Tearing energy and path-dependent J-integral evaluation considering stress softening for carbon black reinforced elastomers

Abstract

For carbon black reinforced Ethylene-Propylene-Diene Monomer Rubber (EPDM) fracture mechanics investigations by using a Single Edge Notched Tension sample (SENT) are presented. Filled elastomers under cyclic loading typically display inelastic effects like permanent set, strong nonlinear S-shaped stress-strain behaviour and stress induced softening (discontinuous damage) as well as cyclic softening (continuous damage) better known as Mullins effect. These unique properties give this material class an interesting and a complex aspect regarding the experimental observations and numerical modelling of fracture mechanics. In simulations with homogenous material, the J-integral given as the evaluation of the Eshelby stress tensor along a path integral around the crack shows no dependency on the chosen integration path. In contrast, dissipative materials show strong path dependency of the J-integral. When the chosen path is near to the crack tip, this effect is pronounced, due to the inelastic effects, which are very high at the crack tip compared to the rest of the sample. In the process zone, the J-integral value depends strongly on the chosen path around the crack tip. This phenomenon occurs due to the intensity of inelastic effects near the crack tip. The path-dependency of J-integral using the variational formulation of a crack problem in a dissipative material has been given in [16]. Stumpf and Le have proposed a new formulation of the boundary value problem for elastoplastic cracked body using variational formulation, where the finite deformation was considered. For cyclic displacement controlled loading, the elastomers show typical stress softening behaviour, i.e. the force-displacement curve of each cycle is lower than the previous cycle and higher than the following cycle. This occurs due to the continuous damage, whereby the bondings between polymer chains and the filler particles are partially damaged. At small external amplitudes, the stress softening effect is significant only in the vicinity of the crack tip, because of the hysteresis which is large compared to the rest of the sample. The evaluation of the J-integral for an SENT sample under cyclic displacement controlled loading shows clearly that the resulting energy flux at the crack tip decreases from the virgin curve until the last repetition. The values found are in good agreement with experimentally evaluated tearing energy. Hence J-integral evaluation while considering a stress softening reflecting material model can be a promising approach used for estimation of the crack propagation or for lifetime prediction.