Abstract
Interface crack problems in graded orthotropic media are considered using analytical and computational techniques. In the analytical formulation an interface crack between a graded orthotropic coating and a homogeneous orthotropic substrate is considered. The principal axes of orthotropy are assumed to be parallel and perpendicular to the crack plane. Mechanical properties of the medium are assumed to be continuous with discontinuous derivatives at the interface. The problem is formulated in terms of the averaged constants of plane orthotropic elasticity and reduced to a pair of singular integral equations which are solved numerically to compute the mixed mode stress intensity factors and the energy release rate. In the second part of the study, enriched finite elements are formulated and implemented for graded orthotropic materials. Comparisons of the finite element and analytical results show that enriched finite element technique is capable of producing highly accurate results for crack problems in graded orthotropic media. Finally, periodic interface cracking and the four point bending test for graded orthotropic solids are modeled using enriched finite elements and the results are briefly discussed.
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Bahr, H.-A., Balke, H., Fett, T., Hofinger, I., Kirchhoff, G., Munz, D., Neubrand, A., Semenov, A.S., Weiss, H.-J. and Yang, Y.Y. (2003). Cracks in functionally graded materials. Materials Science and Engineering A A362, 2–16.
Chen, Y.F. and Erdogan, F. (1990). The Interface Crack Problem in Nonhomogeneous Bonded Materials of Finite Thickness, Semiconductor Research Corporation, Technical Report, Contract No: 89–MP–071.
Chen, Y.F. and Erdogan, F. (1996). Interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate. Journal of the Mechanics and Physics of Solids 44, 771–781.
Chen, J., Liu, Z.X. and Zou, Z.Z. (2002). Transient internal crack problem for a nonhomogeneous orthotropic strip (Mode I). International Journal of Engineering Science 40, 1761–1774.
Cinar, A. and Erdogan, F. (1983). The crack and wedging problem for an orthotropic strip. International Journal of Fracture 19, 83–102.
Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, E.G. (1953). Higher Transcendental Functions, Vol. II, McGraw – Hill, New York.
Erdogan, F. (1962). On the stress distribution in plates with colinear cuts under arbitrary loads. In: Proceedings of the Fourth U.S. National Congress of Applied Mechanics, ASME, Vol. 1, pp. 547–553.
Gu, P. and Asaro, R.J. (1997). Cracks in functionally graded materials. International Journal of Solids and Structures 34, 1–17.
Guo, L.-C., Wu, L.-Z. and Ma, L. (2004). The interface crack problem under a concentrated load for a functionally graded coating – substrate system. Composite Structures 63, 397–406.
Gupta, G.D. and Erdogan, F. (1974). The problem of edge cracks in an infinite strip. Journal of Applied Mechanics – Transactions of the ASME 41, 1001–1006.
Kaya, A.C. and Nied, H.F. (1993). Interface fracture analysis of bonded ceramic layers using enriched finite elements. In: Proceedings of the Symposium on Ceramic Coatings (Edited by Kokini, K.), ASME MD – Vol. 44, pp. 47–71.
Kim, J.-H. and Paulino, G.H. (2002). Mixed – Mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure. Engineering Fracture Mechanics 69, 1557–1586.
Kim, J.-H. and Paulino, G.H. (2003a). The interaction integral for fracture of orthotropic functionally graded materials: Evaluation of stress intensity factors. International Journal of Solids and Structures 40, 3967–4001.
Kim, J.-H. and Paulino, G.H. (2003b). Mixed – Mode J – Integral formulation and implementation using graded elements for fracture analysis of nonhomogeneous orthotropic materials. Mechanics of Materials 35, 107–128.
Kokini, K., DeJonge, J., Rangaraj, S. and Beardsley, B. (2002). Thermal shock of functionally graded thermal barrier coatings with similar thermal resistance. Surface and Coatings Technology 154, 223–231.
Krenk, S. (1979). On the elastic constants of plane orthotropic elasticity. Journal of Composite Materials 13, 108–116.
Ozturk, M. and Erdogan, F. (1996). Axisymmetric crack problem in bonded materials with a graded interfacial region. International Journal of Solids and Structures 33, 193–219.
Ozturk, M. and Erdogan, F. (1997). Mode I crack problem in an inhomogeneous orthotropic medium. International Journal of Engineering Science 35, 869–883.
Ozturk, M. and Erdogan, F. (1999). The mixed mode crack problem in an inhomogeneous orthotropic medium. International Journal of Fracture 98, 243–261.
Sampath, S., Herman, H., Shimoda, N. and Saito, T. (1995). Thermal spray processing of FGMs. M.R.S. Bulletin 20, 27–31.
Shbeeb, N.I. and Binienda, W.K. (1999). Analysis of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness. Engineering Fracture Mechanics 64, 693–720.
Yildirim, B. (2000). Nonlinear Thermal Stress and Fracture Analysis of Multilayer Structures using Enriched Fi-nite Elements, Department of Mechanical Engineering and Mechanics, Ph.D. Dissertation, Lehigh University, Bethlehem, Pennsylvania.
Yildirim, B. and Erdogan, F. (2004). Edge crack problems in homogeneous and functionally graded material thermal barrier coatings under uniform thermal loading. Journal of Thermal Stresses 27, 311–329.
Zienkiewicz, O.C. and Taylor, R.L. (2000). The Finite Element Method, Volume 1, The Basis, 5th edit., Butterworth – Heinemann, Woburn, MA, USA.
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Dag, S., Yildirim, B. & Erdogan, F. Interface crack problems in graded orthotropic media: Analytical and computational approaches. International Journal of Fracture 130, 471–496 (2004). https://doi.org/10.1023/B:FRAC.0000049497.81105.c4
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DOI: https://doi.org/10.1023/B:FRAC.0000049497.81105.c4