On the compressibility of unvulcanized rubber: experiments and theoretical considerations

Abstract

This diploma thesis is motivated by the unsatisfactory performance of state-of-the-art simulation tools used for modeling shape changes of (unvulcanized) rubber compounds and blends during the extrusion process. In this work, it is proposed that one of the reasons for such unrealistic simulation results are incomplete constitutive models fed into such simulation tools. In particular, rubber is standardly assumed to be totally incompressible - a far-reaching assumption requiring careful investigations. The latter are the content of the present thesis. In order to quantify the compressibility of dierent rubber mixtures, a series of hydrostatic compression tests was performed, using a new experimental method. The test protocol comprised loading and unloading of a material specimen put into the entirely closed extrusion canal of a capillary rheometer. In order to quantify variations in compressibility between dierent materials, all tests were performed on one natural rubber and two rubbers of the EPDM (ethylene propylene diene monomer) type. Extensive evaluation of the collected experimental data showed that, based on dissipation considerations, the characteristics of the stress-strain paths allow to consider the material as (non-linearly) elastic. Alternatively, a series of load displacement curves were fitted based on viscoelastic material models, making use of an evolution algorithm, revealing that the resulting fits were actually independent of the viscoelastic parameters - thus also corroborating the inadequacy of viscoelasticity to describe rubber compressibility. To show the stability and consistency of the available data, (non-linear elastic) evaluation was carried out by taking into account dierent strain measures (Green-Lagrange strain, Hencky (logarithmic) strain, linearized strain and strain rates) and their energy-conjugate stress measures (second Piola-Kirchho stress, Kirchho stress, Cauchy stress, Jaumann stress rate), thereby applying both hyper- and hypoelastic constitutive relations. All evaluations - independent of the used stress and strain measures, and independent of whether hyperor hypoelasticity was considered - clearly revealed that the investigated natural and EPDM rubbers are indeed compressible and non-linearly elastic. Considering the most important relations, i.e. stress over strain, bulk modulus over stress, and bulk modulus over strain, the influence of the actually used stressstrain measures is of minor importance. However, the bulk moduli obtained from hypoelastic constitutive relations are much higher than the bulk moduli obtained based on hyperelastic constitutive relations, showing the influence of an incremental approach. Thus, the results collected from the experimental data provide a valuable basis for implementation of improved constitutive relations in structural simulation tools.