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, go, 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 I1 to mode I stress intensity factors at the tip of the kink, i.e., g, is determined directionally by an elliptical region with major and minor axes equal to the fracture resistances of the material, K,, and K,, for pure mode I and pure mode 11, respectively. Points inside the elliptical region are considered safe. When Km is equal to K,, 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, Kn, the angle of inclination of the fracture crack extension to the main crack, a, is in the region of -76", in general agreement with previous well established results. However, when the ratio r ( = K,/K,) is less than r' (=0.82, approximately) a different pattern emerges and, in particular, under pure mode I1 load, the crack advance is co-planar with the main crack, i.e., in mode 11. A lower transition value r" (=0.582, approximately) was also detected under pure mode I applied load. Thus for values of r a 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 1/11 crack extension. Some implications of these results are discussed. NOMENCLATURE a =half crack length of the main crack E' = effective modulus of elasticity g = energy release rate during extension of the kink gc = critical value of g g,, g, = mode I and mode I1 energy release rates for the kinked crack k,, k, = mode I and mode I1 stress intensity factors at the tip of the kinked crack K l , K , = mode I and mode I1 stress intensity factors applied to the tip of the main crack K,, K,, = fracture toughnesses in mode I and mode I1 Kk, Knr = instantaneous fracture resistances in mode I and mode I1 m = K , / K , n = K J K , r = Km/Kk r' = upper transition value of r (r'=0.82) r" = lower transition value of r (r"=0.582)
= k 2 / hx, , x2 = coordinates parallel and normal to the main crack xi. x i = coordinates parallel and normal to the kink a = angle that the kink makes with the main crack u = remotely applied hydrostatic tensile stress 5 = remotely applied shear stress a, = value of a which gives the maximum value of g/g,