Two-zone Hugoniot for porous materials

By decoupling thermal equilibrium conditions in shock loaded porous materials, two regimes resulting in two-zone Hugoniot are revealed, specifically, a stable low-pressure regime characterized by achieving interphase temperature equilibrium and a metastable high-pressure regime. Porous materials, represented as two-phase mixtures, are analyzed with an analytically constructed Hugoniot employing a constant Grüneisen parameter of condensed phase. Results of the analysis agree well with experiments for various porous materials over a wide range of porosities, which confirms the consistency of this interpretation. The two-zone consideration discovers a limitation on the high-temperature states of solid materials accessible via the shock loading of porous materials and suggests that the two-phase nature of porous materials needs to be reflected in the use of Hugoniot data of powders when constructing equations of state for the corresponding condensed materials.

Figure 1

Schematic of the PE and PTE Hugoniots for a porous material and its constituents at a high porosity resulting in the Hugoniot abnormality.

Figure 2

Calculated composite Hugoniots (curves) compared to the experiment (points) for copper powders: $m=1.4$ (1, $\circ$), 2 (2, $\square$), 4 (3, $△$), 5.5 (4, $•$), 7.2 (5, $\blacksquare$), and 10 (6, $\times$).

Figure 3

Calculated composite Hugoniots (curves) compared to the experiment (points) for iron powders: $m=1.13$ (1, $\circ$), 1.65 (2, $\square$), 2.33 (3, $△$), 2.9 (4, $\diamond$), 10 (5, $•$), and 20 (6, $\times$).

Figure 4

Calculated composite Hugoniots (curves) compared to the experiment (points) for tantalum pentoxide powders: $m=1.1$ (1, $\circ$), 2.7 (2, $\square$), 6.8 (3, $△$), and 32.8 (4, $\times$).

Figure 5

Calculated composite Hugoniots (curves) compared to the experiment (points) for polystyrene powders: $m=2.1$ (1, $\circ$), 3.67 (2, $\square$), 5.3 (3, $△$), 7.2 (4, $•$), 10.5 (5, $\blacksquare$), 13.6 (6, $\diamond$), and 19.1 (7, $\times$).

Figure 6

Calculated three-phase composite Hugoniots (curves) compared to the experiment (points) for PTFE powders: $m=1.45$ (1, $\circ$) and 2.82 (2, $\square$).

Figure 7

Calculated three-phase composite Hugoniots (curves) compared to the experiment (points) for silicon dioxide powders: $m=1.5$ (1, $\circ$) and 4.82 (2, $\square$).