Investigation of fragments size resulting from dynamic fragmentation in melted state of laser shock-loaded tin Loïc Signor a, b, * , Thibaut de Rességuier b , André Dragon b , Gilles Roy a , Alain Fanget c , Matthieu Faessel d a Commissariat à l’Energie Atomique, Centre de Valduc, 21120 Is-sur-Tille, France b Institut Pprime (UPR 3346), CNRS e ENSMA e Université de Poitiers, Département Physique et Mécanique des Matériaux, 1 av. Clément Ader, 86961 Chasseneuil Futuroscope Cedex, France c Délégation Générale de l’Armement, Centre d’Etudes de Gramat, 46500 Gramat, France d Centre de Morphologie Mathématique, MINES ParisTech, 35 rue St-Honoré, 77300 Fontainebleau, France article info Article history: Received 29 October 2009 Accepted 14 March 2010 Available online 24 March 2010 Keywords: Dynamic fragmentation Laser-driven shock-wave Shock-induced melting Tin abstract The understanding of dynamic fragmentation in shock-loaded metals and the evaluation of geometrical and kinematical properties of the resulting fragments are issues of considerable importance for both basic and applied science, for instance to predict the evolution of engineering structures submitted to high-velocity impact or explosive detonation. Among dynamic failure processes, spall fracture in solid materials has been extensively studied for many years, while scarce data can be found yet about how such phenomenon could evolve after partial or full melting on compression or on release. In this case, the dynamic fragmentation process, which may be referred to as ‘micro-spalling’, takes place in a liquid medium. It results in the formation of a cloud of fine molten droplets, ejected at high-velocity. The present work is devoted to experimental characterization, theoretical modelling and simulation of the ‘micro-spalling’ process in tin, with a specific emphasis on the size of the resulting fragments, namely the melted droplets. Laser-driven shock-loading experiments on tin have been performed. Post-test observations of the recovered fragments provide an insight into the actual fragmentation process and allow to infer the distribution of the fragments size which are found to be mostly sub-micrometric. Fragmentation modelling is based on a widely employed, energetic approach adapted to the case of liquids. This approach is implemented as a failure criterion in an one-dimensional hydrocode including a multiphase equation of state for tin. A fairly good agreement is obtained between experimental and computed sizes range. Some discrepancies are explained by both experimental uncertainties and model limitations which are carefully pointed out and discussed. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction The understanding of shock-induced failure of materials is an issue of considerable importance to predict the evolution of engineering structures submitted to high-velocity impact or explosive detonation. Extensive experimental and theoretical investigations have been devoted to dynamic failure and fragmentation of solid materials [1,2], particularly in regard to the well-known solid spallation process [3], which occurs upon reflection of a strong compressive pulse at a free surface and leads to the ejection of one or several layers of materials called spalls. However, little data can be found yet about how such process evolves when the material is previously melted partially or fully, upon compression or release, during the propagation of the compressive pulse. In this context, the present work is more specifically dedicated to the fragmentation process referred to as micro-spalling in ref. [4]. This phenomenon arises from the reflection at a free surface of a triangular shock-wave (also called unsupported shock-wave or Taylor-like wave) of sufficiently high peak pressure to cause melting: the interaction of reflected and incident release waves gives rise to tensile stresses which cannot be sustained by the molten material. This one is consequently fragmented into a cloud of fine droplets ejected at high-velocity. The main purpose of the present paper is to address experimental characterization, theoretical modelling and simulation of the micro-spalling process in tin, with a specific focus on the size of the resulting melted droplets, called fragments in the following. Experimental evidence of micro-spalling has been inferred from flash radiography (using either X-ray [5e7] or Proton beam [8,9]) * Corresponding author at: Institut Pprime (UPR 3346), CNRS e ENSMA e Uni- versité de Poitiers, Département Physique et Mécanique des Matériaux, 1 av. Clément Ader, 86961 Chasseneuil Futuroscope Cedex, France. Tel.: þ335 49 49 82 20; fax: þ335 49 49 82 38. E-mail address: loic.signor@lmpm.ensma.fr (L. Signor). Contents lists available at ScienceDirect International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng 0734-743X/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2010.03.001 International Journal of Impact Engineering 37 (2010) 887e900