James S. Stolken

Atomistic Shock Hugoniot simulation of single-crystal copper

Planar shock waves in single-crystal copper were simulated using nonequilibrium molecular dynamics with a realistic embedded atom potential. The simulation results are in good agreement with new experimental data presented here, for the Hugoniot of single-crystal copper along ⟨100⟩. Simulations were performed for Hugoniot pressures in the range 2 GPa – 800 GPa, up to well above the shock induced melting transition. Large anisotropies are found for shock propagation along ⟨100⟩,⟨110⟩, and ⟨111⟩, with quantitative differences from pair potentials results. Plastic deformation starts at Up≳0.75km∕s, and melting occurs between 200 and 220 GPa, in agreement with the experimental melting pressure of polycrystalline copper. The Voigt and Reuss averages of our simulated Hugoniot do not compare well below melting with the experimental Hugoniot of polycrystalline copper. This is possibly due to experimental targets with preferential texturing and/or a much lower Hugoniot elastic limit.

On the importance of geometric nonlinearity in finite-element simulations of trabecular bone failure.

The finite element method, which has been successfully applied to studies of the elastic properties of trabecular bone, is now being used to simulate its failure. These simulations have used a geometrically linear (linear kinematic) approximation to the total stiffness matrix; nonlinear terms in the total stiffness matrix have been excluded from the computation in order to achieve efficiency. Because trabecular bone appears to be a slender (i.e., geometrically nonlinear) structure, we studied the validity of the linear kinematic approximation for simulating its failure. Two cases, designed to bracket the extremes of stability behavior, were explored: a single representative spicule of trabecular bone (case 1) and a volume of trabecular bone consisting of relatively low aspect ratio members (case 2). For case 1, geometrically linear (GL) and nonlinear (GNL) analyses were performed with two different materials models: a plastic damage model and a brittle damage model. When GNL terms were included in the total stiffness matrix, we found that load-path bifurcation preceded tissue failure regardless of the form of the damage model. This bifurcation was the result of a complex coupling between material yield and structural instability. The nature of this coupling was highly sensitive to the form of the damage model. None of these behaviors was observed in the linear analyses, where failure was insensitive to the form of the damage model and where structural instabilities were prevented from occurring. For case 2, compressive loading of a volume of trabecular bone, geometric nonlinear effects were pronounced. There was a bifurcation in load response that resulted in large apparent strain to failure. The GL simulations, on the other hand, precluded this bifurcation. We hypothesize that trabecular bone is a geometric nonlinear structure; nonlinear terms must be included in the total stiffness matrix to accurately simulate its failure.

Densification of fused silica due to shock waves and its implications for 351 nm laser induced damage.

High-power 351 nm (3 ) laser pulses can produce damaged areas in high quality fused silica optics. Recent experiments have shown the presence of a densified layer at the bottom of damage initiation craters. We have studied the propagation of shock waves through fused silica using large-scale atomistic simulations since such shocks are expected to accompany laser energy deposition. These simulations show that the shocks induce structural transformations in the material that persist long after the shock has dissipated. Values of densification and thickness of densified layer agree with experimental observations. Moreover, our simulations give an atomistic description of the structural changes in the material due to shock waves and their relation to Raman spectra measurements.

High-pressure, high-strain-rate lattice response of shocked materials

Laser-based shock experiments have been conducted in thin Si and Cu crystals at pressures above the published Hugoniot Elastic Limit (HEL) for these materials. In situ x-ray diffraction has been used to directly measure the response of the shocked lattice during shock loading. Static film and x-ray streak cameras recorded x rays diffracted from lattice planes both parallel and perpendicular to the shock direction. In addition, experiments were conducted using a wide-angle detector to record x rays diffracted from multiple lattice planes simultaneously. These data showed uniaxial compression of Si (100) along the shock direction and three-dimensional compression of Cu (100). In the case of the Si diffraction, there was a multiple wave structure observed. This is evaluated to determine whether there is a phase transition occurring on the time scale of the experiments, or the HEL is much higher than previously reported. Results of the measurements are presented.

Dislocation stress fields for dynamic codes using anisotropic elasticity: methodology and analysis

Abstract A numerical methodology to incorporate anisotropic elasticity into three-dimensional dislocation dynamics codes has been developed, employing theorems derived by Lothe [J. Lothe, Philos. Mag. 15 (1967) 353], Brown [L.M. Brown, Philos. Mag. 15 (1967) 363], Indenbom and Orlov [V.L. Indenbom, S.S. Orlov, Sov. Phys. Crystallogr. 12 (6) (1968) 849], and Asaro and Bamett [R.J. Asaro, D.M. Barnett, in: R.J. Arsenault, J.R. Beeler Jr., J.A. Simmons (Eds.), Computer Simulation for Materials Applications, Part 2. Nuclear Metallurgy, Vol. 20, p. 313]. The formalism is based on the stress field solution for a straight dislocation segment of arbitrary orientation in three-dimensional space. The general solution is given in a complicated closed integral form. To reduce the computation complexity, look-up tables are used to avoid heavy computations for the evaluation of the angular stress factor ( Σ ij ) and its first derivative term ( Σ ij ′). The computation methodology and error analysis are discussed in comparison with known closed form solutions for isotropic elasticity. For the case of Mo single crystals, we show that the difference between anisotropic and isotropic elastic stress fields can be, for some components of the stress tensor, as high as 15% close to the dislocation line, and decrease significantly away from it. This suggests that short-range interactions should be evaluated based on anisotropic elasticity, while long-range interactions can be approximated using long-range elasticity.

Analysis of the x-ray diffraction signal for the {alpha}-{epsilon} transition in shock-compressed iron: Simulation and experiment

Recent published work has shown that the phase change of shock-compressed iron along the [001] direction does transform to the {epsilon} [hexagonal close-packed (hcp)] phase similar to the case for static measurements. This article provides an in-depth analysis of the experiment and nonequilibrium molecular dynamics simulations, using x-ray diffraction in both cases to study the crystal structure upon transition. Both simulation and experiment are consistent with a compression and shuffle mechanism responsible for the phase change from body-centered cubic to hcp. Also both show a polycrystalline structure upon the phase transition, due to the four degenerate directions in which the phase change can occur.

Metals far from equilibrium: From shocks to radiation damage

Abstract Shock waves and high-energy particle radiation can each drive materials far from thermodynamic equilibrium and enable novel scenarios in the processing of materials. A large number of theoretical and experimental studies of shock deformation have been performed on polycrystalline materials, but shock deformation in single crystals has only recently been studied in some detail. We present molecular dynamics (MD) simulations of the shock response of single crystal copper, modeled using an embedded atom potential that reproduces both defect formation and high pressure behavior. Shock-induced plasticity will also be discussed. Predicting the in-service response of ferritic alloys in future fusion energy environments requires a detailed understanding of the mechanisms of defect accumulation and microstructure evolution in harsh radiation environments, which include a high level of He generation concurrent with primary damage production. The second half of this paper describes results of atomistic MD and kinetic Monte Carlo simulations to investigate the role of He on point defect cluster behaviour and damage accumulation in bcc Fe. The goal of these simulations is to study the mechanisms responsible for the formation of vacancy-He clusters which serve as He bubble and void nuclei in fusion reactor materials.

Determination of the intrinsic temperature dependent thermal conductivity from analysis of surface temperature of laser irradiated materials

An experimental and analytical approach is described to determine the temperature dependent intrinsic lattice thermal conductivity, k(T), for a broad range of materials. k(T) of silica, sapphire, spinel, and lithium fluoride were derived from surface temperature measurements. Surfaces were heated from room temperature up to 3000 K using a CO2-laser irradiance ≤5 kW/cm2. The solution of the nonlinear heat flow equation was used to extract parameters of k(T)=A×Te, where −1.13≤e≤0 depending on the material. Results generally show good agreement with reported k(T). Below evaporation, the phonon-only k remains the dominant heat transport mechanism during laser heating.

Shock Hugoniot of single crystal copper

The shock Hugoniot of single crystal copper is reported for stresses below 66 GPa. Symmetric impact experiments were used to measure the Hugoniots of three different crystal orientations of copper, [100], [110], and [111]. The photonic doppler velocimetry (PDV) diagnostic was adapted into a very high precision time of arrival detector for these experiments. The measured Hugoniots along all three crystal directions were nearly identical to the experimental Hugoniot for polycrystalline Cu. The predicted orientation dependence of the Hugoniot from molecular dynamics calculations was not observed. At the lowest stresses, the sound speed in Cu was extracted from the PDV data. The measured sound speeds are in agreement with values calculated from the elastic constants for Cu.

Multiple film plane diagnostic for shocked lattice measurements (invited)

Laser-based shock experiments have been conducted in thin Si and Cu crystals at pressures above the Hugoniot elastic limit. In these experiments, static film and x-ray streak cameras recorded x rays diffracted from lattice planes both parallel and perpendicular to the shock direction. These data showed uniaxial compression of Si(100) along the shock direction and three-dimensional compression of Cu(100). In the case of the Si diffraction, there was a multiple wave structure observed, which may be due to a one-dimensional phase transition or a time variation in the shock pressure. A new film-based detector has been developed for these in situ dynamic diffraction experiments. This large-angle detector consists of three film cassettes that are positioned to record x rays diffracted from a shocked crystal anywhere within a full π steradian. It records x rays that are diffracted from multiple lattice planes both parallel and at oblique angles with respect to the shock direction. It is a time-integrating measur...