Skip to main content
SpringerLink
Log in

Numerical Simulation of Crack Growth in Brittle Matrix of Particle Reinforced Composites Using the XFEM Technique

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

Crack growth in particle reinforced composites is significantly influenced by the character of the reinforcement particles. To accurately deal with such problems, the extended finite element method (XFEM) was employed and improved. The simulations are accomplished by using a new domain expression of an interaction integral for evaluating stress intensity factors (SIFs), and by adopting the maximum hoop stress criterion for crack-growth direction prediction. Crack deflection/attraction mechanisms and their associated energy release rate variations are investigated. It is shown that the applied numerical method allows a considerable flexibility and can be used in more general situations. The crack-tip shielding and amplifying behaviors are clearly observed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Tamate, O., The effect of a circular inclusion on the stresses around a line crack in a sheet under tension. International Journal of Fracture, 1968, 4(3): 257–65.

    Google Scholar 

  2. Sendechyj, G.P., Interaction of cracks with rigid inclusions in longitudinal shear deformation. International Journal of Fracture, 1974, 10(1): 45–52.

    Article  Google Scholar 

  3. Hwu, C., Liang, Y.K. and Yen, W.J., Interactions between inclusions and various types of cracks. International Journal of Fracture, 1995, 73(4): 301–23.

    Article  Google Scholar 

  4. Kassam, Z.H.A., Zhang, R.J. and Wang, Z.R., Finite element simulation to investigate interaction between crack and particulate reinforcements in metal matrix composites. Materials Science and Engineering, 1995, A203(1–2): 286–299.

    Article  Google Scholar 

  5. Ayyar, A. and Chawla, N., Microstructure-based modeling of crack growth in particle reinforced composites. Composites Science and Technology, 2006, 66(13): 1980–1994.

    Article  Google Scholar 

  6. Bush, M.B., The interaction between a crack and a particle cluster. International Journal of Fracture, 1997, 88(3): 215–232.

    Article  Google Scholar 

  7. Knight, M.G., Wrobel, L.C. and Henshall, J.L., A study of the interaction between a propagating crack and an uncoated/coated elastic inclusion using the BE technique. International Journal of Fracture, 2002, 114(1): 47–61.

    Article  Google Scholar 

  8. Kitey, R., Phan, A.V., Tippur, H.V. and Kaplan, T., Modeling of crack growth through particulate clusters in brittle matrix by symmetric-Galerkin boundary element method. International Journal of Fracture, 2006, 141(1–2): 11–25.

    Article  Google Scholar 

  9. Williams, R.C., Phan, A.V., Tippur, H.V., Kaplan, T. and Gray, L.J., SGBEM analysis of crack-particle(s) interactions due to elastic constants mismatch. Engineering Fracture Mechanics, 2007, 74(3): 314–331.

    Article  Google Scholar 

  10. Lei, J., Yang, Q.S., Wang, Y.S. and Zhang, C.Z., An investigation of dynamic interaction between multiple cracks and inclusions by TDBEM. Composites Science and Technology, 2009, 69(7–8): 1279–1285.

    Article  Google Scholar 

  11. Kurumatani, M. and Terada, K., Finite cover method with multi-cover layers for the analysis of evolving discontinuities in heterogeneous media. International Journal for Numerical Methods in Engineering, 2009, 79(1): 1–24.

    Article  Google Scholar 

  12. Chen, C.Q., Cui, J.Z., Duan, H.L., Feng, X.Q., He, L.H., Hu, G.K., Huang, M.J., Huo, Y.Z., Ji, B.H., Liu, B., Peng, X.H., Shi, H.J., Sun, Q.P., Wang, J.X., Wang, Y.S., Zhao, H.P., Zhao, Y.P., Zheng, Q.S. and Zou, W.N., Perspectives in mechanics of heterogeneous solids. Acta Mechanica Solida Sinica, 2011, 24(1): 1–26.

    Article  Google Scholar 

  13. Jing, L., A review of techniques, advances and outstanding issues in numerical modeling for rock mechanics and rock engineering. International Journal of Rock Mechanics & Mining Sciences, 2003, 40(3): 283–353.

    Article  MathSciNet  Google Scholar 

  14. Belytschko, T., Moës, N., Usui, S. and Parimi, C., Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering, 2001, 50(4): 993–1013.

    Article  Google Scholar 

  15. Daux, C., Moës, N., Dolbow, J., Sukumar, N. and Belyschko, T., Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering, 2000, 48(12): 1741–1760.

    Article  Google Scholar 

  16. Huynh, D.B.P. and Belytschko, T., The extended finite element method for fracture in composite materials. International Journal for Numerical Methods in Engineering, 2009, 77(2): 214–239.

    Article  MathSciNet  Google Scholar 

  17. Sukumar, N. and Prévost, J.H., Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation. International Journal of Solids and Structures, 2003, 40(26): 7513–7537.

    Article  Google Scholar 

  18. Huang, R., Sukumar, N. and Prévost, J.H., Modeling quasi-static crack growth with the extended finite element method Part II: Numerical applications. International Journal of Solids and Structures, 2003, 40(26): 7539–7552.

    Article  Google Scholar 

  19. Belytschko, T. and Black, T., Elastic crack growth in finite elements with minimal re-meshing. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620.

    Article  Google Scholar 

  20. Moës, N., Dolbow, J. and Belytschko, T., A finite element method for crack growth with out re-meshing. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131–150.

    Article  Google Scholar 

  21. Babuška, I. and Melenk, J.M., The partition of unity method. International Journal for Numerical Methods in Engineering, 1997, 40: 727–758.

    Article  MathSciNet  Google Scholar 

  22. Moës, N., Cloirec, M., Cartraud, P. and Remacle, J.F., A computational approach to handle complex microstruture geometries. Computer Methods in Applied Mechani- cs and Engineering, 2003, 192(28–30): 3163–3177.

    Article  Google Scholar 

  23. Dréau, K., Chevaugeon, N. and Moës, N., Studied X-FEM enrichment to handle material interfaces with higher order finite element. Computer Methods in Applied Mechanics and Engineering, 2010, 199(29–32): 1922–1936.

    Article  MathSciNet  Google Scholar 

  24. Yu, H.J., Wu, L.Z., Guo, L.C., Du, S.Y. and He, Q.L., Investigation of mixed-mode stress intensity factors for non-homogeneous materials using an interaction integral method. International Journal of Solids and Structures, 2009, 46(20): 3710–3724.

    Article  Google Scholar 

  25. Yu, H.J., Wu, L.Z., Guo, L.C., He, Q.L. and Du, S.Y., Interaction integral method for the interfacial fracture problems of two non-homogeneous materials. Mechanics of Materials, 2010, 42(4): 435–450.

    Article  Google Scholar 

  26. Rice, J.R., A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics, 1968, 35: 379–386.

    Article  Google Scholar 

  27. Dolbow, J., Moës, N. and Belytschko, T., Discontinuous enrichment in finite element with a partition of unity method. Finite Elements in Analysis and Design, 2000, 36(3–4): 235–260.

    Article  Google Scholar 

  28. Dolbow, J. and Gosz, M., On the computation of mixed-mode stress intensity factors in functionally graded materials. International Journal of Solids and Structures, 2002, 39(9): 2557–2574.

    Article  Google Scholar 

  29. Kim, J.H. and Paulino, G.H., An accurate scheme for mixed-mode fracture analysis of functionally graded materials using the interaction integral and micromechanics models. International Journal for Numerical Methods in Engineering, 2003, 58(10): 1457–1497.

    Article  Google Scholar 

  30. Kim, J.H. and Paulino, G.H., Consistent formulations of the interaction integral method for fracture of functionally graded materials. Journal of Applied Mechanics, 2005, 72(3): 351–364.

    Article  Google Scholar 

  31. Hutchinson, J.W. and Suo, Z., Mixed mode cracking in layered materials. Advances in Applied Mechanics, 1992, 29: 63–191.

    Article  Google Scholar 

  32. Elguedj, T., Gravouil, A. and Combescure, A., Appropriate extended functions for X-FEM simulations of plastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering, 2006, 195(7–8): 501–515.

    Article  Google Scholar 

  33. Kim, J.H. and Paulino, G.H., On fracture criteria for mix-mode crack propagation in functionally graded materials. Mechanics of Advanced Materials and Structures, 2007, 14: 227–244.

    Article  Google Scholar 

  34. Erdogan, F. and Sih, G.C., On the crack extension in plates under plane loading and transverse shear. ASME Journal of Basic Engineering, 1963, 85(4): 519–527.

    Article  Google Scholar 

  35. Civelek, M.B and Erdogan, F., Crack problems for a rectangular plate and an infinite strip. International Journal of Fracture, 1982, 19(2): 139–159.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Composite Materials, Harbin Institute of Technology, Harbin, 150001, China

    Zhiyong Wang, Li Ma, Linzhi Wu & Hongjun Yu

Authors
  1. Zhiyong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Linzhi Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hongjun Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li Ma.

Additional information

Project supported by the Program for New Century Excellent Talents in University (No. NCET-08-0152) and the Program of Excellent Team in Harbin Institute of Technology.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, Z., Ma, L., Wu, L. et al. Numerical Simulation of Crack Growth in Brittle Matrix of Particle Reinforced Composites Using the XFEM Technique. Acta Mech. Solida Sin. 25, 9–21 (2012). https://doi.org/10.1016/S0894-9166(12)60002-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(12)60002-0

Key words

Search

Navigation