Efficient prediction of crack initiation from arbitrary 2D notches

An efficient two-scale approach for predicting mode I crack initiation from 2D notches based on the Coupled Criterion is proposed. On the scale of the local model, a voxel model containing the notch simulates the displacement field. The crack model is introduced on the smaller scale and is defined in an image space. Based on the notch curvature, the precomputed crack model can be transformed to any position on the notch surface. The displacement field of the local model is fitted at the boundaries of the transformed crack model by predefined deformation modes and results can be obtained by a superposition of precomputed crack model results. By introducing the crack in the crack model, the stiffness of this model is reduced and thus, the incremental energy release rate can be inaccurate. Therefore, a boundary relaxation approach is used to obtain more accurate energy release rates. It is shown that the method is very efficient as it requires only 3:20 min to analyze 50 positions on a notch compared to 2:21 h of a conventional approach using full FEM simulations. Thereby, the method is reliable in identifying the critical position. The predicted failure index at this position deviates by at most 10.8%. Since the crack model limits the length of initiating cracks, Irwin’s length KIc2/σc2 of the material must lie below 2.53 times the radius of a circular hole under uniaxial tension. For a brittle material like Al2O3, notches with a curvature radius above 31μm can thus be analyzed.