Two procedures to evaluate fracture resistance of notched components are proposed in this contribution: the Strain Energy Density (SED) over a control volume and the Cohesive Zone Model (CZM). With the aim to simplify the application of the two fracture criteria, the concept of the ‘equivalent local mode I’ is presented. The control volume of the SED criterion and the cohesive crack of the CZM, have been rotated along the notch edge and centered with respect to the point where the elastic principal stress is maximum. Numerical predictions are compared with experimental results from U and V shaped notches under three point bending with notch root radius ranging from 0.2 to 4.0 mm. In parallel the loading conditions vary, from pure mode I to a prevailing mode II. All specimens were made of PMMA and tested at -60°C. The good agreement between theory and experimental results adds further confidence to the proposed fracture criteria.
Numerous failure curves are presented in this manuscript to predict the onset of sudden fracture in V-notched brittle materials under combined tension-shear loading conditions. The curves were developed in a computational manner in terms of the notch stress intensity factors and based on the suitable failure concept of the maximum tangential stress (MTS) utilized frequently in the past by the author and his co-researchers for predicting mixed mode brittle fracture in extensive notched specimens. Three extensively used notch angles and various notch tip radii were considered in the computations. A wide range of brittle materials were also taken into account by defining and using the material critical distance. Through predicting load-bearing capacity and notch bifurcation angle utilizing only the two basic material properties namely the ultimate tensile strength and the plane-strain fracture toughness, engineers can design more rapidly and conveniently the V-notched brittle components with the aim to withstand reliably against sudden fracture.
Extensive brittle fracture curves are presented in the present paper for engineering components weakened by a U-shaped notch under different in-plane loading conditions from pure mode I to pure mode II. The curves were obtained in a computational manner on the basis of an appropriate brittle fracture model, namely the U-notched maximum tangential stress (UMTS) criterion, suggested and employed several times in the past by the author and his co-researchers to assess mixed mode fracture in numerous U-notched samples. Eight different notch tip radii were considered in the computations. Extensive brittle materials were also taken into consideration by using different values of the material critical distance in the calculations. By estimating theoretically the load-carrying capacity and the fracture initiation angle using solely the two basic material properties, namely the ultimate tensile strength and the plane-strain fracture toughness, engineers can design conveniently the U-notched brittle components and structures aiming to avoid abrupt fracture.