Towards a physics-based relationship for crack growth under different loading modes

In an attempt to understand quasi-static delamination growth under mixed mode loading conditions from a physics-based perspective, this work first evaluated cracking in isotropic materials. The critical Strain Energy Density (SED) approach is adopted, because physically the onset of crack growth is expected to occur when the energy available near the crack tip reaches a critical value. The main hypothesis of the present paper is that the critical SED for onset of crack growth is constant for a given material, and independent of the loading mode. The relationship derived from this hypothesis therefore relates the physical onset of crack growth and the angle at which that occurs for any opening mode through the SED. To test this hypothesis, results from literature were taken and shear fracture tests on foam specimens were performed, which both were compared with the derived relationship. The excellent correlation demonstrated the validity of the physics-based relationship, which explains the observed differences between mode I and mode II fracture toughnesses and illustrates why concepts like the Stress Intensity Factor (SIF) alone are insufficient to explain the observations. The developed relationship allows to derive the mode II fracture toughness from mode I fracture toughness tests and the material's mechanical properties.