Determination of the Loading Mode Dependence of the Proportionality Parameter for the Tearing Energy of Embedded Flaws in Elastomers Under Multiaxial Deformations

In this paper, the relationship between the tearing energy and the far-field cracking energy density (CED) is evaluated for an embedded penny-shaped flaw in a 3D elastomer body under a range of loading modes. A 3D finite element model of the system is used to develop a computational-based fracture mechanics approach which is used to evaluate the tearing energy at the crack in different multiaxial loading states. By analysing the tearing energy’s relationship to the far-field CED, the proportionality parameter in the CED formulation is found to be a function of stretch and biaxiality. Using a definition of biaxiality that gives a unique value for each loading mode, the proportionality parameter becomes a linear function of stretch and biaxiality. Tearing energies predicted through the resulting equation show excellent agreement to those calculated computationally.