Nonlinear relationship between the fatigue limit and quantitative parameters of material microstructure

The purpose of this paper is to develop a generalized model for the calculation of the fatigue limit of the material based on the data on its microstructure. Relying on the experimental results of fatigue and cyclic fracture toughness tests and the analysis of the microstructure of two-phase titanium VT3-1 alloy with different structural states obtained by varying the thermo-mechanical treatment (TMT), it is shown that the dependence of the fatigue limit σ−1 on the size of the microstructural element, which is responsible for the material fatigue strength, is of a nonlinear character. The formula is derived to calculate the fatigue limit from the data on the microstructure parameters and from the results of static tensile tests of the material, which shows a very good agreement between the calculated and experimental results. The calculation results of the fatigue limit σ−1 are presented for other titanium alloys of three types, namely, pseudo-alpha alloy IMI 834, alpha + beta alloys (VT6, Ti-6-4, VT16) and beta LCB alloy, as well as for the materials with another type of the crystal lattice, such as steel 0.16%C with a body-centered cubic lattice (bcc) and brass 70%Cu/30%Zn with a face-centered cubic lattice (fcc) which justify the validity of the obtained formula. An effort has been made to explain the physical meaning of the obtained dependence.