Exponential initiation function and flyer optimization

There are two commonly used criteria for describing the shock initiation threshold of high explosives. They are Walker and Wasley, and James criteria that are based on the value of energy flux or a hyperbolic function of energy flux and kinetic energy, respectively. A recent addition is the use of an exponential function^1,2 that is based on energy and power fluxes. This paper explores possible merits and use of the new exponential function and its scaling parameters. When combined with the James observation on the relation between the initiation threshold and Pop-plot, the scaling parameter reduces to an equation that can be analytically inspected for the existence of a domain where a parallel shifting of the two thresholds is a good approximation. We then considered, following the approach discussed by Horie et al.³, the use of the new parameter to determine the optimum flyer property that generates the ‘best’ impact to deliver energy into the target. The resulting equation is a transcendental equation that does not allow a simple analytic solution, but in the case of bounding situations such as a sustained load, it yields a simple closed form solution for the optimum choice of flyer shock impedance relative to that of the target. Additional implication of the equation for the optimized impact velocity is the existence of the minimum shock duration, indicating that thin pulse (un-sustained shock) may not be amenable to the optimization depending on its duration.

1. Damm et al., Proc. JANNAF 2012

2. Welle et al., 15^th Int’l. Det. Symp., 2014

3. Horie et al., 16^th Int’l. Det. Symp., 2018