A phase-transformation based method coupled with entropy to predict fatigue crack initiation of metallic materials

•A new phase transformation model is proposed to predict fatigue crack initiation.•Evolution of damage under fatigue loading is considered with the entropy theory.•Effects of grain size on the crack initiation is investigated. Fatigue crack initiation can be regarded as a generalized phase transformation from the view of breaking energy barrier. A new phase transformation model is proposed to predict fatigue crack initiation based on the second law of thermodynamics. Evolution of dynamic energy during crack initiation and the damage under fatigue loading is considered combining with the entropy theory. The system becomes unstable when the Helmholtz free energy reaches the extremum value, which is adopted to represent fatigue crack initiation. The effects of grain size on the crack initiation and the asymptote of S-shaped S-N curve are discussed. The theoretical predictions are compared with the experimental data and show reasonable accuracy for different metallic materials.