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ON AN ANTIPLANE CRACK PROBLEM FOR FUNCTIONALLY GRADED ELASTIC MATERIALS

Part of: Elliptic equations and systems Material properties given special treatment

Published online by Cambridge University Press:  21 April 2011

DAVID L. CLEMENTS
DAVID L. CLEMENTS*
Affiliation:
School of Mathematics, University of Adelaide, Adelaide, SA 5005, Australia (email: david.clements@adelaide.edu.au)
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Abstract

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This paper examines an antiplane crack problem for a functionally graded anisotropic elastic material in which the elastic moduli vary quadratically with the spatial coordinates. A solution to the crack problem is obtained in terms of a pair of integral equations. An iterative solution to the integral equations is used to examine the effect of the anisotropy and varying elastic moduli on the crack tip stress intensity factors and the crack displacement.

Keywords

crack problemsanisotropyfunctionally graded materials

MSC classification

Secondary: 35J25: Boundary value problems for second-order elliptic equations 74E10: Anisotropy
Type
Research Article
Information
The ANZIAM Journal , Volume 52 , Issue 1 , July 2010 , pp. 69 - 86
Copyright
Copyright © Australian Mathematical Society 2011

References

[1]Azis, M. I. and Clements, D. L., “A boundary element method for anisotropic inhomogeneous elasticity”, Internat. J. Solids Structures 38 (2001) 5747–5764.Google Scholar
[2]Bohr, H., “Cracks in functionally graded materials”, Math. Sci. Eng. A 362 (2003) 40–60.Google Scholar
[3]Chan, Y.-S., Paulino, G. and Fanning, A. C., “The crack problem for nonhomogeneous materials under antiplane shear loading—a displacement based formulation”, Internat. J. Solids Structures 38 (2001) 2989–3005.CrossRefGoogle Scholar
[4]Chen, Y. F. and Erdogan, F., “The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate”, J. Mech. Phys. Solids 44 (1996) 771–787.Google Scholar
[5]Chen, Y. Z., Lin, X. Y. and Wang, Z. X., “Antiplane elasticity crack problem for a strip of functionally graded materials with mixed boundary condition”, Mech. Res. Comm. 37 (2010) 50–53.Google Scholar
[6]Clements, D. L., Boundary value problems governed by second order elliptic systems (Pitman, Bath, 1981).Google Scholar
[7]Clements, D. L. and Ang, W. T., “On a generalised plane strain crack problem for inhomogeneous anisotropic elastic materials”, Internat. J. Engrg. Sci. 44 (2006) 273–284.Google Scholar
[8]Clements, D. L., Atkinson, C. and Rogers, C., “Antiplane crack problems for an inhomogeneous elastic material”, Acta Mech. 29 (1978) 199–211.Google Scholar
[9]Dag, S. and Erdogan, F., “A surface crack in a graded medium loaded by a sliding rigid stamp”, Eng. Fract. Mech. 69 (2002) 1729–1751.CrossRefGoogle Scholar
[10]Erdogan, F., “The crack problem for bonded nonhomogeneous materials under antiplane shear loading”, J. Appl. Mech. Trans. ASME 52 (1985) 823–828.CrossRefGoogle Scholar
[11]Erdogan, F. and Ozturk, M., “The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate”, Internat. J. Engrg. Sci. 30 (1992) 1507–1523.CrossRefGoogle Scholar
[12]Eshelby, J. D., Read, W. T. and Shockley, W., “Anisotropic elasticity with applications to dislocation theory”, Acta Metall. 1 (1953) 251–259.Google Scholar
[13]Gelbstein, Y., Daniel, M. P. and Dashevsky, Z., “Powder metallurgical processing of functionally graded p-Pb 1−xSn xTe materials for thermoelectric applications”, Phys. B: Condensed Matter 391 (2007) 256–265.Google Scholar
[14]Hassanin, H. and Jiang, K., “Functionally graded microceramic components”, Microelectron. Eng. 87 (2010) 1610–1613.Google Scholar
[15]Jin, Z.-H. and Batra, R. C., “Some basic fracture mechanics concepts in functionally graded materials”, J. Mech. Phys. Solids 44 (1996) 1221–1235.Google Scholar
[16]Konda, N. and Erdogan, F., “The mixed mode crack problem in a nonhomogeneous elastic medium”, Eng. Fract. Mech. (1994) 533–545.Google Scholar
[17]Noda, N., “Thermal stress in functionally graded materials”, J. Thermal Stresses 22 (1999) 477–512.Google Scholar
[18]Noda, N. and Wang, B. L., “Transient thermoelastic responses of functionally graded materials containing collinear cracks”, Eng. Fract. Mech. 69 (2002) 1791–1809.CrossRefGoogle Scholar
[19]Paulino, G., “Fracture of functionally graded materials”, Eng. Fract. Mech. 69 (2002) 1519–1520.CrossRefGoogle Scholar
[20]Pompe, W., Worch, H., Epple, M., Friess, W., Galinsky, M., Greil, P., Hempel, U., Scharnweber, D. and Schulte, K., “Functionally graded materials in biomedical applications”, Math. Sci. Eng. A 362 (2003) 40–60.Google Scholar
[21]Riedel, H., Kieback, B. and Neubrand, A., “Processing techniques for functionally graded materials”, Math. Sci. Eng. A 362 (2003) 81–105.Google Scholar
[22]Stroh, A. N., “Dislocations and cracks in anisotropic elasticity”, Philos. Mag. 3 (1958) 625–646.Google Scholar
[23]Zhang, X. H., Mai, Y. W. and Wang, B. L., “Functionally graded materials under severe thermal environments”, J. Amer. Ceram. Soc. 88 (2005) 683–690.Google Scholar