The effect of root radius on the direction of crack extension under combined mode loading

Abstract

The “energy density theory” of G. Sih is extended to investigate the direction of initial crack extension at the tip of blunt cracks (notches) in combined Mode 1-Mode 2 loading. Three different governing strain energy density functions are postulated for comparison, and each is applied to the ideally sharp and the blunt notch cases. It is found that the sharp and blunt notch solutions agree in the limits of pure Mode 1 loading, but their difference grows as K1/K2 value is decreased and becomes most conspicuous in the limit of pure Mode 2 loading. It is also found that the above solution difference is greatest near the crack tip and diminishes at a large distance from the crack tip. For both the sharp and blunt notch solutions, the deviatoric strain energy density function predicts a larger absolute value of the critical angle θc than does the total strain energy density function. The results are compared with those obtained by using the classical method of “maximum tangential (tensile) stress” for predicting the crack trajectories.