On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: plane deformation
Source abstract
Abstract
A new multi-layered model is developed for a functionally graded interfacial zone between two dissimilar elastic solids based on the fact that an arbitrary curve can be approached by a continuous but piecewise linear curve. The interfacial zone with both Young’s modulus and Poisson’s ratio varying continuously in an arbitrary manner is divided into multiple layers with the material properties varying linearly in each sub-layer and continuous at the interfaces between sub-layers. With this new model, we analyze the problem of a Griffith crack in the interfacial zone under plane stress-state deformation. The transfer matrix method and Fourier integral transform technique are used to reduce the mixed boundary-value problem to a set of Cauchy singular integral equations. The stress intensity factors are calculated. The paper compares the new model to other existing models and discusses its advantages.
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Research context
OpenAlex topics: Numerical methods in engineering · Composite Material Mechanics · Mechanical Behavior of Composites
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References (30)
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1. Choi, H.J., Lee, K.Y. and Jin, T.E. (1998a). Collinear cracks in a layered half-plane with a graded nonhomogeneous interfacial zone-Part I: mechanical response. International Journal of Fracture 94, 103–122.10.1023/A:1007524104202 ↗
2. Choi, H.J., Jin, T.E. and Lee, K.Y. (1998b). Collinear cracks in a layered half-plane with a graded nonhomogeneous interfacial zone-Part II: thermal shock response. International Journal of Fracture 94, 123–135.10.1023/A:1007572020132 ↗
3. Craster, R.V. and Atkinson, C. (1994). Mixed boundary value problems in non-homogenerous elastic materials. Quarterly Journal of Mathematics 47, 183–206.
4. Delale, F. and Erdogan, F. (1988). On the mechanical modeling of the interfacial region in bonded half-planes. Journal of Applied Mechanics 55, 317–324.10.1115/1.3173677 ↗
5. Dhaliwal, R.S., Saxena, H.S. and He, W.H. (1992). Stress intensity factor for the cylindrical interface crack between nonhomogeneous coaxial finite elastic cylinders, Engineering Fracture Mechanics 43, 1039–1051.10.1016/0013-7944(92)90033-B ↗
6. Erdogan, F. (1995). Fracture-mechanics of functionally graded materials. Composite Engineering 5, 753–770.10.1016/0961-9526(95)00029-M ↗
7. Erdogan, F. and Gupta, G.D. (1972). On the numerical solution of singular integral equations. Quarterly Journal of Applied Mathematics 29, 525–534.10.1090/qam/408277 ↗
8. Erdogan, F., Kaya, A.C. and Joseph, P.F. (1991). The mode-III crack problem in bonded materials with a nonhomogeneous interfacial zone. Journal of Applied Mechanics 58, 419–427.10.1115/1.2897202 ↗
9. Ewing, W.M., Jardetzky, W.S. and Press, F. (1957). Elastic Waves in Layered Media, McGraw-Hill, New York.
10. Fildis, H. and Yahsi, O.S. (1996). The axisymmetric crack problem in a non-homogeneous interfacial region between homogeneous half-spaces. International Journal of Fracture 78, 139–164.10.1007/BF00034523 ↗
11. Fildis, H. and Yahsi, O.S. (1997). The mode III axisymmetric crack problem in a non-homogeneous interfacial region between homogeneous half-spaces. International Journal of Fracture 85, 35–45.10.1023/A:1007397402482 ↗
12. Huang, G.Y., Wang, Y.S. and Gross, D. (2002). Fracture analysis of functionally graded coatings: antiplane deformation. European Journal Mechanics A/Solids 21, 391–400.10.1016/S0997-7538(02)01223-8 ↗
13. Itou, S. and Shima, Y. (1999). Stress intensity factors around a cylindrical crack in an interfacial zone in composite materials. International Journal of Solids Structures 36, 697–709.10.1016/S0020-7683(98)00041-9 ↗
14. Jin, Z.-H. and Noda, N. (1994). Crack-tip singular fields in nonhomogeneous materials. Journal of Applied Mechanics 61, 738–740.10.1115/1.2901529 ↗
15. Kim, J.H. and Paulino, G.H. (2003). The interaction integral for fracture of orthotropic functionally graded materials: evaluation of stress intensity factors. International Journal of Solids and Structures 40, 3967–4001.10.1016/S0020-7683(03)00176-8 ↗
16. Nozaki, H. and Shindo, Y. (1998). Effect of interface layers on elastic wave propagation in a fiber-reinforced metal-matrix composite. International Journal of Engineering Science 36, 383–394.10.1016/S0020-7225(97)00083-9 ↗
17. Ozturk, M. and Erdogan, F. (1993). Antiplane shear crack problem in bonded materials with a graded interfacial zone. International Journal of Engineering Science 31, 1641–1657.10.1016/0020-7225(93)90080-E ↗
18. Ozturk, M. and Erdogan, F. (1995). An axisymmetrical crack in bonded materials with a nonhomogeneous interfacial zone under torsion. Journal of Applied Mechanics 62, 116–125.10.1115/1.2895891 ↗
19. Ozturk, M. and Erdogan, F. (1996). Axisymmetric crack problem in bonded materials with a graded interfacial region. International Journal of Solids and Structures 33, 193–219.10.1016/0020-7683(95)00034-8 ↗
20. Rao, B.N. and Rahman, S. (2003). Meshfree analysis of cracks in isotropic functionally graded materials. Engineering Fracture Mechanics 70, 1–27.10.1016/S0013-7944(02)00038-3 ↗
21. Rao, B.N. and Rahman, S. (2003). An interaction integral method for analysis of cracks in orthotropic functionally graded materials. Computational Mechanics 32, 40–51.10.1007/s00466-003-0460-1 ↗
22. 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, 693–720.10.1016/S0013-7944(99)00099-5 ↗
23. Shbeeb, N.I., Binienda, W.K. and Kreider, K. (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, 23–50.10.1023/A:1007671920395 ↗
24. Sladek, J., Sladek, V. and Atluri, S.N. (2000). Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties. Computational Mechanics 24, 456–462.10.1007/s004660050005 ↗
25. Slater, L.J. (1960). Confluent Hypergeometric Functions, Cambridge University Press, Cambridge.
26. Wang, X.Y., Wang, D. and Zou, Z.Z. (1996). On the griffith crack in a nonhomogeneous interlayer of adjoining two different elastic materials. International Journal of Fracture 79, R51–R56.10.1007/BF00019385 ↗
27. Wang, B.L., Han, J.C. and Du, S.Y. (1999). Dynamic response for functionally graded materials with penny-shaped cracks. Acta Mechanica Solida Sinica 12, 106–113.
28. Wang, Y.S. and Gross, D. (2000). Analysis of a crack in a functionally gradient interface layer under static and dynamic loading. Key Engineering Materials 183-187, 331–336.10.4028/www.scientific.net/KEM.183-187.331 ↗
29. Wang, Y.S., Huang, G.Y. and Gross, D. (2003). On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: anti-plane deformation. Journal of Applied Mechanics 70, 676–680.10.1115/1.1598476 ↗
30. Yue, Z.Q., Xiao, H.T. and Tham, L.G. (2003). Boundary element analysis of crack problems in functionally graded materials. International Journal of Solids and Structures 40, 3273–3291.10.1016/S0020-7683(03)00094-5 ↗