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Experimental Mechanics

, Volume 56, Issue 1, pp 25–35 | Cite as

High Strain-Rate Tensile Characterization of EPDM Rubber Using Non-equilibrium Loading and the Virtual Fields Method

  • S.-h. Yoon
  • M. Winters
  • C. R. Siviour
Article

Abstract

The dynamic tensile stress-strain behaviour of an EPDM rubber was characterized at quasi-static (<0.01 s−1), medium and high strain rates (100–600 s−1). The quasi-static experiments were conducted by a simple uniaxial tensile test; the medium and high strain-rate tests were performed using drop-weight and gas-gun apparatuses. In these dynamic tests, high speed imaging and digital image correlation were used to measure dynamic displacement fields in the specimen. The dynamic stress state is not in equilibrium, which is a usual requirement for a conventional dynamic experimental analysis. Instead, the non-equilibrium deformation was analysed by the Virtual Fields Method (VFM) using inertial forces, clearly generated due to the non-equilibrium state, as a virtual load cell. The linear VFM associated with a linear isotropic model was applied to the drop-weight test data, in these experiments specimens were subjected to various static pre-stretches before dynamic loading was applied. For the gas gun experiments, in which the dynamic strain and experimental durations were larger, the nonlinear VFM was developed to include the one-term Ogden hyperelastic model so that the long deformation history could be analysed. The material parameters identified by these two techniques were used to reconstruct uniaxial true stress-strain curves which showed a clear and consistent rate dependency.

Keywords

Elastomers High strain rate Finite deformation Tensile Mechanical characterization Virtual fields method Inverse method 

Notes

Acknowledgments

Effort sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF, under grant number FA8655-12-1-2015. The U.S Government is authorized to reproduce and distribute reprints for Governmental purpose notwithstanding any copyright notation thereon. The authors thank S Fuller and JL Jordan of AFOSR and M Snyder and R Pollak of EOARD for their support. The authors would like to thank R Froud and R Duffin for the construction of the experimental apparatus used in this research, and their helpful advice when designing this apparatus. Finally we thank Professor F Pierron for his invaluable help with the Virtual Fields Method.

References

  1. 1.
    Gray GT, Blumenthal WR (2000) Split-Hopkinson pressure bar testing of soft materials. ASM Hanb 8:487–496Google Scholar
  2. 2.
    Chen W, Zhang B, Forrestal MJ (1999) A split Hopkinson bar technique for low-impedance materials. Exp Mech 39:81–85. doi: 10.1007/BF02331109 CrossRefGoogle Scholar
  3. 3.
    Rao S, Shim VPW, Quah SE (1997) Dynamic mechanical properties of polyurethane elastomers using a nonmetallic Hopkinson bar. J Appl Polym Sci 66:619–631. doi: 10.1002/(SICI)1097-4628(19971024)66:4<619::AID-APP2>3.0.CO;2-V CrossRefGoogle Scholar
  4. 4.
    Shim J, Mohr D (2009) Using split Hopkinson pressure bars to perform large strain compression tests on polyurea at low, intermediate and high strain rates. Int J Impact Eng 36:1116–1127. doi: 10.1016/j.ijimpeng.2008.12.010 CrossRefGoogle Scholar
  5. 5.
    Song B, Chen W (2005) Split Hopkinson pressure bar techniques for characterizing soft materials. Lat Am J Solids Struct 2:113–152Google Scholar
  6. 6.
    Shergold OA, Fleck NA, Radford D (2006) The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates. Int J Impact Eng 32:1384–1402. doi: 10.1016/j.ijimpeng.2004.11.010 CrossRefGoogle Scholar
  7. 7.
    Chen W, Lu F, Frew DJ, Forrestal MJ (2002) Dynamic compression testing of soft materials. J Appl Mech 69:214. doi: 10.1115/1.1464871 CrossRefzbMATHGoogle Scholar
  8. 8.
    Cheng M, Chen W (2003) Experimental investigation of the stress–stretch behavior of EPDM rubber with loading rate effects. Int J Solids Struct 40:4749–4768. doi: 10.1016/S0020-7683(03)00182-3 CrossRefGoogle Scholar
  9. 9.
    Roland CM, Twigg JN, Vu Y, Mott PH (2007) High strain rate mechanical behavior of polyurea. Polymer 48:574–578. doi: 10.1016/j.polymer.2006.11.051 CrossRefGoogle Scholar
  10. 10.
    Nie X, Song B, Ge Y et al (2008) Dynamic tensile testing of soft materials. Exp Mech 49:451–458. doi: 10.1007/s11340-008-9133-5 CrossRefGoogle Scholar
  11. 11.
    Niemczura J, Ravi-Chandar K (2011) On the response of rubbers at high strain rates—I. Simple waves. J Mech Phys Solids 59:423–441. doi: 10.1016/j.jmps.2010.09.006 CrossRefzbMATHGoogle Scholar
  12. 12.
    Niemczura J, Ravi-Chandar K (2011) On the response of rubbers at high strain rates—II. Shock waves. J Mech Phys Solids 59:442–456. doi: 10.1016/j.jmps.2010.09.007 CrossRefzbMATHGoogle Scholar
  13. 13.
    Pierron F, Grédiac M (2012) The virtual fields method : extracting constitutive mechanical parameters from full-field deformation measurements. Springer, New YorkCrossRefGoogle Scholar
  14. 14.
    Palmieri G, Sasso M, Chiappini G, Amodio D (2011) Virtual fields method on planar tension tests for hyperelastic materials characterisation. Strain 47:196–209. doi: 10.1111/j.1475-1305.2010.00759.x CrossRefGoogle Scholar
  15. 15.
    Promma N, Raka B, Grédiac M et al (2009) Application of the virtual fields method to mechanical characterization of elastomeric materials. Int J Solids Struct 46:698–715. doi: 10.1016/j.ijsolstr.2008.09.025 CrossRefzbMATHGoogle Scholar
  16. 16.
    Moulart R, Pierron F, Hallett S, Wisnom M (2011) Full-field strain measurement and identification of composites moduli at high strain rate with the virtual fields method. Exp Mech 51:509–536. doi: 10.1007/s11340-010-9433-4 CrossRefGoogle Scholar
  17. 17.
    Pierron F, Zhu H, Siviour C (2014) Beyond Hopkinson’s bar. Philos Trans R Soc A Math Phys Eng Sci 372:20130195. doi: 10.1098/rsta.2013.0195 CrossRefGoogle Scholar
  18. 18.
    Pierron F, Sutton MA, Tiwari V (2010) Ultra high speed DIC and virtual fields method analysis of a three point bending impact test on an aluminium bar. Exp Mech 51:537–563. doi: 10.1007/s11340-010-9402-y CrossRefGoogle Scholar
  19. 19.
    Pierron F, Forquin P (2012) Ultra-high-speed full-field deformation measurements on concrete spalling specimens and stiffness identification with the virtual fields method. Strain 48:388–405. doi: 10.1111/j.1475-1305.2012.00835.x CrossRefGoogle Scholar
  20. 20.
    Yoon S, Giannakopoulos I, Siviour CR (2015) Application of the virtual fields method to the uniaxial behaviour of rubbers at medium strain rates. Int J Solids Struct 1–16. doi: 10.1016/j.ijsolstr.2015.04.017
  21. 21.
    Ogden RW (1972) Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc Lond A Math Phys Sci 326:565–584. doi: 10.1098/rspa.1972.0026 CrossRefzbMATHGoogle Scholar
  22. 22.
    Sasso M, Chiappini G, Rossi M et al (2013) Visco-hyper-pseudo-elastic characterization of a fluoro-silicone rubber. Exp Mech 54:315–328. doi: 10.1007/s11340-013-9807-5 CrossRefGoogle Scholar
  23. 23.
    ABAQUS (2011) ABAQUS 6.11 analysis user’s manual. Abaqus 6.11 DocGoogle Scholar
  24. 24.
    LaVision (2006) Product Manual: DaVis StrainMaster SoftwareGoogle Scholar
  25. 25.
    Avril S, Grédiac M, Pierron F (2004) Sensitivity of the virtual fields method to noisy data. Comput Mech 34:439–452. doi: 10.1007/s00466-004-0589-6 CrossRefzbMATHGoogle Scholar
  26. 26.
    Grédiac M, Toussaint E, Pierron F (2002) Special virtual fields for the direct determination of material parameters with the virtual fields method. 1––Principle and definition. Int J Solids Struct 39:2691–2705. doi: 10.1016/S0020-7683(02)00127-0 CrossRefzbMATHGoogle Scholar
  27. 27.
    Russell BP, Karthikeyan K, Deshpande VS, Fleck NA (2013) The high strain rate response of ultra high molecular-weight polyethylene: from fibre to laminate. Int J Impact Eng 60:1–9. doi: 10.1016/j.ijimpeng.2013.03.010 CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2015

Authors and Affiliations

  1. 1.Department of Engineering ScienceUniversity of OxfordOxfordUK

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