Abstract
In several previous studies, strain rate sensitivity parameters are given for universal stress strain curves for true Cauchy stress and true (logarithmic) strain data; however, the required true strain rate was approximated using nominal (engineering) strain rate. The problem with this is that for finite viscoplastic deformations, both Eulerien and Lagrangian variables are being combined within the proposed viscoplasic constitutive models which makes the models inconsistent with the exact equations of motion, and required deformation power requirements. To be consistent, it is required that the true Cauchy stress be the work energy conjugate to the true strain measure whose rate is the rate of deformation tensor along with the current density per current unit volume. Therefore, in this study, the objective is to illustrate the difference associated with using the strain rate sensitivity constants from true stress versus true strain data obtained at several nominal axial strain rates with the true axial rates of deformation.
Similar content being viewed by others
References
Song B, Chen W, Antoun BR, Frew DJ (2007) Determination of early flow stress for ductile specimens at high strain rates by using a SHPB. Exp Mech 47:671–679
Frew DJ, Forrestal MJ, Chen W (2002) Pulse shaping techniques for testing brittle materials with a split Hopkinson pressure bar. Exp Mech 42:93–106
Frew DJ, Forrestal MJ, Chen W (2005) Pulse shaping techniques for testing elastic-plastic materials with a split Hopkinson pressure bar. Exp Mech 45:186–195
Lubliner J (1990) Plasticity Theory. Macmillan Publishing, New York
Warren TL, Forrestal MJ (1998) Effects of strain hardening and strain rate sensitivity on the penetration of aluminum targets with spherical-nosed rods. Int J Solids Struct 35:3737–3753
Piekutowski AJ, Forrestal MJ, Poormon KL, Warren TL (1999) Penetration of 6061–T6511 Aluninum targets by ogive-nose steel projectiles with striking velocities between 0.5 and 3.0 km/s. Int J Impact Eng 23:723–734
Hopkins HG (1960) Dynamic expansion of spherical cavities in metals. progress in solid mecanics, vol 1, 1st edn. Sneddon and R Hill, New York, pp 85–164
Warren TL, Tabbara MR (2000) Simulations of the penetration of 6061–T6511 aluminum targets by spherical-nosed VAR 4340 steel projectiles. Int J Solids Struct 37:4419–4435
Warren TL, Poormon KL (2001) Penetration of 6061–T6511 aluminum targets by ogive-nosed VAR 4340 steel projectiles at oblique angles: experiments and simulations. Int J Impact Eng 25:993–1022
Peirce D, Shih CF, Needleman A (1984) A tangent modulus method for rate dependent solids. Comp and Struct 18(5):875–887
Warren TL (2002) Simulations of the penetration of limestone targets by ogive–nose 4340 steel projectiles. Int J Impact Eng 27:475–496
Warren TL, Hanchak SJ, Poormon KL (2004) Penetration of limestone targets by ogive-nosed VAR 4340 steel projectiles at oblique angles: experiments and simulations. Int J Impact Eng 30:1307–1331
Taylor LM, Flanagan DP (1998) PRONTO 3D a three dimensional transient solid dynamics program. SAND87–1912. Sandia National Laboratories, Albuquerque
Ramesh KT, Narasimhan S (1996) Finite deformations and the dynamic measurement of radial strains in compression kolsky bar experiments. Int J Solids Struct 33(25):3723–3738
Lee EH (1969) Elastic-plastic deformation at finite strains. ASME J Appl Mech 36:1–6
Yadav S, Chichili DR, Ramesh KT (1995) The mechanical response of a 6061–T6 Al/Al2O3 metal matrix at high rates of deformation. Acta Metall Mater 43(12):4453–4464
Hill R (1950) The mathematical theory of plasticity. OxfordUniversityPress, London
Luk V, Forrestal MJ, Amos DE (1991) Dynamic spherical cavity-expansion of strain-hardening materials. ASME J Appl Mech 58:1–6
Forrestal MJ, Piekutowski AJ (2000) Penetration experiments with 6061–T6511 aluminum targets and spherical-nose steel projectiles at striking velocities between 05 and 30 km/s. Int J Impact Engng 24:57–67
Funding
N/A.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The author declares no known competing financial interests or personal relationships that could have appeared to influence the work done in this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Warren, T.L. Approximation of Strain Rate Parameters for Use with Eulerian Viscoplastic Constitutive Models Based on True Cauchy Stresses and True Strains Obtained at Nominal Strain Rates. J. dynamic behavior mater. 10, 98–110 (2024). https://doi.org/10.1007/s40870-023-00394-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40870-023-00394-7