Effect of strains and temperatures on the stress relaxation of unfilled natural rubber

Many rubber-based components are required to withstand long-term stress or strain without developing excessive stress relaxation or creep. A model was implemented for simple shear which used the Boltzmann superposition principle (BSP) to predict the stress relaxation following changes in strain and the William–Landel–Ferry transformation to allow for changes in temperature. Stress relaxation was modelled as linear with the logarithmic of time with a Prony series deduced from two independent parameters. By means of small-time increments, the model can be used to model the stress relaxation under arbitrary strain and temperature histories. Stress relaxation measurements were carried out for two types of deformations: simple shear and compression. The samples were made of an unfilled natural rubber and tested under varying strains and temperatures and the results compared to the predictions of the model. The agreement was generally good, and the discrepancies are discussed. The model parameters were also used within the linear viscoelastic model in the commercial finite element analysis package ABAQUS, which enables modelling in deformation modes other than simple shear.