Skip to main content
SpringerLink
Log in

Solution of multiple cracks in a finite plate of an elastic isotropic material with the distributed dislocation method

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

This paper presents a numerical solution to model multiple cracks in a finite plate of an elastic isotropic material. Both the boundaries and the cracks are modeled by distributed dislocations. This method results in a system of singular integral equations with Cauchy kernels which can be solved by Gauss-Chebyshev quadrature method. Four examples are provided to assess the capability of this method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Erdogan, F. and Gupta, G.D., Layered composites with an interface flaw. International Journal of Solids and Structures, 1971, 7(8): 1089–1107.

    Article  Google Scholar 

  2. Erdogan, F., Gupta, G.D. and Ratwani, M., Interaction between a circular inclusion and an arbitrarily oriented crack. Journal of Applied Mechanics, 1974, 41(4): 1007–1013.

    Article  Google Scholar 

  3. Comninou, M. and Schmeuser, D., The interface crack in a combined tension–compression and shear field. Journal of Applied Mechanics, 1979, 46: 345–348.

    Article  Google Scholar 

  4. Comninou, M. and Dundurs, J., Effect of friction on the interface crack loaded in shear. Journal of Elasticity, 1982, 10(2): 203–212.

    Article  MathSciNet  Google Scholar 

  5. Comninou, M. and Chang, F.K, Effects of partial closure and friction on a radial crack emanating from a circular hole. International Journal of Fracture, 1985, 28: 29–36.

    Google Scholar 

  6. Hills, D.A. and Comninou, M., A normally loaded half plane with an edge crack. International Journal of Solids and Structures, 1985, 21(4): 399–410.

    Article  Google Scholar 

  7. Nowell, D. and Hills, D.A., Open cracks at or near free of positive radial stresses along the crack line in the edges. Journal of Strain Analysis for Engineering Design, 1987, 22(3): 177–185.

    Article  Google Scholar 

  8. Hills, D.A. and Nowell, D., Stress intensity calibrations for closed cracks. Journal of Strain Analysis for Engineering Design, 1989, 24(1): 37–43.

    Article  Google Scholar 

  9. Hills, D.A., Kelly, P.A., Dai, D.N. and Korsunsky, A.M., Solution of Crack Problems-the Distributed Dislocation. Dordrecht: Kluwer Academic Publishers, 1996.

    Book  Google Scholar 

  10. Weertman, Dislocation Based Fracture Mechanics. Singapore: World Scientific, 1996.

    Book  Google Scholar 

  11. Sheng, C.F., Boundary element method by dislocation distribution. Journal of Applied Mechanics, 1987, 54(1): 105–109.

    Article  Google Scholar 

  12. Dai, D.N., Modeling cracks in finite bodies by distributed dislocation dipoles. Fatigue and Fracture of Engineering Materials and Structures, 2002, 25(1):27–39.

    Article  MathSciNet  Google Scholar 

  13. Han, J, J. and Dhanasekar, M., Modeling cracks in arbitrarily shaped finite bodies by distribution of dislocation. International Journal of Solids and Structures, 2004, 41(2): 399–411.

    Article  Google Scholar 

  14. Jin, X.Q. and Keer, N., Solution of multiple edge cracks in an elastic plane. International Journal of Fracture, 2006, 137: 121–137.

    Article  Google Scholar 

  15. Zhou, Z.G., Zhang, P.W. and Wu, L.Z., Multiple parallel sysmetric permeable model-Ill cracks in a piezo-electric/piezomagenetic composite material plane. Acta Mechanica Solida Sinica, 2010, 23(4): 336–351.

    Article  Google Scholar 

  16. Chen, Y.Z. and Wang, Z.X., Solution of multiple crack problems in a finite plate using coupled integral equations. International Journal of Solids and Structures, 2012, 49(1): 87–94.

    Article  MathSciNet  Google Scholar 

  17. Chen, Y.Z., Solution of multiple crack problems in a finite plate using an alternating method based on two kinds of integral equation. Engineering Analysis with Boundary Elements, 2011, 35(10):1109–1115.

    Article  MathSciNet  Google Scholar 

  18. Jin.X.Q., Analysis of Some Two Dimensional Problems Containing Cracks and Holes. Northwestern university, 2006: 138–140.

  19. Erdogan, F., Gupta, G.D. and Cook, T.S., Numerical solution of singular integral equations. In: Methods of Analysis and Solutions of Crack Problems, Noordhoff, Leyden, 1973: 368–425.

    Chapter  Google Scholar 

  20. He, M. and Hutchinson, J.W., Kinking of a crack out of aninterface. J Appl Mech, 1989, 56: 270–278.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Aeronautics, Northwestern Polytechnical University, 710072, Xi’an, China

    Jiong Zhang, Zhan Qu & Qiqing Huang

  2. School of Materials Science and Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

    Lechun Xie

  3. School of Mechanical and Vehicular Engineering, Beijing Institute of Technology, 100081, Beijing, China

    Cenbo Xiong

Authors
  1. Jiong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhan Qu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiqing Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lechun Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Cenbo Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiong Zhang.

Additional information

Project supported by National Natural Science Foundation of China (No. 51174162).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Qu, Z., Huang, Q. et al. Solution of multiple cracks in a finite plate of an elastic isotropic material with the distributed dislocation method. Acta Mech. Solida Sin. 27, 276–283 (2014). https://doi.org/10.1016/S0894-9166(14)60036-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(14)60036-7

Key Words

Search

Navigation