Journal of Materials Science

, Volume 34, Issue 19, pp 4665–4670 | Cite as

Failure criteria for multiply flawed anisotropic materials

  • Tsung-Lin Wu
  • Jin H. Huang


This study presents overall failure criteria for an infinite anisotropic solid containing multiple flaws subjected to a set of uniform applied loads. Based on the inclusion method, flaws are treated as elliptical inclusions where their elastic moduli are considered to be zero. The explicit expression of elastic fields is obtained for a cubic crystal multiply flawed solid through the use of the Mori-Tanaka mean field theory. The resulting expression is further utilized to find an interaction energy function between the applied loads and flaws. With this energy function, the energy release rates and critical stresses are acquired separately in a closed form for Mode I, II, and III. The closed forms for energy release rates and critical stresses reveal that they are a function of the aspect ratio and the volume fraction of flaws, the modes of the loading, and the material properties. As an illustrated numerical example, the energy release rates and the critical stresses that vary with both the aspect ratio and the volume fraction of the flaws in a cubic crystal material are discussed.


Polymer Field Theory Aspect Ratio Material Property Interaction Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. A. Griffith, Trans. R. Soc. A221 (1921) 163.Google Scholar
  2. 2.
    R. A. Sack, Proc. Phys. Soc. 58 (1946) 729.Google Scholar
  3. 3.
    I. N. Sneddon, Proc. R. Soc. A187 (1946) 229.Google Scholar
  4. 4.
    M. K. Kassir and G. C. Sih, Int. J. Engng. Sci. 5 (1967) 899.Google Scholar
  5. 5.
    J. R. Willis, ibid. 6 (1968) 253–263.Google Scholar
  6. 6.
    D. M. Barnett and R. J. Asaro, J. Mech. Phys. Solids 20 (1972) 353.Google Scholar
  7. 7.
    T. Mura and S. C. Lin, J. Appl. Mech. 41 (1974) 209.Google Scholar
  8. 8.
    T. Mura and T. C. Cheng, ibid. 21 (1978) 1165.Google Scholar
  9. 9.
    J. H. Huang and H. K. Liu, Int. J. Engng. Sci. 36 (1998) 143.Google Scholar
  10. 10.
    T. Mura, "Micromechanics of Defects in Solids," (Martinus Nijhoff Publishers, Dordrecht).Google Scholar
  11. 11.
    J. D. Eshelby, Proc. Roy. Soc. A241 (1957) 376.Google Scholar
  12. 12.
    T. Mori and K. Tanaka, Acta Metall. 21 (1973) 571.Google Scholar
  13. 13.
    J. H. Huang and J. S. Yu, Comp. Engng. 4 (1994) 1169.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Tsung-Lin Wu
    • 1
  • Jin H. Huang
    • 2
  1. 1.Automative Division of Mechanical Engineering DepartmentNan Tai Technology InstituteTainan, TaiwanRepublic of China
  2. 2.Department of Mechanical EngineeringFeng Chia UniversityTaichung, TaiwanRepublic of China

Personalised recommendations