A novel approach to fracture prediction in flat notched PMMA components under pure torsion: integration of theory of critical distances with equivalent and fictitious material concepts

This study investigates the ability of selected brittle fracture criteria to predict crack initiation in V-notched PMMA components subjected to pure torsion. The analysis employs the Theory of Critical Distances (TCD) together with the Maximum Tangential Stress (MTS) and Mean Stress (MS) criteria. The critical distance parameters were identified using three independent approaches, including method base on experimentally determined stress intensity factors, finite element simulations, and stress distributions obtained from pre-cracked specimens. In addition, the classical criteria were extended by incorporating the Equivalent Material Concept (EMC) and the Fictitious Material Concept (FMC), allowing plastic deformation effects under shear-dominated loading to be taken into account. The results show a pronounced dependence of prediction accuracy on specimen thickness as well as notch geometry. Linear-elastic solutions were found to be reliable only for relatively large notch radii, whereas sharp notches required the inclusion of nonlinear effects through EMC or FMC. The most consistent predictions were obtained using the MS criterion combined with the FMC approach, particularly for intermediate notch radii. The study demonstrates that the critical distance cannot be treated as a universal material constant, but should instead be interpreted as an effective fracture process length scale influenced by the stress state, stress gradient, and three-dimensional constraint conditions.