Development of semiempirical equation of state of binary functionally graded materials and its influence on generation of ramp compression: Comparison with bilayer graded density impactors

Abstract

Ramp wave study involving graded impactors with discrete or continuous variation of material density is of immense interest for investigation of shock induced structural changes in solids. Hydrodynamic simulation of ramp wave generated by continuously changing functionally graded materials (FGM) requires accurate knowledge of its equation of state (EOS) parameters. However, theoretical as well as experimental EOS data for the same are not readily available. Current work is an attempt towards development of semiempirical EOS model for binary FGM (bFGM) wherein the density is a continuous function of position, either linearly or quadratically. This has been achieved by deriving analytical functions for density dependence of hugoniot parameters using the recently proposed kinetic energy average (KEA) model as well as commonly employed interpolation based methods. Six bFGMs with Al, Mg, and paraffin as low-impedance components and Cu and W as high-impedance ones are considered for the present study. It is shown that shock impedance of linear and quadratic bFGM can be expressed as superlinear/superquadratic functions of position. Subsequently, hydrodynamic simulation results of impact loading of thus constructed bFGMs on ultrathin Ta target are reported. The time profile of target pressure displayed signatures of quasi-isentropic compression (shock ramp). Ramp profiles obtained in our simulation are compared with those generated by recently reported [Phys. Rev. B 99, 214105 (2019)] alternate material bilayer graded density impactor (blGDI) with programmable layer thicknesses. Time profile of ramp pulse is shown to have direct correlation with spatial profile of shock impedance. Influence of associated physical parameters, such as impedance of front layer material, impedance ratio of two components, impact velocity, and mixture model of EOS on shock-ramp adiabats are explored in great detail. The merits of using low and high impedance material as one component of bFGM or blGDI in lowering target heating and enhancing peak ramp pressure are investigated theoretically. Study reveals that paraffin based bFGM with quadratic density function produces the lowest temperature and entropy.