On the Relation between Indentation Hardness and Young's Modulus

Abstract A relation between British Standard and International rubber hardness and Young's modulus is derived from classical elasticity theory, and compared with the empirical relation given in B.S.903:1950. An experimental examination of the load-indentation relationship for a rigid sphere pressed into a flat rubber pad is described ; it indicates that the theoretical relation is more appropriate than the empirical one for small indentations, corresponding to hardnesses exceeding about 60° B.S. & I.R.H., and equally valid for hardnesses between about 40° and 60°. Moreover, the numerical constants are not subject to experimental uncertainty. If reduced major loads are stipulated for determining the hardness of rubbers of less than 35° to 40° B.S. & I.R.H., the theoretical relation should apply over the entire useful range. An approximate relation between Shore hardness and Young's modulus is derived similarly. The approximate equivalence of the British Standard and International rubber hardness and Shore hardness scales over the major part of the hardness range is confirmed.