International Journal of Fracture

, Volume 140, Issue 1–4, pp 243–254 | Cite as

Study on the fragmentation of shells

  • Falk K. Wittel
  • Ferenc Kun
  • Bernd H. Kröplin
  • Hans J. Herrmann


Fragmentation can be observed in nature and in everyday life on a wide range of length scales and for all kinds of technical applications. Most studies on dynamic failure focus on the behaviour of bulk systems in one, two and three dimensions under impact and explosive loading, showing universal power law behaviour of fragment size distribution. However, hardly any studies have been devoted to fragmentation of shells. We present a detailed experimental and theoretical study on the fragmentation of closed thin shells of various materials, due to an excess load inside the system and impact with a hard wall. Characteristic fragmentation mechanisms are identified by means of a high speed camera and fragment shapes and mass distributions are evaluated. Theoretical rationalisation is given by means of stochastic break-up models and large-scale discrete element simulations with spherical shell systems under different extreme loading situations. By this we explain fragment shapes and distributions and prove a power law for the fragment mass distribution. Satisfactory agreement between experimental findings and numerical predictions of the exponents of the power laws for the fragment shapes is obtained


Computer simulation explosion fragmentation scaling shell 


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  1. Alby, F.,  et al. 2004The European space debris safety and mitigation standardAdvances in Space Research3412601263CrossRefADSGoogle Scholar
  2. Åstrøm, J., Timonen, J. 1997Fragmentation by crack branchingPhysical Review Letters783677CrossRefADSGoogle Scholar
  3. Åstrøm, J.A., Ouchterlony, F., Linna, R.P., Timonen, J. 2004Universal dynamic fragmentation in D dimensionsPhysical Review Letters92245506CrossRefADSGoogle Scholar
  4. Ching, E.S.C., Liu, S., Xia, K.-Q. 2000Energy dependence of impact fragmentation of long glass rodsPhysica A28783CrossRefADSGoogle Scholar
  5. Hernandez, G., Herrmann, H.J. 1995Discrete models for two- and three-dimensional fragmentationPhysica A215420CrossRefADSGoogle Scholar
  6. Inaoka, H., Toyosawa, E., Takayasu, H. 1997Aspect ratio dependence of impact fragmentationPhysical Review Letters783455CrossRefADSGoogle Scholar
  7. Kadono, T., Arakawa, M. 2002Crack propagation in thin glass plates caused by high velocity impactPhysical Review E65035107CrossRefADSGoogle Scholar
  8. Katsuragi, H., Sugino, D., Honjo, H. 2003Scaling of impact fragmentation near the critical pointPhysical Review E68046105CrossRefADSGoogle Scholar
  9. Kun, F., Herrmann, H.J. 1999Transition from damage to fragmentation in collision of solidsPhysical Review E592623CrossRefADSGoogle Scholar
  10. Kun, F., Wittel, F.K., Kun Herrmann, H.J., Kröplin, B.H. and Måløy, K.J. (2005). Scaling behavior of fragment shapes. cond-mat/0506686Google Scholar
  11. MacLeod, N., Bain, M.M., Solomon, S.E. and Hancock, J.W. (2005). Failure mechanisms of hens’ eggs. Proceedings of the International Conference of Fracture ICF11, Torino, 4499.Google Scholar
  12. Meibom, A., Balslev, I. 1996Composite power laws in shock fragmentationPhysical Review Letters762492CrossRefADSGoogle Scholar
  13. Oddershede, L., Dimon, P., Bohr, J. 1993Self-organized criticality in fragmentingPhysical Review Letters713107CrossRefADSGoogle Scholar
  14. Turcotte, D.L. 1986Fractals and fragmentationJournal of Geophysical Research911921ADSGoogle Scholar
  15. Wittel, F.K., Kun, F., Herrmann, H.J., Kröplin, B.H. 2004Fragmentation of shellsPhysical Review Letters93035504CrossRefADSGoogle Scholar
  16. Wittel, F.K., Kun, F., Herrmann, H.J., Kröplin, B.H. 2005Breakup of shells under explosion and impactPhysical Review E71016108CrossRefADSGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Falk K. Wittel
    • 1
  • Ferenc Kun
    • 2
  • Bernd H. Kröplin
    • 1
  • Hans J. Herrmann
    • 3
  1. 1.Institute for Statics and Dynamics of Aerospace StructuresUniversity of StuttgartStuttgartGermany
  2. 2.Department of Theoretical PhysicsUniversity of DebrecenDebrecenHungary
  3. 3.Institute for Computer PhysicsUniversity of StuttgartStuttgartGermany

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