1 ? Comparaison des courants obtenus par Gourdin (1989) et par notre modélisation 1D. Un bon accord jusqu'à t = 22 µs est observé. Au-delà, en raison des essais avec charge creuse de Gourdin, des différences notoires existent naturellement, 1989. ,
Une résolution spatiale supérieure à celle de la caméra Imacon ,
objectif de cette partie est essentiellement de montrer la faisabilité d'une telle procédure. (a) Image de l'anneau en expansion (b) Traitement 1 : extraction de l'anneau (c) Traitement 2 : évaluation des contours Fig. C.1 ? Traitement d'une image d'expansion d'anneau obtenue grâce à la caméra Imacon 200. Le premier traitement revient à extraire de l'image l'anneau ,
Increased ductility in high velocity electromagnetic ring expansion, Met. and Mat. Trans. 27A, pp.1837-1844, 1996. ,
Ring fragmentation predictions using the Gurson model with material stability conditions as failure criteria, International Journal of Solids and Structures, vol.39, issue.13-14, pp.3555-3580, 2002. ,
DOI : 10.1016/S0020-7683(02)00170-1
Characterization of Necking Phenomena in High-Speed Experiments by Using a Single Camera, EURASIP Journal on Image and Video Processing, 2010. ,
DOI : 10.1016/S0143-8166(98)00052-9
URL : https://hal.archives-ouvertes.fr/hal-00497354
A statistical method for verifying mesh convergence in Monte Carlo simulations with application to fragmentation, International Journal for Numerical Methods in Engineering, vol.150, issue.11, pp.279-306, 2011. ,
DOI : 10.1007/978-1-4612-0871-6
Turbulences en mécanique des fluides. Collection Polytech, 2000. ,
Shaped charge jet breakup measurements and surface instability calculations, 1977. ,
DOI : 10.21236/ada040444
URL : http://www.dtic.mil/dtic/tr/fulltext/u2/a040444.pdf
Mémoire sur l'emploi du fer et de l'acier dans les constructions, Annales des Ponts et Chaussées, vol.9, issue.34, pp.574-775, 1885. ,
A damage model for the dynamic fragmentation of brittle solids, Computer Methods in Applied Mechanics and Engineering, vol.183, issue.3-4, pp.247-258, 2000. ,
DOI : 10.1016/S0045-7825(99)00221-2
URL : https://hal.archives-ouvertes.fr/hal-00013966
Inertia and thermal effects on the localization of plastic flow, Acta Metallurgica, vol.33, issue.3, pp.387-396, 1985. ,
DOI : 10.1016/0001-6160(85)90081-1
Fragmentation of rapidly stretching sheets, Eur, 1994. ,
Dynamic pre-strain and inertia effects on the fracture of metals, Journal of the Mechanics and Physics of Solids, vol.28, issue.1, pp.17-26, 1980. ,
DOI : 10.1016/0022-5096(80)90009-5
Investigation of the fracture and fragmentation of explosively driven rings and cylinders, International Journal of Impact Engineering, vol.35, issue.12, pp.1547-1556, 2008. ,
DOI : 10.1016/j.ijimpeng.2008.07.081
Application du test d'expansion d'anneau à l'étude du comportement dynamique du cuivre, 1994. ,
Metallurgical effects on the constitutive and fragmentation behavior of ofhc copper rings, Conference on Shock Compression of Condensed Matter, 1987. ,
Analysis and assessment of electromagnetic ring expansion as a high???strain???rate test, Journal of Applied Physics, vol.12, issue.2, pp.411-422, 1989. ,
DOI : 10.1007/BF00542818
Fragmentation of solids under impulsive stress loading, Journal of Geophysical Research: Solid Earth, vol.44, issue.B2, pp.1047-1054, 1981. ,
DOI : 10.1115/1.3424150
Fragmentation of Rings and Shells -The Legacy of N.F. Mott, 2006. ,
Fragmentation of metal rings by electromagnetic loading, Experimental Mechanics, vol.47, issue.B2, pp.393-400, 1983. ,
DOI : 10.1007/978-1-4613-3219-0_8
A statistics and energy based theory of dynamic fragmentation, International Journal of Impact Engineering, vol.29, issue.1-10, pp.293-306, 2003. ,
DOI : 10.1016/j.ijimpeng.2003.09.026
The Influence of a Surface Coating on the High-rate Fragmentation of a Ductile Material, International Journal of Fracture, vol.23, issue.1-4, pp.89-108, 2006. ,
DOI : 10.1007/s10704-005-3066-0
The dynamics of multiple neck formation and fragmentation in high rate extension of ductile materials, International Journal of Solids and Structures, vol.39, issue.21-22, pp.5615-5632, 2002. ,
DOI : 10.1016/S0020-7683(02)00367-0
Effect of inertia on the necking as a precursor to dynamic fracture, Eur. J. Mech. A/Solids, vol.14, pp.287-307, 1995. ,
Bifurcation phenomena in the plane tension test, Journal of the Mechanics and Physics of Solids, vol.23, issue.4-5, 1975. ,
DOI : 10.1016/0022-5096(75)90027-7
Deformation and fragmentation behaviour of exploded metal cylinders and the effects of wall materials, configuration, explosive energy and initiated locations, International Journal of Impact Engineering, vol.35, issue.12, pp.1578-1586, 2008. ,
DOI : 10.1016/j.ijimpeng.2008.07.002
Fracture Behavior of Tubular Bombs, Journal of Applied Physics, vol.58, issue.3, pp.1856-1862, 1968. ,
DOI : 10.1115/1.3629585
Stress-strain data obtained at high rates using an expanding ring, Experimental Mechanics, vol.8, issue.1, pp.441-448, 1969. ,
DOI : 10.1007/BF02410405
Computational comparisons of homogeneous and statistical descriptions of AerMet100 steel subjected to high strain rate loading, International Journal of Impact Engineering, vol.38, issue.6, 2011. ,
DOI : 10.1016/j.ijimpeng.2010.10.016
Influence of strain-rate sensitivity on necking under uniaxial tension, Acta Metallurgica, vol.25, issue.8, pp.839-846, 1977. ,
DOI : 10.1016/0001-6160(77)90168-7
Dynamic Necking of Rods at High Strain Rates, Le Journal de Physique IV, vol.07, issue.C3, 1997. ,
DOI : 10.1051/jp4:19973119
URL : https://hal.archives-ouvertes.fr/jpa-00255404
Dynamic fracture and spallation in ductile solids, Journal of Applied Physics, vol.99, issue.4, pp.2812-2825, 1981. ,
DOI : 10.1115/1.3443401
Reaction kinetics in processes of nucleation and growth, Trans. AIMME, vol.135, pp.414-458, 1939. ,
Etude analytique de l'instabilité plastique de striction pour une plaque sollicitée en traction biaxiale, 2010. ,
An estimate of the strength of a copper shaped charge jet and the effect of strength on the breakup of a stretching jet, 1976. ,
Pulsed High Magnetic Fields, 1970. ,
Expanding Ring Test : Numerical Simulation - Application to the Analysis of Experimental Data, Le Journal de Physique IV, vol.07, issue.C3, pp.235-240, 1997. ,
DOI : 10.1051/jp4:1997342
URL : https://hal.archives-ouvertes.fr/jpa-00255499
Multiple necking during the dynamic expansion of hemispherical metallic shells, from experiments to modelling, Journal of the Mechanics and Physics of Solids, vol.58, issue.7, pp.955-982, 2010. ,
DOI : 10.1016/j.jmps.2010.05.001
Predictions of bifurcation and instabilities during dynamic extension, International Journal of Solids and Structures, vol.40, issue.8, pp.1995-2016, 2003. ,
DOI : 10.1016/S0020-7683(03)00020-9
Analysis of multiple necking in rings under rapid radial expansion, International Journal of Impact Engineering, vol.30, issue.4, pp.403-419, 2004. ,
DOI : 10.1016/S0734-743X(03)00063-0
CTH simulations of an expanding ring to study fragmentation, International Journal of Impact Engineering, vol.35, issue.12, pp.1661-1665, 2008. ,
DOI : 10.1016/j.ijimpeng.2008.07.066
Fragmentation behavior of Armco iron and HF???1 steel explosive???filled cylinders, Journal of Applied Physics, vol.189, issue.5, pp.2344-2351, 1983. ,
DOI : 10.1098/rspa.1947.0042
Fragmentation of Shell Cases, Proceedings of The Royal Society . Series A. pp, pp.300-308, 1947. ,
DOI : 10.1098/rspa.1947.0042
URL : http://rspa.royalsocietypublishing.org/content/royprsa/189/1018/300.full.pdf
Finite Deformations of an Elastic Solid, American Journal of Mathematics, vol.59, issue.2, 1951. ,
DOI : 10.2307/2371405
Random process model of rough surfaces. Transactions of the ASME, Journal of Lubrication Technology, pp.398-407, 1971. ,
DOI : 10.1115/1.3451608
A unit for testing materials at high strain rates, Experimental Mechanics, vol.11, issue.1, pp.29-32, 1965. ,
DOI : 10.1007/BF02320901
Rupture behaviour of metals in explosive expansion, Inst. Phys. Conf. Ser, vol.47, pp.242-251, 1979. ,
Finite element simulation of ring expansion and fragmentation, International Journal of Fracture, vol.95, issue.1/4, pp.279-297, 1999. ,
DOI : 10.1023/A:1018672922734
On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion, Journal of Physics: Condensed Matter, vol.17, issue.1, 2005. ,
DOI : 10.1088/0953-8984/17/1/R01
Materials under Extreme Loadings, pp.313-332, 2010. ,
Constitutive relations for copper under shock wave loading: Twinning activation, Mechanics of Materials, vol.38, issue.3, pp.173-185, 2006. ,
DOI : 10.1016/j.mechmat.2005.06.005
Breakup of Copper shaped-charge jets: Experiment, numerical simulations, and analytical modeling, Journal of Applied Physics, vol.80, issue.12, 2005. ,
DOI : 10.1016/S0924-0136(98)00099-5
URL : https://hal.archives-ouvertes.fr/hal-00119280
A model of the shear modulus, Solid State Communications, vol.81, issue.3, pp.277-281, 1992. ,
DOI : 10.1016/0038-1098(92)90514-A
An acetylene cylinder explosion: A most probable cause analysis, Engineering Failure Analysis, vol.13, issue.4, 2006. ,
DOI : 10.1016/j.engfailanal.2005.04.014
On the complete extinction of selected imperfection wavelengths in dynamically expanded ductile rings, Mechanics of Materials, vol.60, pp.107-120, 2013. ,
DOI : 10.1016/j.mechmat.2013.01.009
Finite element simulation of steel ring fragmentation under radial expansion, International Journal of Impact Engineering, vol.34, issue.4, pp.799-822, 2007. ,
DOI : 10.1016/j.ijimpeng.2006.01.003
URL : https://e-archivo.uc3m.es/bitstream/10016/7341/3/finite_zaera_ijie_2007_ps.pdf
Necking bifurcations during high strain rate extension, Journal of the Mechanics and Physics of Solids, vol.47, issue.11, pp.2209-2233, 1999. ,
DOI : 10.1016/S0022-5096(99)00031-9
The rupture behaviour of metals at high strain rates, J. Inst. Metals, vol.95, pp.244-251, 1967. ,
Unstable neck formation in a ductile ring subjected to impulsive radial loading, International Journal of Solids and Structures, vol.37, issue.16, pp.2265-2283, 2000. ,
DOI : 10.1016/S0020-7683(98)00315-1
The fragmentation of tubular bomb Scientific papers of G.I. Taylor Vol III, pp.387-390, 1963. ,
Dynamic fracture of 6061-T6 aluminium cylinders, 1977. ,
DOI : 10.1115/1.3424150
Dislocation???mechanics???based constitutive relations for material dynamics calculations, Journal of Applied Physics, vol.46, issue.5, pp.1816-1825, 1987. ,
DOI : 10.1063/1.1707363
URL : https://zenodo.org/record/1232906/files/article.pdf
On the dynamics of necking and fragmentation ??? I. Real-time and post-mortem observations in Al 6061-O, International Journal of Fracture, vol.21, issue.6, pp.183-217, 2006. ,
DOI : 10.1098/rspa.1950.0050
On the dynamics of necking and fragmentation???II. Effect of material properties, geometrical constraints and absolute size, International Journal of Fracture, vol.33, issue.1, pp.3-36, 2008. ,
DOI : 10.1007/978-1-4613-2880-3_6
An elastic???visco-plastic analysis of ductile expanding ring, International Journal of Impact Engineering, vol.33, issue.1-12, pp.880-891, 2006. ,
DOI : 10.1016/j.ijimpeng.2006.09.070
The formation of multiple adiabatic shear bands, Journal of the Mechanics and Physics of Solids, vol.54, issue.7, pp.1376-1400, 2006. ,
DOI : 10.1016/j.jmps.2006.01.006