Fracture analysis near the interface crack tip for mode Ⅰ of orthotropic bimaterial

• Published in: Science China. Physics, mechanics & astronomy Vol. 56; no. 4; pp. 785 - 797
• Main Authors: Yang, XiaoMei, Yang, WeiYang, Li, JunLin, Zhang, XueXia
• Format: Journal Article
• Language: English
• Published: Heidelberg SP Science China Press 01.04.2013; Springer Nature B.V
• Subjects: Astronomy; Boundary conditions; Classical and Continuum Physics; Complex numbers; Crack tips; Exact solutions; Fracture mechanics; Interfacial cracks; Linear equations; Mathematical analysis; Observations and Techniques; Physics; Physics and Astronomy; Real numbers; Singularity (mathematics); Stress functions; Stress intensity factors; 双材料; 奇异性指数; 断裂分析; 正交各向异性材料; 正交异性; 界面; 裂纹尖端; 非齐次线性方程组; stress; interface crack for mode I; displacement; orthotropic bimaterial; stress intensity factor
• ISSN: 1674-7348; 1869-1927
• DOI: 10.1007/s11433-013-5035-3

The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.