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Title: Analytic EoS and PTW strength model recommendation for Starck Ta

Abstract

The purpose of this document is to provide an analytic EoS and PTW strength model for Starck Ta that can be consistently used between different platforms and simulations at three labs. This should provide a consistent basis for comparison of the results of calculations, but not the best implementation for matching a wide variety of experimental data. Another version using SESAME tables should follow, which will provide a better physical representation over a broader range of conditions. The data sets available at the time only include one Hopkinson bar at a strain rate of 1800/s; a broader range of high-rate calibration data would be preferred. The resulting fit gives the PTW parameter p = 0. To avoid numerical issues, p = 0:001 has been used in FLAG. The PTW parameters that apply above the maximum strain rate in the data use the values from the original publication.

Authors:
 [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1304821
Report Number(s):
LA-UR-16-26427
DOE Contract Number:
AC52-06NA25396
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Sjue, Sky K., and Prime, Michael B. Analytic EoS and PTW strength model recommendation for Starck Ta. United States: N. p., 2016. Web. doi:10.2172/1304821.
Sjue, Sky K., & Prime, Michael B. Analytic EoS and PTW strength model recommendation for Starck Ta. United States. doi:10.2172/1304821.
Sjue, Sky K., and Prime, Michael B. Thu . "Analytic EoS and PTW strength model recommendation for Starck Ta". United States. doi:10.2172/1304821. https://www.osti.gov/servlets/purl/1304821.
@article{osti_1304821,
title = {Analytic EoS and PTW strength model recommendation for Starck Ta},
author = {Sjue, Sky K. and Prime, Michael B.},
abstractNote = {The purpose of this document is to provide an analytic EoS and PTW strength model for Starck Ta that can be consistently used between different platforms and simulations at three labs. This should provide a consistent basis for comparison of the results of calculations, but not the best implementation for matching a wide variety of experimental data. Another version using SESAME tables should follow, which will provide a better physical representation over a broader range of conditions. The data sets available at the time only include one Hopkinson bar at a strain rate of 1800/s; a broader range of high-rate calibration data would be preferred. The resulting fit gives the PTW parameter p = 0. To avoid numerical issues, p = 0:001 has been used in FLAG. The PTW parameters that apply above the maximum strain rate in the data use the values from the original publication.},
doi = {10.2172/1304821},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Sep 01 00:00:00 EDT 2016},
month = {Thu Sep 01 00:00:00 EDT 2016}
}

Technical Report:

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  • The purpose of this document is to provide a calibration of the Preston-Tonks- Wallace (PTW) strength model for use with the new SESAME equation of state (EoS) 93524. The calibration data included in this t spans temperatures from 198 K to 673 K and strain rates from 0.001/s to 3200/s.
  • Abstract A thermodynamically consistent and fully general equation–of– state (EOS) for multifield applications is described. EOS functions are derived from a Helmholtz free energy expressed as the sum of thermal (fluctuational) and collisional (condensed–phase) contributions; thus the free energy is of the Mie–Gr¨uneisen1 form. The phase–coexistence region is defined using a parameterized saturation curve by extending the form introduced by Guggenheim,2 which scales the curve relative to conditions at the critical point. We use the zero–temperature condensed–phase contribution developed by Barnes,3 which extends the Thomas–Fermi–Dirac equation to zero pressure. Thus, the functional form of the EOS could be called MGGBmore » (for Mie– Gr¨uneisen–Guggenheim–Barnes). Substance–specific parameters are obtained by fitting the low–density energy to data from the Sesame4 library; fitting the zero–temperature pressure to the Sesame cold curve; and fitting the saturation curve and latent heat to laboratory data,5 if available. When suitable coexistence data, or Sesame data, are not available, then we apply the Principle of Corresponding States.2 Thus MGGB can be thought of as a numerical recipe for rendering the tabular Sesame EOS data in an analytic form that includes a proper coexistence region, and which permits the accurate calculation of derivatives associated with compressibility, expansivity, Joule coefficient, and specific heat, all of which are required for multifield applications. 1« less
  • A new Sesame EOS table for Ta has been released for testing. It is a limited range table covering T ≤ 26, 000 K and ρ ≤ 37.53 g/cc. The EOS is based on earlier analysis using DFT phonon calculations to infer the cold pressure from the Hugoniot. The cold curve has been extended into compression using new DFT calculations. The present EOS covers expansion into the gas phase. It is a multi-phase EOS with distinct liquid and solid phases. A cold shear modulus table (431) is included. This is based on an analytic interpolation of DFT calculations.