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Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (9): 1177-1192.doi: https://doi.org/10.1007/s10483-016-2123-6

• 论文 • 上一篇    下一篇

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

Tiemei YANG, Weiyang YANG, Junlin LI, Xuexia ZHANG   

  1. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China
  • 收稿日期:2015-11-11 修回日期:2016-04-01 出版日期:2016-09-01 发布日期:2016-09-01
  • 通讯作者: Tiemei YANG E-mail:yangtie01@sina.com
  • 基金资助:

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

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

Tiemei YANG, Weiyang YANG, Junlin LI, Xuexia ZHANG   

  1. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China
  • Received:2015-11-11 Revised:2016-04-01 Online:2016-09-01 Published:2016-09-01
  • Contact: Tiemei YANG E-mail:yangtie01@sina.com
  • Supported by:

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

摘要:

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 △1 > 0 and △2 > 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.

关键词: uniqueness, interface crack, characteristic equation, orthotropic bimaterial, stress intensity factor, stress

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 △1 > 0 and △2 > 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.

Key words: orthotropic bimaterial, stress, characteristic equation, interface crack, stress intensity factor, uniqueness

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