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Crack propagating in a functionally graded strip under the plane loading

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Abstract

In the present paper, a finite crack with constant length (Yoffe type crack) propagating in the functionally graded strip under the plane loading is investigated by means of the Schmidt method. By using the Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of the material properties, the thickness of the functionally graded strip, and speed of the crack propagating upon the dynamic fracture behavior.

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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.

    Article  Google Scholar 

  • Babaei, R. and Lukasiewicz, S.A. (1998). Dynamic response of a crack in a functionally graded material between two dissimilar half places under anti-plane impact load. Engineering Fracture Mechanics 60, 479–487.

    Article  Google Scholar 

  • Bi, X.S., Cheng, J. and Chen, X.L. (2003). Moving crack for functionally graded material in an infinite length strip under antiplane shear. Theoretical and Applied Fracture Mechanics 39, 89–97.

    Article  Google Scholar 

  • Butcher, R.J., Rousseau, C.E. and Tippur, H.V. (1999). A functionally graded particulate composite: preparation, measurements and failure analysis. Acta Materialia 47 259–268.

    Google Scholar 

  • Carpenter, R.D., Liang, W.W., Paulino, G.H., Gibeling, J.C. and Munir, Z.A. (1999). Fracture testing and analysis of a layered functionally graded Ti/TiB beam in 3-point bending. Materials Science Forum 308-311, 837–842.

    Google Scholar 

  • Carpenter, R.D., Paulino, G.H., Munir, Z.A. and Gibeling, J.C. (2000) A novel technique to generate sharp cracks in metallic/ceramic functionally graded materials by reverse 4-point bending. Scripta Materialia 43, 547–552.

    Article  Google Scholar 

  • Chen, J., Liu, Z. and Zou, Z. (2002). Transient internal crack problem for a nonhomogeneous orthotropic strip (mode I). International Journal of Engineering Science 40, 1761–1774.

    Google Scholar 

  • Chen, J., Liu, Z. and Zou, Z. (2003). Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes. Archive of Applied Mechanics 72, 686–696.

    Google Scholar 

  • Chen, J., Liu, Z. and Zou, Z. (2003). Electromechanical impact of a crack in a functionally graded piezoelectric medium. Theoretical and Applied Fracture Mechanics 39, 47–60.

    Google Scholar 

  • Chiang, C.R. (1989). Mode III interface crack propagation. Engineering Fracture Mechanics 32, 545–550.

    Article  Google Scholar 

  • Choi, H.J. (2001). The problem for bonded half-planes containing a crack at an arbitrary angle to the graded interfacial zone. International Journal of Solids and Structures 38, 6559–6588.

    Article  MATH  Google Scholar 

  • Delale, F. and Erdogan, F. (1983). The crack problem for a nonhomogeneous plane. Journal of Applied Mechanic 50, 609–614.

    Google Scholar 

  • Delale, F. and Erdogan, F. (1988). On the mechanical modeling of the interfacial region in bonded half-planes. ASME Journal of Applied Mechanics 55, 317–324.

    Google Scholar 

  • Dhaliwal, R.S., He, W., Saxena, H.S. and Rokne, J.G. (1992). A moving Griffith crack at the interface of two dissimilar elastic layers. Engineering Fracture Mechanics 43, 923–930.

    ADS  Google Scholar 

  • Erdelyi, A. (ed.). (1954). Table of the integral transforms, Vol. 1, McGraw-Hill, New York.

    Google Scholar 

  • Gradshteyn, I.S. and Ryzhik, I.M. (1980). Table of Integral, Series and Products, Academic Press, New York.

    Google Scholar 

  • Itou, S. (1978). Three dimensional waves propagation in a cracked elastic solid. ASME Journal of Applied Mechanics 45, 807–811.

    MATH  Google Scholar 

  • Itou, S. (1997). Dynamic stress intensity factors around two parallel cracks in an infinite-orthotropic plane subjected to incident harmonic stress waves. International Journal of Solids and Structures 34, 1145–1165.

    Article  MATH  Google Scholar 

  • Jiang, L.Y. and Wang, X.D. (2002). On the dynamic propagation in an interphase with spatially varying elastic properties under inplane loading. International Journal of Fracture 114, 225–244.

    Article  Google Scholar 

  • Jin, Z.H. and Batra, R.C. (1996). Some basic fracture mechanics concepts in functionally graded materials. Journal of Mechanics Physics and Solids 44, 1221–1235.

    Google Scholar 

  • Koizumi, M. (1993). The concept of FGM. In: Ceramic Transactions (Edited by Holt, J.B., et al.) Vol. 34. Functionally Graded Materials. American Ceramic Society, Ohio, pp. 3–10.

    Google Scholar 

  • Konda, N. and Erdogan, F. (1994). The mixed mode crack problem in a nonhomogeneous elastic plane. Engineering Fracture Mechanics 47, 533–545.

    Article  Google Scholar 

  • Lee, Y.D. and Erdogen, F. (1994). Residual/thermal stress in FGM and laminated thennal barrier coating. International Journal of Fracture 69, 145–165.

    Google Scholar 

  • Li, H., Lambros, J., Cheeseman, B.A. and Santare, M.H. (2000). Experimental investigation of the quasi-static fracture of functionally graded materials. International Journal of Solids and Structures 37, 3715–3732.

    Google Scholar 

  • Ma, L. Wu, L.Z. and Guo., L.C. (2002). Dynamic behavior of two collinear anti-plane shear cracks in a functionally graded layer bonded to dissimilar half planes. Mechanics Research Communications 29, 207–215.

    Article  Google Scholar 

  • Marur, P.R. and Tippur, H.V. (1998). Evaluation of mechanical properties of functionally graded materials. Journal of Testing and Evaluation 26, 539–545.

    Google Scholar 

  • 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 of Solids and Structures 37, 5353–5370.

    Google Scholar 

  • Meguid, S.A. Wang, X.D. and Jiang, L.Y. (2002). On the dynamic propagation of a finite crack in functionally graded materials. Engineering Fracture mechanics 69, 1753–1768.

    Article  Google Scholar 

  • Morse, P.M. and Feshbach, H. (1958). Methods of Theoretical Physics, Vol. 1. McGraw-Hill, New York.

    Google Scholar 

  • Nakagaki, M., Sasaki, H. and Hagihara, S. (1995). A study of crack in functionally graded material under dynamic loading. ASME Pressure Vessels and Piping Division (Publication) PVP, Dynamic Fracture, Failure and Deformation. 300, 1–6.

    Google Scholar 

  • Parameswaran, V. and Shukla, A. (1998). Dynamic fracture of a functionally gradient material having discrete property variation. Journal of Materials Science 33, 3303–3311.

    Article  Google Scholar 

  • Parameswaran, V. and Shukla, A. (1999). Crack-tip stress fields for dynamic fracture in functionally gradient materials. Mechanics of Materials 31, 579–596.

    Article  Google Scholar 

  • Rousseau, C.E. and Tippur, H.V. (2000). Compositionally graded materials with cracks normal to the elastic gradient. Acta Materialia 48, 4021–4033.

    Article  Google Scholar 

  • Shbeeb, N.I., Binenda, W.K. and Kreider, K.L. (1999). Analysis of the driving forces for multiple cracks in an infinite nonhomogeneous plate, Part I: theoretical analysis. Journal of Applied Mechanics 66, 492–500.

    Google Scholar 

  • Shbeeb, N.I., Binenda, W.K. and Kreider, K.L. (1999). Analysis of the driving forces for multiple cracks in an infinite nonhomogeneous plate, Part II: numerical solution. Journal of Applied Mechanics 66, 501–505.

    Google Scholar 

  • Shbeeb, N.I., Binenda, W.K. and Kreider, K.L. (2000). Analysis of the driving force for a generally oriented crack in a functionally graded strip sandwiched between two homogeneous half planes. International Journal of Fracture 104, 23–50.

    Article  Google Scholar 

  • Sih, G.C. and Chen, E.P. (1972). Crack propagation in s strip of material under plane extension. International Journal of Engineering Science 10, 537–551.

    Article  Google Scholar 

  • Sih, G.C. and Chen, E.P. (1982). Moving cracks in layered composites. International Journal of Engineering Science 20, 1181–1192.

    Article  Google Scholar 

  • Suresh, S. and Mortensen, A. (1997). Functionally graded metals and metal-ceramic composites: part 2 thermomechanical behavior. International Materials Reviews 29, 306–312.

    Google Scholar 

  • Yau, W.F. (1967). Axisymmetric slipless indentation of an infinite elastic cylinder. SIAA Journal of Applied Mathematics 15, 219–227.

    MATH  Google Scholar 

  • Wang, B.L., Han, J.C. and Du, S.Y. (2000). Crack problem for non-homogeneous composite materials subjected to dynamic loading. International Journal of Solids and Structures 37, 1251–1274.

    Google Scholar 

  • Wang, X.D. and Meguid, S.A. (1994). On the dynamic crack propagation in an interface with spatially varying elastic properties. International Journal of Fracture 69, 87–99.

    Google Scholar 

  • Yoffe, E.H. (1951). The moving Griffith crack. Philosophical Magazine 7, 739–750.

    MathSciNet  Google Scholar 

  • Zhou, Z.G. and Shen, Y.P. (1999). Investigation of the scattering of harmonic shear waves by two collinear cracks using the non-local theory. ACTA Mechanica 135, 169–179.

    Article  Google Scholar 

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Authors and Affiliations

  1. Center for Composite Materials, Harbin Institute of Technology, Harbin, 150001, P.R. China

    Li Ma, Lin-Zhi Wu, Zhen-Gong Zhou & Tao Zeng

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  1. Li Ma
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  2. Lin-Zhi Wu
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  3. Zhen-Gong Zhou
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  4. Tao Zeng
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Ma, L., Wu, LZ., Zhou, ZG. et al. Crack propagating in a functionally graded strip under the plane loading. International Journal of Fracture 126, 39–55 (2004). https://doi.org/10.1023/B:frac.0000025301.01917.9f

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  • DOI: https://doi.org/10.1023/B:frac.0000025301.01917.9f

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