Equivalent thermo-mechanical parameters for perfect crystals

Thermo-elastic behavior of perfect single crystal is considered. The crystal is represented as a set of interacting particles (atoms). The approach for determination of equivalent continuum values for the discrete system is proposed. Averaging of equations of particles' motion and long wave approximation are used in order to make link between the discrete system and equivalent continuum. Basic balance equations for equivalent continuum are derived from microscopic equations. Macroscopic values such as Piola and Cauchy stress tensors and heat flux are represented via microscopic parameters. Connection between the heat flux and temperature is discussed. Equation of state in Mie-Gruneisen form connecting Cauchy stress tensor with deformation gradient and thermal energy is obtained from microscopic considerations.Comment: To be published in proceedings of IUTAM Simposium on "Vibration Analysis of Structures with Uncertainties", 2009; 14 pages

Test of a theoretical equation of state for elemental solids and liquids

We propose a means for constructing highly accurate equations of state (EOS) for elemental solids and liquids essentially from first principles, based upon a particular decomposition of the underlying condensed matter Hamiltonian for the nuclei and electrons. We also point out that at low pressures the neglect of anharmonic and electron-phonon terms, both contained in this formalism, results in errors of less than 5% in the thermal parts of the thermodynamic functions. Then we explicitly display the forms of the remaining terms in the EOS, commenting on the use of experiment and electronic structure theory to evaluate them. We also construct an EOS for Aluminum and compare the resulting Hugoniot with data up to 5 Mbar, both to illustrate our method and to see whether the approximation of neglecting anharmonicity et al. remains viable to such high pressures. We find a level of agreement with experiment that is consistent with the low-pressure results.Comment: Minor revisions for consistency with published versio

Low-Melting Metal Resistance to Plastic Strain in Shock-Compressed State

The measuremental results are presented for the main stresses, σx and σy, behind the plane stationary shock wave front in the low-melting metals (Mg, Cd, Sn, Zn, Bi). In every test the piesoresistive gauges were employed for the measurements, placed in two mutually perpendicular planes of a sample. The gauge measuring element is a linear piece of the manganine wire of 0.05 mm in diameter and 10 mm long. The total gauge thickness with polymer insulation was 0.23 mm at low stresses and 0.53 mm at high ones behind the shock wave front. Stationary shock waves of duration about ~1 µs entered into the sample from the screen where the shock wave propagates being generated by a detonation wave incident along the normal. The measured values correctness for the main stresses, σx and σy, is supported by the special tests with paraffin, steel (elastic and plastic deformation regions), ceramics (elastic deformation regions) and vanadium. For the low-melting metals investigation in the normal stresses range, σx = 4-25 GPa, the strong strengthening was recorded at the high-speed deformation by the shock waves. The dependence of dynamic ultimate yield, Yg = σx-σy on σx approaches a linear one the range investigation.Les résultats des mesures des contraintes principales σx et σy ayant lieu derrière le front de l'onde de choc plate stationnaire dans les métaux fusibles (Mg, Cd, Sn, Zn, Bi) sont présentés. Les mesures sont été réalisées par les capteurs piézorésistants disposés dans deux plans d'échantillon réciproquement perpendiculaires. Les ondes de choc stationnaires de durée ~1 µs ont été introduites dans l'échantillon de l'écran dans lequel l'onde de choc produite par l'onde de détonation normale se propageait. Le durcissement fort a été enregistré pour les métaux fusibles examinés dans la gamme des contraintes normales σx= 4-25 GPa à la déformation ultra-rapide dans les ondes de choc. Dans la gamme examinée la relation entre la limite élastique dynamique Yg = σx-σy et σx ressemblait beaucoup à la relation linéaire

Application of kinetic conception to the numerical simulation of spall fracture of metals

The results of application of kinetic two-stage microstatistical model with internal values (of the NAG type) to describe the spall fracture of metals are presented. The model describes adequately experimental data for natural uranium, copper, aluminum and some other metals. Some peculiarities of transient process of spall fracture are under analysis

Peculiarities of metal balls deformation by quasi-spherical shock waves

The paper presents results of experimental studies of metal balls deformation by quasi-spherical shock waves. With use of sequential increase of explosive layer thickness characterizing level of shock-wave loading for ball surface, we recorded various extents of ball : from saving of material continuity to fragmentation. Results of explosive loading of metals with different strength and plastic properties are discusse