A method to numerically predict the loading ratio dependency of long crack propagation rates under cyclic loading

The investigation of cyclic crack propagation rates (CPR) for different loading ratios is very elaborate. A multiscale numerical approach to predict high cycle fatigue (HCF) strength for a ferritic-pearlitic steel has been modified to be applicable for the numerical calculation of its cyclic CPR. The original approach involves a series of numerical and mechanism-based analytical models. Microstructural features of the material are statistically characterized for the generation of synthetically representative volume element (RVE) models of the microstructure. A combined isotropic and kinematic hardening model for crystal plasticity is used to include the microdeformation behavior under cyclic loading in the model. The simulation of cyclic loading with numerous of these statistically equivalent RVEs results in fatigue indicator parameter (FIP) fields which differ from one RVE to the other. With regard to the weakest link theory, only the highest FIP in each RVE is extracted for further fatigue calculations. Theses FIPs are distributed by an extreme value distribution function which can be uniquely described by two parameters. These parameters are used to determine the crack propagation rate. For the comparison of results from experiment and simulations, a concept is proposed which links the globally applied stress amplitude on the RVEs to the cyclic stress intensity factor. The model needs to be calibrated by cyclic CPR results conducted with arbitrarily chosen loading ratios. The validation of the calibrated model is achieved by the prediction and comparison of cyclic CPR at a different loading ratio. The obtained numerical values are in good agreement with the experimental results.