This study investigated the relationship between fracture toughness (Kc) and energy release rate (Gc) through fracture morphology analysis, emphasizing the critical role of fractal dimensions in accurately characterizing fracture surfaces. Traditional linear elastic fracture mechanics (LEFM) models relate Gc to Kc by combining energy principles with the nominal area of the fracture surface. However, real materials often exhibit plasticity, and their fracture surfaces are not regular planes. To address these issues, this research applied fractal theory and introduced the concept of ubiquitiform surface area to refine the calculation of fracture surfaces, leading to more accurate estimates of Gc and Kc. The method was validated through standard compact tensile specimen tests on a nickel-based superalloy at 550 °C. Additionally, the analysis of fractal dimension differences and dispersion in various fracture regions provides a novel perspective for evaluating the fracture toughness of materials.

The rotor system supported by rolling bearings usually provides a resonance effect due to the nonlinearity of bearings. In this paper, the causes of these anomalous resonance effects are discussed by establishing coupling dynamic model of the flexible rotor-roller bearings system. The 4-degrees of freedom (DOF) Timoshenko finite element and the free interface modal synthesis technique are used to model the elastic rotor. Then, a piece-wise flexible rotor model coupling with a 5-DOF dynamic bearing model is obtained by fixing the inner race to rotor. And waterfall plots are mainly obtained using the method of adaptive Runge-Kutta. Comparisons are made between the simulated response of the rotor-simplified bearing and rotor-bearing coupling models. Firstly, the vibration of cage can cause supercritical anomaly vibration except for the subcritical vibration induced by the variable compliance vibration. Secondly, the vibration amplitude of the coupling model is lower than the rotor-nonlinear springs model.