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Modified boundary layer analysis for a mode III crack problem

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Abstract

A modified boundary layer problem of a semi-infinite crack in an elastic-perfectly plastic material under a Mode III load is analyzed. The analytic solution of elastic fields is derived by using complex function theory. It is found that the size and the shape of the plastic zone near the crack tip depend on the elastic T-stress given on the remote boundary. A method for determining higher order singular solutions of elastic fields is also proposed. In order to determine the higher order singular solutions of the elastic fields, Williams expansion of the solution is used. Higher order terms in the Williams expansion are obtained through simple mathematical manipulation. The coefficients of each term in the Williams expansion are also calculated numerically with the J-based mutual integral

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References

  1. S. G. Larsson and A. J. Carlsson, Influence of nonsingular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials, J. Mech. Phys. Solids 21 (1973) 263–277.

    Article  Google Scholar 

  2. J. R. Rice, Limitations to the small scale yielding approximation for crack tip plasticity, J. Mech. Phys. Solids 22 (1974) 17–26.

    Article  Google Scholar 

  3. B. Cotterell and J. R. Rice, Slightly curved or kinked cracks, Int. J. Fracture 16 (1980) 155–169.

    Article  Google Scholar 

  4. Z.-Z. Du and J. W. Hancock, The effect of nonsingular stresses on crack-tip constraint, J. Mech. Phys. Solids 39 (1991) 555–567.

    Article  Google Scholar 

  5. J. A. H. Hult and F. A. McClintock, Elastic-plastic stress and strain distributions around sharp notches under repeated shear, Proc. of the 9th Int. Congr. Applied Mechanics, Belgium, (1957) 51–58.

  6. E. Turska and E. Wisniewski, On semi-infinite crack problems in elastic-plastic bodies: uniqueness and examples, Int. J. Eng. Sci. 41 (2003) 1767–1783.

    Article  MathSciNet  Google Scholar 

  7. Y. J. Cho, H. G. Beom and Y. Y. Earmme, Application of a conservation integral to an interface crack interacting with singularities, Int. J. Fracture 65 (1994) pp.63–73.

    Article  Google Scholar 

  8. I. Jeon and S. Im, The role of higher order eigenfields in elastic-plastic cracks, J. Mech. Phys. Solids 49 (2001) 2789–2818.

    Article  MATH  Google Scholar 

  9. G. P. Cherepanov, Mechanics of Brittle Fracture, McGraw-Hill, New-York, USA, (1979)

    MATH  Google Scholar 

  10. F. H. K. Chen and R. T. Shield, Conservation laws in elasticity of the J integral type, Z. Angew. Math. Phys. 28 (1977) 1–22.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Inha University, 253 Yonghyun-dong, Incheon, 402-751, Korea

    Hyeon Gyu Beom, Yu Hwan Kim, Chongdu Cho & Chang-Boo Kim

Authors
  1. Hyeon Gyu Beom
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  2. Yu Hwan Kim
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  3. Chongdu Cho
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  4. Chang-Boo Kim
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Correspondence to Hyeon Gyu Beom.

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Beom, H.G., Kim, Y.H., Cho, C. et al. Modified boundary layer analysis for a mode III crack problem. J Mech Sci Technol 22, 653–661 (2008). https://doi.org/10.1007/s12206-008-0113-6

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  • DOI: https://doi.org/10.1007/s12206-008-0113-6

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