Averaged strain energy density evaluated rapidly from the singular peak stresses by FEM: cracked components under mixed-mode (I + II) loading

The strain energy averaged in a material-dependent structural volume (SED parameter) proved to efficiently account for notch effects in static as well as fatigue structural strength problems. In this work, a method is presented to rapidly evaluate the SED parameter from the singular peak stresses determined by the finite element (FE) method at the tip of cracks subjected to mixed mode (I + II) loading. Coarse finite element meshes automatically obtained from the free mesh generation algorithm available in a commercial software program can be used. Therefore, mesh refinement close to the crack tip can be avoided. The proposed approach takes advantage of the existing Peak Stress Method (PSM), which provides some expressions to estimate the mode I and mode II stress intensity factors (SIFs) starting from the elastic crack tip stresses evaluated by FEM. Because a closed-form expression of the SED parameter as a function of the SIFs is available and the latter can be evaluated from the crack tip stresses, the proposed method can be formulated in a straightforward manner. By using the new approach, geometrical modelling of the structural volume, inside which strain energy should be averaged, is no longer necessary. Several analyses have been carried out on cracked plates subjected to tension loading, varying the length and the inclination of the crack (i.e., the mode mixity) as well as the size of the adopted finite elements. The approximated SED values calculated by the singular peak stresses using coarse meshes have been systematically compared with those obtained directly from the FE strain-energy using very refined meshes to verify the range of applicability of such an approach.