Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (5): 585-594.doi: https://doi.org/10.1007/s10483-009-0505-z

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Interface crack problems for mode II of double dissimilar orthotropic composite materials

杨维阳1 张少琴1 李俊林1 马玉兰1,2   

  1. 1. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, P. R. China;
    2. Department of Mathematics and Physics, Beijing Technology and Business University, Beijing 100037, P. R. China
  • 收稿日期:2008-10-18 修回日期:2009-03-23 出版日期:2009-05-01 发布日期:2009-05-01

Interface crack problems for mode II of double dissimilar orthotropic composite materials

Wei-Yang YANG1, Shao-Qin ZHANG1, Jun-Lin LI1, Yu-Lan MA1,2   

  1. 1. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, P. R. China;
    2. Department of Mathematics and Physics, Beijing Technology and Business University, Beijing 100037, P. R. China
  • Received:2008-10-18 Revised:2009-03-23 Online:2009-05-01 Published:2009-05-01

摘要: The fracture problems near the interface crack tip for mode II of double dissimilar orthotropic composite materials are studied. The mechanical models of interface crack for mode II are given. By translating the governing equations into the generalized bi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.

关键词: interface crack for mode II, stress intensity factor, double materials, orthotropic

Abstract: The fracture problems near the interface crack tip for mode II of double dissimilar orthotropic composite materials are studied. The mechanical models of interface crack for mode II are given. By translating the governing equations into the generalized bi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.

Key words: interface crack for mode II, stress intensity factor, double materials, orthotropic

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