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A novel singular element is presented to evaluate the stress intensity factor (SIF) of the through-thickness crack in this paper. The new element takes into account the special variation of the displacements around the intersection of the crack front and the free surface. The intersection between the crack front and the free surface is named singular point. The proposed element has a vertex which coincides with the singular point. Accurately capturing the distribution of displacements in the vicinity of the singular point is of crucial importance in the implementation of dual boundary element method (DBEM) for the through-thickness crack problems. The element with usual shape functions doesn’t lead to accurate solutions unless extremely fine meshes are used. With these new singular elements, more accurate results for the displacement filed around the singular point and the SIF can be obtained. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.
dual boundary element method, stress intensity factor, through-thickness crack, vertex singularity
[1] Yan, A.M. & Nguyen-Dang, H., Multiple-cracked fatigue crack growth by BEM. Computational Mechanics, 16(5), pp. 273–280, 1995. http://dx.doi.org/10.1007/BF00350716
[2] Liu, Y.J. & Xu, N., Modeling of interface cracks in fiber-reinforced composites with the presence of interphases using the boundary element method. Mechanics of Materials, 32(12), pp. 769–783, 2000. http://dx.doi.org/10.1016/S0167-6636(00)00045-4
[3] Telles, J.C.F., Castor, G.S. & Guimaraes, S., A numerical Green’s function approach for boundary elements applied to fracture mechanics. International Journal for Numerical Methods in Engineering, 38(19), pp. 3259–3274, 1995. http://dx.doi.org/10.1002/nme.1620381906
[4] Blandford, G.E., Anthony, R.I. & James, A.L., Two-dimensional stress intensity factor computations using the boundary element method. International Journal for Numerical Methods in Engineering, 17(3), pp. 387–404, 1981. http://dx.doi.org/10.1002/nme.1620170308
[5] Crouch, S.L., Antony, M.S. & Rizzo, F.J., Boundary element methods in solid mechanics. Journal of Applied Mechanics, 50, p. 704, 1983. http://dx.doi.org/10.1115/1.3167130
[6] Sirtori, S., Maier, G., Novati, G. & Miccoli, S., A Galerkin symmetric boundary-element method in elasticity: formulation and implementation. International Journal for Numerical Methods in Engineering, 35(2), pp. 255–282, 1992. http://dx.doi.org/10.1002/nme.1620350204
[7] Xie, G., Zhang, J., Huang, C., Lu, C. & Li, G., A direct traction boundary integral equation method for three-dimension crack problems in infinite and finite domains. Computational Mechanics, 53(4), pp. 575–586, 2014. http://dx.doi.org/10.1007/s00466-013-0918-8
[8] Hong, H.K. & Chen, J.T., Derivations of integral equations of elasticity. Journal of Engineering Mechanics, 114(6), pp. 1028–1044, 1988. http://dx.doi.org/10.1061/(ASCE)0733-9399(1988)114:6(1028)
[9] Chen, J.T. & Hong, H.K., Review of dual boundary element methods with emphasis on hyprsingular integrals and divergent series. Applied Mechanics Reviews, 52, pp. 17–33, 1999. http://dx.doi.org/10.1115/1.3098922
[10] Mi, Y. & Aliabadi, M.H., Dual boundary element method for three-dimensional fracture mechanics analysis. Engineering Analysis with Boundary Elements, 10(2), pp. 161–171, 1992. http://dx.doi.org/10.1016/0955-7997(92)90047-B
[11] Pan, E. & Yuan, F.G., Boundary element analysis of three-dimensional cracks in anisotropic solids. International Journal for Numerical Methods in Engineering, 48(2), pp. 211–237, 2000. http://dx.doi.org/10.1002/(SICI)1097-0207(20000520)48:2%3C211::AIDNME875%3E3.0.CO;2-A
[12] Chen, W.H. & Chen, T.C., An efficient dual boundary element technique for a two-dimensional fracture problem with multiple cracks. International Journal for Numerical Methods in Engineering, 38(10), pp. 1739–1756, 1995. http://dx.doi.org/10.1002/nme.1620381009
[13] Ariza, M.P., Saez, A. & Dominguez, J., A singular element for three-dimensional fracture mechanics analysis. Engineering Analysis with Boundary Elements, 20(4), pp. 275–285, 1997. http://dx.doi.org/10.1016/S0955-7997(97)00070-2
[14] Mi, Y. & Aliabadi, M.H., Discontinuous crack-tip elements: application to 3D boundary element method. International Journal of Fracture, 67(3), pp. R67–R71, 1994. http://dx.doi.org/10.1007/BF00016267
[15] Benthem, J.P., State of stress at the vertex of a quarter-infinite crack in a half-space. International Journal of Solids and Structures, 13(5), pp. 479–492, 1977. http://dx.doi.org/10.1016/0020-7683(77)90042-7
[16] Bažant, Z.P. & Luis F.E., Surface singularity and crack propagation. International Journal of Solids and Structures, 15(5) pp. 405–426, 1979. http://dx.doi.org/10.1016/0020-7683(79)90062-3
[17] Shivakumar, K.N. & Raju, I.S., Treatment of singularities in cracked bodies. International Journal of Fracture, 45(3), 159–178, 1990. http://dx.doi.org/10.1007/BF00693347
[18] Kwon, S.W. & Sun, C.T., Characteristics of three-dimensional stress fields in plates with a through-the-thickness crack. International Journal of Fracture, 104(3), pp. 289–314, 2000. http://dx.doi.org/10.1023/A:1007601918058
[19] Aliha, M.R.M. & Saghafi, H., The effects of thickness and Poisson’s ratio on 3D mixedmode fracture. Engineering Fracture Mechanics, 98, pp. 15–28, 2013. http://dx.doi.org/10.1016/j.engfracmech.2012.11.003
[20] Raju, I.S. & Newman, J.C., Three dimensional finite-element analysis of finite-thickness fracture specimens. NASA, Washington, DC, 1977.
[21] Murakami, Y. & Hasebe, N. (eds), Stress Intensity Factors Handbook, Elsevier Science: Amsterdam/New York, 2001.