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XFEM simulation of cracks, holes and inclusions in functionally graded materials

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Abstract

The present work aims at the numerical simulation of inhomogeneities/discontinuities (cracks, holes and inclusions) in functionally graded materials (FGMs) using extended finite element method (XFEM). A FGM with unidirectional gradation in material properties is modeled under plane strain condition. The domain contains a major crack either at the center or at the edge of the domain along with multiple minor discontinuities/flaws such as minor cracks and/or voids/inclusions distributed all over the domain. The effect of the variation in stress intensity factor (SIF) of the major crack due to the presence of the minor cracks and voids/inclusions is studied in detail. The simulations show that the presence of minor discontinuities significantly affects the values of SIFs.

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References

  • Bordas, S., Nguyen, P., Dunant, C., Guidoum, A., Dang, H.: An extended finite element library. Int. J. Numer. Methods Eng. 71, 703–732 (2007)

    Article  MATH  Google Scholar 

  • Carpinteri, A., Paggi, M., Pugno, N.: An analytical approach for fracture and fatigue in functionally graded materials. Int. J. Fract. 141, 535–547 (2006)

    Article  MATH  Google Scholar 

  • Chen, S.C., Wang, T.C.: Finite element solutions for plane strain mode-I crack with strain gradient effects. Int. J. Solids Struct. 39, 1241–1257 (2002)

    Article  MATH  Google Scholar 

  • Cheng, Z., Zhong, Z.: Analysis of a moving crack in a functionally graded strip between two homogeneous layers. Int. J. Mech. Sci. 49, 1038–1046 (2007)

    Article  Google Scholar 

  • Cheng, Z., Gao, D., Zhong, Z.: Crack propagating in functionally graded coating with arbitrarily distributed material properties bonded to a homogeneous substrate. Acta Mech. Solida Sin. 23, 437–446 (2011)

    Google Scholar 

  • Chudnovsky, A., Kachanov, M.: Interaction of a crack with a field of micro cracks. Appl. Eng. Sci. 21, 1009–1018 (1983)

    MATH  Google Scholar 

  • Comi, C., Mariani, S.: Extended finite element simulation of quasi-brittle fracture in functionally graded materials. Comput. Methods Appl. Mech. Eng. 196, 4013–4026 (2007)

    Article  MATH  Google Scholar 

  • Dag, S., Yildirim, B., Sarikaya, D.: Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads. Int. J. Solids Struct. 44, 7816–7840 (2007)

    Article  MATH  Google Scholar 

  • Dolbow, J.E., Gosz, M.: On the computation of mixed-mode stress intensity factors in functionally graded materials. Int. J. Solids Struct. 39, 2557–2574 (2002)

    Article  MATH  Google Scholar 

  • Gong, S.X., Horii, H.: General solution to the problem of micro cracks near the tip of a main crack. J. Mech. Phys. Solids 37, 27–46 (1989)

    Article  MATH  Google Scholar 

  • Gong, S.X., Meguid, S.A.: A general solution to the antiplane problem of an arbitrarily located elliptical hole near the tip of a main crack. Int. J. Solids Struct. 28, 249–263 (1991)

    Article  MATH  Google Scholar 

  • Guo, L.-C., Noda, N.: Modeling method for a crack problem of functionally graded materials with arbitrary properties-piecewise exponential model. Int. J. Solids Struct. 44, 6768–6790 (2007)

    Google Scholar 

  • Huang, G.Y., Wang, Y.S., Dietmar, G.: Fracture analysis of functionally graded coatings: plane deformation. Eur. J. Mech. A Solids 22, 535–544 (2003)

    Article  MATH  Google Scholar 

  • Lee, S., Song, J., Yoon, Y., Zi, G., Belytschko, T.: Combined extended and superimposed finite element method for cracks. Int. J. Numer. Methods Eng. 59, 1119–1136 (2009)

    Article  Google Scholar 

  • Ma, J., Zhong, Z., Zhang, C.: Analysis of a crack in a functionally graded strip with a power form shear modulus. Acta Mech. Solida Sin. 22(5), (2009)

  • Meguid, S.A., Gaultier, P.E., Gong, S.X.: A comparison between analytical and finite element analysis of main crack-micro crack interaction. Eng. Fract. Mech. 38, 451–465 (1991)

    Article  Google Scholar 

  • Meguid, S.A., Gong, S.X.: Stress concentration around interacting circular holes: a comparison between theory and experiments. Eng. Fract. Mech. 44, 247–256 (1993)

    Article  Google Scholar 

  • Meguid, S.A., Wang, X.D.: The dynamic interaction of a micro crack with a main crack under antiplane loading. Int. J. Solids Struct. 31, 1085–1097 (1994)

    Article  MATH  Google Scholar 

  • Meguid, S.A., Zhu, Z.-H.: A novel finite element for treating inhomogeneous solids. Int. J. Numer. Methods Eng. 38, 1579–1592 (1995a)

    Article  MATH  Google Scholar 

  • Meguid, S.A., Zhu, Z.-H.: Stress distribution in dissimilar materials containing inhomogeneities near the interface using novel finite element. Finite Elem. Anal. Des. 20, 283–298 (1995b)

    Article  MATH  Google Scholar 

  • Meguid, S.A.: Main crack-micro crack interaction of hydrogenated and outgassed austenitic steels. Int. J. Hydrogen Energy 22, 377–381 (1997)

    Article  Google Scholar 

  • Meguid, S.A., Wang, X.D.: On the dynamic behavior of interacting micro defects in advanced composite materials. Int. J. Impact Eng. 19(5–6), 503–514 (1997)

    Article  Google Scholar 

  • Moes, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46, 131–150 (1999)

    Article  MATH  Google Scholar 

  • Mohammadi, S.: Extended Finite Element Method for Fracture Analysis of Structures, 1st edn. Blackwell Publishing Limited, Oxford (2008)

    Book  MATH  Google Scholar 

  • Mori, T., Saito, K., Mura, T.: An inclusion model for crack arrest in a composite reinforced by sliding fibers. Mech. Mater. 7, 49–58 (1988)

    Article  Google Scholar 

  • Mori, K., Tabarrok, B., Tong, X.: A new method for analysis of arbitrarily shaped cracks by the body force method. Int. J. Mech. Sci. 36, 881–895 (1994)

    Article  MATH  Google Scholar 

  • Nelli Silva, E.C., Paulino, G.H.: Topology optimization applied to the design of functionally graded materials (FGM) structures. In: XXI ICTAM, Warsaw, Poland, 15–21 Aug 2004

  • Prabhakar, R.M., Tippur, H.V.: Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient. Int. J. Solids Struct. 37, 5353–5370 (2000)

    Article  MATH  Google Scholar 

  • Rao, B.N., Rahman, S.: An interaction integral method for analysis of cracks in orthotropic functionally graded materials. Comput. Mech. 32, 40–51 (2003)

    Article  MATH  Google Scholar 

  • Rao, B.N., Rahman, S.: A continuum shape sensitivity method for fracture analysis of orthotropic functionally graded materials. Mech. Mater. 37, 1007–1025 (2005)

    Article  Google Scholar 

  • Rao, B.N., Rahman, S.: A continuum shape sensitivity method for fracture analysis of isotropic functionally graded materials. Comput. Mech. 38, 133–150 (2006)

    Article  MATH  Google Scholar 

  • Sukumar, N., Chopp, D., Moes, N., Belytschko, T.: Modeling holes and inclusions by level sets in the extended finite element method. Comput. Methods Appl. Mech. Eng. 190, 6183–6200 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, X.D., Meguid, S.A.: Dynamic interaction between a matrix crack and a circular inhomogenity with a distinct interphase. Int. J. Solids Struct. 36, 517–531 (1999)

    Article  MATH  Google Scholar 

  • Wang, B.-L., Mai, Y.-W.: Multiple surface cracks in a piezoelectric layer bonded to an elastic substrate under transient electromechanical loads. Mech. Mater. 39, 564–579 (2007)

    Article  Google Scholar 

  • Wang, S., Dempsey, J.P.: A cohesive edge crack. Eng. Fract. Mech. 78, 1353–1373 (2011)

    Article  Google Scholar 

  • Zhang, Ch., Sladek, J., Sladek, V.: Crack analysis in unidirectionally and bidirectionally functionally graded materials. Int. J. Fract. 129, 385–406 (2004)

    Article  MATH  Google Scholar 

  • Zhang, Ch., Sladek, J., Sladek, V.: Antiplane crack analysis of a functionally graded material by a BIEM. Comput. Mater. Sci. 32, 611–619 (2005)

    Article  Google Scholar 

  • Zhang, L., Kim, J.-H.: A complex variable approach for asymptotic mode-III crack-tip fields in an anisotropic functionally graded material. Eng. Fract. Mech. 76, 2512–2525 (2009)

    Article  Google Scholar 

  • Zhu, Z.-H., Meguid, S.A.: On the thermoelastic stress of multiple interacting inhomogeneities. Int. J. Solids Struct. 37, 2313–2330 (2000)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    I. V. Singh, B. K. Mishra & S. Bhattacharya

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  1. I. V. Singh
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  2. B. K. Mishra
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  3. S. Bhattacharya
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Correspondence to I. V. Singh.

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Singh, I.V., Mishra, B.K. & Bhattacharya, S. XFEM simulation of cracks, holes and inclusions in functionally graded materials. Int J Mech Mater Des 7, 199–218 (2011). https://doi.org/10.1007/s10999-011-9159-1

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  • DOI: https://doi.org/10.1007/s10999-011-9159-1

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