A constitutive model for the fatigue life prediction of rubber

Automotive rubber components such as engine mounts or vibration isolators are subjected to dynamic loading in service. Computation of their fatigue lives is necessary in order to assure their safety and reliability. When subjected to cyclic loading, rubbers exhibit an important stretch-induced stress-softening phenomenon known as the Mullins' effect. This stress-softening occurs mostly during the first few cycles, after which the response of the material is unchanged by additional reloading. A constitutive model is proposed for the description of the stabilized state of such a behaviour. The response is supposed to depend only on some cyclic variables. Therefore this state is assumed to be independent of the transition period during which the stress-softening occurs. The damage parameters are the maximum stretches reached in a finite number of material directions, in order to describe the anisotropy induced by the Mullins' effect. Viscous effects are not represented. Uniaxial fatigue tests were performed on axi-symmetric samples made of carbon black filled natural rubber. Comparisons are made between tests where the load was monitored in term of displacements and tests where the load was monitored in term of forces. A finite element analysis is performed in order to obtain the strain and stress distributions over the sample. The code ABAQUS is used with the constitutive model described above implemented in a user subroutine. Fatigue lives and maximum principal stretches are shown to be well correlated. The constitutive model is thus shown to be relevant for the assessment of the fatigue life of rubber.