Abstract
A model for the spall fracture and compaction of a damaged material based on a description of the motion of a single pore is proposed. The model takes into account the strength properties, the effect of pressure, surface tension, and viscosity of materials and inertial forces. Equations describing the dynamics of growth and collapse of pores are presented. The proposed model can be used to calculate the spall fracture and compaction of liquids and metals in both solid and liquid (molten) states.
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O. N. Ignatova, V. A. Raevskii, and I. S. Tselikov, “Kinetic Model for the Compaction of Damage in Materials with Strength,” Vopr. Atom. Nauki Tekh., Ser. Mat. Model. Fiz. Prots., No. 1, 18–23 (2014).
S. P. Kiselev, G. A. Ruev, A. P. Trunev, V. M. Fomin, and M. Sh. Shavaliev, Shock-Wave Processes in Two-Component and Two-Phase Media (Nauka, Novosibirsk, 1992) [in Russian].
S. P. Kiselev, “On Propagation of a Shock Wave in a Porous Material upon Collision of Plates, Fiz. Goreniya Vzryva 31 (4), 79–83 (1995) [Combust., Expl., Shock Waves 31 (4), 473–477 (1995)].
Ya. I. Zel’dovich, “On the Theory of Formation of a New Phase. Cavitation,” Zh. Eksp. Teoret. Fiz. 12 (11/12), 525–538 (1942).
V. K. Kedrinskii, “The Experimental Research and Hydrodynamic Models of a Sultan,” Arch. Mech. 26 (3), 535–540 (1974).
V. K. Kedrinskii, “Nonlinear Problems of Cavitation Breakdown of Liquids under Explosive Loading (Review),” Prikl. Mekh. Tekh. Fiz. 34 (3), 74–91(1993) [J. Appl. Mech. Tech. Phys. 34 (3), 74–91(1993)].
A. A. Bogach and A. V. Utkin, “Strength of Water under Pulsed Loading,” Prikl. Mekh. Tekh. Fiz. 41 (4), 198 (2000) [J. Appl. Mech. Tech. Phys. 41 (4), 752–758 (2000)].
A. V. Utkin, V. A. Sosikov, and A. A. Bogach, “Impulsive Tension of Hexane and Glycerin under Shock Wave Loading,” Prikl. Mekh. Tekh. Fiz. 44 (2), 27–33 (2003) [J. Appl. Mech. Tech. Phys. 44 (2), 174–179 (2003)].
G. I. Kanel et al., “Dynamic Strength of Tin and Lead Melts,” Pis’ma Zh. Eksp. Teoret. Fiz. 102 (8), 615–619 (2015).
M. Furlanetto et al., “The ORTEGA Experiment: Radiographic and Velocimetric Damage Measurements,” Ortega Preshot Report No. LA-UR-10-05028 (2010).
D. B. Holtkamp, D. A. Clark, E. N. Ferm, et al., “A Survey of High Explosive-Induced Damage and Spall in Selected Metals using Proton Radiography,” in Shock Compression of Condenses Mater., Proc. of the Conf., Portland, OR, July 2003 (Amer. Inst. Phys., Melville, 2003), pp. 477–482.
Zhang Chongyu, Hu Haibo, et al., “Dynamic Behaviors of Pb Flyer Driven by Head-on Detonation,” in Extreme States of Matter. Detonation. Shock Waves (VNIIEF, Sarov, 2009), pp. 422–426 [in Russian].
M. M. Carroll and A. C. Holt, “Static and Dynamic Pore-Collapse Relations for Ductile Porous Materials,” J. Appl. Phys. 43, 1626–1635 (1972).
N. F. Gavrilov, G. G. Ivanova, V. I. Selin and V. N. Sofronov, “The UP-OK Program for Solving One-Dimensional Problems of Continuum Mechanics in a One-Dimensional Complex,” Vopr. Atom. Nauki Tekh. 3 (11), 11–14 (1982).
M. Meyers and C. Aimone, “Dynamic Fracture (Spalling) of Metals,” Prog. Mater.Sci. 28, 1–96 (1983).
A. S. Besov, V. K. Kedrinskii, and E. I. Pal’chikov, “The Initial Stage of Cavitation Using a Diffractive Optical Technique,” Pis’ma Zh. Tekh. Fiz. 10 (4), (1984).
Physical Quantities: Handbook, Ed. by I. C. Grigor’ev and E. Z. Meilikhov (Energoatomisdat, Moscow, 1991) [in Russian].
W. Herrmann, “Constitutive Equation for the Dynamic Compaction of Ductile Porous Materials,” J. Appl. Phys. 40 (6), 2490–2499 (1969).
B. L. Glushak, O. N. Ignatova, S. S. Nadezhin, and V. A. Raevskii, “Relaxation Model for the Shear Strength of Five Metals,” Vopr. Atom. Nauki Tekh., Ser. Mat. Model. Fiz. Prots., No. 2, 25–36 (2012).
E. Hairer and G. Wanner, Solving Ordinary Differential Equations. Stiff and Differential-Algebraic Problems (Mir, Moscow, 1999) [Russian translation].
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Original Russian Text © M.A. Desyatnikova, O.N. Ignatova, V.A. Raevskii, I.S. Tselikov.
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Desyatnikova, M.A., Ignatova, O.N., Raevskii, V.A. et al. Dynamic model of the growth and collapse of pores in liquids and solids. Combust Explos Shock Waves 53, 103–109 (2017). https://doi.org/10.1134/S0010508217010142
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DOI: https://doi.org/10.1134/S0010508217010142