Theoretical Estimation of Fatigue Life Before Crack Initiation in Metal Materials

A model for theoretically estimating the number of loading cycles before fatigue crack initiation at a constant applied cycle stress range and a power law equation to describe the kinetics of damage accumulation at this stage of fatigue failure are proposed. It is shown that the level of relaxation of local stress from the top of the blunt concentrator, which occurs due to local plastic deformations, depends on the value of the applied cycle stress and is nonlinear. A power law equation is proposed to estimate this local stress following the concept of critical distance, thus considering fatigue damage accumulation's kinetics. The correlation between the power-law exponents in the above equations and the equation for the growth rate of a newly initiated fatigue crack is established. In addition to the loading parameters and geometric dimensions of the concentrator, the initial data for the theoretical evaluation are the static strength characteristics (elastic modulus, Poisson's ratio, and macroscopic yield onset stress, which are determined from short-term tensile tests of standard specimens) and microstructure characteristics (grain size, Taylor's factor, Burgers vector, and grain misorientation angle, which are determined from the analysis of the microstructure of the starting material). No fitting parameters or experimentally determined data on material fatigue are used. The calculations based on the proposed model of the number of loading cycles before fatigue crack initiation in 45 steel specimens show good agreement with the experimental results.