Influence of cyclic softening on the energy release rate of an edge crack under simple tension

Under cyclic straining, an elastomer's nonlinear elastic behavior depends strongly on its memory of the most extreme prior strain state through the Mullins effect. Although this behavior strongly influences crack tip fields, yet there is no information available in the literature documenting the effect on the crack, and no guidance on how to account for it in fatigue analysis. Using Finite Element Analysis, the case of an edge-cracked simple tension strip under cyclic load is investigated here. The model features a pseudo-elastic representation of the Mullins effect, following Ogden and Roxburgh. The energy release rate of the crack is computed for scenarios involving a purely hyperelastic material (ie, no Mullins effect), and for two pseudo-elastic materials (ie, Mullins effect turned on). For the hyperelastic material, there is a oneto- one relationship between the energy release rate and the strain energy density in the strip. For material exhibiting Mullins effect, however, a more complex relationship is documented. It is shown that at strains approaching the most extreme prior strain state, the energy release rate exceeds the estimate obtained for a purely hyperelastic material, by as much as 30% when the material is capable of softening by 50%.