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In order to verify and validate the newly developed thermoelectron equation of state (EOS) model that is based on the Wu-Jing (W-J) EOS, calculations of shock compression behavior have been made on five different porous metals-iron, copper, lead, tungsten, and aluminum-which are commonly used as standards. The model was used to calculate the Hugoniot, shock temperature, sound velocity, and unloading isentrope for these materials and comparisons were made to previous calculations and available data. Based on these comparisons, it is felt that the model provides information in good agreement with the corresponding experimental and theoretical data published previously. This suggests that the new model can satisfactorily describe the properties of shocked porous materials over a wide range of pressure and porosity., 27 pages, 11 figures, appeared at J. Appl. Phys. 92, 5917 (2002)

Structure evolution under dynamic compression condition (high temperature, high pressure and high strain rate) is one of the most important problems in engineering and applied physics, which is vital for understanding the kinetic mechanism of shock-induced phase transition. In this work, an in-situ dynamic X-ray diffraction (DXRD) diagnostic method is established to probe the lattice response driven by shock waves. The geometry is suitable for the study of laser-shocked crystals. In order to eliminate the measurement error arising from the difference in experimental setup, the static and dynamic lattice diffraction signals are measured simultaneously in one shot by using a nanosecond burst of X-ray emitted from a laser-produced plasma. Experimental details in our investigation are as follows. 1) The laser driven shock wave transit time △ tShock and the shock pressure in sample are accurately determined from the shock-wave profile measurement by dual laser heterodyne velocimetry. 2) A laser pump-and-probe technique for adjusting the time-delay of DXRD diagnosis during △ tShock, with a series of repeated shock loadings is then employed to generate and measure the dynamic structure evolution. Using this method, the dynamic lattice response of[111] single-crystal iron is studied on Shenguang-Ⅱ facility. Single-shot diffraction patterns from both unshocked and shocked crystal are successfully obtained. An elastic-plastic transition process –elastic wave followed by a plastic wave– is observed in shocked[111] single-crystal iron on a lattice scale. The lattice compressibility values of the elastic wave and plastic wave are in agreement with those derived from the wave profiles. It is found that the Hugoniot elastic limit is measured to be about 6 GPa under nanosecond-pulsed laser shock compression. Such a high yield strength is consistent with recent laser ramp compression experimental results in polycrystalline Fe[Smith et al. 2011 J. Appl. Phys. 110 123515], suggesting that the peak pressure of elastic wave is dependent on the loading rate and the thickness of sample. Based on the analysis of diffraction patterns, the BCC phase is determined to be stable till 23.9 GPa, the highest pressure explored in this work, which might indicate that the phase transition strongly couples with the crystal orientation and loading rate. Some possible physical mechanisms remain to be further studied:whether the transition time hysteresis occurs or the metastable FCC phase exists in shocked[111] single crystal Fe, or the phase transition onset pressure increases under high strain-rate compression. Our DXRD results provide a primary experimental reference for the follow-up study on the phase kinetics.

Porous material contains a large number of pores, and once the pore space collapses, it changes into a dense material with the great increase of temperature because of the energy deposition by porosity collapsing. In the process of shock compression, the temperature is extremely increased, which influences the thermodynamic state of porous material significantly. Therefore, the calculation of temperature is important for the shock compression of porous material, yet it has not been solved well in the literature. In this paper, based on the study of Grneisen general function v(v), the Debye temperature function of solid material is extended to the region of porous material, and the equivalent Debye temperature function (v) of porous material is formulated, from which the isentropic temperature function Ts(v) of porous material is obtained. Furthermore, a computation model is established, in which the isentropic work of porous is assumed to be equal to that of compact material under the same pressure at 0 K. With this model, the isentropic pressure function ps(v) of the porous material is acquired. Hence, the reference equation for calculating temperature and pressure of porous material, i.e., Ts(v) and ps(v), is completed. To demonstrate this method, the p-v and T-v curves of the Hgoniot state of porous copperare computed, and the values of porosity are m 1.13, 1.22, 1.41, 1.56 and 1.98, respectively. The calculated results are in good agreement with the experimental data. A comparison with other calculation is also made, indicating a better reliability of the present method.

A thermodynamic equation of state (EOS) for thermoelectrons is derived which is appropriate for investigating the thermodynamic variations along isobaric paths. By using this EOS and the Wu-Jing (W-J) model, an extended Hugoniot EOS model is developed which can predict the compression behavior of highly porous materials. Theoretical relationships for the shock temperature, bulk sound velocity, and the isentrope are developed. This method has the advantage of being able to model the behavior of porous metals over the full range of applicability of pressure and porosity, whereas methods proposed in the past have been limited in their applicability., 18 pages, 1 figure, appeared at J. Appl. Phys. 92, 5924 (2002)

Based on the crystal lattices oscillator model, a thermodynamic equation of state is derived using a statistical dynamics method. The new parameter R of this equation of state is independent of the Grüneisen parameter, as compared with its predecessor, which was given by Q. Wu and F. Q. Jing. The calculated shock Hugoniot loci based on this new parameter are in good agreement with those calculated by the original parameter over a wide pressure range. This validates the new form of the R parameter.