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Analysis on non-oscillatory singularity behaviors of mode II interface crack tip in orthotropic bimaterial

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Abstract

The fracture behaviors near the mode II interface crack tip for orthotropic bimaterial are studied. The non-oscillatory field, where the stress singularity exponent is a real number, is discussed by the complex function method and the undetermined coefficient method. From the research fracture problems, the stress functions with ten undetermined coefficients and an unknown singularity exponent are introduced when Δ1 > 0 and Δ2 > 0. By the existence theorem of non-trival solutions for the system of eight homogeneous linear equations, the characteristic equation, the stress singularity exponent, and the discriminating condition of the non-oscillatory singularity are found. By the uniqueness theorem of the solutions for the system of twelve non-homogeneous linear equations with ten unknowns, the ten undermined coefficients in the stress functions are uniquely determined. The definitions of the stress intensity factors are given with the help of one-sided limit, and their theoretical formulae are deduced. The analytic solutions of the stresses near the mode II interface crack tip are derived. The classical results for orthotropic material are obtained.

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Authors and Affiliations

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

    Tiemei Yang, Weiyang Yang, Junlin Li & Xuexia Zhang

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  1. Tiemei Yang
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  2. Weiyang Yang
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  4. Xuexia Zhang
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Correspondence to Tiemei Yang.

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Project supported by the Natural Science Foundation of Shanxi Province (No. 2014011009-2)

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Yang, T., Yang, W., Li, J. et al. Analysis on non-oscillatory singularity behaviors of mode II interface crack tip in orthotropic bimaterial. Appl. Math. Mech.-Engl. Ed. 37, 1177–1192 (2016). https://doi.org/10.1007/s10483-016-2123-6

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  • DOI: https://doi.org/10.1007/s10483-016-2123-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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