Thermo-Mechanical Modelling of High Energy Particle Beam Impacts

  • M. ScapinEmail author
  • L. Peroni
  • A. Dallocchio
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 35)


The unprecedented energy intensities of modern hadron accelerators yield special problems with the materials that are placed close to or into the high intensity beams. The energy stored in LHC in a single beam is equivalent to about 80 kg of TNT explosive, stored in a transverse beam area of 0.2 mm × 0.2 mm. The materials placed close to the beam are used at, or even beyond, their damage limits. However, it is very difficult to predict structural efficiency and robustness accurately: beam-induced damage occurs in a regime where practical experience does not exist. This study is performed in order to estimate the damage on a copper component due to the impact with a 7 TeV proton beam generated by LHC. The case study represents an accidental case consequent to an abnormal release of the beam, in which 8 bunches irradiate the target directly. The energy delivered on the component is calculated using the FLUKA code and then used as input in the numerical simulations, that are carried out via the FEM code LS-DYNA. Different numerical models are realized trying to obtain the simplest model able to correctly describe the material response without affecting the goodness of the results.


CERN Equation of state High energy impact LS-DYNA Shockwaves 



This work was performed within the WP 8 “Collmat” of the FP7 European Project EUCARD. The financial support of the European Commission by means of the EUCARD project, the Fluka Team and Gerald Kerley (Kerley Technical Services) are gratefully acknowledged.


  1. 1.
    Wiedemann, H.: Particle accelerator physics I. Springer, Berlin (1993)CrossRefGoogle Scholar
  2. 2.
    Petterson, T.S., Lefèvre, P.: The large hadron collider: conceptual design. CERN Desktop Publishing Service, Geneve (1995)Google Scholar
  3. 3.
    LHC Design Report, vol. I, The LHC Main Ring. CERN Editorial Board (2004)Google Scholar
  4. 4.
    LHC Design Report, vol. III, The LHC Injector Chain. CERN Editorial Board (2004)Google Scholar
  5. 5.
    Gladman, B et al.: LS-DYNA® Keyword User’s Manual—Volume I—Version 971. LSTC (2007)Google Scholar
  6. 6.
    Fasso, A. et al.: FLUKA: A Multi-Particle Transport Code (2005)Google Scholar
  7. 7.
    Dallocchio, A.: Study of termo-mechanical effects induced in solids by high energy particle beam: analytical and numerical methods. Ph.D Thesis, Politecnico di Torino (2008)Google Scholar
  8. 8.
    Bennett, J.R.J., Booth, C.N., Brownsword R.A et al.: LS-DYNA calculation of shock in solid. Nucl. Phys. B (Proc. Suppl.) 155, 293–294 (2006)Google Scholar
  9. 9.
    Bennett, J.R.J., Skoro, G.P., Booth, C., et al.: Thermal shock measurements and modeling for solid high-power targets at high temperatures. Nucl. Mater. 377, 285–289 (2008)CrossRefGoogle Scholar
  10. 10.
  11. 11.
    Tahir, N.A., Goddard, B., Kain, V et al.: Impact of 7-TeV/c large hadron collider proton beam on a copper target. Appl. Phys. 97 (2005)Google Scholar
  12. 12.
    Tahir, N.A., Shutov, A., Lomonosov IV et al.: Thermo-mechanical effects induced by beam impact on the LHC Phase II collimators: preliminary analysis using hydrodynamic approachGoogle Scholar
  13. 13.
    Le Blanc G, Petit J, Chanal P et al.: Modelling the dynamic magneto-thermomechanical behavior of materials using a multi-phase EOS. In: 7th European LS-DYNA Conference (2008)Google Scholar
  14. 14.
    Johnson, J.R., Cook, W.H.: A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: 7th International Symposium on Ballistics, pp. 541–547 (1983)Google Scholar
  15. 15.
    Cowper, G.R., Symonds, P.S.: Strain hardening and strain rate effects in the impact loading of cantilever beam. Brown University Division of Application of Mechanical Report 28 (1952) Google Scholar
  16. 16.
    Zerilli, F.J., Armstrong, R.W.: Dislocation-mechanics-based constitutive relations for material dynamics calculations. J. Appl. Phys, Vol. 61 (1987)Google Scholar
  17. 17.
    Peroni, M., Peroni, L., Dallocchio, A.: Thermo-mechanical model identification of strengthened copper with an inverse method. 9th International DYMAT Conference (2009)Google Scholar
  18. 18.
    Peroni, M.: Experimental methods for material characterization at high strain-rate: analytical and numerical improvements. Ph.D thesis, Politecnico di Torino (2008)Google Scholar
  19. 19.
    Peroni, L., Scapin, M., Peroni, M.: Identification of strain-rate and thermal sensitive material model with an inverse method. In: 14th International Conference on Experimental Mechanics (2010)Google Scholar
  20. 20.
    Steinberg, D.J., Cochran, S.G., Guinan, M.W.: A constitutive model for metals applicable at high-strain rate. J. Appl. Phys. 51, 1498 (1980)CrossRefGoogle Scholar
  21. 21.
    Steinberg, D.J., Lund, C.M.: A constitutive model for strain rates from 10−4 to 106 s−1. Journal de physique, Symposium C3(49), 433–440 (1988)Google Scholar
  22. 22.
    Macdougall, D.: Determination of the plastic work converted to heat using radiometry. Exp. Mech. 40, 298–306 (2000)Google Scholar
  23. 23.
    Hodowany, J., Ravichandram, G., Rosakis, A.J., et al.: Partition of plastic work into heat and stored energy in metals. Exp. Mech. 40, 113–123 (2000)Google Scholar
  24. 24.
  25. 25.
    Kerley, G.I.: Equation of State for Copper and Lead. Kerley Technical Services Report KTS02-1 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Politecnico di TorinoTorinoItaly
  2. 2.Mechanical and Materials Group, EngineeringCERNGeneva 23Switzerland

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