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Analysis of stress intensity factor in orthotropic bi-material mixed interface crack

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Abstract

Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With consideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial differential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant ɛ t and the real stress singularity exponents λ t are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit, undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship between the bi-material stress intensity factor and the ratio of bi-material Young’s modulus are given in the numerical analysis.

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Authors and Affiliations

  1. School of Applied Sciences, Taiyuan University of Science and Technology, Taiyuan, 030024, P. R. China

    Wen-bin Zhao  (赵文彬), Xue-xia Zhang  (张雪霞), Xiao-chao Cui  (崔小朝) & Wei-yang Yang  (杨维阳)

Authors
  1. Wen-bin Zhao  (赵文彬)
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  2. Xue-xia Zhang  (张雪霞)
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  3. Xiao-chao Cui  (崔小朝)
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  4. Wei-yang Yang  (杨维阳)
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Corresponding author

Correspondence to Wen-bin Zhao  (赵文彬).

Additional information

Project supported by the National Key Basic Research Program of China (973 Program) (No. 2009CB724201), the Science and Technology Major Project of the Ministry of Education of China (No. 208022), the Postgraduate Scientific and Technological Innovation Project of Taiyuan University of Science and Technology (No. 20125027), and the Scientific Research Funds for Doctoral Students of Taiyuan University of Science and Technology (No. 20122005)

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Zhao, Wb., Zhang, Xx., Cui, Xc. et al. Analysis of stress intensity factor in orthotropic bi-material mixed interface crack. Appl. Math. Mech.-Engl. Ed. 35, 1271–1292 (2014). https://doi.org/10.1007/s10483-014-1864-9

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  • DOI: https://doi.org/10.1007/s10483-014-1864-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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