Rapid finite element evaluation of the averaged strain energy density of mixed-mode (I + II) crack tip fields including the T-stress contribution

The strain energy density (SED) averaged over a material dependent control volume has been demonstrated to control fracture and fatigue behaviour of different materials in many engineering design situations. A method to rapidly calculate the averaged SED at the tip of long cracks under in-plane mixed mode (I + II) loading has been recently proposed. It was based on the peak stresses evaluated from finite element (FE) analyses, according to the peak stress method (PSM). The aim of this work is to extend this FE approach to short cracks. In the present paper short cracks are distinguished from long cracks by considering that the stress fields within the control volume of short cracks are no longer governed solely by the stress intensity factors (SIFs), but the contribution of higher order terms, and primarily the T-stress, becomes significant to estimate the averaged SED. Therefore the averaged SED is calculated using the linear elastic nodal stresses evaluated by FEM either at the crack tip, to account for the SIF contribution, and at selected FE nodes of the crack free edges, to include the T-stress contribution. The proposed approach is referred to as nodal stress approach. The advantage of the nodal stress approach is two-fold: there is no need of mesh refinements in the close neighbourhood of the points of singularity, so that coarse FE meshes can be adopted; moreover, geometrical modelling of the control volume in FE models is no longer necessary. Infinite plates weakened by central small cracks subjected to mixed mode I + II loading and a lap joint geometry have been analysed taking into consideration different crack lengths, mode mixities and average finite element sizes of the employed meshes. A comparison between approximate values of the averaged SED according to the nodal stress approach and those derived directly from the FE strain energy adopting very refined FE meshes has been successfully performed within a range of applicability.