Strength of porous α-SiO2 in a shock loaded environment: Calibration via Richtmyer–Meshkov instability and validation via Mach lens

Abstract

The strength of brittle porous media is of concern in numerous applications, for example, earth penetration, crater formation, and blast loading. Thus, it is of importance to possess techniques that allow for constitutive model calibration within the laboratory setting. The goal of the current work is to demonstrate an experimental technique allowing for strength assessment of porous media subjected to shock loading, which can be implemented into pressure-dependent yield surfaces within numerical simulation schemes. As a case study, the deviatoric response of distended α-SiO2 has been captured in a tamped Richtmyer–Meshkov instability (RMI) environment at a pressure regime of 4–10 GPa. Hydrocode simulations were used to interpret RMI experimental data, and a resulting pressure-dependent yield surface akin to the often employed modified Drucker–Prager model was calibrated. Simulations indicate that the resulting jet length generated by the RMI is sensitive to the porous media strength, thereby providing a feasible experimental platform capable of capturing the pressurized granular deviatoric response. Furthermore, in efforts to validate the RMI-calibrated strength model, a set of Mach-lens experiments was performed and simulated with the calibrated pressure-dependent yield surface. Excellent agreement between the resulting Mach-lens length in experiment and simulation provides additional confidence to the RMI yield-surface calibration scheme.

Tamped Richtmyer–Meshkov Instability Experiments to Probe High-Pressure Material Strength

“…Strain rates in these experiments were of order 10 7 s −1 , though strain rates and total strain varied across the regions of the sample. Most were performed into vacuum ( A = −1 ), with only the work by Olles et al [26] and Hudspeth et al [27] involving a tamped configuration ( A > −1 ); they are discussed in the next section.…”

“…Olles et al [26] examined copper drivers tamped by deuterated water. Hudspeth et al [27] utilized the same configuration, but their objective was to probe the strength behavior of the tamper material, a SiO 2 powder. This was possible because the strength of the copper was independently established in the two studies.…”

“…In lieu of a fluid, a soft metal that readily deforms can be used. Copper [26,27] is a good choice since it is readily available and widely studied.…”

“…Liquids also have the advantage that they will conform to perturbations such as those examined here. Water (1.0 g/cm 3 ) or deuterated (heavy) water are well characterized and have been used in recent studies [26,27]. The densest fluid at ambient conditions is mercury (13.6 g/cm 3 ), though it presents numerous concerns for experimental work.…”

“…• The tamper material chosen has implications for the instrumentation that can be utilized. For example, synchrotron radiation such as that available at the Advanced Photon Source [16] has been used to image through water [26] and SiO 2 powder [27], but it would not penetrate any reasonable thickness of mercury or Wood's metal. On the other hand, proton radiography [15,28,29] has much greater penetrating capability and could be used with, in principle, almost any tamper material.…”