Constitutive relation of thermal aged filled rubber

A constitutive relation with respect to the thermal aging parameters is presented based on the one-order Ogden model to describe the mechanical behaviors of filled rubber with or without thermal aging. It was found that the parameter α in the Ogden model was nearly independent of the aging temperature and aging time in the early stage of aging. The superposition principle between aging time and aging temperature was used to determine the activation energy in controlling the change of the stiffness of the filled rubber in thermal aging, and then an empirical temperature-time-dependent constitutive relation was established using an Arrhenius's shift factor, by which the fatigue properties of the filled rubber were studied as an example. Test results show that the variation of the crack growth rate with the strain energy release rate calculated by considering the thermal aging effect follows the Paris law; and a closer estimation for the fatigue life with thermal aging consideration is obtained than that without thermal aging consideration.