Session J25: Focus Session: Simulation of Matter at Extreme Conditions: Shock Compression and Other High-Strain-Rate Phenomena

Single two-zone elastic-plastic shock waves in solids

A new regime of shock wave propagation in solids, corresponding to a single two-zone elastic-plastic shock-wave, was discovered using a novel moving window molecular dynamics technique. Both leading low-pressure elastic and trailing high-pressure plastic fronts move with the same speed and have a fixed separation that can extend to several microns. The material in the elastic zone is in a metastable state, having a pressure that substantially exceeds the critical shock strength characteristic of the onset of the well-known split-elastic-plastic, two-wave regime. The single two-zone elastic-plastic shock wave is a quite general phenomenon observed in our simulations for a broad class of crystalline materials, including aluminum, nickel, diamond, and Lennard-Jones crystals. It is the existence of the two-zone, elastic-plastic regime that allows for a consistent explanation of the anomalously high elastic wave amplitudes observed in recent experiments.   

The Role of Shock Induced Defect Structure in Spall Failure

Spall failure is a complex multiscale, multirate process. On the macroscale the process involves a period of shock compression followed by dynamic tension set up by the stress wave interactions. During the shock compression, the material undergoes a myriad of shock stress magnitude and pulse duration dependent microscopic processes that may include dislocation multiplication, nucleation, trapping, pile-up, annihilation, recovery, cell evolution, as well as vacancy generation and clustering. In addition to shock hardening the material, this new shock induced defect structure seeds the material with potential void nucleation sites that may be activated during the proceeding period of dynamic tensile loading. Upon nucleation, the voids undergo dynamic growth to coalescence, constrained by inertia and viscoplastic resistance to deformation. A multiscale predictive framework is developed to analyze the role of these time-dependent processes in the experimentally observed spall strength dependence on initial microstructure, preheated temperature, tensile loading rate, pulse duration, and shock stress magnitude.   

Physics of hyper-velocity impacts of micrometer and sub-micrometer sized particles

The phenomena occurring during hypervelocity microparticle impact are manyfold and the basis for the variety of applications. The processes of interest are particle fragmentation, impact ionization, impact flashes, and TOF mass spectrometry. To relate the parameters of individual particle impacts with the resulting measured values, a comprehensive program of impact experiments under well known experimental conditions for a wide variety of impact parameters is needed. For this, dust particles are accelerated to hypervelocity speeds with an electrostatic accelerator and the resulting plasma cloud is analyzed with suitable instruments. A detailed investigation using latest analyzing techniques like high-speed cameras and sensitive high-resolution spectrometers promises new instrument concepts and insights into short timescale high-pressure states of matter. Linear TOF mass spectroscopy provides the opportunity to measure the dynamic and thermodynamic properties of the impact ions. Together with a deeper theoretical understanding of the impact process and the subsequent expansion and other experimental approaches, this method can be a powerful tool to investigate the state of the hot compressed matter due to the related residual ion species.   

Shock Ejecta Entrainment in Gas

In a continuation of earlier work, paired metal shock ejecta experiments, with and without helium fill, are used to measure shock ejecta motion in gas. The vacuum ejecta experiments use Asay foils and PDV to characterize ejecta properties, and the gas ejecta experiments use PDV. FFT analysis of the PDV signals gives a qualitative indication of the presence of such ejecta and of its motion; this can be ``calibrated'' via the Asay foil data. For modest amounts of ejecta (allowing enough light to reach the free surface and return to the probe to give a strong free surface velocity signal), the FFT amplitudes are roughly proportional to the ejecta areal density, where the proportionality constant depends on the shape and size distribution of the ejecta particles. We assume these are consistent for the two samples in each experiment pair, although limitations to this assumption (e.g. ejecta disruption by the gas) are discussed. An additional caveat is that PDV only measures the motion of ejecta with particle sizes exceeding the 1550 nm light wavelength. Experiments to assess optimal generators of shock ejecta detectable by PDV are also presented. Indium was found to work well in the pressure regime studied.   

Why nano-projectiles work differently than macro-impactors- role of plastic flow

Hypervelocity impacts provide a way to take localized regions of a target to extreme pressure and temperature conditions. Resulting crater features can be challenging for hydrocode simulations and test the validity of constitutive models. We will present atomistic simulation data on crater formation due to hypervelocity impact of nanoprojectiles of up to 55 nm diameter and with targets containing up to ten billion atoms, and compare them to available experimental data on micron-, mm-, and cm-sized projectiles. We show that previous scaling laws do not hold in the nano-regime and outline the reasons: within our simulations we observe that the cratering mechanism changes, going from the smallest to the largest simulated scales, from an evaporative regime to a regime where melt and plastic flow dominate, as it is expected in larger micro-scale experiments. The importance of strain-rate dependence of strength and of dislocation production and motion under these extreme conditions will be discussed.   

Elastic-plastic response and polymorphic phase transition in shock-compressed diamond

Shock wave propagation in diamond along the < 110 > crystallographic direction was simulated by molecular dynamics (MD) using the reactive empirical bond order (REBO) potential. In addition to known regimes of shock wave propagation, such as single elastic, split elastic-plastic, and single plastic shock wave, two new regimes were observed: 1) a split elastic-elastic shock wave associated with a polymorphic phase transition; 2) a single two-zone elastic-plastic shock wave with the leading elastic zone followed by the plastic zone. In the case of the split elastic-elastic shock wave, the onset of phase transition occurs at a pressure below the Hugoniot elastic limit (HEL); therefore, the solid-solid transformation takes place in the uniaxially compressed material in the absence of plasticity. Within the single two-zone elastic-plastic shock wave, the material in the elastic zone is in a metastable state at a pressure exceeding the HEL. The metastable elastic state decays into the plastic state within the plastic zone, both elastic and plastic fronts moving with the same speed.   

The Shock Response of Granular and Consolidated Ta2O5

The dynamic behavior of granular and nearly fully dense tantalum pentoxide (Ta$_{2}$O$_{5}$) has been explored through planar impact experiments. The experiments span from the compaction regime to the ultra-high pressure range utilizing gas guns and the Z machine. These data provide a valuable data set for the extension of the P-$\lambda$ model to the high-pressure regime. A thermodynamic approach due to Rice and Walsh is employed in the model to treat highly distended materials that can display anomalous compressibility. When the model is calibrated to the gas gun and Z data, we test its applicability against the data of Miller et al. from laser experiment on low-density aerogels. Even in these very different conditions, the model does a credible job of predicting the material behavior, suggesting that the approach may be useful as a general modeling tool for the high-pressure regime.   

Optical emission from Gd$_{3}$Ga$_{5}$O$_{12}$ single crystals shock compressed from 40 to 300 GPa

The question of the shock pressure at which a strong material reaches thermal equilibrium is an important one that depends on strength and has never been answered for any strong material. To answer the range of shock pressures in which shock dissipation is dominated by entropy (damage and disorder) or by shock heating (T), we have performed time-resolved optical emission and transmission measurements on strong GGG single crystals under wide-range uniaxial compression from $\sim $40 GPa to $\sim $300 GPa with a sixteen-wavelength pyrometer. Temperatures T and emissivities e were derived from gray-body fits up to 300 GPa. These data: (i) determine shock pressures at which GGG reaches thermal equilibrium and melting, (ii) essentially confirm previously calculated shock temperatures of GGG, (iii) demonstrate the complete transition from heterogeneous shock heating at lower pressures (small e) to thermally-equilibrated bulk heating (large e) at higher pressure (never before been done in strong materials), and (iv) characterize GGG as an anvil for use in studying metallic fluid hydrogen.   

Laser-driven focusing shock waves in a thin liquid layer

Direct real-time visualization of converging shock waves in a few micron thick liquid layer is demonstrated in an all-optical experiment. The set-up includes an axicon that focuses an intense picosecond excitation pulse into a ring-shaped pattern in a water layer. Optical excitation induces a shock wave that propagates in the plane of the sample and converges toward the center resulting in cylindrical focusing of the shock front. Streak-camera images with a quasi-cw probe beam yield real-time records of the entire shock propagation. Talbot imaging and interferometry with a femtosecond probe pulse are used to obtain full field images at variable delays. Shock pressure values calculated from the velocity of the shock front demonstrate the effect of shock focusing and agree with density profiles obtained by quantitative analysis of interferometric images. The configuration of the experiment provides ample access for optical diagnostics of the shocked material and can be combined with a wide range of spectroscopic probes.   

From fingering to fracture in a complex fluid

We present a novel experiment -- a specific Hele-Shaw cell with mobile sides which can be pulled at a prescribed velocity - with which both liquids and solids can be loaded with the same boundary conditions, beyond the small deformation regime. With such a system, one can examine quantitatively the response of a viscoelastic material when the loading rate is varied. In the case of viscous Newtonian liquids, an air bubble is shown to destabilize in a Saffman-Taylor manner, forming a finger which elongates in the direction in which the mobile sides are pulled. In contrast, in a Maxwell liquid, we observe a different kind of instability, which gives rise to more complex patterns. This instability leading to local stress concentrations, it is immediately followed by fracture. The displacement field is evaluated in each case by using tracers and image correlations.   

Nonlinear Elasticity as a Guide for Exploring High Pressure/Shear Stability

Recent constitutive representation theorems for nonlinear anisotropic elasticity, Wright [2011], show the characteristics of elastic response for materials in any point group. All anisotropic representations consist of a sum of six terms, and each term consists of a scalar function of anisotropic invariants times a ``tensor generator,'' which has the same invariance under group transformations as the stress itself. Knowledge of these representations shows promise as a guide for exploring material stability under extreme loading conditions. Although much is known both experimentally and theoretically about material stability under high pressure, far less is known about the effect of large shear stress superimposed on high pressure. Stress has six independent components, so study of the effects of pressure alone leaves the other five dimensions unexplored. Rather than random DFT calculations in the five dimensional deviatoric space, the known structure of the six term representations suggests that systematic study of just one additional dimension at a time could be accomplished by following changes in just one additional term in the representation at a time. These ideas will be illustrated in the context of a program designed to explore the effect of shear on amorphization in B4C, a ceramic often used for ballistic protection. \textit{T.W. Wright, Bootstrap elasticity: From linear to nonlinear constitutive representations, accepted for publication, J. Elasticity}.   

Multi million-to-Billion Atom Molecular Dynamics Simulations of Cavitation-Induced Damage on a Silica Slab

Cavitation bubble collapse causes severe damage to materials. For example, cavitation erosion is a major threat to the safety of nuclear power plants. The cavitation bubbles may also be utilized for preventing stress corrosion cracking with water jet peening technology. We have performed multi million-to-billion atoms molecular dynamics simulations to investigate the shock-induced cavitation damage mechanism on an amorphous silica slab in water. The system consists of a 60nm thick silica slab immersed in water in an MD box of dimension 285 x 200 x 200 nm3. A nanobubble is created by removing water molecules within a sphere of radius 100 nm. To apply a planar shock, we assign a uniform particle velocity vp on the entire system towards a planar momentum mirror. We have performed the simulation with two kinds of bubbles, an empty bubble and a bubble filled with inert gas. The simulation results reveal nanojet formation during bubble collapse causing damage on the silica surface; however, the damage was significantly reduced in the case of the filled bubble. We will discuss the effect of the presence of inter gas inside the nanobubble on the pressure distribution, the extent of damage, and collapse behavior corresponding the shock front.   

Akrology; the physics of the extreme behaviour of metals and energetics

Structures designed for extreme environments must be designed not only for the magnitude of the load that they will experience, but also the time for which that load acts upon them. At the core of the problem lies the loading impulse experienced by materials and the operating deformation mechanisms that are excited. Our experience of materials' physics, gathered by investigating response to mechanical loads, has suggested a series of descriptive constructs within which we build our picture of behaviour. At the highest loadings and the shortest loading times this perception is coloured by experience gathered from historical considerations. This paper suggests a framework by which to interpret data collected on the response of metals and explosives. It suggests that strength is a quantity that decays over time and that fundamentally approaches zero in the limit of infinite time. Controlling this decay is the business of engineering to design structures that will survive in the environments our times of interest define.   

Equation of State of a Solid: Potts-Percolation Model

We include stress and strain in a Potts-percolation model of a solid, see J. Phys.: Condens. Matter 20, 075222 (2008) and Phys Rev E80, 031116 (2009). Neighboring atoms are connected by a bond of Lennard-Jones energy. If the energy is larger than a threshold the bond is more likely to fail, while if the energy is lower than the threshold the bond is more likely to be alive. We compute the equation of state: stress as function of strain and temperature by using renormalization group and Monte Carlo simulations. The phase diagram and the equation of state are determined. When the Potts heat capacity is divergent the continuous transition is replaced by a weak first-order transition through the van der Waals loop mechanism. When the Potts transition is first order the stress exhibits a large discontinuity as function of the strain.