A FRACTURE CRITERION FOR CRACKS UNDER MIXED‐MODE LOADING

Abstract

Abstract A fracture criterion is proposed, based on maximum energy release rates at the tips of short kinks when the main cracks are subjected to mixed mode loading. The criterion differs from existing energy based criteria in that the fracture toughness, gc, is not independent of the stress mode prevailing in the region of the tip of the kink but is a function of the ratio of the mode II to mode I stress intensity factors at the tip of the kink, i.e., gc is determined directionally by an elliptical region with major and minor axes equal to the fracture resistances of the material, KIr and KIIr, for pure mode I and pure mode II, respectively. Points inside the elliptical region are considered safe. When KIIr is equal to KIr the ellipse degenerates into a circle and the fracture criterion reverts to the existing familiar maximum energy release rate criterion based on a single value of the fracture toughness, irrespective of the active mode prevailing in the region at the tip of the kink. In this case, under pure shear (mode II) applied load, KII, the angle of inclination of the fracture crack extension to the main crack, α, is in the region of −76°, in general agreement with previous well established results. However, when the ratio r (=KIIrKIr) is less than r′ (=0.82, approximately) a different pattern emerges and, in particular, under pure mode II load, the crack advance is co‐planar with the main crack, i.e., in mode II. A lower transition value r″ (=0.582, approximately) was also detected under pure mode I applied load. Thus for values of r≥r″, the crack extension is in pure mode I and is co‐planar with the main crack but when r < r″, the crack branches out at an angle (which can be positive or negative) in mixed modes I/II crack extension. Some implications of these results are discussed.