High Pressure Hugoniot Measurements in Solids Using Mach Reflections

Shock compression experiments provide access to extreme pressures in a laboratory setting. Matter at these pressures is often studied by utilizing a well controlled planar impact between two flat plates to generate a one dimensional shock wave. While these experiments are a powerful tool in equation of state (EOS) development, they are inherently limited by the velocity of the impacting plate. In an effort to dramatically increase the range of pressures that can be studied with available impact velocities, a new experimental technique is examined. The target plate is replaced by a composite assembly consisting of two concentric cylinders and is designed such that the initial shock velocity in a well characterized outer cylinder is higher than in the inner cylinder material of interest. After impact, conically converging shocks are generated at the interface due to the impedance mismatch between the two materials and the axisymmetric geometry. Upon convergence, an irregular reflection occurs and the conical analog of a Mach reflection develops. The Mach reflection grows until it reaches a steady state, for which an extremely high-pressure state is concentrated behind the Mach stem. The Mach lens composite target comprising of the concentric cylinders is studied using a combination of analytical, numerical, and experimental techniques. A simple analytical method for calculating the form of the Mach reflection is determined through classic concepts in gas dynamics. Traditionally, oblique shock reflection phenomena in gases can be treated through a shock polar analysis, which provides an intuitive graphical method for solving such problems. By translating the classic Lagrangian treatment of a 1-D plane shock wave in a solid to the Eulerian oblique shock framework for gases, a similar methodology is developed to treat shock reflections in solids. Numerical simulations using a hydrocode are also conducted to gain further insight into the problem. These simulations reveal quantitative details about the shock propagation and interaction in the Mach lens and are used to both validate the shock polar analysis and design the experiments. The Mach lens concept is validated experimentally by examining a copper inner cylinder in conjunction with outer materials of either 6061-T6 aluminum or molybdenum. Since, in the steady state, the axial velocity of the Mach reflection is equal to the far field shock velocity in the outer cylinder, the shock velocity can be calculated through impedance matching between the well characterized impactor and outer cylinder materials from a measurement of the projectile velocity. A vi second measurement of the Mach reflection is made through velocity interferometry at the rear surface of the target using either VISAR, which provides a point measurement of the velocity, or ORVIS, which provides the velocity spatially resolved along a line. The VISAR experiments provide a time resolved free surface velocity measurement at the center of the target which allows for an inference of the in situ particle velocity, and, in conjunction with the calculated shock velocity, provides the necessary information to calculate the shocked state behind the Mach stem. Measurements of this shocked state have been found to be in excellent agreement with Hugoniot measurements in copper using traditional plane shock techniques. These Hugoniot states illustrate multiplications in the pressure between 1.7 and 4.4 over the equivalent plate impact experiments. These types of high pressures traditionally require impact velocities between 2 and 5 km/s, which can only be obtained with two-stage launcher technology. The spatial properties of the Mach reflection are investigated using either multiple VISAR point measurements or the ORVIS diagnostic. The measurements are found to be in good agreement with both the shock polar analysis, and numerical simulations. The possibilities of using this type of full field information to extract an entire Hugoniot curve in a single experiment are also discussed. The effects of phase transitions on the Mach lens target are also examined through the use of an iron inner cylinder. Iron undergoes a well known α (bcc) (hcp) polymorphic transition along the Hugoniot, and the effects of this response are examined through the use of numerical simulations and VISAR measurements.