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.
Similar content being viewed by others
References
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.
Cotterell, B. and Rice, J.R., Slightly curved or kinked cracks. International Journal of Fracture, 1980, 6: 155–169.
Shen, I.Y., Perturbation eigensolutions of elastic structures with cracks. Journal of Applied Mechanics, Transactions ASME, 1993, 60: 438–442.
Martin, P.A., Perturbed cracks in two dimensions: an integral-equation approach. International Journal of Fracture, 2000, 104: 317–327.
Helsing, J., A fast and stable solver for singular integral equations on piecewise smooth curved. SIAM Journal on Scientific Computing, 2011, 33: 153–174.
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.
Chen, Y.Z., Hasebe, N. and Lee, K.Y., Multiple Crack Problems in Elasticity. WIT Press, Southampton, 2003.
Chen, Y.Z., A numerical solution technique of hypersingular integral equation for curved cracks. Communication in Numerical Methods in Engineering, 2003, 19: 645–655.
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.
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.
Leonel, E.D. and Venturini, W.S., Multiple random crack propagation using a boundary element formulation. Engineering Fracture Mechanics, 2011, 78: 1077–1090.
Oliveira, H.L. and Leonel, E.D., Dual BEM formulation applied to analysis of multiple crack propagation. Key Engineering Materials, 2013, 560: 99–106.
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.
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.
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.
Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory Of Elasticity. Noordhoff International Publishing, Leyden, 1957.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
The second author would like to thank Ministry of Science, Technology and Innovation (MOSTI), Malaysia for the Science Fund, Vot No. 5450657.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S0894-9166(16)30243-9