Averaged strain energy density estimated rapidly from the singular peak stresses by FEM: Cracked bars under mixed-mode (I + III) loading

The strain energy density (SED) averaged over a material dependent control volume proved to control fracture and fatigue behaviour of different materials in many engineering problems. A method to rapidly estimate the averaged SED at the tip of cracks under in-plane mixed mode I + II loading has been recently proposed. It is based on the peak stresses evaluated from finite element (FE) analyses, according to the peak stress method (PSM). Coarse finite element meshes automatically obtained from the free mesh generation algorithm available in a commercial FE code can be adopted. In the present paper Ansys software has been adopted. The aim of the present contribution is to extend the FE approach to cracks subjected to out-of-plane mixed mode I + III loading. The advantage of the proposed approach is two-fold: there is no need of mesh refinement in the close neighbourhood of the points of singularity, so that coarse FE meshes can be adopted; moreover, geometrical modeling the control volume in FE models is no longer necessary. Bars weakened by circumferential outer cracks subjected to out-of-plane mixed mode (I + III) loading have been analysed taking into consideration different crack lengths, mode mixities and average sizes of the adopted FE meshes. A comparison between approximate values of the averaged SED according to the peak stress approach and accurate values calculated directly from the FE strain energy by adopting very refined FE meshes has been successfully performed within a range of applicability.