The determination of Young's modulus from the indentation of rubber sheets by spherically tipped indentors

Abstract

Rubber hardness is a parameter which vaguely characterizes the more fundamental material property, Young's modulus. The determination of Young's modulus via penetration techniques has not yet been possible for no theory directly expressed this quantity in terms of radius of contact or depth of penetration. The Hertz contact theory has been used but is inapplicable as it does not consider the major variable of sheet thickness. The present work derives equations for this purpose: E= 9PR 16H 3 H a 3 −0.339+0.342 a H 2 −0.1465 a H 5 and E= 9PR 16H 3 Rd a 1 2 +0.252 Rd H 2 +0.1588 Rd H 2 2 2 +0.2245 Rd H 2 2+0.2245 +0.3069 Rd H 2 3 2 +0.2245 where E is Young's modulus, P is normal load, R is the radius of the spherically tipped indentor, H is the sheet thickness, a is the contact radius and d is the depth of indentor penetration. The first of these equations is verified by use of the published and unpublished data of R. C. Drutowski and compared to the results one would get from the Hertz contact theory. The second equation is verified by use of the published and unpublished data of N. E. Waters.