Mark Lieber

Novel measurements of shock pressure decay in PMMA using detonator loading

An empirical model equation for shock-pressure decay in PMMA was determined through a unique set of experiments employing detonator loading. Custom polymethyl methacrylate (PMMA) witness blocks were designed with monolithic architecture to house precise PMMA gaps with thicknesses ranging from 0-10 mm in nominal increments of 1 mm. The PMMA gaps separated detonator working surfaces from windowed photonic Doppler velocimetry (PDV) probes, and were designed to provide undistorted optical access for ultra-high-speed framing and digital-streak cameras. The shock wave image framing technique (SWIFT), and a new laser-backlit digital-streak diagnostic, simultaneously captured the temporal evolution of detonator-induced diverging shock waves within the PMMA gaps. The PDV diagnostic measured critical mass-velocity histories as the shocks exited the variable gap thicknesses. The multi-diagnostic data package was used to characterize the shock-pressure decay in PMMA as a function of shock-propagation time and PMMA thickness.An empirical model equation for shock-pressure decay in PMMA was determined through a unique set of experiments employing detonator loading. Custom polymethyl methacrylate (PMMA) witness blocks were designed with monolithic architecture to house precise PMMA gaps with thicknesses ranging from 0-10 mm in nominal increments of 1 mm. The PMMA gaps separated detonator working surfaces from windowed photonic Doppler velocimetry (PDV) probes, and were designed to provide undistorted optical access for ultra-high-speed framing and digital-streak cameras. The shock wave image framing technique (SWIFT), and a new laser-backlit digital-streak diagnostic, simultaneously captured the temporal evolution of detonator-induced diverging shock waves within the PMMA gaps. The PDV diagnostic measured critical mass-velocity histories as the shocks exited the variable gap thicknesses. The multi-diagnostic data package was used to characterize the shock-pressure decay in PMMA as a function of shock-propagation time and PMMA th...

On a physics-based model equation for shock-position evolution in PMMA

A governing differential equation for shock position in PMMA was derived from momentum conservation and an experimentally determined decay law for shock pressure. A new multi-diagnostic characterization method for measuring detonator pressure and wave shape output in PMMA witness blocks provided temporally resolved, 1-D, shock-position data that was iteratively fit by solutions to the governing equation via a unique genetic algorithm solver. The goal was to calculate a solution that describes the temporal evolution of shock pressure in PMMA starting at the detonator interface. The empirical decay law was investigated using experimental data, where different regimes were considered for the decay coefficients. A successful solution provides extensive performance information that is directly relevant to the understanding and characterization of detonator function.A governing differential equation for shock position in PMMA was derived from momentum conservation and an experimentally determined decay law for shock pressure. A new multi-diagnostic characterization method for measuring detonator pressure and wave shape output in PMMA witness blocks provided temporally resolved, 1-D, shock-position data that was iteratively fit by solutions to the governing equation via a unique genetic algorithm solver. The goal was to calculate a solution that describes the temporal evolution of shock pressure in PMMA starting at the detonator interface. The empirical decay law was investigated using experimental data, where different regimes were considered for the decay coefficients. A successful solution provides extensive performance information that is directly relevant to the understanding and characterization of detonator function.

Enhancing impact velocity with shock interactions in a restricting die

Shock compression and impact studies could benefit from the ability to increase impact velocities that can be achieved with gun systems. Single-stage guns have modest performance (0.2-2 km/s) that limits their utility for high-pressure and high-velocity studies, while more capable systems are expensive and complex. We are developing a technique that uses a low-strength sabot with a tapered die to increase the impact velocity without modifying the gun itself. Impact of the projectile with the die generates a converging shock wave in the sabot that acts to accelerate the front of the projectile, while decelerating the rear portion. Preliminary experiments using this technique have observed a velocity enhancement of up to a factor of two.

Study of energy partitioning using a set of related explosive formulations

Condensed phase high explosives convert potential energy stored in the electro-magnetic field structure of complex molecules to high power output during the detonation process. Historically, the explosive design problem has focused on intramolecular energy storage. The molecules of interest are derived via molecular synthesis providing near stoichiometric balance on the physical scale of the molecule. This approach provides prompt reactions based on transport physics at the molecular scale. Modern material design has evolved to approaches that employ intermolecular ingredients to alter the spatial and temporal distribution of energy release. State of the art continuum methods have been used to study this approach to the materials design. Cheetah has been used to produce data for a set of fictitious explosive formulations based on C-4 to study the partitioning of the available energy between internal and kinetic energy in the detonation. The equation of state information from Cheetah has been used in ALE3D to develop an understanding of the relationship between variations in the formulation parameters and the internal energy cycle in the products.

INTEGRATED EXPERIMENT AND MODELING OF INSENSITIVE HIGH EXPLOSIVES

New design paradigms for insensitive high explosives are being sought for use in munitions applications that require enhanced safety, reliability and performance. We describe recent work of our group that uses an integrated approach to develop predictive models, guided by experiments. Insensitive explosive can have relatively longer detonation reaction zones and slower reaction rates than their sensitive counterparts. We employ reactive flow models that are constrained by detonation shock dynamics (DSD) to pose candidate predictive models. We discuss the variation of the pressure dependent reaction rate exponent and reaction order on the length of the supporting reaction zone, the detonation velocity curvature relation, the computed critical energy required for initiation, the relation between the diameter effect curve and the corresponding normal detonation velocity curvature relation.