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

  • N. Muthu (a1), S. K. Maiti (a2), B. G. Falzon (a3) and I. Guiamatsia (a4)
Abstract
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.

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Corresponding author
brian.falzon@monash.edu
References
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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.
2. Mortensen A. and Suresh S. Functionally graded metals and metal-ceramic composites: Part 1 Processing, Int Material Reviews, 1995, 30, pp 8393.
3. Cherradi N., Kawasaki A. and Gasik M. Worldwide trends in functional gradient materials research and development, Composites Engineering, 1994, 8, pp 883–94.
4. Neubrand A. and Rode J. Gradient materials: An overview of a novel concept, Zeitschrift Fur Metallkunde, 1997, 88, pp 358–71.
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.
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.
7. Li C., Zou Z. and Duan Z. Stress intensity factors for functionally graded solid cylinders, Engineering Fracture Mechanics, 1999, 63, pp 735–49.
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.
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.
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.
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.
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.
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.
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.
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.
16. Rao B.N. and Rahman S. Mesh-free analysis of cracks in isotropic functionally graded materials, Engineering Fracture Mechanics, 2003, 70, pp 127.
17. Delale F. and Erdogan F. The crack problem for a nonhomogeneous plane, J Applied Mechanics, 1983, 50, pp 609614.
18. Erdogan F. Stress intensity factors, J Applied Mechanics, 1983, 50, pp 9921002.
19. Eischen J.W. Fracture of nonhomogeneous materials, Int J of Fracture, 1987, 34, pp 322.
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.
21. Watwood V.B. The finite element method for prediction of crack behaviour, Nuclear Engineering and Design, 1969, 11, pp 323332.
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.
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.
24. Raju I.S. Calculation of strain-energy release rates with higher order and singular finite elements, Engineering Fracture Mechanics, 1987, 28, pp 251274.
25. Maiti S.K. Finite element computation of crack closure integrals and stress intensity factors, Engineering Fracture Mechanics, 1992, 41, pp 339348.
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.
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.
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.
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.
30. Lancaster P. and Salkauskas K. Surfaces generated by moving least square methods, Mathematics of Computation, 1981, 37, pp 141158.
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.
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.
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.
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.
35. Dundurs J. Edge-bonded dissimilar orthogonal elastic wedges, ASME J Applied Mechanics, 1969, 36, pp 650–2.
36. Williams M.L. On the stress distribution at the base of a stationary crack, ASMe J Applied Mechanics, 1957, 24, pp 109–14.
37. Anderson T.L. Fracture Mechanics, Fundamentals and Applications, Second edition, 1995, CRC, New York, USA.
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