J. E. Hammerberg

Nonlinear dynamics and the problem of slip at material interfaces

Abstract The problem of dry friction between two metallic interfaces is discussed from the perspective of large scale molecular dynamics (MD) simulations. For flat interfaces between identical metals, two-dimensional MD simulations using embedded-atom-method potentials for copper have shown a variety of phenomena associated with a velocity weakening of the tangential force at high relative velocities (approaching significant fractions of the transverse sound speed). These include dislocation generation, dislocation motion both parallel and normal to the sliding interface, large plastic deformation, nucleation of microstructure, diffusive coarsening of microstructure, and material mixing. The early time behavior of a flat sliding interface is dominated by dislocation motion parallel to the interface. For this early stage, lower-dimensional models are useful in interpreting some of the simulation data. A two-chain forced Frenkel-Kontorova model reproduces some of the behavior of the larger scale simulations when the phenomenological damping is taken to be consistent with the MD simulations. This model exhibits four velocity regimes of steady state flow which will be discussed. Some of the implications for the nucleation of microstructure will be addressed.

Effects of shock-breakout pressure on ejection of micron-scale material from shocked tin surfaces

This effort investigates the relation between ejecta production and shock-breakout pressure (PSB) for Sn shocked with a Taylor shockwave (unsupported) to pressures near the solid-on-release/partial melt-on-release phase transition region. The shockwaves were created by detonation of high explosive (HE) PBX-9501 on the front side of Sn coupons. Ejecta production at the backside or free side of the Sn coupons was characterized through use of piezoelectric pins, optical shadowgraphy, x-ray attenuation radiography, and optical-heterodyne velocimetry. Ejecta velocities, dynamic volume densities, and areal densities were then correlated with the shock-breakout pressure of Sn surfaces characterized by roughness average of Ra=16 μin or Ra=32 μin.

Piezoelectric characterization of ejecta from shocked tin surfaces

Using piezoelectric diagnostics, we have measured densities and velocities of ejected particulate as well as “free-surface velocities” of bulk tin targets shock loaded with high explosive. The targets had finely grooved, machined finishes ranging from 10 to 250μin. Two types of piezoelectric sensor (“piezopins”), lithium niobate and lead zirconate titanate, were compared for durability and repeatability; in addition, some piezopins were “shielded” with foam and metal foil in order to mitigate premature failure of the pins in high ejecta regimes. These experiments address questions about ejecta production at a given shock pressure as a function of surface finish; piezopin results are compared with those from complementary diagnostics such as x-ray radiography and time-resolved optical transmission techniques. The mass ejection shows a marked dependence on groove characteristics and cannot be described by a groove defect theory alone.

Probing the underlying physics of ejecta production from shocked Sn samples

This effort investigates the underlying physics of ejecta production for high explosive (HE) shocked Sn surfaces prepared with finishes typical to those roughened by tool marks left from machining processes. To investigate the physical mechanisms of ejecta production, we compiled and re-examined ejecta data from two experimental campaigns [W. S. Vogan et al., J. Appl. Phys. 98, 113508 (1998); M. B. Zellner et al., ibid. 102, 013522 (2007)] to form a self-consistent data set spanning a large parameter space. In the first campaign, ejecta created upon shock release at the back side of HE shocked Sn samples were characterized for samples with varying surface finishes but at similar shock-breakout pressures PSB. In the second campaign, ejecta were characterized for HE shocked Sn samples with a constant surface finish but at varying PSB.

Dynamic comparisons of piezoelectric ejecta diagnostics

We investigate the quantitative reliability and precision of three different piezoelectric technologies for measuring ejected areal mass from shocked surfaces. Specifically we performed ejecta measurements on Sn shocked at two pressures, P≈215 and 235 kbar. The shock in the Sn was created by launching a impactor with a powder gun. We self-compare and cross-compare these measurements to assess the ability of these probes to precisely determine the areal mass ejected from a shocked surface. We demonstrate the precision of each technology to be good, with variabilities on the order of ±10%. We also discuss their relative accuracy.

Experimental observations on the links between surface perturbation parameters and shock-induced mass ejection

We have assembled together our ejecta measurements from explosively shocked tin acquired over a period of about ten years. The tin was cast at 0.99995 purity, and all of the tin targets or samples were shocked to loading pressures of about 27 GPa, allowing meaningful comparisons. The collected data are markedly consistent, and because the total ejected mass scales linearly with the perturbations amplitudes they can be used to estimate how much total Sn mass will be ejected from explosively shocked Sn, at similar loading pressures, based on the surface perturbation parameters of wavelength and amplitude. Most of the data were collected from periodic isosceles shapes that approximate sinusoidal perturbations. Importantly, however, we find that not all periodic perturbations behave similarly. For example, we observed that sawtooth (right triangular) perturbations eject more mass than an isosceles perturbation of similar depth and wavelength, demonstrating that masses ejected from irregular shaped perturbatio...

On shock driven jetting of liquid from non-sinusoidal surfaces into a vacuum

Previous work employed Richtmyer-Meshkov theory to describe the development of spikes and bubbles from shocked sinusoidal surfaces. Here, we discuss the effects of machining different two-dimensional shaped grooves in copper and examine the resulting flow of the material after being shocked into liquid on release. For these simulations, a high performance molecular dynamics code, SPaSM, was used with machined grooves of kh0 = 1 and kh0 = 1/8, where 2h0 is the peak-to-valley height of the perturbation with wavelength λ, and k = 2π/λ. The surface morphologies studied include a Chevron, a Fly-Cut, a Square-Wave, and a Gaussian. We describe extensions to an existing ejecta source model that better captures the mass ejected from these surfaces. We also investigate the same profiles at length scales of order 1 cm for an idealized fluid equation of state using the FLASH continuum hydrodynamics code. Our findings indicate that the resulting mass can be scaled by the missing area of a sinusoidal curve with an effe...

INFLUENCE OF SHOCKWAVE PROFILE ON EJECTA

We investigate the relation between shock‐pulse shape and the amount of micron‐scale fragments ejected upon shock release at the metal/vacuum interface of shocked Sn targets. These micron‐scale particles are commonly referred to as ejecta. Two shock‐pulse shapes are considered: a supported shock created by impacting a Sn target with a sabot that was accelerated using a powder gun; and an unsupported or Taylor Shockwave, created by detonation of high explosive that was press‐fit to the front‐side of the Sn target. Ejecta production at the back‐side or free‐surface of the Sn coupons were characterized through use of piezoelectric pins, Asay foils, optical shadowgraphy, and x‐ray attenuation.

Second shock ejecta measurements with an explosively driven two-shockwave drive

We develop and apply an explosively driven two-shockwave tool in material damage experiments on Sn. The two shockwave tool allows the variation of the first shockwave amplitude over range 18.5 to 26.4 GPa, with a time interval variation between the first and second shock of 5 to 7 μs. Simulations imply that the second shock amplitude can be varied as well and we briefly describe how to achieve such a variation. Our interest is to measure ejecta masses from twice shocked metals. In our application of the two-shockwave tool, we observed second shock ejected areal masses of about 4 ± 1 mg/cm2, a value we attribute to unstable Richtmyer-Meshkov impulse phenomena. We also observed an additional mass ejection process caused by the abrupt recompression of the local spallation or cavitation of the twice shocked Sn.

Dry friction: modeling and energy flow

Abstract A model of dry, wearless friction between two atomistically flat, two-dimensional workpieces is introduced. This isotropic elastic model allows us to study the flow of energy away from the sliding interface during the frictional process. Although a direct quantitative comparison of the model with molecular dynamics data is not possible, qualitative comparisons indicate that much of the early-time nonplastic behavior of molecular dynamics data can be described by a simple elastic model. Also our results support previous speculation that it is appropriate to introduce viscous damping effects when formulating lower-dimensional models of such physical processes.