High-Pressure Shock Compression of Solids VI pp 169-213 | Cite as

# Meso-Macro Energy Exchange in Shock Deformed and Fractured Solids

## Abstract

One of primary problems in the dynamics of materials is developing an understanding of the coupling between microstructural features of a material and its macroscopic response on impact. Many theoretical models based on the microstructure dynamics, in particular on dislocation dynamics, have been developed to describe the macroscopic behavior of material under both uniaxial stress and uniaxial strain conditions. Nevertheless, this coupling is poorly understood both qualitatively and quantitatively. This is due to the incorrect, but commonly used, approach of linking the macroscopic response on impact with data describing the microstructural state that prevails *after* dynamic loading. In reality, adequate mathematical modeling of dynamic processes should be based on microstructural kinetics data obtained in real time, i.e., during the dynamic deformation and fracture processes. This requires that experimental technique provide not only measurements of macroscopic response such as the time-resolved freesurface-velocity profile for impacted specimens, but also kinetic characteristics of their internal structure. These characteristics provide information on the relative mobility of elementary carriers of deformation (ECD). Because the motion of ECDs in a heterogeneous medium is stochastic in nature, their kinetics must normally be described in the language of the particle velocity distribution function and its statistical moments. The term mesoparticle kinetics, as used herein, has the same meaning as in the physical kinetics of fluids and gases, i.e., it refers to the behavior of the particles as characterized by a distribution in velocity space. The width of that distribution, or the square root of the particle velocity dispersion, is defined in Section 5.2 as a mean velocity fluctuation of the mesostructure. This mean velocity fluctuation is a quantitative characteristic of mesoparticle kinetics.

## Keywords

Particle Velocity Impact Velocity Fracture Solid Velocity Fluctuation Velocity Dispersion## Preview

Unable to display preview. Download preview PDF.

## References

- [1]J.N. Johnson., O.E. Jones and T.E. Michaels, “Dislocation dynamics and single-crystal constitutive relation.”
*J. Appl. Phys*.**41**, pp 2770–2779 (1970).Google Scholar - [2]V.E. Panin, V.Yu. Grinjaev, T.F. Elsukova and A.G. Ivanchin, “Structure levels of deformation of solids”.
*Isvestja Vuzov. Fizika***6**, pp. 5–22 (1982).Google Scholar - [3]V.I. Vladimirov, V.N. Nikolaev, and N.M. Priemski, “Mesoscopic level of plastic deformation,” In:
*Physics of strength and plasticity*(ed. S.I. Zhurkov).Nauka. Leningrad, pp. 69–80, (1986).Google Scholar - [4]V.V. Rybin, “Large plastic deformations and fracture of metals,”
*M. Mettalurgy*. 224 p. (1986) (in Russian).Google Scholar - [5]E.L. Aero, “Microscale deformation in two-dimentional lattice: structural transitions and bifurcations at critical shear,”
*Physics Solid State***42**, pp. 1147–1153 (2000). (Translated from*Fizika Tverdogo Tela*.**42**, pp. 1113-1119 (2000)).ADSCrossRefGoogle Scholar - [6]Yu.I. Mescheryakov, N.A. Makhutov, and S.A. Atroshenko, “Micromechanisms of dynamic fracture of ductile high-strength steels,”
*J. Mech. Phys. Solids***42**, pp. 1435–1450 (1994).ADSCrossRefGoogle Scholar - [7]Yu.I. Mescheryakov., A.K. Divakov, and L.P. Fadienko, “On the particle velocity distribution at the elastic precursor of compression wave in Aluminum,”
*J. Tech. Phys*.**53**, p. 2050 (1983).Google Scholar - [8]T.A. Khantuleva and Yu.I. Mescheryakov, “Kinetics and non-local hydrodynamics of mesostructure formation in dynamically deformed media,”
*Int. J. Phys. Mesomechanics***2**, pp. 5–17 (1999).Google Scholar - [9]J.R. Asay and L.M. Barker, “Interferometric measurements of shock-induced internal particle velocity and spatial variation of particle velocity,”
*J. Appl. Phys*.**45**, pp. 2540–2546 (1974).ADSCrossRefGoogle Scholar - [10]Yu.I. Mescheryakov, and A.K. Divakov, “Multiscale kinetics of microstructure and strain-rate dependence of materials,”
*Dymat Journal***1**, pp. 271–287 (1994).Google Scholar - [11]L.M. Barker, “Multi-beam VISAR for simultaneous velocity vs. time measurements” In:
*Shock Compression of Condensed Matter—1999*(ed. M.D. Funlish, L.C. Chhabildas, and R.S. Hixson., American Institute of Physics, Melville, New York, pp 999–1002 (2000).Google Scholar - [12]G.E. Duvall, “Maxwell-like relations in condensed matter. Decay of shock waves,”
*Irish J. Phys. Tech*.**7**, pp. 57–69 (1978).Google Scholar - [13]J. Hubburd, “The friction and diffusion coefficients of the Fokker-Plank equation in a plasma,”
*Proc. Roy. Soc. A***260**, pp 114–126 (1961).ADSCrossRefGoogle Scholar - [14]T.A. Khantuleva, this volume, Chapter 6.Google Scholar
- [15]A.M. Kosevich,
*Dislocation in the theory of elasticity*, Moscow. Nauka. (1978).Google Scholar - [16]T. Mura, “Continuous distribution of moving dislocations,”
*Phil. Mag*.**8**, pp. 843–853 (1963).ADSCrossRefGoogle Scholar - [17]J.J. Gilman. “The plastic wave myth” In:
*Shock Compression of Condensed Matter—1991*(eds. S.C. Schmidt, R.D. Dick, J.W. Forbes, and D.G. Tasker), North Holland, Amsterdam, pp 387–389 (1992).Google Scholar - [18]T. Kihara and O. Aono, “Unified theory of relaxation in plasma. Basic theorem”,
*J. Phys. Soc. Japan***18**, pp. 837–851 (1963).MathSciNetADSCrossRefGoogle Scholar - [19]G.E. Uhlenbeck, L.S. Ornstein, “On the theory of Brownian motion,”
*Phys. Rev*.**36**, p. 823 (1930).ADSzbMATHCrossRefGoogle Scholar - [20]V. Horsthemke and R. Lefever,
*Noise-induced transitions*, Springer-Verlag, New York, p. 297 (1984).zbMATHGoogle Scholar - [21]J.J. Gilman, “Dislocation dynamics and the response of materials to impact,”
*Appl. Mech. Rev*.**21**, p. 767 (1968).ADSGoogle Scholar