singular exponents and the material parameters are discussed systematically. We get that there are two kinds of real singularity exponents that are λ=-1/2and λ=-1/2+ε, two kinds of complex singularity exponents that are λ=-1/2+iε and λ=-1/2+c+iε. Meanwhile, the stress fields have a constant singularity at λ=-1/2, a non-constant singularity at λ=-1/2+ε, a constant oscillatory singularity at λ=-1/2+iε and a non-constant oscillatory singularity at λ=-1/2+c+iε. The existence of four kinds of singularities near the interface crack tip of orthotropic bi-material is verified by examples and it expands the scope of singularity exponents. Simultaneously, foreach case, the analytic expressions for stress intensity factors, stress fields anddisplacement fields near the central-penetrated interface crack tip for mode I andmode II of orthotropic bi-material are obtained. By the principle of superposition,we can establish corresponding results of central-penetrated interface crack formixed mode.