Mathematical Modeling of Fatigue Fracture at High-Frequency Bending Vibrations

Abstract

A two-criterion kinetic damage model is proposed to describe the development of the fatigue fracture process under cyclic loading. On this basis, a procedure is proposed for calculating the coefficients of the kinetic equation for various modes of fatigue fracture from low-cycle to very-high-cycle fatigue. A uniform numerical method has been developed based on an implicit approximation of the differential equation for damage. This method makes it possible to carry out an end-to-end calculation of the evolution of crack-like zones of fatigue fracture in the material without considering cracks in their classical sense, as well as to estimate the durability of samples from the first nucleation to macrofracture. Calculations were made of the fatigue fracture of specimens under long-term cyclic loading according to the three-point bending scheme with the development of crack-like fracture zones in the modes from HCF to VHCF. Comparison of numerical and experimental results for specimens of titanium alloys is carried out.