Experimental investigations of the normal loading of elastic spherical and conical indenters on to elastic flats

Abstract

Results obtained from a series of experimental investigations are described in which an elastic polyisoprene hemisphere and elastic rubber cones of included angles 60°, 90°, 120° and 150° were loaded normally on to smooth blocks of soda–lime glass and polydimethylsiloxane (PDMS) containing 10% and 20% by volume of the curing agent. The load versus displacement data were continuously recorded with an instrumented indentation machine. It is shown that, whereas the loading behaviour of the hemisphere on to the blocks of the soda–lime glass and PDMS closely follows the theory of Hertz (see equation (1)), the load versus displacement behaviour of the rubber cones of included angles 60°, 90° and 120° could not be fitted by the Sneddon equation (see equation (5)) for rigid conical indenters loading on to an elastic half-space or by the modified Sneddon equation (see equation (6)) employing the combined moduli of the indenter and the half-space. The discrepancy between the predictions of the modified Sneddon equation and the experimental measurements is very significant, thus confirming our recent concern about the validity of using the modified Sneddon equation for analysing the experimental data obtained from nanoindentation experiments. Estimates of the errors caused by the use of the modified Sneddon equation have been made to further illustrate our contention. On the other hand, the behaviour of the 150° included angle cone loading on to the blocks of rubber, PDMS (1 : 10) and PDMS (1 : 20), has been shown to be particularly striking, as the rubber cone behaved as if it were rigid; moreover, the experimental data are well fitted by the Sneddon equation corresponding to a 150° rigid cone loading on to an elastic half-space. Finally, it has been proposed that, in order to determine the elastic modulus of a very stiff solid (i.e. Young's modulus close to that of the indenter) correctly using the technique of instrumented indentation, including nanoindentation, the included angle of the indenter, made of diamond, should be 150° and the measured load versus displacement data should be analysed using the Sneddon equation corresponding to a rigid cone of an included angle of 150°.