Session H25: Focus Session: Simulation of Matter at Extreme Conditions - Shock Compression of Metals

Invariance of the Dissipative Action at Ultrahigh Strain Rates above the Strong Shock Threshold

We have directly resolved shock structures in pure aluminum in the first few hundred picoseconds subsequent to a dynamic load, at peak stresses up to 43 GPa and strain rates of in excess of 10$^{10}$ s$^{-1}$. For strong shocks we obtain peak stresses, strain rates, and rise times. From these data, we directly validate$^{1}$ the invariance$^{2}$ of the dissipative action in the strong shock regime, and by comparing with data obtained at much lower strain rates show that this invariance is observed over at least 5 orders of magnitude in the strain rate. Over the same range, we similarly validate the fourth-power scaling of strain rate with peak stress (the Swegle-Grady relation). 1. J. C. Crowhurst, M. R. Armstrong, K. B. Knight, J. M. Zaug, E. M. Behymer, Phys. Rev. Lett, 107, 144302 (2011). 2. D. E. Grady, J. Appl. Phys. 107, 013506 (2010). This work was also supported by the EFree, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Grant No. DESC0001057.   

Ultrashort elastic and plastic shock waves in nickel generated by femtosecond laser pulses

The structure and evolution of ultrashort shock waves generated by femtosecond laser pulses in thin nickel films were investigated by molecular dynamics and two-temperature hydrodynamics simulations. Ultrafast laser energy deposition results in the formation of a highly-pressurized 100-nm-thick layer below the surface of the film. Relaxation of the stress-confined state leads to the creation of a strong compression wave that later transforms into an ultrashort shock wave. Analysis of experimental data shows that such a shock wave, generated by low absorbed laser fluence, can exhibit a pure elastic structure despite an amplitude exceeding the conventional Hugoniot elastic limit. For absorbed fluences above $\sim 0.6 \rm{\:J/cm^{2}},$ two independent processes of elastic and plastic wave breaking are observed with the elastic precursor appearing before formation of the plastic wave. It is found that the amplitude of the elastic precursor is almost independent of the absorbed fluence, but closely related to the pressure at the melting front. The decay rate of the plastic wave amplitude is much higher than that of the elastic wave, which may result in the complete disappearance of the plastic wave within the metal film.   

Molecular dynamics simulations of steady shock waves in nickel

Shock waves in single-crystal nickel samples were investigated by molecular dynamics (MD) simulations. Standard piston simulations were used to investigate the elastic-plastic split-shock-wave regime, whereas regimes having a single steady shock-wave structure were studied by a novel moving window (MW-MD) technique. Two distinct regimes were investigated, including the regimes of split elastic and plastic shock waves and the steady two-zone elastic-plastic single wave. Split shock waves were shown to form at moderate piston velocities out of a metastable high-pressure elastic state that decays into a two-wave structure consisting of a slow plastic wave and fast elastic precursor. At higher piston velocities, the plastic wave overtakes the elastic precursor but does not overrun it. Instead, both waves were found to move in tandem with the same average speed while maintaining a finite, and in some cases strongly fluctuating, separation width that may extend to several microns. The dependence of shock wave structure on crystallographic orientation and concentration of defects was investigated.   

A Molecular dynamics study of a Richtmyer-Meshkov instability

We simulated a single-mode Richtmyer-Meshkov instability (RMI) using the SPaSM (Scalable Parallel Short-range Molecular-dynamics) code on the RoadRunner supercomputer and its Cerrillos counterpart. The simulations consisted of approximately 60 million atoms shocked along the $<111>$ direction. The single crystal simulations had a sinusoidal groove with a wavelength of 257 nm. We conclude from the simulations that the RMI interfaces shows an inversion for most of the conditions we studied. For certain amplitudes and stresses, we observe the spike saturating. Simulations have been carried out at shock strengths both above and below the melt transition. A discussion of the spike and bubble characteristics will be discussed.   

Orientation dependence of shock-induced melting in crystalline aluminum

The complete evolution of metastable states during shock-induced solid-liquid phase transitions in crystalline aluminum was observed in moving window molecular dynamics simulations. The orientation-dependent transition pathways towards orientation-independent final equilibrium states include both ``cold melting'' followed by resolidification in [110]- and [111]-oriented shock waves, and crystal overheating followed by melting in [100] shock waves. Such orientation-dependent dynamics of solid-liquid phase transitions takes place within an extended zone up to hundreds of nanometers behind the shock front, which makes it accessible for experimental observation.   

Strain rate influence on the Hall-Petch effect in Cu

The increased strength of materials with a decreasing grain size has been known for several decades as the Hall-Petch effect. This trend is true down to a specific grain size below which the strength starts decreasing again, due to a change in the underlying plasticity mechanisms caused by the increased grain boundary network density. We are interested in the strain rate influence on the Hall-Petch and ``reverse Hall-Petch" effects. We use molecular dynamics simulations to study polycrystalline samples of copper of different grain sizes between 5 nm and 30 nm, and under uniaxial compression at a wide range of strain rates (10$^{8}$ to 10$^{11}$ s$^{-1}$). We verify that the yield stress of the material increases with the strain rate, due to the time scale required to generate plasticity. Moreover, we observe that the grain size for which the yield stress is highest depends on the strain rate studied. These results are of particular importance for high strain rate loading conditions, such as shock compression.   

High Strain Rate and Shock-Induced Deformation in Metals

Large-scale non-equilibrium molecular Dynamics (MD) simulations are now commonly used to study material deformation at high strain rates (10$^9$-10$^{12}$ s$^{-1}$). They can provide detailed information-- such as defect morphology, dislocation densities, and temperature and stress profiles, unavailable or hard to measure experimentally. Computational studies of shock-induced plasticity and melting in fcc and bcc single, mono-crystal metals, exhibit generic characteristics: high elastic limits, large directional anisotropies in the yield stress and pre-melting much below the equilibrium melt temperature for shock wave propagation along specific crystallographic directions. These generic features in the response of single crystals subjected to high strain rates of deformation can be explained from the changes in the energy landscape of the uniaxially compressed crystal lattice. For time scales relevant to dynamic shock loading, the directional-dependence of the yield strength in single crystals is shown to be due to the onset of instabilities in elastic-wave propagation velocities. The elastic-plastic transition threshold can accurately be predicted by a wave-propagation stability analysis. These strain-induced instabilities create incipient defect structures, which can be quite different from the ones, which characterize the long-time, asymptotic state of the compressed solid. With increase compression and strain rate, plastic deformation via extended defects gives way to amorphization associated with the loss in shear rigidity along specific deformation paths. The hot amorphous or (super-cooled liquid) metal re-crystallizes at rates, which depend on the temperature difference between the amorphous solid and the equilibrium melt line. This plastic-amorphous transition threshold can be computed from shear-waves stability analyses. Examples from selected fcc and bcc metals will be presented employing semi-empirical potentials of the embedded atom method (EAM) type as well as results from density functional theory calculations.   

Metallurgical Effects Upon the Shock Response of Tantalum: Cold Work and Dilute Alloying

The response of the body centred cubic metal tantalum to shock loading has been studied for several decades, due to its use by the military in explosively formed projectiles. It can also be considered as an ideal body centred cubic metal, thus rendering it ideal for studies of fundamental mechanical and microstructural behaviour. Previous studies on well controlled, annealed specimens has shown that deformation is controlled by the motion of rather than the generation of a/2$<$111$>${\{}110{\}} screw dislocations in straight segments, which result in little if any post shock hardening. In situ-shear strength measurements have also shown a significant strength reduction behind the shock front, suggesting that the motion of these dislocations acts as a stress relief mechanism. Similar effects have also been noted in tungsten and its alloys, but very recently, measurements in niobium and molybdenum show shear strength to be near constant behind the shock front. Other factors, such as variation of Peierls stress effecting ease of dislocation generation and the propensity to twin also have a strong effect upon the shock response. In this presentation, we return to tantalum, investigating the differences in shock response between a low dislocation density (annealed) and high dislocation density (cold rolled) material. We also examine the effects of dilute alloying through the addition of 2.5wt{\%} tungsten to tantalum. Results are discussed in terms of the shear strength and its variation with time behind the shock front.   

High Strain Rate Behavior of Nanoporous Tantalum

Nano-scale failure under extreme conditions is not well understood. In addition to porosity arising from mechanical failure at high strain rates, porous structures also develop due to radiation damage. Therefore, understanding the role of porosity on mechanical behavior is important for the assessment and development of materials like metallic foams, and materials for new fission and fusion reactors, with improved mechanical properties. We carry out molecular dynamics (MD) simulations of a Tantalum (a model body-centered cubic metal) crystal with a collection of nanovoids under compression. The effects of high strain rate, ranging from $10^{7}$$s^{-1}$ to $10^{10}$$s^{-1}$, on the stress strain curve and on dislocation activity are examined. We find massive total dislocation densities, and estimate a much lower density of mobile dislocations, due to the formation of junctions. Despite the large stress and strain rate, we do not observe twin formation, since nanopores are effective dislocation production sources. A significant fraction of dislocations survive unloading, unlike what happens in fcc metals, and future experiments might be able to study similar recovered samples and find clues to their plastic behavior during loading.   

High-Pressure Strength Determination via Quasi-Elastic Optimization Analysis

The analysis of unloading profiles from ramp wave experiments on Sandia's Z machine for the purposes of extracting strength information can be greatly influenced by the presence of a window. An impedance mismatch between the sample and the window generates a reflected ramp wave which perturbs the incoming wave, particularly at later times when, during unloading, the material strength becomes evident. In an effort to analyze the waveforms for an accurate estimate of the strength, the experimental data is coupled with optimized numerical simulations. Simulations were performed with LASLO, a one-dimensional magneto-hydrodynamics code. The deviatoric response was calculated using a modified rate-independent Steinberg - Guinan model in which a quasi-elastic response was implemented during unloading by linearly varying the shear modulus. A best fit of relevant parameters in this strength model along with the magnetic field at the drive surface were estimated over the course of thousands of simulations using the Dakota optimization package. These results may then be used to estimate the in situ wave profiles from which the strength can be extracted. Initial results will be presented for ramp wave compression of tantalum with a lithium fluoride window to peak stresses of $\sim $120 GPa. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin company, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Calculation of diffusivity and viscosity of Al-Cu molten mixtures using molecular dynamics

We use equilibrium classical molecular dynamics and Green-Kubo techniques to calculate the diffusivity and viscosity of Al-Cu molten mixtures. We calculate both the self-diffusivities and the Maxwell-Stefan diffusivities, and evaluate the validity of the Darken relation for this system. We compare the results with those from experiments reported in the literature. We have constructed an analytic model that is fit to the MD results. This transport model has been implemented in a continuum hydrodynamics code. Both the continuum code and extremely large-scale molecular dynamics have been used to simulate the development of vortices due to the Kelvin-Helmholtz instability in a shear layer, and we discuss the results of that comparison.   

Mechanical Behaviour of Light Metal Alloys at High Strain Rates. Computer Simulation on Mesoscale Levels

Researches of the last years have allowed to establish that the laws of deformation and fracture of bulk ultrafine-grained and coarse-grained materials are various both in static and in dynamic loading conditions. Development of adequate constitutive equations for the description of mechanical behavior of bulk ultrafine-grained materials at intensive dynamic influences is complicated in consequence of insufficient knowledge about general rules of inelastic deformation and nucleation and growth of cracks. Multi-scale computational model was used for the investigation of deformation and fracture of bulk structured aluminum and magnesium alloys under stress pulse loadings on mesoscale level. The increment of plastic deformation is defined by the sum of the increments caused by a nucleation and gliding of dislocations, the twinning, meso-blocks movement, and grain boundary sliding. The model takes into account the influence on mechanical properties of alloys an average grains size, grain sizes distribution of and concentration of precipitates. It was obtained the nucleation and gliding of dislocations caused the high attenuation rate of the elastic precursor of ultrafine-grained alloys than in coarse grained counterparts.   

Estimation of spectral characteristics of particles ejected from free surfaces of metals and liquids under shock wave effect

The authors present approximated relations for estimations of the basic characteristics of flow of particles ejected from free surface of substance after shock wave arrival (shock-wave ejecta). The problem is considered as a particular case of the Richtmayer-Meshkov instability. Periodic perturbations on free surface, which are sinusoidal and having triangular shape, are considered as the initial perturbations causing formation of jets and particles. The medium is assumed to be liquid with surface tension. The role of viscosity is estimated. In the work, the authors obtained equations for estimations of the following characteristics of the particle flow: -~dependence of integral mass of ejected substance on time; -~space-time distribution of density of ejected substance; -~space-time distribution of velocity of ejected substance; -~distribution of particles in sizes; -~correlation of sizes and velocities of particles. Estimations are presented concerning influence of shear strength and plasticity on substance ejecta. Analytical relations are compared with results of numerical calculations and experiments.''