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Stress intensity factor for the interaction between a straight crack and a curved crack in plane elasticity

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Abstract

Formulation in terms of hypersingular integral equations for the interaction between straight and curved cracks in plane elasticity is obtained using the complex variable functions method. The curved length coordinate method and a suitable numerical scheme are used to solve such integrals numerically for the unknown function, which are later used to find the stress intensity factor, SIF.

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References

  1. Panasyuk, V.V., Savruk, M.P. and Datsyshyn, A.P., A general method of solution of two-dimensional problems in the theory of cracks. Engineering Fracture Mechanics, 1977, 9: 481–497.

    Article  Google Scholar 

  2. Cotterell, B. and Rice, J.R., Slightly curved or kinked cracks. International Journal of Fracture, 1980, 6: 155–169.

    Article  Google Scholar 

  3. Shen, I.Y., Perturbation eigensolutions of elastic structures with cracks. Journal of Applied Mechanics, Transactions ASME, 1993, 60: 438–442.

    Article  Google Scholar 

  4. Martin, P.A., Perturbed cracks in two dimensions: an integral-equation approach. International Journal of Fracture, 2000, 104: 317–327.

    Article  Google Scholar 

  5. Helsing, J., A fast and stable solver for singular integral equations on piecewise smooth curved. SIAM Journal on Scientific Computing, 2011, 33: 153–174.

    Article  MathSciNet  Google Scholar 

  6. Helsing, J. and Peters, G., Integral equation methods and numerical solutions of crack and inclusion problems in planar elastostatics. SIAM Journal on Applied Mathematics, 1999, 59: 965–982.

    MathSciNet  MATH  Google Scholar 

  7. Chen, Y.Z., Hasebe, N. and Lee, K.Y., Multiple Crack Problems in Elasticity. WIT Press, Southampton, 2003.

    MATH  Google Scholar 

  8. Chen, Y.Z., A numerical solution technique of hypersingular integral equation for curved cracks. Communication in Numerical Methods in Engineering, 2003, 19: 645–655.

    Article  MathSciNet  Google Scholar 

  9. Nik Long, N.M.A. and Eshkuvatov, Z.K., Hypersingular integral equation for multiple curved crack problem in plane elasticity. International Journal of Solids and Stuctures, 2009, 46: 2611–2617.

    Article  Google Scholar 

  10. Chen, Y.Z., Gross, D. and Huang, Y.J., Numerical solution of the curved crack problem by means of polynomial approximation of the dislocation distribution. Engineering Fracture Mechanics, 1991, 39: 791–797.

    Article  Google Scholar 

  11. Leonel, E.D. and Venturini, W.S., Multiple random crack propagation using a boundary element formulation. Engineering Fracture Mechanics, 2011, 78: 1077–1090.

    Article  Google Scholar 

  12. Oliveira, H.L. and Leonel, E.D., Dual BEM formulation applied to analysis of multiple crack propagation. Key Engineering Materials, 2013, 560: 99–106.

    Article  Google Scholar 

  13. Guo, J.H., Lu, Z.X., Han, H.T. and Yang, Z., Exact solutions for anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material. International Journal of Solids and Structures, 2009, 46: 3799–3809.

    Article  Google Scholar 

  14. Guo, J.H. and Lu, Z.X., Anti-plane analysis of multiple cracks originating from a circular hole in a magnetoelectroelastic solid. International Journal of Solids and Structures, 2010, 47: 1847–1856.

    Article  Google Scholar 

  15. Guo, J.H., Lu, Z.X., Han, H.T. and Yang, Z., The behavior of two non-symmetrical permeable cracks emanating from an elliptical hole in a piezoelectric solid. European Journal of Mechanics A/Solids, 2010, 29: 654–663.

    Article  Google Scholar 

  16. Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory Of Elasticity. Noordhoff International Publishing, Leyden, 1957.

    Google Scholar 

  17. Mayrhofer, K. and Fischer, F.D., Derivation of a new analytical solution for a general two dimensional finite-part integral applicable in fracture mechanics. International Journal of Numerical Method in Engineering, 1992, 33: 1027–1047.

    Article  MathSciNet  Google Scholar 

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Correspondence to M. R. Aridi.

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The second author would like to thank Ministry of Science, Technology and Innovation (MOSTI), Malaysia for the Science Fund, Vot No. 5450657.

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Aridi, M.R., Nik Long, N.M.A. & Eshkuvatov, Z.K. Stress intensity factor for the interaction between a straight crack and a curved crack in plane elasticity. Acta Mech. Solida Sin. 29, 407–415 (2016). https://doi.org/10.1016/S0894-9166(16)30243-9

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  • DOI: https://doi.org/10.1016/S0894-9166(16)30243-9

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