Skip to main content
Top
Published in: Journal of Materials Engineering and Performance 10/2019

23-09-2019

Mechanical Behavior of Lead at High Strain Rates

Authors: Xiaoyun Zhang, Yihui Zhu, Yuzhao Yang, Cheng Xu

Published in: Journal of Materials Engineering and Performance | Issue 10/2019

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper presents a study on the material behaviors and constitutive models of lead at high strain rates. Quasi-static compressive tests and split Hopkinson pressure bar (SHPB) tests were conducted at room temperature. The results of the SHPB tests were verified by high-speed photography, and the error of strain is less than 3% at high strain rate (5000/s). Our results show that the yield stress and flow stress increase at high strain rates. This result indicates that lead is sensitive to the strain rate at high strain rates, but the dependence is not linear during 3000-5000/s. The strain-rate dependence of lead was fitted by a quadratic polynomial curve. To describe the nonlinear strain-rate relationship of lead, modified Johnson–Cook and Cowper–Symonds material models were used to fit the experimental stress–strain curves. The modified Cowper–Symonds model agrees better with the experimental results and can better describe the dynamic mechanical behavior of lead under high strain rates.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Y.M. Parulekar et al., Lead Extrusion Dampers for Reducing Seismic Response of Coolant Channel Assembly, Nucl. Eng. Des., 2004, 227(2), p 175–183CrossRef Y.M. Parulekar et al., Lead Extrusion Dampers for Reducing Seismic Response of Coolant Channel Assembly, Nucl. Eng. Des., 2004, 227(2), p 175–183CrossRef
2.
go back to reference K. Zeynali et al., Experimental and Numerical Investigation of Lead-Rubber Dampers in Chevron Concentrically Braced Frames, Arch. Civ. Mech. Eng., 2018, 18(1), p 162–178CrossRef K. Zeynali et al., Experimental and Numerical Investigation of Lead-Rubber Dampers in Chevron Concentrically Braced Frames, Arch. Civ. Mech. Eng., 2018, 18(1), p 162–178CrossRef
3.
go back to reference N. Loizou and R.B. Sims, The Yield Stress of Pure Lead in Compression, J. Mech. Phys. Solids, 1953, 1, p 234–243CrossRef N. Loizou and R.B. Sims, The Yield Stress of Pure Lead in Compression, J. Mech. Phys. Solids, 1953, 1, p 234–243CrossRef
4.
go back to reference H. Kolsky, An Investigation of the Mechanical Properties of Materials at Very High Rates of Loading, Proc. Phys. Soc. B, 1949, 62(11), p 676–700CrossRef H. Kolsky, An Investigation of the Mechanical Properties of Materials at Very High Rates of Loading, Proc. Phys. Soc. B, 1949, 62(11), p 676–700CrossRef
5.
go back to reference M. Malatyński and J. Klepaczko, Experimental Investigation of Plastic Properties of Lead Over a Wide Range of Strain Rates, Int. J. Mech. Sci., 1980, 22(3), p 173–183CrossRef M. Malatyński and J. Klepaczko, Experimental Investigation of Plastic Properties of Lead Over a Wide Range of Strain Rates, Int. J. Mech. Sci., 1980, 22(3), p 173–183CrossRef
6.
go back to reference J. Duffy, R.H. Hawley, and R.A. Frantz, The Deformation of Lead in Torsion at High Strain Rates, J. Appl. Mech., 1972, 39(3), p 651CrossRef J. Duffy, R.H. Hawley, and R.A. Frantz, The Deformation of Lead in Torsion at High Strain Rates, J. Appl. Mech., 1972, 39(3), p 651CrossRef
7.
go back to reference G.R. Johnson and W.H. Cook, A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain-Rates and High Temperatures, in Proceedings of the Seventh International Symposium on Ballistics, The Hague, The Netherlands (1983), p 541–547. G.R. Johnson and W.H. Cook, A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain-Rates and High Temperatures, in Proceedings of the Seventh International Symposium on Ballistics, The Hague, The Netherlands (1983), p 541–547.
8.
go back to reference G. Cowper and P. Symonds, Strain Hardening and Strain-Rate Effects in the Impact Loading of Cantilever Beams, Report No. 28, Brown University Division of Applied Mathematics (1957) G. Cowper and P. Symonds, Strain Hardening and Strain-Rate Effects in the Impact Loading of Cantilever Beams, Report No. 28, Brown University Division of Applied Mathematics (1957)
9.
go back to reference H. Huh and W.J. Kang, Crash-Worthiness Assessment of Thin-Walled Structures with the High-Strength Steel Sheet, Int. J. Veh. Des., 2002, 30(1–2), p 1–21CrossRef H. Huh and W.J. Kang, Crash-Worthiness Assessment of Thin-Walled Structures with the High-Strength Steel Sheet, Int. J. Veh. Des., 2002, 30(1–2), p 1–21CrossRef
10.
go back to reference T.J. Holmquist and G.R. Johnson, Determination of Constants and Comparison of Results for Various Constitutive Models. J. Phys. IV Colloq., 1991, 1(C3), p C3-853-C3-860 T.J. Holmquist and G.R. Johnson, Determination of Constants and Comparison of Results for Various Constitutive Models. J. Phys. IV Colloq., 1991, 1(C3), p C3-853-C3-860
11.
go back to reference B.J. Tuazon et al., Integration of a New Data Acquisition/Processing Scheme in SHPB Test and Characterization of the Dynamic Material Properties of High-Strength Steels Using the Optional Form of Johnson-Cook Model, J. Mech. Sci. Technol., 2014, 28(9), p 3561–3568CrossRef B.J. Tuazon et al., Integration of a New Data Acquisition/Processing Scheme in SHPB Test and Characterization of the Dynamic Material Properties of High-Strength Steels Using the Optional Form of Johnson-Cook Model, J. Mech. Sci. Technol., 2014, 28(9), p 3561–3568CrossRef
12.
go back to reference A.A. Al Salahi and R. Othman, Constitutive Equations of Yield Stress Sensitivity to Strain Rate of Metals: A Comparative Study, J. Eng., 2016, 2016, p 1–7CrossRef A.A. Al Salahi and R. Othman, Constitutive Equations of Yield Stress Sensitivity to Strain Rate of Metals: A Comparative Study, J. Eng., 2016, 2016, p 1–7CrossRef
13.
go back to reference T. Grunenwald, F. Llorca, and J. Farre, A Modeling of Visco-Plastic Behavior of Lead and a Lead Alloy Over a Wide Range of Strain Rate and Temperature, J. Phys. IV, 2003, 110, p 99–104 T. Grunenwald, F. Llorca, and J. Farre, A Modeling of Visco-Plastic Behavior of Lead and a Lead Alloy Over a Wide Range of Strain Rate and Temperature, J. Phys. IV, 2003, 110, p 99–104
14.
go back to reference G.S. Sohoni, M.V. Walame, V. Tandon, R.S. Mahajan, and S. Raju. ASME 2005. Dynamic Dynamic Behavior Characterization of Lead at High Strain Rates Using High Speed Photography for Finite Element Simulation, in International Mechanical Engineering Congress and Exposition (2005). G.S. Sohoni, M.V. Walame, V. Tandon, R.S. Mahajan, and S. Raju. ASME 2005. Dynamic Dynamic Behavior Characterization of Lead at High Strain Rates Using High Speed Photography for Finite Element Simulation, in International Mechanical Engineering Congress and Exposition (2005).
15.
go back to reference G.T. Gray, Classic Split-Hopkinson Bar Testing, in ASM Handbook. Mechanical Testing and Evaluation, vol. 8 (ASM International, Detroit, 2000), p 1027–1067. G.T. Gray, Classic Split-Hopkinson Bar Testing, in ASM Handbook. Mechanical Testing and Evaluation, vol. 8 (ASM International, Detroit, 2000), p 1027–1067.
16.
go back to reference S. Li and H. Shisheng, Two-Wave and Three-Wave Method in SHPB Data Processing, Explos. Shock Waves, 2005, 25(4), p 368–373 ((in Chinese)) S. Li and H. Shisheng, Two-Wave and Three-Wave Method in SHPB Data Processing, Explos. Shock Waves, 2005, 25(4), p 368–373 ((in Chinese))
17.
go back to reference W. Chen and W. Chen. Split Hopkinson (Kolsky) Bar (2011), p 180. W. Chen and W. Chen. Split Hopkinson (Kolsky) Bar (2011), p 180.
18.
go back to reference M. Alves, Material Constitutive Law for Large Strains and Strain Rates, J. Eng. Mech., 2000, 126(2), p 215–218CrossRef M. Alves, Material Constitutive Law for Large Strains and Strain Rates, J. Eng. Mech., 2000, 126(2), p 215–218CrossRef
19.
go back to reference W.Q. Song, P. Beggs, and M. Easton, Compressive Strain-Rate Sensitivity of Magnesium–Aluminum Die Casting Alloys, Mater. Des., 2009, 30(3), p 642–648CrossRef W.Q. Song, P. Beggs, and M. Easton, Compressive Strain-Rate Sensitivity of Magnesium–Aluminum Die Casting Alloys, Mater. Des., 2009, 30(3), p 642–648CrossRef
20.
go back to reference C. Zhi-jian, Y. Jian-hong, and Z. Yao, Impact Experiment Study of Ship Building Steel at 450 MPa Level and Constitutive Model of Cowper-Symonds, J. Ship Mech., 2007, 6(11), p 933–941 C. Zhi-jian, Y. Jian-hong, and Z. Yao, Impact Experiment Study of Ship Building Steel at 450 MPa Level and Constitutive Model of Cowper-Symonds, J. Ship Mech., 2007, 6(11), p 933–941
Metadata
Title
Mechanical Behavior of Lead at High Strain Rates
Authors
Xiaoyun Zhang
Yihui Zhu
Yuzhao Yang
Cheng Xu
Publication date
23-09-2019
Publisher
Springer US
Published in
Journal of Materials Engineering and Performance / Issue 10/2019
Print ISSN: 1059-9495
Electronic ISSN: 1544-1024
DOI
https://doi.org/10.1007/s11665-019-04343-1

Other articles of this Issue 10/2019

Journal of Materials Engineering and Performance 10/2019 Go to the issue

Premium Partners