The multiphase equation of states (EOSs) of both the solid and liquid phases of Al and Ta are presented. These EOSs are carried out on the basis of the Helmholtz free energy, where the ion vibration free energy is evaluated from the mean field potential (MFP) model we recently proposed [Physica B 406 (2011) 4163]. The calculated results show that our multiphase EOSs can give a good reproduction of the measured phase diagrams and other experimental data, including static high-pressure measurements, shock Hugoniots and the thermodynamic quantities of these metals.

Element bismuth (Bi) will experience complex phase transitions under high temperature and high pressure, which means significant changes in physical properties, such as density, energy, etc. Multiphase equations of states (EOSs) of both solid and liquid phases for Bi are presented. The EOSs are based on the three-term expression for Helmholtz free energy, where the ion vibration free energy is evaluated from the mean field potential model we recently proposed. The calculated results show that our multiphase EOSs can well reproduce the experimental data, including phase diagram, isotherms of solid phases, density measurements of liquid phase and shock-wave compression data, which proves the rationality of the parameter values and the universal nature of this model.

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The Hugoniot elastic limit (HEL) of ceramics is explained as the limit of elastic response and the onset of failure under dynamic uniaxial strain loading, which is an important parameter for understanding the dynamic properties of ceramic materials. Previous experimental impact studies showed an interesting phenomenon that the HEL decreases with the increase of sample thickness, which is termed the elastic precursor decay. This phenomenon has not been explained by a suitable mechanism to date. Recently it has become apparent that mechanical response of polycrystalline ceramics is governed by mechanism operating at a grain level. So the objective of the present work is to develop a mechanism that can illustrate this phenomenon on a mesoscale. In this paper, the plate impact experiments of alumina with varying thickness values are conducted by using one-stage light gas gun. The histories of the rear free surface velocity of the samples are recorded by a Velocity Interferometer System for Any Reflector (VISAR). The HELs of alumina samples with different thickness values are obtained from turning point of elastic phase to inelastic phase in the temporal curves of free surface velocity. It is confirmed that the HEL of alumina decreases with increasing the sample thickness obviously, namely elastic precursor decay phenomenon. It is considered that this phenomenon is related to the failure mechanism of shocked alumina at a grain level. Thus, the mesoscopic model of alumina, including alumina grain phase and glass binder phase, is developed according to the microstructure properties of tested sample observed experimentally. Mesoscale simulations are presented to study the mesoscale failure properties of alumina at various impact velocities. The results show that inelastic responses, such as microcracking, grain plasticity, are observed in microstructure of alumina even when the peak-shock stress is less than the magnitude of HEL. As is well known, the evolution process of cracking or plasticity is the energy dissipation process essentially, which will reduce the amplitude of elastic wave. Furthermore, the properties of elastic precursor wave propagation in microstructure of alumina are also captured in the present simulations. Since the acoustic impedance of glass binder phase is much lower than that of alumina grain phase, complex reflection and transmission of elastic wave will occur at grain boundaries. Due to a large number of randomly oriented crystals, the wave front, well defined at the continuum, is dispersed to lateral or reverse directions at these length-scales, which can also decay the elastic precursor amplitude in the initial propagating direction. Therefore, the results suggest that energy dissipation caused by the failure process should occur below HEL and energy dispersion due to reflection and transmission of elastic wave at grain boundaries should play a dominant role in the phenomenon of elastic precursor decay.