Nonlinear Elastic Analysis of the Hardness Test on Rubber-Like Materials

Abstract

Abstract Both the Ogden-Tschoegl nonlinear elastic constitutive law and a contact algorithm in the general-purpose finite-element program AFEM have been used to examine the use of IRHD values to relate the elastic properties of elastomers. We are aware that large deformations of rubber specimens and complicated interface conditions are involved in this so-called simple test. However, from the finite-element results, we find that the linearly elastic Hertz contact solution is a reasonably accurate model. This can be attributed to several points. First, the hardness test involves mainly compression and shear deformation and the linearly elastic behavior is more closely followed in rubbers for the above two types of deformation. Second, although nonlinear effects become significant in soft rubbers and higher indentation cases, the ASTM D 1415 standard defines larger indentation depth differences for smaller IRHD values. The definition itself compensates for the nonlinear effects. Third, although the interfacial stress field changed due to different frictional conditions, we calculated the IRHD values only from indentation depth difference and total load applied to the steel ball. Both the indentation depth difference and the total load are obtained from far-field conditions and do not change significantly. 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.