A thermodynamically complete multi-phase equation of state for dense and porous metals at wide ranges of temperature and pressure

A thermodynamically complete multi-phase equation of state (EOS) applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed. A standard three-term decomposition of the Helmholtz free energy as a function of specific volume and temperature is presented, where the cold component models both compression and expansion states, the thermal ion component introduces the Debye approximation and melting entropy, and the thermal electron component employs the Thomas–Fermi–Kirzhnits (TFK) model. The porosity of materials is considered by introducing the dynamic porosity coefficient α and the constitutive P–α relation, connecting the thermodynamic properties between dense and porous systems, allowing for an accurate description of the volume decrease caused by void collapse while maintaining the quasi-static thermodynamic properties of porous systems identical to the dense ones. These models enable the EOS applicable and robust at wide ranges of temperature, pressure and porosity. A systematic evaluation of the new EOS is conducted with aluminum (Al) as an example. 300 K isotherm, shock Hugoniot, as well as melting curves of both dense and porous Al are calculated, which shows great agreements with experimental data and validates the effectiveness of the models and the accuracy of parameterizations. Notably, it is for the first time Hugoniot P–σ curves up to 10⁶ GPa and shock melting behaviors of porous Al are derived from analytical EOS models, which predict much lower compression limit and shock melting temperatures than those of dense Al.