The paper describes various analytical procedures that account for the influence of the geometry of a rigid indenter upon the measured contact compliance of a smooth perfectly elastic half space. The analytical solutions provide a means of interrelating the reaction force, P, and the displacement, h, characteristics in terms of the contact geometry and the reduced elastic modulus E*. The general form is P=gE*hn, where g and n are functions only of the indenter geometry. This relationship is incorporated into a curve-fitting procedure and used to evaluate the influence of the indenter geometry upon the computed modulus of a poly(isobutylene) rubber. The method described provides a viable means of incorporating the imperfections, associated with the geometry of an indenter, into the interpretation of contact compliance data.
The mechanics of the indentation of elastomers by the “Durometer” (Shore A) hardness tester is analysed using the theory of elasticity to derive an interrelation between the Shore hardness number and the Young's modulus. Experimental compliance curves, for different elastomers, are provided to support the theory. The theoretical interrelationships between the International Rubber Hardness and the Shore A Hardness and the corresponding elastic modulus are also compared. The effects of the time dependent deformations are examined. Finally, the error introduced by computing the Young's modulus using an equivalent punch solution is examined and a means of improving the predictions is provided.
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