Assessment of Analytical Equations for the Derivation of Young’s Modulus of Bonded Rubber Materials

Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

Abstract:

The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: Bonded rubber, quasi-static test, shape factor, apparent Young’s modulus.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3300388

References:

[1] J.C. Snowdon, ‘‘Vibration isolation: Use and characterization’’, The Journal of the Acoustical Society of America, vol.66, pp.1245-1274, 1979.
[2] H. C. Tsai and C. C. Lee, ‘‘Compressive stiffness of elastic layers bonded between rigid plates’’, International Journal of Solids and Structures, vol. 35, no. 23, pp. 3053-3069, 1998.
[3] C.G. Koh and H.L. Lim, ‘‘Analytical solution for compression stiffness of bonded rectangular layers’’, International Journal of Solids and Structures, vol. 38, no. 1, p. 445-455, 2001
[4] H.C. Tsai, ‘‘Compression analysis of rectangular elastic layers bonded between rigid plates’’, International Journal of Solids and Structures, vol. 42, no. 11-12, pp. 3395-3410, 2005.
[5] A.N. Gent and, P.B. Lindley, ‘‘The compression of bonded rubber blocks’’, Proceedings of the Institution of Mechanical Engineers, vol. 173, no. 1, pp. 111-122, 1959
[6] P.B. Lindley, ‘‘Load-compression relationship of rubber units’’, Journal of strain analysis, vol. 1, no. 1, pp. 190-195, 1966.
[7] D. Koblar, J. Skofic, and M. Boltezar, ‘‘Evaluation of the Young’s Modulus of Rubber-Like Materials Bonded to Rigid Surfaces with Respect to Poisson’s Ratio’’, Journal of Mechanical Engineering, vol. 60, no. 7-8,pp. 506-511, 2014
[8] S. Qiao and N. Lu, ‘‘Analytical solutions for bonded elastically compressible layers’’, International Journal of Solids and Structures, vol. 58, pp. 353-36, 2015.
[9] S.R. Moghe and H.F. Neef, ‘‘Elastic deformations of constrained cylinders’’, Journal of strain analysis, vol. 1, no. 1, pp. 190-195, 1966.
[10] J.M. Horton, G.E. Tupholme and M.J.C. Gover, ‘‘Axial loading of bonded rubber blocks’’, Journal of Applied Mechanics, vol. 69, no. 6, pp. 836-843, 2002
[11] J.M. Horton, M.J.C. Gover and G.E. Tupholme, ‘‘Stiffness of Rubber Bush Mountings Subjected to Tilting Deflection’’, Rubber Chem. Technol., vol. 73, pp. 619–633, 2000.
[12] J.G. Williams and C, Gamonpilas, ‘‘Using the simple compression test to determine young’s modulus, Poisson’s ratio and coulomb friction coefficient’’, International Journal of Solids and Structures, vol. 45, no. 16, pp. 4448-4459, 2008.
[13] D. Koblar and M. Boltezar, ‘‘Evaluation of the frequency-dependent young’s modulus and damping factor of rubber from experiment and their implementation in a finite-element analysis’’, Journal of Experimental Techniques, vol. 40, no. 1, pp. 235-244, 2013.
[14] L. R. G. Treloar, ‘‘The physics of rubber elasticity’’ 3rd ed., Oxford University Press Inc., New York, pp. 59-62, 1975.
[15] A. L. Gent, ‘‘Engineering with rubber: how to design rubber components’’, 3rd ed., Carl Hanser Verlag, Munich 2012.