NONLINEAR ELASTIC ANALYSIS OF THE HARDNESS TEST ON RUBBER-LIKE MATERIALS

The hardness test has been widely used in the rubber industry for many years and has become the standard method for characterizing a rubber compound. In this paper, we present a nonlinear elastic analysis of the hardness test. Nonlinear finite-element analysis theories are applied in our numerical simulations of the hardness test. The objective of the finite-element analysis is to elucidate the relationship between material properties and hardness scale values in the nonlinear region. The IRHD method is selected for our analysis because of its several advantages. This means that we are not dealing with those compounds that have unusually high rates of stress relaxation or deformation hysteresis, all time-dependent factors are excluded. Following this, we use the Ogden-Tschoegl rubber-like material constitutive law and contact algorithm in the general-purpose finite-element program AFEM to solve materially and geometrically nonlinear conditions. From the finite-element results, we find that the linearly elastic Hertz contact solution is a reasonably accurate model. We should note that using linear elasticity to correlate the elastic moduli and IRHD values is simply a special case in rubber elasticity. We conveniently get rubber's elastic moduli from IRHD values based on linear elasticity, but the complete rubber-like material behavior has to be obtained from more general experiments and described by a nonlinear constitutive law such as the Ogden-Tschoegl model.