Averaged strain energy density estimated rapidly from the nodal stresses by FEM for cracks under mixed mode loadings including the T-stress contribution

The present contribution reviews a recently proposed method to rapidly estimate the averaged SED at the tip of short as well as long cracks under in-plane I+II and long cracks under out-of-plane I+III mixed mode loadings. 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. According to the proposed method, the averaged SED is calculated using the linear elastic nodal stresses evaluated by FEM either at the crack tip, to account for the SIFs contribution, and at selected FE nodes of the crack free edges, to include the T-stress contribution. The advantage of the proposed approach is two-fold: coarse FE meshes can be adopted; moreover, geometrical modelling the control volume is no longer necessary. To validate the approach, cracked plates subjected to in-plane I+II mixed mode loading as well as bars weakened by circumferential outer cracks subjected to out-of-plane mixed mode I+III loading have been analysed. 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.