Session D1: EM-3: Mechanical Effects and Initiation

Presentation of an approach for the analysis of the mechanical response of propellant under a large spectrum of loadings: numerical and mechanical issues

Many authors claim that to understand the response of a propellant, specifically under quasi static and dynamic loading, the mesostructural morphology and the mechanical behaviour of each of its components have to be known. However the scale of the mechanical description of the behaviour of a propellant is relative to its heterogeneities and the wavelength of loading. The shorter it is, the more important the topological description of the material is. In our problems, involving the safety of energetic materials, the propellant can be subjected to a large spectrum of loadings. This presentation is divided into five parts. The first part describes the processes used to extract the information about the morphology of the meso-structure of the material and presents some results. The results, the difficulties and the perspectives for this part will be recalled. The second part determines the physical processes involved at this scale from experimental results. Taking into account the knowledge of the morphology, two ways have been chosen to describe the response of the material. One concerns the quasi static loading, the object of the third part, in which we show how we use the mesoscopic scale as a base of development to build constitutive models. The fourth part presents for low but dynamic loading the comparison between numerical analysis and experiments.   

Evidence for Friction Between Crack Surfaces During Deformation of Composite Plastic Bonded Explosives

The compressive strength has been found to increase linearly with hydrostatic pressure in a low pressure range in which work softening due to crack damage is observed. Analysis indicates that this linear increase can be attributed to friction between the surfaces of closed cracks and a friction coefficient is obtained from the linear slope and the measured angle of the failure plane. Analysis also indicates that the plane of maximum shear stress, the failure plane, is greater than 45 degrees when friction is present* as observed and a friction coefficient is also calculated directly from this angle. In addition, a relationship between the ratio of compressive to tensile strengths and the friction coefficient has been given by Zuo and Dienes*. The observed ratio is greater than the predicted value without friction and a friction coefficient is obtained which is in agreement with the two values obtained as discussed above. This agreement of three independent measures of the friction coefficient is taken a strong evidence for the presence of friction. This friction can be the source of hot spots and ignition during deformation*. *Zuo, Q. H., and Dienes, J. K., LA-13962-MS (2002).   

Effects of shear strain on initiation of chemical reactions in HMX

We performed a theoretical study of detonation initiation reactions in crystalline $\beta $-HMX using ab-initio methods. A HONO formation and elimination and direct N-NO$_{2}$ bond dissociation are considered to be main mechanisms of detonation initiation in HMX. We calculated the activation barriers of these two reactions using nudged elastic band method. We studied the same reactions in HMX exposed to the shear strain in (001) and (101) directions. The shear strain has been modeled by constructing an interface between different layers of HMX. We observed a significant change in energy barriers with respect to bulk calculations. This indicates that the shear strain plays an important role in detonation initiation in HMX. The results obtained are consistent with previously observed trends in DADNE and TATB and may be used to reveal common features of high explosive initiation behaviors.   

Defect Characterization in Crystalline Explosives

While microstructural defects such as dislocations, voids, and impurities may dramatically affect ignition sensitivity of energetic materials, the use of non-destructive techniques to accurately characterize the nature of internal defects and how they correlate to initiation is lacking. The objective of this work is to investigate the application of various defect characterization methods to crystalline explosives. X-ray Topography imaging, performed at on oriented, crystal slabs of RDX, shows that for a $<210>$ crystal slab, dislocation structure was only observed in the 020 transmission image compared to the 002, 102, 111, and 021 images. XRT images of the $<111>$ sliced sample taken through the 102 and 202 crystal planes show features including dislocations, grain boundaries, and the seed origin. Small and Ultra Small Angle Neutron Scattering experiments were performed on standard grade and reduced sensitivity grade RDX powder samples using the contrast variation method. Significant differences in scattering profiles were observed from these two versions of RDX, likely due to the existence of sub-micron voids or impurity pockets in the standard grade RDX sample. Large Scale Gap Test (LSGT) data from IHDIV NSWC for formulations containing these powder samples were then used to correlate neutron scattering to shock sensitivity.   

Session D2: MD-1: Molecular Dynamics 1

Phase diagram and thermodynamic properties of nanocarbons in detonation conditions from atomistic simulations using the LCBOPII potential

Several earlier studies showed that the detonation of oxygen deficient explosives produces substantial amounts of nanometre-sized carbon residues. The presence of these carbon nanoparticles needs to be accounted for in thermochemical models to obtain accurate estimations of the thermodynamic properties of the detonation products. Thus the determination of the thermodynamic properties of nanocarbons, and in particular of the size-dependence of their phase diagram, is highly desirable for pressure and temperature ranges close to those achieved at the Chapman-Jouguet point. In this communication we will present the carbon phase diagram obtained by Monte Carlo simulations with the LCBOPII potential, an empirical potential for carbon developed by Los et al. which is known to give a good description of bulk carbon phases under high pressure and temperature [1]. In particular we will emphasize on the region of the phase diagram of interest for detonation products (close to the CJ point) and extrapolations of the coexistence lines to the nanometer-sized carbon clusters will be provided using a simple model. Our results will then be compared to the structure and phase transitions of nanocarbons obtained by Molecular Dynamics simulations. \\[3pt] [1] Phys. Rev. B 72, 214102 (2005)   

Molecular dynamics simulation of shock-induced phase transition in Germanium

Results from shock-wave and ramp-wave uniaxial loading of Germanium will be presented. Germanium is known to transition from ambient cubic diamond (cd) phase to the high-pressure body-centered tetragonal (bct) or $\beta$-tin phase at pressures between 10 and 12 GPa. Large-scale molecular dynamics (MD) simulations were used to study the phase transition in single-crystal Germanium under uniaxial compression along several different crystal axes. We observed that the transition from the cd phase to the bct phase nucleates through shear banding and advances to relieve uniaxial strain. The macroscopic properties are compared with experimental results for both the Modified Embedded Atom Method (MEAM) and Tersoff potentials. Simulation techniques included standard non-equilibrium MD, as well as alternative computational methods, such as the Continuous Hugoniot Method and homogeneous uniaxial ramp methods. \\[4pt] This work is supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.   

An abundance of mechanisms for plastic flow in an extremely brittle material: dislocations and phase transformations in RDX

Orientation-dependent anisotropies in the initiation sensitivity of PETN can be rationalized elegantly by the availability and activity of dislocation slip systems for a given crystallographic orientation of the shock propagation direction. The true power of the resulting steric hindrance model is that it provides a framework for predicting anisotropies in the initiation sensitivity of any pristine energetic molecular crystal once its slip systems have been identified and characterized rigorously. I will present a review of recent molecular dynamics simulations and experiments that demonstrate that the energetic molecular crystal RDX is a rather plastic material under compression owing to a surprising number of mechanisms for plastic flow and stress relaxation. I will focus on the homogeneous nucleation of dislocations under shock compression and surface indentation, complex patterns of spatially localized melting and flow during void collapse, and the discussion of two shock-induced phase transformations in oriented RDX single crystals.   

Ab Initio Studies of Shock-Induced Chemical Reactions of Inter-Metallics

Shock-induced and shock assisted chemical reactions of intermetallic mixtures are studied by many researchers, using both experimental and theoretical techniques. The theoretical studies are primarily at continuum scales. The model frameworks include mixture theories and meso-scale models of grains of porous mixtures. The reaction models vary from equilibrium thermodynamic model to several non-equilibrium thermodynamic models. The shock-effects are primarily studied using appropriate conservation equations and numerical techniques to integrate the equations. All these models require material constants from experiments and estimates of transition states. Thus, the objective of this paper is to present studies based on ab initio techniques. The ab inito studies, to date, use ab inito molecular dynamics. This paper presents a study that uses shock pressures, and associated temperatures as starting variables. Then intermetallic mixtures are modeled as slabs. The required shock stresses are created by straining the lattice. Then, ab initio binding energy calculations are used to examine the stability of the reactions. Binding energies are obtained for different strain components super imposed on uniform compression and finite temperatures. Then, vibrational frequencies and nudge elastic band techniques are used to study reactivity and transition states. Examples include Ni and Al.   

Molecular Dynamics and Hydrodynamics Simulations of Detonation Wave Refraction at the Boundary of TATB-like HE and Beryllium

Here we present results of investigations of the process of detonation wave refraction on the border with inert material. The effects of broad reaction zone in TATB-like HE and high sound speed in Be were of particular interest. Molecular Dynamics (MD) was chosen as an instrument of the investigation. An atomistic approach to the contrast of HydroDynamics (HD) does not use any phenomenological models for physical processes but intreatomic potentials. Therefore MD allows for the direct and explicit simulation of such phenomena as detonation kinetics, elastic-plastic transition mechanism and shear stress relaxation kinetics from the microscopic point of view. Nevertheless it was very interesting and important to compare results of MD and HD approaches to the same problem. To make possible hydrodynamics modeling the parameters of the models used in HD were determined from MD simulations. In the course, we used MD results to choose parameters for Be and TATB-like HE equations of state and to evaluate parameters of elastic- plastic transition models for these materials. HD and MD results have been compared and analyzed.   

Session D3: ED-1a: PDV Fundamentals

Fundamental Experiments in Velocimetry

One can understand what velocimetry does and does not measure by understanding a few fundamental experiments. Photon Doppler Velocimetry (PDV) is an interferometer that will produce fringe shifts when the length of one of the legs changes, so we might expect the fringes to change whenever the distance from the probe to the target changes. However, by making PDV measurements of tilted moving surfaces, we have shown that fringe shifts from diffuse surfaces are actually measured only from the changes caused by the component of velocity along the beam. This is an important simplification in the interpretation of PDV results, arising because surface roughness randomizes the scattered phases.   

Heterodyne Velocimetry measurements on solids shock driven by high power lasers

A new Heterodyne Velocimeter (PDV) is under development at CEA for high explosive experimentations. Recently, we used it onto metallic target shock driven by high power laser. The aim is to test the ability of this means to reveal the propagation and the effects of shocks into materials, at extremely high strain rate and fast variations into the loading evolution. Spallation and fragmentation experiments carried out on aluminum samples, were performed on the LULI lasers at the Ecole Polytechnique, with both VISAR and HV diagnostics. Comparisons reveal a very good consistency of both experimental results. In addition, HV diagnostic evidence several levels of velocity in the experiment of fragmentation. Interpretation of these measurements is supported by transverse shadowgraphy analysis.   

Velocity Extraction from PDV Data Using Advanced Fourier Transform Techniques

Photon Doppler Velocimetry (PDV) experiments return surface velocimetry data encoded in the form of time-dependent amplitudes. Typically, these data are analyzed by sliding short-time Fourier transforms (STFTs), which return frequency (velocity) distributions at a number of discrete time windows. The parameters for these STFTs -- sample length, window size and parameters, and overlap -- are often chosen empirically. However, the analysis procedure is usually the largest single source of uncertainty in the returned velocity data, and although the STFT parameters affect the accuracy and precision of the result, their precise impact has not been quantified. Using synthetic PDV data sets, this study has investigated the accuracy with which a single velocity can be extracted by STFT techniques. The impact of the STFT parameters on the resulting accuracy has been measured computationally. Additionally, the increased accuracy gained by the use of multi-resolution and fractional Fourier techniques have been measured, along with the increased computational cost.   

High-Resolution Projectile Velocity and Acceleration Measurement using Photonic Doppler Velocimetry

This paper describes the new photonic Doppler velocimetry (PDV) technique for measuring time-resolved projectile velocity and acceleration profiles. This technique is shown to provide excellent temporal and spatial resolution in measurement for full flight of the launch package launched from single- and two-stage guns. The PDV method measures the minute Doppler shift in the monochromatic light reflected from the moving surface, which is directly proportional to its velocity. The Doppler-shifted laser signal is mixed with the unshifted signal to generate a beat signal. Short-time Fourier analysis of the beat signal produces highly resolved and accurate velocity profiles. Off-the-shelf components developed for the telecommunications industry are used, producing a system that is robust and inexpensive. Other examples of PDV measurements are provided in a companion paper on impact response of glass bars.   

What does ``velocity'' interferometry really measure?

Optical interferometers (\textit{e.g.}, VISAR and PDV) are commonly used to measure velocity in dynamic compression experiments. Although the basic function of these interferometers is typically straightforward, there are situations where their operation becomes unclear. Both VISAR and PDV are displacement interferometers because they respond to changes in target position; approximate velocities are determined over a finite time duration of the measured signal(s). However, this distinction becomes muddled in various measurements. Interference fringes can be observed despite the lack of any obvious displacement, while in other situations, no interference fringes are observed even when displacement is seemingly evident. This presentation attempts to reconcile the apparent inconsistencies in optical velocimetry. Many of these inconsistencies stem from intuitive, but incorrect, notions of interferometer operation. Ultimately, ``velocity'' interferometry provides a measure of displacement, though the origin of this displacement may be subtle.   

Session D4: MS-2: Rheology of Various Metals

The Young's modulus of 1018 steel and 6061-T6 aluminum measured from quasi-static to elastic precursor strain-rates

It is commonly assumed in engineering and physics that the elastic moduli of metals is independent of strain-rate, but is a weak function of temperature. An extensive literature search however has failed to find any citable reference in which the Young's modulus of any pedigreed metal was measured over a wide variety of strain-rates. To rectify this, samples of pedigreed 1018 steel and 6061-T6 aluminum have been tested at strain-rates from $10^{-4}$~s$^{-1}$ to $10^{6}$~s$^{-1}$. Low strain-rate data ($10^{-4}-10^{-2}$~s$^{-1}$)was obtained from commercial bonded strain gauges. Intermediate rate data ($\approx10^{-4}$~s$^{-1}$) was obtained from time of flight ultrasonic measurements. Shock rate data was obtained by examining the elastic precursor using shock pins and PDV (photonic Doppler velocimetry). Correction for the adiabatic versus thermal nature of the disparate strain-rate regimes have been made. Additionally, the implications of the uniaxial strain nature of the shock elastic precursor are examined with respect to comparison with uniaxial stress lower rate data.   

Strain Rate Dependence of a Single Crystal Alloy

In order to provide data for constitutive modelling, and to better understand mechanisms behind strain rate dependence of metals, characterisation experiments have been performed on the nickel based single crystal alloy CMSX-4. This material has received extensive characterisation in the literature, concentrating on metallurgical aspects as well as creep and fatigue behaviour, giving a good background to the high rate research. The current paper will report data from compression experiments performed at strain rates from 10$^{-3}$ to 10$^3$ s$^{-1}$, and Taylor Impact tests. Data obtained will be evaluated in the light of previous thermo-mechanical characterisation of this alloy, and compared to the high rate response of polycrystalline materials.   

Dynamic Shear Strength Measurements in Shock Loaded Molybdenum

Dynamic shear strength measurements in shock-loaded molybdenum have been performed in the pressure range 2-20 GPa using plate-impact techniques. Shear strength is monitored using managnin stress gauges mounted such that they are sensitive to the lateral component of stress, combined with knowledge of the shock-induced impact stress in the longitudinal direction. In previous work on the shock response of body centred cubic (BCC) metals, increases in lateral stress with duration behind the shock front have been interpreted as a decrease in shear strength. In tantalum, this interpretation is supported by post-shock microstructural analysis which reveals a minor increase in dislocation density associated with a high Peierl's stress. Our current measurements in molybdenum metal further extend this work in BCC structures.   

Modeling high-rate straining of cerium in shock waves and explosive experiments

The paper presents numerical results from calculations simulating experiments which were focused on the investigation of stress profiles in high-purity and high-grade cerium. The experiments were taken in recent years at LANL with use of light-gas guns for loading samples and the VISAR technique for recording stress profiles and at RFNC-VNIITF where samples were loaded with the sliding and normal detonation of HE and the registration of stress profiles was done with photo- chronographic optic lever technique. Provided is information on the multiphase equation of state and the elastic-plastic models used in calculations. Calculated and experimental profiles are compared. Specific features and characteristics of high-rate straining of cerium are discussed.   

Shock Driven Twinning in Tantalum Single Crystals

Recovery based observations of high pressure material behavior generated under high explosively driven flyer based loading conditions are reported. Two shock pressures, 25, and 55 GPa and four orientations {\{}(100), (110), (111), (123){\}} were considered. Recovered material was characterized using electron backscatter diffraction along with a limited amount of transmission electron microscopy to assess the occurrence of twinning under each test condition. Material recovered from 25 GPa had a very small fraction of twinning for the (100), (110), and (111) oriented crystals while a more noticeable fraction of the (123) oriented crystal was twinned. Material recovered from 55 GPa showed little twinning for (100) orientation slightly more for the (111) orientation and a large area fraction for the (123) orientation. The EBSD and TEM observations of the underlying deformation substructure are rationalized by comparing with previous static and dynamic results along with the crystal plasticity based hydrodynamic modeling.   

Shock Response of Cu-Nb Nanolayer Composites

Large-scale classical molecular dynamics (MD) simulations and laser-launched flyer plate experiments have been used to study the shock response of Cu-Nb nanolayered composites. At a layer thickness of 5 nm, the hardness of such metallic multilayers (as measured by quasistatic indentation or compression tests) reaches a maximum due to the difficulty of dislocation transmission across the interfaces. We observe a similar strengthening effect under dynamic shock loading, both in the MD simulations and in \textit{post mortem} examinations of shock-recovered samples subjected to $\sim $20 GPa shock loading. The MD simulations provide insight into the dislocation nucleation and transmission processes that occur under compression, as well as the subsequent annihilation upon release.   

Session D5: ID-2: Aluminum Spall and Strength

Laser-Driven Spall in Al: Velocity Interferometry and Target Recovery

Using the HELEN laser at AWE we have done spall experiments on pure Al at strain rates between $\sim $6x10$^{5}$ and 2x10$^{6}$s$^{-1}$. A heterodyne velocity interferometer (Het-V) recorded rear-surface velocity profiles and the majority of targets were recovered. We have compared the behaviour of polycrystalline and single-crystal Al of four different crystal orientations. The results allow the correlation of pre-shot target structure -- determined by electron backscatter diffraction -- with the velocity profiles and recovered-target metallurgy.   

Temporal Softening and its Effect upon Spall Strength

Experimental observation has revealed that the effects of shock wave loading are extremely complex, often resulting in morphological changes that result in a hardening of the material. Temporal softening that precedes the aforementioned hardening has also been observed. In Al and Cu, the duration of this softening is on the order of 0.3 to 0.5 ms. This work has revealed that, at least in some cases, this temporal softening phenomenon is attributable to the formation of complex bi-periodic twin structures. The overall morphology of these structures is rather complex, consisting of what we shall refer to as ``packages,'' with each ``package'' being composed of two sets of parallel twins aligned in a quasi-herringbone pattern. It is probable that the temperature within the ``package'' is much higher than the temperature of the surrounding material during ``package'' formation. The formation of bi-periodic twin structures and concomitant temporal softening has an effect upon spall strength. That effect is explored in the work to be presented. Samples are loaded by short duration pulses (0.2 - 1 ms) in such a way that the onset of damage occurs within the period of temporal softening. This has enabled an assessment of the softening effect on spall strength.   

Spall and Dynamic Yielding of Aluminum and Aluminum Alloys at Strain Rates of 3x10$^{6}$ s$^{-1}$

We have explored the role that grain size, impurity particles and alloying in aluminum play in dynamic yielding and spall fracture at tensile strain rates of $\sim $3x10$^{6}$ s$^{-1}$. We achieved these strain rates shocking the aluminum specimens via laser ablation using the Z-Beamlet Laser at Sandia National Laboratories. The high purity aluminum and Al-1100 produced very different spall strengths and nearly the same yield strengths. Various grain-sized Al + 3 wt. {\%} Mg specimens presented the lowest spall strength, but the greatest dynamic yield strength. Fracture morphology results and particle analysis will be presented along with hydrodynamic simulations to put these results in context with previous publications. Impurity particles appeared to play a vital role in spall fracture at these fast strain rates. With respect to dynamic yielding, alloying elements such as Mg seem to be the dominant factor.   

Shock Behavior of 2139-T8 Aluminum

Plane shock wave experiments have been conducted on an aluminum alloy, Al 2139-T8, to determine its response under high rates of loading. The alloying elements, copper, magnesium, and silver, have been found to improve the fatigue life and fracture toughness of Al 2139 and mitigate impact induced damage. The present suite of experiments provide measurements of the Hugoniot Elastic Limit (HEL), compression, shear strength, and spall threshold to 5 GPa. Longitudinal measurements are made with a VISAR system and shear strength is determined through direct measurements of lateral stress with manganin gages. Preliminary results indicate an HEL of approximately 0.9 GPa, a value consistent with yield stress measured at rates as high as 40k/s, and a constant spall pull-back velocity of approximately 180 m/s. The results also show that it continues to retain shear strength like other aluminum alloys. The EPIC code (Elastic Plastic Impact Calculations) is used to simulate the experimental results.   

Investigation of aluminum 6061-T6 strength properties to 160 GPa

Shock compression experiments were performed on aluminum 6061-T6 up to 160 GPa to probe aluminum strength through the melt regime. A careful set of experiments, using established two and three stage flyer plate launch techniques were conducted using symmetric impact loading conditions to compress the aluminum through the solid to liquid phase boundary. Velocity interferometry provides the fine structure almost as an in-situ particle velocity wave profile at the aluminum/lithium-fluoride window interface. Results will be detailed in terms of wave speeds in the shocked state for estimates of strength of the material. Results of these experiments will be discussed in detail. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.