Peridynamic numerical investigation of asymmetric strain-controlled fatigue behaviour using the kinetic theory of fracture

Numerical fatigue process modelling is complex and still an open task. Discontinuity caused by fatigue cracks requires special finite element techniques based on additional parameters, the selection of which has a strong effect on the simulation results. Moreover, the calculation of fatigue life according to empirical material coefficients (e.g., Paris law) does not explain the process, and coefficients should be set from experimental testing, which is not always possible. A new nonlocal continuum mechanics formulation without spatial derivative of coordinates, namely, peridynamics (PD), which was created 20 y ago, provides new opportunities for modelling discontinuities, such as fatigue cracks. The fatigue process can be better described by using the atomistic approach-based kinetic theory of fracture (KTF), which includes the process temperature, maximum and minimum stresses, and loading frequency in its differential fatigue damage equation. Standard 316L stainless steel specimens are tested, and then the KTF-PD fatigue simulation is run in this study. In-house MATLAB code, calibrated from the material S‒N curve, is used for the KTF-PD simulation. A novel KTF equation based on the cycle stress‒strain hysteresis loop is proposed and applied to predict fatigue life. The simulation results are compared with the experimental results, and good agreement is observed for both symmetric and asymmetric cyclic loading.