The novel equivalent material concept, proposed originally by the author, was utilized together with the mean stress and the point stress failure concepts to predict the load-carrying capacity of O-notched ductile steel plates under pure tension. Unlike for V and U-notches, it was found that the point stress criterion combined with the equivalent material concept could estimate successfully the limited available experimental results reported in literature regarding four O-notched plates made of very ductile steel. By using the model, one may predict well the onset of tensile crack initiation in O-notched ductile components without requiring performing experiments or elastic-plastic analysis.

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.

The aim of the present work was to develop a guideline for approving the railway axles made of C35 steel and containing surface and/or in-body defects after manufacturing. First, several through and part-through circular cracks were modeled on the surface and in the body of the axle at its critical cross-section. Then, the permissible size of such cracks was determined by using the fracture mechanics. To verify the validity of the guideline, the theoretical result for the semi-circular surface crack was compared with the allowable size prescribed by the international railway standard. A very good agreement was found to exist between the predicted and the standard values.