Fundamental structure of steady plastic shock waves in metals

Abstract

The propagation of steady plane shock waves in metallic materials is considered. Following the constitutive framework adopted by R. J. Clifton ͓Shock Waves and the Mechanical Properties of Solids, edited by J. J. Burke and V. Weiss ͑Syracuse University Press, Syracuse, N.Y., 1971͒, p. 73͔ for analyzing elastic-plastic transient waves, an analytical solution of the steady state propagation of plastic shocks is proposed. The problem is formulated in a Lagrangian setting appropriate for large deformations. The material response is characterized by a quasistatic tensile ͑compression͒ test ͑providing the isothermal strain hardening law͒. In addition the elastic response is determined up to second order elastic constants by ultrasonic measurements. Based on this simple information, it is shown that the shock kinetics can be quite well described for moderate shocks in aluminum with stress amplitude up to 10 GPa. Under the later assumption, the elastic response is assumed to be isentropic, and thermomechanical coupling is neglected. The model material considered here is aluminum, but the analysis is general and can be applied to any viscoplastic material subjected to moderate amplitude shocks. Comparisons with experimental data are made for the shock velocity, the particle velocity and the shock structure. The shock structure is obtained by quadrature of a first order differential equation, which provides analytical results under certain simplifying assumptions. The effects of material parameters and loading conditions on the shock kinetics and shock structure are discussed. The shock width is characterized by assuming an overstress formulation for the viscoplastic response. The effects on the shock structure of strain rate sensitivity are analyzed and the rationale for the J. W. Swegle and D. E. Grady ͓J. Appl. Phys. 58, 692 ͑1985͔͒ universal scaling law for homogeneous materials is explored. Finally, the ability to deduce information on the viscoplastic response of materials subjected to very high strain rates from shock wave experiments is discussed.

The atomistic modeling of wave propagation in nanocrystals

“…As the shock pressure increases, plasticity also increases, but the overall result is a decrease in the width of the front, as seen in experiments and predicted by viscoplastic models 34 . This leads to a steep increase of the strain rate with pressure, as measured for strong, overdriven shocks.…”

Simulation of the shock waves propagation through the interface of bipartite bimetallic Ni-Al particles

“…Инициирование ударных волн может быть осу-ществлено посредством мощного лазерного излу-чения, при значениях интенсивности в пределах 10 12 -10 13 Вт / см 2 , либо при бомбардировке поверхности металла тяжелыми ионами [16,17].…”

Impact Mechanics and High-Energy Absorbing Materials: Review

“…The results in Jones et al (1997) match the continuum results for the analysis of plastic wave propagation in the Taylor impact test, in which a cylindrical specimen impacts a rigid flat target perpendicularly in order to determine its mechanical behavior at high strain rates. Molinari and Ravichandran (2004) use the Lagrangian multiplier method to formulate the solution of steady plastic shocks in metals. An explicit formula is obtained for the characteristic shock width, and the effect of parameters like strain rate sensitivity and flow stress resistance on the shock profile is analyzed.…”