Crack-tip field on mode Ⅱ interface crack of double dissimilar orthotropic composite materials

• Published in: Applied mathematics and mechanics Vol. 30; no. 12; pp. 1489 - 1504
• Main Author: 张雪霞 崔小朝 杨维阳 李俊林
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.12.2009
• Subjects: Applications of Mathematics; Classical Mechanics; Composite materials; Cracks; Displacement; Exponents; Fluid- and Aerodynamics; Linear equations; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Singularities; Stress functions; Stresses; 复合材料; 奇异性指数; 应力函数; 应力强度因子; 正交异性材料; 界面裂纹; 裂纹尖端; 非齐次线性方程组; stress intensity factors; double materials; mode II interface crack; orthotropic; 74R20; O174.5; 35Q72; O346.3
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-009-1202-4

Two systems of non-homogeneous linear equations with 8 unknowns are obtained.This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions.By solving the above systems of non-homogeneous linear equations,the two real stress singularity exponents can be determined when the double material parameters meet certain conditions.The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit.By substituting these parameters into the corresponding mechanics equations,theoretical solutions to the stress intensity factor,the stress field and the displacement field near the crack tip of each material can be obtained when both discriminants of the characteristic equations are less than zero.Stress and displacement near the crack tip show mixed crack characteristics without stress oscillation and crack surface overlapping.As an example,when the two orthotropic materials are the same,the stress singularity exponent,the stress intensity factor,and expressions for the stress and the displacement fields of the orthotropic single materials can be derived.