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General solutions of plane problem for power function curved cracks

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Abstract

A new exact and universal conformal mapping is proposed. Using Muskhelishvili's complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors (SIFs) for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.

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References

  1. Shen, D. W. and Fan, T. Y. Exact solutions of two semi-infinite collinear cracks in a strip. Engineering Fracture Mechanics, 70(6), 813–822 (2003)

    Article  Google Scholar 

  2. Muskhelishvili, N. I. Some Basic Problems of Mathematical Theory of Elasticity, Springer-Verlag, Berlin (1975)

    MATH  Google Scholar 

  3. Yan, X. Q. A numerical analysis of cracks emanating from an elliptical hole in a 2-D elasticity plate. European Journal of Mechanics-A / Solids, 25(1), 142–153 (2006)

    Article  MATH  Google Scholar 

  4. Guo, J. H. and Liu, G. T. Stress analysis for an elliptical hole with two straight cracks (in Chinese). Chinese Journal of Theoretical and Applied Mechanics, 39(5), 699–703 (2007)

    Google Scholar 

  5. Abdelmoula, R., Semani, K., and Li, J. Anaysis of cracks originating at the boundary of a circular hole in an infinite plate by using a new conformal mapping approach. Applied Mathematics and Computation, 188(2), 1891–1896 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, Y. Z. Stress intensity factors for curved and kinked cracks in plane extension. Theoretical and Applied Fracture Mechanics, 31(3), 223–232 (1999)

    Article  Google Scholar 

  7. Hu, Y. T. and Zhao, X. H. Curve crack lying along a parabolic curve in anisotropic body. Applied Mathematics and Mechanics (English Edition), 16(2), 115–124 (1995) DOI 10.1007/BF02451451

    Article  MathSciNet  MATH  Google Scholar 

  8. Wei, X. X. and Dong, J. An analytical solution for the elastic plane problem with a symmetric parabolic crack (in Chinese). Transactions of Beijing Institute of Technology, 24(5), 380–382 (2004)

    Google Scholar 

  9. Guo, H. M., Liu, G. T., and Pi, J. D. Analytical solutions for the elastic plane problem with symmetric power function cracks (in Chinese). Journal of Inner Mongolia Normal University (Natural Science Edition), 36(5), 533–536 (2007)

    MathSciNet  MATH  Google Scholar 

  10. Fan, T. Y. Foundation of Fracture Theory (in Chinese), Science Press, Beijing (2003)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Institute of Solid Mechanics, Beihang University, Beijing, 100191, P. R. China

    Jun-hong Guo  (郭俊宏), Ze-shuai Yuan  (袁泽帅) & Zi-xing Lu  (卢子兴)

Authors
  1. Jun-hong Guo  (郭俊宏)
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  2. Ze-shuai Yuan  (袁泽帅)
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  3. Zi-xing Lu  (卢子兴)
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Corresponding author

Correspondence to Zi-xing Lu  (卢子兴).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 10932001, 11072015, and 10761005), the Scientific Research Key Program of Beijing Municipal Commission of Education (No. KZ201010005003), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20101102110016), and the Ph. D. Innovation Foundation of Beijing University of Aeronautics and Astronautics (No. 300351)

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Guo, Jh., Yuan, Zs. & Lu, Zx. General solutions of plane problem for power function curved cracks. Appl. Math. Mech.-Engl. Ed. 32, 563–570 (2011). https://doi.org/10.1007/s10483-011-1438-9

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  • DOI: https://doi.org/10.1007/s10483-011-1438-9

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