Criterion for combined mode I-II brittle fracture

Abstract

The Griffith concept of energy equilibrium for brittle mode I crack propagation was extended to mode II and combined mode I-II crack extensions. First, the maximum energy release rate for an infinitesimally kinked crack extension under combined mode I-II loading analyzed by Kageyama and Okamura was successfully expressed by a combined mode stress intensity factor. Second, the ratio between mode I and mode II fracture energy rates was estimated from the areas of the frontal process zone estimated from the area enclosed in the iso-stress contours of both the maximum principal stress and the maximum shear stress. Third, those considerations led to a predicted KIIC/KIC ratio of 1.20, which was quite near the experimental results of 1.1 to 1.3 obtained earlier. Finally, the combined mode I-II fracture criterion was formulated by the same technique, and the predicted criterion coincided well with Singh and Shetty's empirical criterion. The fracture toughness values of modes I and II, and the combined mode I-II criterion for polycrystalline alumina were also estimated experimentally using a disk method. The estimated result of KIIC/KIC ratio was 1.17, which was very close to the predicted value of 1.20. The experimentally assessed combined mode fracture criterion was closely related to the predicted one.