International Journal of Fracture

, Volume 163, Issue 1–2, pp 109–119 | Cite as

Dynamic fragmentation of laser shock-melted tin: experiment and modelling

Original Paper


Dynamic fragmentation of shock-loaded metals is an issue of considerable importance for both basic science and a variety of technological applications, such as pyrotechnics or inertial confinement fusion, the latter involving high energy laser irradiation of thin metallic shells. Whereas spall fracture in solid materials has been extensively studied for many years, little data can be found yet about the evolution of this phenomenon after partial or full melting on compression or on release. Here, we present an investigation of dynamic fragmentation in laser shock-melted tin, from the “micro-spall” process (ejection of a cloud of fine droplets) occurring upon reflection of the compressive pulse from the target free surface, to the late rupture observed in the unspalled melted layer (leading to the formation of larger spherical fragments). Experimental results consist of time-resolved velocity measurements and post-shock observations of recovered targets and fragments. They provide original information regarding the loss of tensile strength associated with melting, the cavitation mechanism likely to occur in the melted metal, the sizes of the subsequent fragments and their ejection velocities. A theoretical description based on an energetic approach adapted to the case of a liquid metal is implemented as a failure criterion in a one-dimensional hydrocode including a multi-phase equation of state for tin. The resulting predictions of the micro-spall process are compared with experimental data. In particular, the use of a new experimental technique to quantify the fragment size distributions leads to a much better agreement with theory than previously reported. Finally, a complementary approach focused on cavitation is proposed to evaluate the role of this phenomenon in the fragmentation of the melted metal.


Dynamic fragmentation Micro-spall Laser shock Shock-induced melting Cavitation Tin 


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  1. Andriot P, Chapron P, Olive F (1982) Ejection of material from shocked surfaces of tin, tantalum and lead alloys. In: Nellis WJ, Seaman L, Graham RA (eds) Shock waves in condensed matter – 1981, AIP conference proceedings, vol 78, pp 505–508Google Scholar
  2. Andriot P, Chapron P, Lambert V, Olive F (1984) Influence of melting on shocked free surface behaviour using Doppler laser interferometry and X-ray densitometry. In: Asay JR, Graham RA, Straub GK (eds) Shock waves in condensed matter – 1983. North-Holland Amsterdam, pp 277–280Google Scholar
  3. Antoun T, Seaman L, Curran DR, Kanel GI, Razorenov SV, Utkin AV (2002) Spall fracture. Springer, New YorkGoogle Scholar
  4. Asay JR, Mix LP, Perry FC (1976) Ejection of material from shocked surfaces. Appl Phys Lett 29(5): 284–287CrossRefADSGoogle Scholar
  5. Barker LM, Hollenbach RE (1970) Shock-wave studies of PMMA, fused silica and sapphire. J Appl Phys 41: 4208–4226CrossRefADSGoogle Scholar
  6. Blink JA, Hoover WG (1985) Fragmentation of suddenly heated liquids. Phys Rev A 32(2): 1027–1035CrossRefPubMedADSGoogle Scholar
  7. Buy F, Voltz C, Llorca F (2006) Thermodynamically based equation of state for shock wave study: application to the design of experiments on tin. In: Furnish MD, Elert M, Russell TP, White CT (eds) Shock compression of condensed matter – 2005, AIP conference proceedings, vol 845, pp 41–44Google Scholar
  8. Chapron P, Elias P, Laurent B (1988) Experimental determination of the pressure inducing melting in release for shock-loaded metallic samples. In: Schmidt SC, Holmes NC (eds) Shock waves in condensed matter – 1987, Elsevier, Amsterdam, pp 171–174Google Scholar
  9. Cheret R, Chapron P, Elias P, Martineau J (1986) Mass ejection from the free surface of shock-loaded metallic samples. In: Gupta YM (ed) Shock waves in condensed matter – 1985. Plenum, New York, pp 651–654Google Scholar
  10. Davison L, Grady DE, Shahinpoor M (1996) High pressure shock compression of solids II, dynamic fracture and fragmentation. Springer, New YorkMATHGoogle Scholar
  11. de Rességuier T, Signor L, Dragon A, Boustie M, Roy G, Llorca F (2007a) Experimental investigation of liquid spall in laser shock-loaded tin. J Appl Phys 101(1): 013506CrossRefADSGoogle Scholar
  12. de Rességuier T, Signor L, Dragon A, Severin P, Boustie M (2007b) Spallation in laser shock-loaded tin below and just above melting on release. J Appl Phys 102(7): 073535CrossRefADSGoogle Scholar
  13. de Rességuier T, Signor L, Dragon A, Boustie M, Berthe L (2008) On the dynamic fragmentation of laser shock-melted tin. Appl Phys Lett 92(13): 131910CrossRefADSGoogle Scholar
  14. Denoual C, Diani JM (2002) Cavitation in compressible visco-plastic materials. In: Furnish MD, Thadhani NN, Horie Y (eds) Shock compression of condensed matter – 2001, AIP conference proceedings, vol 620, pp 495–498Google Scholar
  15. Elias P, Chapron P, Laurent B (1988) Detection of melting in release for a shock-loaded tin sample using the reflectivity measurement method. Opt Commun 66(2–3): 100–106CrossRefADSGoogle Scholar
  16. Eliezer S, Gilath I, Bar-Noy T (1990) Laser-induced spall in metals: experiment and simulation. J Appl Phys 67: 715–724CrossRefADSGoogle Scholar
  17. Grady DE (1988) The spall strength of condensed matter. J Mech Phys Solids 36(3): 353–384CrossRefADSGoogle Scholar
  18. Grady DE (1996) Spall and fragmentation in high-temperature metals. In: High-pressure shock compression of solids II (see ref. Davison et al. (1996) above), Chap. 9, pp 219–236Google Scholar
  19. Hemsing WF (1979) Velocity sensing interferometer (VISAR) modification. Rev Sci Instrum 50: 73–78CrossRefPubMedADSGoogle Scholar
  20. Johnson JN (1981) Dynamic fracture and spallation in ductile solids. J Appl Phys 52(4): 2812–2825CrossRefADSGoogle Scholar
  21. Kanel GI, Razorenov SV, Utkin AV, Grady DE (1996) The spall strength of metals at elevated temperature. In: Schmidt SC, Tao WC (eds) Shock compression of condensed matter – 1995, AIP conference proceedings, vol 370, pp 503–506Google Scholar
  22. Lescoute E, de Rességuier T, Chevalier JM, Boustie M, Cuq-Lelandais JP, Berthe L (2009) Transverse shadowgraphy and new recovery techniques to investigate dynamic fragmentation of laser shock-loaded metals. 16th APS Shock conference, NashvilleGoogle Scholar
  23. Mabire C, Héreil PL (2000) Shock induced polymorphic transition and melting of tin. In: Furnish MD, Chhabildas LC, Hixson RS (eds) Shock compression of condensed matter – 1999, AIP conference proceedings, vol 505, pp 93–96Google Scholar
  24. Mercier P, Benier J, Sollier A, Lescoute E, Cuq-Lelandais JP, Gay E, de Rességuier T, Berthe L, Boustie M, Nivard M, Claverie A (2009) Heterodyne Velocimetry measurements on solids under shock driven by high power lasers. 16th APS Shock conference, NashvilleGoogle Scholar
  25. Moshe E, Eliezer S, Dekel E, Henis Z, Ludmirsky A, Goldberg IB, Eliezer D (1999) Measurements of laser driven spallation of tin and zinc using an optical recording velocity interferometer system. J Appl Phys 86(8): 4242–4248CrossRefADSGoogle Scholar
  26. Rybakov AP, Rybakov IA (1995) Reaction of condensed matter to extremely short-duration and intense loading. Strength of solids and liquids under dynamic damage. Eur J Mech B/Fluids 14(2): 197–205Google Scholar
  27. Signor L, de Rességuier T, Roy G, Dragon A, Llorca F (2007a) Fragment-size prediction during dynamic fragmentation of shock-melted tin: recovery experiments and modeling issues. In: Elert M, Furnish MD, Chau R, Holmes M, Nguyen J (eds) Shock compression of condensed matter – 2007, AIP conference proceedings, vol 955, pp 593–596Google Scholar
  28. Signor L, Dragon A, de Rességuier T, Roy G, Llorca F (2007b) EMMC10, fragmentation of melted metals upon intense shock-wave loading. Experiment and modelling for a tin target. In: Nowacki WK, Zhao H (eds) Multi-phase and multi-components materials under dynamic loading, pp 273–282. ISBN 978-83-89687-16-6Google Scholar
  29. Signor L (2008) PhD Thesis. Université de Poitiers, FranceGoogle Scholar
  30. Signor L, Dragon A, Roy G, de Rességuier T, Llorca F (2008) Dynamic fragmentation of melted metals upon intense shock wave loading. Some modelling issues applied to a tin target. Arch Mech 60(4): 323–343MATHGoogle Scholar
  31. Signor L, Roy G, Chanal PY, Héreil PL, Buy F, Voltz C, de Rességuier T, Dragon A (2009) Debris cloud ejection from shock-loaded tin melted on release or on compression. 16th APS Shock conference, NashvilleGoogle Scholar
  32. Stebnovskii SV (1998) Experimental investigation of pulsed stretching of cavitating media. J Appl Mech Tech Phys 39(5): 758–761CrossRefADSGoogle Scholar
  33. Stebnovskii SV (2007) Fragmentation of liquid and liquid-plastic media under unsteady strains. J Appl Mech Tech Phys 48(4): 519–524CrossRefADSGoogle Scholar
  34. Zellner MB, Grover M, Hammerberg JE, Hixson RS, Iverson AJ, Macrum GS, Morley KB, Obst AW, Olson RT, Payton JR, Rigg PA, Routley N, Stevens GD, Turley WD, Veeser L, Buttler WT (2007) Effects of shock-breakout pressure on ejection of micron-scale material from shocked tin surfaces. J Appl Phys 102: 013522CrossRefADSGoogle Scholar
  35. Zhiembetov AK, Mikhaylov AL, Smirnov GS (2002) Experimental study of explosive fragmentation of metals melts. In: Furnish MD, Thadhani NN, Horie Y (eds) Shock compression of condensed matter – 2001, AIP conference proceedings, vol 620, pp 547–550Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • T. de Rességuier
    • 1
  • L. Signor
    • 2
    • 3
  • A. Dragon
    • 2
  • G. Roy
    • 3
  1. 1.Laboratoire de Combustion et de DétoniqueCNRS/ENSMAFuturoscopeFrance
  2. 2.Laboratoire de Mécanique et Physique des MatériauxCNRS/ENSMAFuturoscopeFrance
  3. 3.Commissariat à l’Energie AtomiqueCentre de ValducIs-sur-TilleFrance

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