Advertisement

Continuum Mechanics and Thermodynamics

, Volume 29, Issue 4, pp 977–988 | Cite as

Phase field modelling of dynamic thermal fracture in the context of irradiation damage

  • Alexander SchlüterEmail author
  • Charlotte Kuhn
  • Ralf Müller
  • Marilena Tomut
  • Christina Trautmann
  • Helmut Weick
  • Carolin Plate
Original Article

Abstract

This work presents a continuum mechanics approach to model fracturing processes in brittle materials that are subjected to rapidly applied high-temperature gradients. Such a type of loading typically occurs when a solid is exposed to an intense high-energy particle beam that deposits a large amount of energy into a small sample volume. Given the rapid energy deposition leading to a fast temperature increase, dynamic effects have to be considered. Our existing phase field model for dynamic fracture is thus extended in a way that allows modelling of thermally induced fracture. A finite element scheme is employed to solve the governing partial differential equations numerically. Finally, the functionality of our model is illustrated by two examples.

Keywords

Phase field Thermal fracture Irradiation damage 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amor H., Marigo J.J., Maurini C.: Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J. Mech. Phys. Solid. 57(8), 1209–1229 (2009)ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    Boettinger W.J., Warren J.A., Beckermann C., Karma A.: Phase-field simulation of solidification 1. Annu. Rev. Mater. Res. 32(1), 163–194 (2002). doi: 10.1146/annurev.matsci.32.101901.155803 CrossRefGoogle Scholar
  3. 3.
    Borden M.J., Verhoosel C.V., Scott M.A., Hughes T.J.R., Landis C.M.: A phase-field description of dynamic brittle fracture. Comput. Methods Appl. Mech. Eng. 217–220, 77–95 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bourdin B.: Numerical implementation of the variational formulation of quasi-static brittle fracture. Interfaces Free Bound. 9, 411–430 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Chambolle A.: An approximation result for special functions with bounded deformation. J. Math. Pure Appl. 83(7), 929–954 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Francfort G.A., Marigo J.J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solid. 46(8), 1319–1342 (1998)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Griffith A.A.: The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. Lond. A 221, 163–198 (1921)ADSCrossRefGoogle Scholar
  8. 8.
    Hofacker M., Miehe C.: A phase field model for ductile to brittle failure mode transition. PAMM 12(1), 173–174 (2012)CrossRefGoogle Scholar
  9. 9.
    Hofacker M., Miehe C.: A phase field model of dynamic fracture: robust field updates for the analysis of complex crack patterns. Int. J. Numer. Methods Eng. 93(3), 276–301 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kuhn, C.: Numerical and analytical investigation of a phase field model for fracture. Phd thesis, Technische Universität Kaiserslautern (2013)Google Scholar
  11. 11.
    Kuhn C., Müller R.: Phase field simulation of thermomechanical fracture. PAMM 9(1), 191–192 (2009)CrossRefGoogle Scholar
  12. 12.
    Kuhn, C., Müller, R.: A continuum phase field model for fracture. Eng. Fract. Mech. 77(18), 3625–3634 (2010). Computational mechanics in fracture and damage: a special issue in Honor of Prof. GrossGoogle Scholar
  13. 13.
    Richter, H., Aiginger, H., Noah Messomo, E.: Simulating transient effects of pulsed beams on beam intercepting devices. Ph.D. thesis, Vienna, Tech. U., Vienna (2011). Presented 14 Oct 2011Google Scholar
  14. 14.
    Schlueter, A., Willenbuecher, A., Kuhn, C., Mueller, R.: Phase field approximation of dynamic brittle fracture. Comput. Mech. 54, 1–21 (2014)Google Scholar
  15. 15.
    Schmitt R., Kuhn C., Mueller R., Bhattacharya K.: Crystal plasticity and martensitic transformations—a phase field approach. Technische Mechanik 34(1), 23–38 (2014)Google Scholar
  16. 16.
    Schrade D., Mueller R., Xu B.X., Gross D.: Domain evolution in ferroelectric materials: a continuum phase field model and finite element implementation. Comput. Methods Appl. Mech. Eng. 196(41–44), 4365–4374 (2007)ADSCrossRefzbMATHGoogle Scholar
  17. 17.
    Tahir N.A., Hoffmann D.H.H., Maruhn J.A., Spiller P., Bock R.: Heavy-ion-beam-induced hydrodynamic effects in solid targets. Phys. Rev. E 60, 4715–4724 (1999)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Alexander Schlüter
    • 1
    Email author
  • Charlotte Kuhn
    • 1
  • Ralf Müller
    • 1
  • Marilena Tomut
    • 2
  • Christina Trautmann
    • 2
    • 3
  • Helmut Weick
    • 2
  • Carolin Plate
    • 1
  1. 1.University of KaiserslauternKaiserslauternGermany
  2. 2.GSI Helmholtzzentrum für Schwerionenforschung GmbHDarmstadtGermany
  3. 3.TU DarmstadtDarmstadtGermany

Personalised recommendations