Crack-face interaction for a Griffith crack in biaxial stress

The work described herein is an investigation of the influence of crack-face interaction on unstable crack propagation in brittle materials. For this study, interaction results from the interference of wedge-shaped protrusions on the faces of a Griffith crack when subjected to arbitrarily oriented biaxial stress at infinity. A mathematical model based on solutions from linear elastic theory is presented for a single interference site and then expanded to include multiple interference sites. The importance of protrusion interference is measured as the change in the fracture toughness required to prevent unstable crack propagation in the presence of interference from that required in the absence of interference. The dependence of the required fracture toughness on the applied stress (orientation and magnitude), wedge geometry (size and vertex angle), and configuration of the interference sites (location and number) is examined, with all results obtained for dimensionless variables. It is concluded that a single interference site has little effect on the required fracture toughness, except under certain special conditions. For multiple sites, although the effect on the required fracture toughness increases monotonically with the number of sites, it appears to approach some limit asymptotically.