×

zbMATH — the first resource for mathematics

An axisymmetric problem of an embedded crack in a graded layer bonded to a homogeneous half-space. (English) Zbl 1194.74311
Summary: In an attempt to simulate non-uniform coating delamination, the elasto-static problem of a penny shaped axisymmetric crack embedded in a functionally graded coating bonded to a homogeneous substrate subjected to crack surface tractions is considered. The coating’s material gradient is parallel to the axisymmetric direction and is orthogonal to the crack plane. The graded coating is modeled as a non-homogeneous medium with an isotropic constitutive law. Using Hankel transform, the governing equations are converted into coupled singular integral equations, which are solved numerically to yield the crack tip stress intensity factors. The Finite Element Method was additionally used to model the crack problem. The main objective of this paper is to study the influence of the material non-homogeneity and the crack position on the stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.

MSC:
74R10 Brittle fracture
74G70 Stress concentrations, singularities in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Erdogan, F.: Fracture mechanics of functionally graded materials, Composites engineering 5, 753-770 (1995)
[2] Lanutti, J. J.: Functionally graded materials: properties, potential and design guidelines, Composites engineering 4, 81-94 (1994)
[3] Dhaliwal, R. S.; Singh, B. M.: On the theory of elasticity of a nonhomogeneous medium, Journal of elasticity 8, 211-219 (1978) · Zbl 0372.73015
[4] Delale, F.; Erdogan, F.: The crack problem for a nonhomogeneous plane, ASME journal of applied mechanics 50, 609-614 (1983) · Zbl 0542.73118
[5] Erdogan, F.: The crack problem for bonded nonhomogeneous materials under antiplane shear loading, ASME journal of applied mechanics 52, 823-828 (1985) · Zbl 0584.73125
[6] Ozturk, M.; Erdogan, F.: The axisymmetric crack problem in a nonhomogeneous medium, ASME journal of applied mechanics 44, 631-636 (1993) · Zbl 0774.73053
[7] Konda, N.; Erdogan, F.: Mixed mode crack problem in a nonhomogeneous elastic medium, Engineering fracture mechanics 47, 533-547 (1994)
[8] Jin, Z-H.; Noda, N.: Crack tip singular fields in nonhomogeneous materials, ASME journal of applied mechanics 61, 738-740 (1994) · Zbl 0825.73567
[9] Noda, N.; Jin, Z-H.: Steady thermal stresses in an infinite nonhomogeneous elastic solid containing a crack, Journal of thermal stresses 16, 181-196 (1993)
[10] El-Borgi, S.; Erdogan, F.; Hidri, L.: A partially insulated embedded crack in an infinite functionally graded medium under thermo-mechanical loading, International journal of engineering science 42, 371-393 (2004)
[11] Jin, Z-H.; Noda, N.: An internal crack parallel to the boundary of a nonhomogeneous half plane under thermal loading, International journal of engineering science 31, 793-806 (1993) · Zbl 0773.73073
[12] Jin, Z. -H.; Noda, N.: Transient thermal stress intensity factors for a crack in a semi-infinite plate of a functionally gradient material, International journal of solids structures 31, 203-218 (1994) · Zbl 0799.73055
[13] Lee, Y. D.; Erdogan, F.: Interface cracking of FGM coatings under steady state heat flow, Engineering fracture mechanics 59, 361-380 (1998)
[14] Chen, Y. F.; Erdogan, F.: The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate, Journal of mechanics and physics of solids 44, 771-787 (1996)
[15] El-Borgi, S.; Erdogan, F.; Ben Hatira, F.: Stress intensity factors for an interface crack between a functionally graded coating and a homogeneous substrate, International journal of fracture 123, 139-162 (2003)
[16] El-Borgi, S.; Hidri, L.; Abdelmoula, R.: An embedded crack in a graded coating bonded to a homogeneous substrate under thermo-mechanical loading, Journal of thermal stresses 29, 439-466 (2006)
[17] El-Borgi, S.; Keer, L.; Ben Said, W.: An embedded crack in a functionally graded coating bonded to a homogeneous substrate under frictional Hertzian contact, Wear, an international journal on the science and technology of friction, lubrication and wear 257, 760-776 (2004)
[18] El-Borgi, S.; Aloulou, W.; Zghal, A.: Buckling of a functionally graded coating with an embedded crack bonded to a homogeneous substrate, International journal of fracture 142, 137-150 (2006) · Zbl 1197.74039
[19] Aloulou, W.; Yildirim, B.; El-Borgi, S.; Zghal, A.: Buckling of an orthotropic graded coating with an embedded crack bonded to a homogeneous substrate, International journal of solids and structures 46, No. 9, 1890-1900 (2009) · Zbl 1217.74049
[20] Ozturk, M., 1992. Axisymmetric and anti-plane shear crack problem in bonded nonhomogeneous material. Ph.D. Thesis, Lehigh University, Department of Mechanical engineering and Mechanics 1992.
[21] Ozturk, M.; Erdogan, F.: Axisymmetric crack problem in bonded materials with a graded interfacial region, International journal of solids and structures 33, No. 2, 193-216 (1996) · Zbl 0929.74096
[22] Sahin, A., Erdogan, F., 1997. The axisymmetric crack problem in a semi-infinite nonhomogeneous medium. Master Thesis, Lehigh University, Department of Mechanical engineering and Mechanics, 1997.
[23] Erdogan, F.; Gupta, G.: On the numerical solutions of singular integral equations, Quarterly journal of applied mathematics 29, 525-534 (1972) · Zbl 0236.65083
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.