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Title: Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

Abstract

Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes the rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methodsmore » are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.« less

Authors:
 [1];  [2];  [3];  [4]
  1. US Army, Aberdeen Proving Grounds, MD (United States). Impact Physics Branch; Georgia Inst. of Technology, Atlanta, GA (United States). Woodruff School of Mechanical Engineering
  2. US Army, Aberdeen Proving Grounds, MD (United States). Impact Physics Branch
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Materials Modeling and Simulation Group
  4. Georgia Inst. of Technology, Atlanta, GA (United States). Woodruff School of Mechanical Engineering and School of Materials Science
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1249149
Report Number(s):
LLNL-JRNL-663743
Journal ID: ISSN 2213-7467
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Advanced Modeling and Simulation in Engineering Sciences
Additional Journal Information:
Journal Volume: 2; Journal Issue: 1; Journal ID: ISSN 2213-7467
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Lloyd, Jeffrey T., Clayton, John D., Austin, Ryan A., and McDowell, David L.. Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions. United States: N. p., 2015. Web. https://doi.org/10.1186/s40323-015-0036-6.
Lloyd, Jeffrey T., Clayton, John D., Austin, Ryan A., & McDowell, David L.. Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions. United States. https://doi.org/10.1186/s40323-015-0036-6
Lloyd, Jeffrey T., Clayton, John D., Austin, Ryan A., and McDowell, David L.. Fri . "Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions". United States. https://doi.org/10.1186/s40323-015-0036-6. https://www.osti.gov/servlets/purl/1249149.
@article{osti_1249149,
title = {Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions},
author = {Lloyd, Jeffrey T. and Clayton, John D. and Austin, Ryan A. and McDowell, David L.},
abstractNote = {Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes the rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.},
doi = {10.1186/s40323-015-0036-6},
journal = {Advanced Modeling and Simulation in Engineering Sciences},
number = 1,
volume = 2,
place = {United States},
year = {2015},
month = {7}
}

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    Works referencing / citing this record:

    Dynamic Strength of AZ31B-4E and AMX602 Magnesium Alloys Under Shock Loading
    journal, January 2020