Thermodynamic equation of state and application to Hugoniot predictions for porous materials

Abstract

A thermodynamic equation of state (EOS) is derived which is appropriate for investigating the thermodynamic variations along isobaric paths. By using this EOS, a Hugoniot EOS model with a unified theoretical basis is proposed for predicting the shock compression behavior of porous materials. The model is tested on 2024 aluminum, copper, and tungsten which are the typical materials with low, intermediate, and high shock impedance, respectively, and commonly used as standards. The calculated Hugoniots for these three materials with different initial densities are in good agreement with the corresponding experimental data published previously. It shows that this Hugoniot EOS model can satisfactorily predict the Hugoniot of porous materials over a wide pressure range.

On predicting the shock densification response of heterogeneous powder mixtures

“…(1) and (2) and used by Wu and Jing [1] is a rate independent compaction model for ductile metal powders. While more phenomenological in formulation, the model of Fischmeister and Artz [3] is also based on rate independent compaction of ductile metallic powders.…”

“…In doing so, it was necessary to choose an analysis framework which permitted direct exchange between quasi-static and dynamic model parameters, and one which could also be applied to a wide range of initial configurations. With regard to dynamic compaction models, that of Wu and Jing [1] is ideally suited for this application because it does not rely directly on the Grüneisen parameter to extrapolate the porous response from that of the solid, and can thus be applied to low (< 50 % theoretical) density powders/mixtures. Furthermore, it incorporates densification along a cold compaction curve through the simplified Carrol-Holt [2] model, which depends only on porosity and the yield strength of the matrix material.…”

“…2, resulting in a value of σ D = 1,683 MPa. With σ D determined, the dynamic crush-up response of the equivolumetric mixture of Ta + Fe 2 O 3 is predicted using the model of Wu and Jing [1] and Eqns.…”

Intense shock compression of porous solids: Application to wc and ta2O5

“…The RW parameter is a dimensionless measure of the increase in volume when thermal energy is added to a body while maintaining the pressure of the body constant. The seminal, thermodynamic approach introduced by Rice and Walsh is espoused and assimilated in our EOS model [3,4]. Equation 2 can be integrated holding pressure P constant from some reference volume υ R (P) and reference enthalpy H R (P) to yield a relation for specific volume as a function of pressure and enthalpy, 3 is analogous to the Mie Grüneisen EOS obtained when Eq.…”

The influence of particle morphology on the dynamic densification of metal powders

“…Prior to the experiments, the Hugoniot and crushup curves for the three mixtures were calculated using the Wu-Jing model [4], which constructs the powder states based upon an isobaric shift from the Hugoniot of the solid. For the low stress regime, the Wu-Jing model implements the Carrol-Holt form of the P − α model [5].…”