We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shap
e for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long duration ramps are desired.
The plastic response of beryllium was investigated during loading by laser-induced shock waves, using surface velocimetry and in-situ x-ray diffraction. Results from loading by thermal x-rays (hohlraum) were consistent with more extensive studies usi
ng laser ablation. Strong elastic waves were observed, up to ~1 km/s in free surface speed, with significant structure before the arrival of the plastic shock. The magnitude and shape of the precursor could be reproduced with a plasticity model based on dislocation dynamics. Changes in lattice spacing measured from the x-ray diffraction pattern gave a direct measurement of uniaxial compression in the elastic wave, triaxial flow from the decay of the precursor, and triaxial compression in the plastic shock; these were consistent with the velocity data. The dynamic strength behavior deduced from the laser experiments was used to help interpret surface velocity data around the onset of shock-induced melting. A model of heterogeneous mixtures is being extended to treat anisotropic components, and spall.
The pressure-volume-temperature equation of state of the intermetallic compound NiAl was calculated theoretically, and compared with experimental measurements. Electron ground states were calculated for NiAl in the CsCl structure, using density funct
ional theory, and were used to predict the cold compression curve and the density of phonon states. The Rose form of compression curve was found to reproduce the ab initio calculations well in compression but exhibited significant deviations in expansion. A thermodynamically-complete equation of state was constructed for NiAl. Shock waves were induced in crystals of NiAl by the impact of laser-launched Cu flyers and by launching NiAl flyers into transparent windows of known properties. The TRIDENT laser was used to accelerate the flyers to speeds between 100 and 600m/s. Point and line-imaging laser Doppler velocimetry was used to measure the acceleration of the flyer and the surface velocity history of the target. The velocity histories were used to deduce the stress state, and hence states on the principal Hugoniot and the flow stress. Flyers and targets were recovered from most experiments. The effect of elasticity and plastic flow in the sample and window was assessed. The ambient isotherm reproduced static compression data very well, and the predicted Hugoniot was consistent with shock compression data.
Neutron resonance spectrometry (NRS) has been used to measure the temperature inside Mo samples during shock loading. The temperatures obtained were significantly higher than predicted assuming ideal hydrodynamic loading. The effect of plastic flow a
nd non-ideal projectile behavior were assessed. Plastic flow was calculated self-consistently with the shock jump conditions: this is necessary for a rigorous estimate of the locus of shock states accessible. Plastic flow was estimated to contribute a temperature rise of 53K compared with hydrodynamic flow. Simulations were performed of the operation of the explosively-driven projectile system used to induce the shock in the Mo sample. The simulations predicted that the projectile was significantly curved on impact, and still accelerating. The resulting spatial variations in load, including radial components of velocity, were predicted to increase the apparent temperature that would be deduced from the width of the neutron resonance by 160K. These corrections are sufficient to reconcile the apparent temperatures deduced using NRS with the accepted properties of Mo, in particular its equation of state.
A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to calculate response to shock and ramp compression, and ramp decompression, generalizing previous solutions for scal
ar equations of state. The numerical methods were found to be flexible and robust, and matched analytic results to a high accuracy. The basic ramp and shock solution methods were coupled to solve for composite deformation paths, such as shock-induced impacts, and shock interactions with a planar interface between different materials. These calculations capture much of the physics of typical material dynamics experiments, without requiring spatially-resolving simulations. Example calculations were made of loading histories in metals, illustrating the effects of plastic work on the temperatures induced in quasi-isentropic and shock-release experiments, and the effect of a phase transition.
