Advertisement

Phase Field Crack Growth Model with Hydrogen Embrittlement

  • Takeshi TakaishiEmail author
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 26)

Abstract

As an application of the phase field model for crack propagation in elastic body, chemical-diffuse crack growth model with the effect of the hydrogen embrittlement is considered. Numerical results show the difference of crack path between data with the effects and data without the effect. Temporal evolution of the normalized difference of phase field depict the time when start the difference of crack path.

Keywords

Fracture Toughness Phase Field Crack Path Hydrogen Embrittlement Phase Field Model 
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.

Notes

Acknowledgments

This work is in collaboration with M.Kimura.

References

  1. 1.
    Belytschko, T., Black, T.: Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Methods Eng. 45, 602–620 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Takaishi, T., Kimura, M.: Phase field model for mode III crack growth. Kybernetika 45, 605–614 (2009)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Kimura, M., Takaishi, T.: A phase field approach to matehmatical modeling of crack propagation. A mathematical approach to research problems of science and technology mathematics for industry 5, 161–170 (2014)Google Scholar
  4. 4.
    Francfort, G.A., Marigo, J.-J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46, 1319–342 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ambrosio, L., Tortorelli, V.M.: On the approximation of free discontinuity problems. Boll. Un. Mat. Ital. 7, 105–123 (1992)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Troiano, A.R.: The role of Hydrogen and other interstitials in the mechanical behaviour of metals. Trans. ASM 52, 54–80 (1960)Google Scholar
  7. 7.
    Beachem, C.D.: A new model for hydrogen-asisted cracking. Metall. Trans. 3, 437–451 (1972)CrossRefGoogle Scholar
  8. 8.
    Griffith, A.A.: The phenomenon of rupture and flow in solids. Philos. Trans. Roy. Soc. Lond. A221, 163–198 (1921)CrossRefGoogle Scholar
  9. 9.
    Bourdin, B.: Numerical implementation of the variational formulation of brittle fracture. Interfaces Free Bound. 9, 411–430 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Buliga, M.: Energy minimizing brittle crack propagation. J. Elast. 52, 201–238 (1998/99)Google Scholar
  11. 11.
    Kobayashi, R.: Modeling and numerical simulations of dendritic crystal growth. Physica D 63, 410–423 (1993)CrossRefzbMATHGoogle Scholar
  12. 12.
    Hecht, F.: New development in FreeFem++. J. Numer. Math. 20, 251–265 (2012)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Hiroshima Kokusai Gakuin UniversityHiroshimaJapan

Personalised recommendations