Abstract
The static crack problem of a functionally graded coating-substrate structure with an internal or edge crack perpendicular to the interface is investigated under an in-plane load. The structure is made up of a functionally graded coating with an internal or edge crack and a homogeneous substrate of finite thickness. The material properties are assumed to vary continuously from the coating to the substrate. By use of Fourier transform method, the mixed boundary value problem is reduced to a singular integral equation which can be solved numerically. During the analysis, a higher-order term is obtained in the asymptotic analysis of the singular kernel to improve the convergence efficiency of numerical integrals. The influences of material constants and the geometry parameters on the stress intensity factors (SIFs) are studied. In Part II of this paper, the transient response of the structure subjected to an in-plane impact is investigated.
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References
Anlas, G., Santare, M.H. and Lambros, J. (2000). Numerical calculation of stress intensity factors in functionally graded materials. International Journal of Fracture 104, 131–143.
Bao, G. and Wang, L. (1995). Multiple cracking in functionally graded ceramic/metal coatings. International Journal of Solids and Structures 32, 2853–2871.
Butcher, R.J., Rousseau, C.E. and Tippur, H.V. (1999). A functionally graded particulate composite: preparation, Measurements and Failure Analysis. Acta Mater. 47, 259–268.
Chen, Y.F. and Erdogan, F. (1996). The interface problem for a nonhomogeneous coating bonded to a homogeneous substrate. Journal Mechanical Physics Solids 44, 771–787.
Chi, S.H. and Chung Y.L. (2003). Cracking in coating-substrate composites with multi-layered and FGM coatings. Engineering Fracture Mechanics 70, 1227–1243.
Choi, H.J. (1996a). An analysis of cracking in a layered medium with a functionally graded nonhomogeneous interface. ASME, Journal of Applied Mechanics 63, 479–486.
Choi, H.J. (1996b). Bonded dissimilar strips with a crack perpendicular to the functionally graded interface. International Journal of Solids and Structures 33, 4101–4117.
Choi, H.J., Jin, T.E. and Lee, K.Y. (1998). Collinear cracks in a layered half-plane with a graded nonhomogeneous interfacial zone-Part I: Mechanical response. International Journal of Fracture 94, 103–122.
Delale, F. and Erdogan, F. (1983). The crack problem for a nonhomogeneous plane. Journal of Applied Mechanics 50, 609–614.
Delale, F. and Erdogan, F. (1988). On the Mechanical modeling of the interfacial region in bonded half-planes. Journal of Applied Mechanics 55, 317–324.
Erdogan, F. and Gupta, G.D. (1972). On the numerical solution of singular integral equations. Quarterly of Applied Mathematics 30, 525–534.
Erdogan, F. and Ozturk, M. (1995). Periodic cracking of functionally graded coatings. International Journal Engeneering Science 33, 2179–2195.
Erdogan, F. and Wu, B.H. (1996). Crack problem in functionally graded material layers under thermal stresses. Journal of Thermal Stresses 19, 237–265.
Erdogan, F. and Wu, B.H. (1997). The surface crack problem for a plate with functionally graded properties. Journal of Applied Mechanics 64, 449–456.
Huang, G.Y., Wang, Y.S. and Gross, D. (2002). Fracture analysis of functionally graded coatings: antiplane deformation. European Journal of Mechanics A/Solids 21, 391–400.
Itou, S. (2001). Stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes. International Journal of Fracture 110, 123–135.
Jin, Z.H. and Noda, N. (1994). Crack-tip singular fields in nonhomogeneous materials. Journal of Applied Mechanics 61, 738–740.
Kadioglu, S., Dag, S. and Yahsi, S. (1998). Crack problem for a functionally graded layer on an elastic foundation. International Journal of Fracture 94, 63–77.
Kawasaki, A. and Watanabe, R. (2002). Thermal fracture behavior of metal/ceramic functionally graded materials. Engineering Fracture Mechanics 69, 1713–1728.
Marur, P.R. and Tippur, H.V. (2000). Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient. International Journal Solids Structures 37, 5353–5370.
Rousseau, C.E. and Tippur, H.V. (2000). Compositionally graded materials with cracks normal to the elastic gradient. Acta Materials 48, 4021–4033.
Shbeeb, N.I., Binienda, W.K. and Kreider, K. (1999a). Analysis of the driving force for multiple cracks in an infinite nonhomogeneous plate, Part I: theoretical analysis. Journal of Applied Mechanics 66, 492–500.
Shbeeb, N.I., Binienda, W.K. and Kreider, K. (1999b). Analysis of the driving force for multiple cracks in an infinite nonhomogeneous plate, Part II: numerical solutions. Journal of Applied Mechanics 66, 501–506.
Ueda, S. and Shindo, Y. (2000). Crack kingking in functionally graded materials due to an initial strain resulting from stress relation. Journal of Thermal Stresses 23, 285–290.
Ueda, S. (2001). The surface crack problem for a layered plate with a functionally graded nonhomogeneous interface. International Journal of Fracture 110, 189–204.
Wang, B.L., Mai, Y.W. and Noda, N. (2002). Fracture mechanics analysis model for functionally graded materials with arbitrarily distributed properties. International Journal of Fracture 116, 161–177.
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Guo, LC., Wu, LZ., Ma, L. et al. Fracture analysis of a functionally graded coating-substrate structure with a crack perpendicular to the interface - Part I: Static problem. International Journal of Fracture 127, 21–38 (2004). https://doi.org/10.1023/B:FRAC.0000035049.26772.2d
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DOI: https://doi.org/10.1023/B:FRAC.0000035049.26772.2d