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A spherical indentation technique for property evaluation of hyperelastic rubber

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Abstract

The numerical approach of Lee et al. [Trans. Korean Soc. Mech. Eng., A28, 816–825 (2004)] to spherical indentation technique for property evaluation of hyperelastic rubber is enhanced. The Yeoh model is adopted as the constitutive form of rubber material because it can express well large deformation and cover various deformation modes with a simple form. We first determine the friction coefficient between a rubber specimen and a spherical indenter in a practical viewpoint and perform finite element simulations for a deeper indentation depth than that selected by Lee et al. [Trans. Korean Soc. Mech. Eng., A 28, 816–825 (2004)]. An optimal data acquisition spot is selected, which features sufficiently large strain energy density and negligible frictional effect. We improve then two normalized functions mapping an indentation load–displacement curve onto a strain energy density–invariant curve, the latter of which gives the Yeoh model constants. The enhanced spherical indentation approach successfully produces the rubber material properties with an average error of less than 5%. The validity of our developed approach is verified by experimental evaluation of material properties with three kinds of rubber materials.

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References

  1. W.D. Kim, D.J. Kim, W.S. Kim, and Y.S. Lee: A study on the equi-biaxial tension test of rubber material. Trans. KSAE 11, 95–104 (2003).

    Google Scholar 

  2. H. Lee, D.W. Kim, J.H. Lee, and S.H. Nahm: Software and hardware development of micro-indenter for material property evaluation of hyper-elastic rubber. Trans. Korean Soc. Mech. Eng. A 28, 816–825 (2004).

    Article  Google Scholar 

  3. O.H. Yeoh: Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber Chem. Technol. 63, 792–805 (1990).

    Article  CAS  Google Scholar 

  4. O.H. Yeoh: Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66, 754–771 (1993).

    Article  CAS  Google Scholar 

  5. O.H. Yeoh and P.D. Fleming: A new attempt to reconcile the statistical and phenomenological theories of rubber elasticity. J. Polym. Sci., Part B: Polym. Phys. 35, 1919–1931 (1997).

    Article  CAS  Google Scholar 

  6. M. Mooney: A theory of large elastic deformation. J. Appl. Phys. 11, 582–592 (1940).

    Article  Google Scholar 

  7. L.R.G. Treloar: The elastic of a network of long-chain molecules-II.Trans. Faraday Soc. 39, 241–246 (1943).

    Article  CAS  Google Scholar 

  8. L.R.G. Treloar: The Physics of Rubber Elasticity (Clarendon Press, Oxford, 1975).

    Google Scholar 

  9. R.S. Rivlin: Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Philos. Trans. R. Soc. London, Ser. A 241, 379–397 (1948).

    Article  Google Scholar 

  10. R.S. Rivlin: Large Elastic Deformations in Rheology: Theory and Application (Academic Press, New York, 1956).

    Google Scholar 

  11. R.W. Ogden: Large deformation isotropic elasticity–on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. London, Ser. A 326, 565–584 (1972).

    Article  CAS  Google Scholar 

  12. E.M. Arruda and M.C. Boyce: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41, 389–412 (1993).

    Article  CAS  Google Scholar 

  13. M.C. Boyce and E.M. Arruda: Constitutive models for rubber elasticity: A review. Rubber Chem. Technol. 3, 504–523 (2000).

    Article  Google Scholar 

  14. ABAQUS: ABAQUS User’s Manual, Version 6.8 (Simulia, Providence, RI, 2008).

    Google Scholar 

  15. A. Ali, M. Hosseini, and B.B. Sahari: A review of constitutive models for rubber-like materials. Am. J. Eng. Appl. Sci. 3, 232–239 (2010).

    Article  Google Scholar 

  16. T. Beda: Reconciling the fundamental phenomenological expression of the strain energy of rubber with established experimental facts. J. Polym. Sci., Part B: Polym. Phys. 43, 125–134 (2005).

    Article  CAS  Google Scholar 

  17. G.B. McKenna and L.J. Zapas: Experiments on the small-strain behaviour of crosslinked natural rubber: 1. Torsion. Polymer 24, 1495–1501 (1983).

    Article  CAS  Google Scholar 

  18. G.B. McKenna and L.J. Zapas: Experiments on the small-strain behaviour of crosslinked natural rubber: 2. Extension and compression. Polymer 24, 1502–1506 (1983).

    Article  CAS  Google Scholar 

  19. M.J. Gregory: The stress–strain behaviour of filled rubber at moderate strains rubber at moderate strains. Plast. Rubber Mater. Appl. 4, 184–188 (1979).

    CAS  Google Scholar 

  20. H.J. Qi and M.C. Boyce: Constitutive model for stretch-induced softening of the stress-stretch behavior of elastomeric materials. J. Mech. Phys. Solids 52, 2187–2205 (2004).

    Article  CAS  Google Scholar 

  21. W.D. Kim, W.S. Kim, D.J. Kim, C.S. Woo, and H.J. Lee: Mechanical testing and nonlinear material properties for finite element analysis of rubber components. Trans. Korean Soc. Mech. Eng. A 28, 848–859 (2004).

    Article  Google Scholar 

  22. L. Mullins: Effect of stretching on the properties of rubber. Rubber Chem. Technol. 16, 275–289 (1947).

    CAS  Google Scholar 

  23. H. Lee, J.H. Lee, and G.M. Pharr: A numerical approach to spherical indentation technique for material property evaluation. J. Mech. Phys. Solids 53, 2037–2069 (2005).

    Article  CAS  Google Scholar 

  24. W.D. Kim, D.J. Kim, C.W. Na, and Y.S. Lee: A study on the frictional characteristics of vulcanized rubber plates. J. Korean Rubber Soc. 36, 121–129 (2001).

    CAS  Google Scholar 

  25. J.H. Lee, T.H. Kim, and H. Lee: A study on robust indentation techniques to evaluate elastic–plastic properties of metals. Int. J. Solids Struct. 47, 647–664 (2010).

    Article  Google Scholar 

  26. J.H. Lee, H. Lee, H.C. Hyun, and M. Kim: Numerical approaches and experimental verification of the conical indentation techniques for residual stress evaluation. J. Mater. Res. 25, 2212–2223 (2010).

    Article  CAS  Google Scholar 

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Acknowledgment

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (Grant No. 2009-0086135).

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Hyun, H.C., Lee, J.H., Kim, M. et al. A spherical indentation technique for property evaluation of hyperelastic rubber. Journal of Materials Research 27, 2677–2690 (2012). https://doi.org/10.1557/jmr.2012.241

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