Elastic and fully plastic J-integrals for mixed mode fracture induced by inclined surface cracks in plates under biaxial loading

Mixed mode fractures can be triggered by either multi-axial stresses or inclined cracks or both. Little research has been undertaken on J-integral for inclined surface cracks in plates under biaxial loading. This paper intends to determine the elastic and fully plastic J-integral for mixed mode fracture induced by inclined surface cracks in plates under biaxial loading conditions, using three-dimensional finite element method. Various geometries, biaxiality and material properties of cracked plates, including crack depth to plate thickness ratios, inclination angles, strain hardening exponents and biaxiality ratios, are considered. From numerical results, it is found that for elastic analysis, the equivalent influence coefficients increases with the increase of the relative crack depth and the magnitude of the biaxiality ratios. It is also found that for a given crack and plate geometry, the values of normalized fully plastic J-integral h₁ decrease along the whole crack front for different strain hardening exponents n with the increase of the inclination angles from 0° to 45° for uniaxial loading. It can be concluded that the method presented in the paper can determine the J-integral for inclined surface cracks in plates with reasonable accuracy. The results presented in the paper can equip practitioners for more accurate prediction of plate failures under various loads.