On the failure of cracks under mixed-mode loads

Fracture of plates containing a crack under mixed-mode, I and II, loading conditions is investigated. Fracture mechanisms are first examined from fracture surface morphology to correlate with the macroscopic fracture behavior. Two distinct features are observed and they are typical of shear and tensile types of failure. From this correlation, a fracture criterion based on the competition of the attainment of a tensile fracturing stress σ_C and a shear fracturing stress τ_C at a fixed distance around the crack tip is proposed. Material ductility is incorporated using τ_C/σ_C determined from classical material failure theories. The type of fracture is predicted by comparing τ_max/σ_max at r=r_C for a given mixed mode loading to the material ductilityτ_C/σ_C , i.e. τ_max/σ_max)<(τ_C /σ_C) for tensile type of fracture and (τ_max/σ_max) r (τ_C/ σ_C) for shear type of fracture. It is found that, for typical engineering structural metals with certain ductility, (1) crack propagation initiates according to the maximum hoop stress criterion when the the mode mixity is near mode I and according to the maximum shear stress criterion when the mode mixity is near mode II, and (2) the transition of the failure from tensile to shear type can be predicted by the proposed criterion. For brittle materials the maximum hoop (opening) stress always reaches the tensile fracturing stress before the maximum shear stress reaches the shear fracturing stress of the material at a crack tip. Therefore, specimens made of brittle materials tend to fail under the maximum hoop stress criterion, as demonstrated by Erdogan and Sih (1963) and others.