J-Integral Solution for Elastic Fracture Toughness for Plates with Inclined Cracks under Biaxial Loading

Surface cracks with different orientations have been recognized as a major cause of potential failures of thin metal structures, which are often under biaxial loading. It has been known that, for cracked ductile metals, plasticity results in an easing of stress intensity at the crack front and ultimately increases the total fracture toughness of the metal. To enable the use of linear elastic fracture mechanics for ductile material failure prediction, the plastic portion of fracture toughness must be excluded. This paper aims to develop a J-integral based method for determining the elastic fracture toughness of ductile metal plates with inclined cracks under biaxial loading. The derived elastic fracture toughness is a function of the plate and crack geometry, strain-hardening coefficient, yield strength, fracture toughness, biaxiality ratio, and inclination angle. It is found that an increase in yield strength or relative crack depth, or a decrease in Mode-I fracture toughness, leads to a larger ratio of elastic fracture toughness to total fracture toughness. It is also found that the effect of biaxiality ratio and inclination angle on elastic fracture toughness is highly dependent on total fracture toughness. It can be concluded that the developed model can accurately predict the fracture failure of ductile thin metal structures with inclined cracks under biaxial loading.