An Improved Fracture Criterion for Three-Dimensional Stress States

A theory is developed to predict the onset of fracture in isotropic, brittle materials when subjected to three dimensional states of applied stress. It is assumed that fracture is precipitated by stress concentrations emanating from material flaws. The flaw model which has been adopted consists of randomly oriented, microscopic, flat triaxial ellipsoidal voids imbedded in an otherwise defect-free material. It is shown that the ensuing fracture criterion may be expressed as a parabolic Mohr’s envelope. These results are qualitatively similar to Paul’s earlier three-dimensional generalization of Griffith’s two-dimensional stress fracture criterion. To handle three-dimensional states of applied stress, Paul used an approximation based on two-dimensional elasticity to obtain the state of stress around a flat spheroid. Newly developed results for flat ellipsoidal cavaties are utilized herein to analyze the three-dimensional cavity. Pertinent effects due to Poisson’s ratio and ellipsoid geometry are reported.