Application of a Multiscale Model of Tantalum Deformation at Megabar Pressures Page: 3 of 7
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Application of a Multiscale Model of Tantalum Deformation at Megabar Pressures
Robert Cavallo, Hye-Sook Park, Nathan Barton, Bruce Remington, Stephen Pollaine, Shon Prisbrey, Joel
Bernier, Mark May, Brian Maddox, David Swift and the Materials Integrated Experimental Team
(Lawrence Livermore National Laboratory), Rich Becker (Army Research Laboratory) and Russell Olson
(Los Alamos National Laboratory)
A new multiscale simulation tool has been developed to model the strength of tantalum under high-
pressure dynamic compression. This new model combines simulations at multiple length scales to
explain macroscopic properties of materials. Previously known continuum models of material response
under load have built upon a mixture of theoretical physics and experimental phenomenology.
Experimental data, typically measured at static pressures, are used as a means of calibration to
construct models that parameterize the material properties; e.g., yield stress, work hardening, strain-
rate dependence, etc. The pressure dependence for most models enters through the shear modulus,
which is used to scale the flow stress. When these models are applied to data taken far outside the
calibrated regions of phase space (e.g., strain rate or pressure) they often diverge in their predicted
behavior of material deformation.
The new multiscale model, developed at Lawrence Livermore National Laboratory, starts with
interatomic quantum mechanical potential and is based on the motion and multiplication of
dislocations'. The basis for the macroscale model is plastic deformation by phonon drag and thermally
activated dislocation motion and strain hardening resulting from elastic interactions among dislocations.
The dislocation density, p, and dislocation velocity, v, are connected to the plastic strain rate, EP, via
Orowan's equation: EP = -V, where b is the Burger's vector, the shear magnitude associated with a
dislocation, and M is the Taylor factor, which accounts for geometric effects in how slip systems
accommodate the deformation. The evolution of the dislocation density and velocity is carried out in
the continuum model by parameterized fits to smaller scale simulations, each informed by calculations
on smaller length scales down to atomistic dimensions.
We apply this new model for tantalum to two sets of experiments and compare the results with more
traditional models. The experiments are based on the Barnes's2 technique in which a low density
material loads against a metal surface containing a pre-imposed rippled pattern. The loaded sample is
Rayleigh-Taylor unstable and the rippled amplitudes grow with time. The rate of growth differs
depending on the material strength, with stronger materials growing less, even to the point of
saturation. One set of experiments was conducted at the pRad facility at LANSCE at Los Alamos National
Laboratory in 2007 using high-explosive (HE) driven tantalum samples. The other set of experiments
was done at the Omega laser at the Laboratory for Laser Energetics at the University of Rochester, which
used high-powered lasers to create plasmas to dynamically compress a rippled tantalum sample (see,
e.g., Park et al.3,4). The two techniques provide data at different pressures and strain rates: The HE
technique drives the samples at around 2 x 105 s-' strain rate and pressures near 500 kbar, while the
laser technique hits strain rates around 2 x 107 s-' and pressures close to 1.4 Mbar.
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Cavallo, R M; Park, H; Barton, N R; Remignton, B A; Pollaine, S M; Prisbrey, S T et al. Application of a Multiscale Model of Tantalum Deformation at Megabar Pressures, article, May 13, 2010; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc837084/m1/3/: accessed September 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.