Nonhomogenized Displacement Discontinuity Method for Calculation of Stress Intensity Factors for Cracks in Anisotropic FGMs
Publication: Journal of Engineering Mechanics
Volume 140, Issue 12
Abstract
A numerical method is proposed for calculation of the mixed-mode stress intensity factors at a crack tip in anisotropic functionally graded materials (FGMs). The method is constructed by introducing the nonhomogenized displacement discontinuities technique. With this method, the stress intensity factors can be effectively determined by direct use of the finite-element results of the near-tip displacement discontinuities across the crack surfaces. The result from the proposed method can also be used as an effective indicator for evaluating the accuracy of the calculation. This proposed approach is applicable for problems containing curved cracks of arbitrary shape in general anisotropic FGMs.
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Acknowledgments
This work has been partially supported by National Science Council Grant No. NSC101-2221-E-008-076 to National Central University.
References
Banks-Sills, L. (1991). “Application of the finite element method to linear elastic fracture mechanics.” Appl. Mech. Rev., 44(10), 447–461.
Banks-Sills, L., Hershkovitz, I., Wawrzynek, P. A., Eliasi, R., and Ingraffea, A. R. (2005). “Methods for calculating stress intensity factors in anisotropic materials: Part I— is a symmetric plane.” Eng. Fract. Mech., 72(15), 2328–2358.
Beom, H. G., Earmme, Y. Y., and Choi, S. Y. (1994). “Energy release rates for an arbitrarily curved interface crack.” Mech. Mater., 18(3), 195–204.
Boone, T. J., Wawrzynek, P. A., and Ingraffea, A. R. (1987). “Finite element modelling of fracture propagation in orthotropic materials.” Eng. Fract. Mech., 26(2), 185–201.
Budiansky, B., and Rice, J. R. (1973). “Conservation laws and energy-release rates.” J. Appl. Mech., 40(1), 201–203.
Chang, J. H., and Tang, D. S. (2013). “Calculation of stress intensity factors for curved cracks in anisotropic FGMs.” J. Chin. Inst. Eng., 36(8), 1045–1058.
Chang, J. H., and Wu, D. J. (2007). “Computation of mixed-mode stress intensity factors for curved cracks in anisotropic elastic solids.” Eng. Fract. Mech., 74(8), 1360–1372.
Chen, F. H. K., and Shield, R. T. (1977). “Conservation laws in elasticity of the type.” Z. Angew. Math. Phys., 28(1), 1–22.
Chu, S. J., and Hong, C. S. (1990). “Application of the integral to mixed mode crack problems for anisotropic composite laminates.” Eng. Fract. Mech., 35(6), 1093–1103.
Delale, F., and Erdogan, F. (1983). “The crack problem for a nonhomogeneous plane.” J. Appl. Mech., 50(3), 609–614.
Dolbow, J. E., and Gosz, M. (2002). “On the computation of mixed-mode stress intensity factors in functionally graded materials.” Int. J. Solids Struct., 39(9), 2557–2574.
Eischen, J. W. (1987). “Fracture of non-homogeneous materials.” Int. J. Fract., 34(1), 3–22.
Gu, P., Dao, M., and Asaro, R. J. (1999). “A simplified method for calculating the crack-tip field of functionally graded materials using the domain integral.” J. Appl. Mech., 66(1), 101–108.
Kim, J.-H., and Paulino, G. H. (2003). “The interaction integral for fracture of orthotropic functionally graded materials: Evaluation of stress intensity factors.” Int. J. Solids Struct., 40(15), 3967–4001.
Lim, I. L., Johnston, I. W., and Choi, S. K. (1992). “Comparison between various displacement-based stress intensity factor computation techniques.” Int. J. Fract., 58(3), 193–210.
Lorentzon, M., and Eriksson, K. (2000). “A path independent integral for the crack extension force of the circular arc crack.” Eng. Fract. Mech., 66(5), 423–439.
Rao, B. N., and Rahman, S. (2003). “An interaction integral method for analysis of cracks in orthotropic functionally graded materials.” Comput. Mech., 32(1–2), 40–51.
Shih, C. F., deLorenzi, H. G., and German, M. D. (1976). “Crack extension modeling with singular quadratic isoparametric elements.” Int. J. Fract., 12(4), 647–651.
Sih, G. C., Paris, P. C., and Erdogan, F. (1962). “Crack tip, stress-intensity factors for plane extension and plate bending problems.” J. Appl. Mech., 29(2), 306–312.
Stern, M., Becker, E. B., and Dunham, R. S. (1976). “A contour integral computation of mixed-mode stress intensity factors.” Int. J. Fract., 12(3), 359–368.
Su, R. K. L., and Sun, H. Y. (2003). “Numerical solutions of two-dimensional anisotropic crack problems.” Int. J. Solids Struct., 40(18), 4615–4635.
Tilbrook, M. T., Moon, R. J., and Hoffman, M. (2005). “Finite element simulations of crack propagation in functionally graded materials under flexural loading.” Eng. Fract. Mech., 72(16), 2444–2467.
Yehia, N. A. B., and Shephard, M. S. (1985). “On the effect of quarter-point element size on fracture criteria.” Int. J. Numer. Methods Eng., 21(10), 1911–1924.
Zhang, C., Cui, M., Wang, J., Gao, X. W., Sladek, J., and Sladek, V. (2011). “3D crack analysis in functionally graded materials.” Eng. Fract. Mech., 78(3), 585–604.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 12 • December 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Sep 9, 2013
Accepted: Mar 26, 2014
Published online: May 9, 2014
Discussion open until: Oct 9, 2014
Published in print: Dec 1, 2014
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