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Computation of stress intensity factors in functionally graded materials using partition-of-unity meshfree method

Published online by Cambridge University Press:  27 January 2016

N. Muthu
Affiliation:
IITB-Monash Research Academy, IIT Bombay Powai, India
S. K. Maiti
Affiliation:
Department of Mechanical Engineering, IIT Bombay Powai, India
B. G. Falzon*
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Australia
I. Guiamatsia
Affiliation:
School of Civil Engineering, The University of Sydney, Sydney, Australia

Abstract

This paper describes the computation of stress intensity factors (SIFs) for cracks in functionally graded materials (FGMs) using an extended element-free Galerkin (XEFG) method. The SIFs are extracted through the crack closure integral (CCI) with a local smoothing technique, non-equilibrium and incompatibility formulations of the interaction integral and the displacement method. The results for mode I and mixed mode case studies are presented and compared with those available in the literature. They are found to be in good agreement where the average absolute error for the CCI with local smoothing, despite its simplicity, yielded a high level of accuracy.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2012 

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References

1. Marin, L. Numerical solution of the Cauchy problem for steady-state heat transfer in two dimensional functionally graded material, Int J Solids and Structures, 2005, 42, pp 4338–51.Google Scholar
2. Mortensen, A. and Suresh, S. Functionally graded metals and metal-ceramic composites: Part 1 Processing, Int Material Reviews, 1995, 30, pp 8393.Google Scholar
3. Cherradi, N., Kawasaki, A. and Gasik, M. Worldwide trends in functional gradient materials research and development, Composites Engineering, 1994, 8, pp 883–94.Google Scholar
4. Neubrand, A. and Rode, J. Gradient materials: An overview of a novel concept, Zeitschrift Fur Metallkunde, 1997, 88, pp 358–71.Google Scholar
5. Shanmugavel, P. and Bhaskar, G.B., Chandrasekaran, M, Mani, P.S. and Srinivasan, S.P. An overview of fracture analysis in functionally graded materials, European J Scientific Research, 2012, 68, pp 412439.Google Scholar
6. Tilbrook, M.T., Moon, R.J. and Hoffman, M. Finite element simulations of crack propagation in functionally graded material under flexural loading, Engineering Fracture Mechanics, 2005, 72, pp 2444–67.Google Scholar
7. Li, C., Zou, Z. and Duan, Z. Stress intensity factors for functionally graded solid cylinders, Engineering Fracture Mechanics, 1999, 63, pp 735–49.Google Scholar
8. Kim, J.H. and Paulino, G.H. Finite element evaluation of mixed mode stress intensity factors in functionally graded materials, Int J Numerical Methods in Engineering, 2002, 53, pp 1903–35.Google Scholar
9. Moës, N., Dolbow, J. and Belytschko, T. A finite element for crack growth without remeshing, Int J Numerical Methods in Eng, 1999, 46, pp 131150.Google Scholar
10. Nguyen, V.P., Rabczuk, T., Bordas, S. and Duflot, M. Meshless methods: A review and computer implementation aspects, Mathematica and Computers in Simulation, 2008, 79, pp 763813.Google Scholar
11. Comi, C. and Mariani, S. Extended finite element simulation of quasi-brittle fracture in functionally graded materials, Computer Methods in Applied Mechanics and Eng, 2007, 196, pp 40134026.Google Scholar
12. Belytschko, T., Gu, L. and Lu, Y.Y. Fracture and crack growth by element-free Galerkin methods, Modelling and Simulation Material Science Eng, 1994, 2, pp 519534.Google Scholar
13. Ventura, G., Xu, J.X. and Belytschko, T. A vector level set method and new discontinuity approximations for crack growth by EFG, Int J Numerical Methods in Eng, 2002, 54, pp 923944.Google Scholar
14. Ching, H.K. and Yen, S.C. Meshless local Petrov-Galerkin analysis for 2d functionally graded elastic solids under mechanical and thermal loads, Composites Part B: Engineering, 2005, 36, pp 223240.Google Scholar
15. Gilhooley, D.F., Xiao, J.R., Batra, R.C., McCarthy, M.A. and Gillespie, J.W. Two-dimensional stress analysis of functionally graded solids using the MLPG method with radial basis functions, Computational Materials Science, 2008, 41, pp 467481.Google Scholar
16. Rao, B.N. and Rahman, S. Mesh-free analysis of cracks in isotropic functionally graded materials, Engineering Fracture Mechanics, 2003, 70, pp 127.Google Scholar
17. Delale, F. and Erdogan, F. The crack problem for a nonhomogeneous plane, J Applied Mechanics, 1983, 50, pp 609614.Google Scholar
18. Erdogan, F. Stress intensity factors, J Applied Mechanics, 1983, 50, pp 9921002.Google Scholar
19. Eischen, J.W. Fracture of nonhomogeneous materials, Int J of Fracture, 1987, 34, pp 322.Google Scholar
20. Chan, S.K., Tuba, I.S. and Wilson, W.K. On the finite element method in linear fracture mechanics, Engineering Fracture Mechanics, 1970, 30, pp 227231.Google Scholar
21. Watwood, V.B. The finite element method for prediction of crack behaviour, Nuclear Engineering and Design, 1969, 11, pp 323332.Google Scholar
22. Rice, J.R. A path independent integral and the approximate analysis of strain concentration by notches and cracks, J Applied Mechanics, 1968, 35, pp 379386.Google Scholar
23. Rybicki, E.F. and Kanninen, M.F. A finite element calculation of stress intensity factors by a modified crack closure integral, Engineering Fracture Mechanics, 1977, 9, pp 931938.Google Scholar
24. Raju, I.S. Calculation of strain-energy release rates with higher order and singular finite elements, Engineering Fracture Mechanics, 1987, 28, pp 251274.Google Scholar
25. Maiti, S.K. Finite element computation of crack closure integrals and stress intensity factors, Engineering Fracture Mechanics, 1992, 41, pp 339348.Google Scholar
26. Yau, J.F., Wang, S.S. and Corten, H.T. A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity, J Applied Mechanics, 1980, 47, pp 335364.Google Scholar
27. Kim, J-H. and Paulino, G.H. Consistent Formulations of the interaction integral method for fracture of functionally graded materials, J Applied Mechanics, 2005, 72, pp 351–41.Google Scholar
28. Xueping, C., Jun, L. and Shirong, L. EFG virtual crack closure technique for the determination of stress intensity factor, Advanced Materials Research, 2011, 250-253, pp 37523758.Google Scholar
29. Guiamatsia, I., Falzon, B., Davies, G.A.O. and Iannucci, L. Element-free Galerkin modelling of composite damage, Composites Science and Technology, 2009, 69, pp 26402648.Google Scholar
30. Lancaster, P. and Salkauskas, K. Surfaces generated by moving least square methods, Mathematics of Computation, 1981, 37, pp 141158.Google Scholar
31. Maiti, S.K., Mukhopadhyay, N.K. and Kakodkar, A. Boundary element method based computation of stress intensity factor by modified crack closure integral, Computational Mechanics, 1997, 19, pp 203210.Google Scholar
32. Dolbow, J.E. and Gosz, M. On the computation of mixed-mode stress intensity factors in functionally graded materials, Int J of Solids and Structures, 2002, 39, pp 2557–74.Google Scholar
33. Erdogan, F. and Wu, B.H. The surface crack problem for a plate with functionally graded properties, J Applied Mechanics, 1997, 64, pp 449–56.Google Scholar
34. Chen, J., Wu, L. and Du, S. Element free Galerkin methods for fracture of functionally graded materials, Key Engineering Materials, 2000, 183–187, pp 487–92.Google Scholar
35. Dundurs, J. Edge-bonded dissimilar orthogonal elastic wedges, ASME J Applied Mechanics, 1969, 36, pp 650–2.Google Scholar
36. Williams, M.L. On the stress distribution at the base of a stationary crack, ASMe J Applied Mechanics, 1957, 24, pp 109–14.Google Scholar
37. Anderson, T.L. Fracture Mechanics, Fundamentals and Applications, Second edition, 1995, CRC, New York, USA.Google Scholar