Criterion for combined mode I-II of brittle fracture

The Griffith concept of energy equilibrium for brittle mode I crack propagation was extended to a combined mode I-II crack extension. First, the maximum energy release rate for an infinitesimally kinked crack extension under combined mode I-II loading, analyzed by other researchers, was successfully expressed with a combined mode stress intensity factor. Second, the fracture energy rate was estimated from the area of the frontal process zone estimated from the area enclosed by the isostress contours of both the maximum principal stress and the maximum shear stress. Third, these considerations led to the estimated K-IIC/K-IC ratio of 1.20, which was close to the experimental results of 1.1 to 1.3 obtained previously. Lastly, the combined mode I-II fracture criterion was formulated by adopting the same procedure, and the predicted criterion coincided well with Shetty's empirical criterion. The fracture toughness values of mode I and mode II, and the combined mode I-II criterion for polycrystalline alumina, float glass and PMMA (polymethyl methacrylate) were also estimated experimentally using a disk method and a rectangular test. The estimated results of the K-IIC/K-IC ratio using the disk method ranged from 1.1 to 1.3, which was very close to the predicted value of 1.20, whereas the rectangular test specimens exhibited considerable stable crack growth at the crack tip and yielded a smaller K-IIC/K-IC ratio, which was related to the mode transformation and stress shielding.