Wavelet transformation based multi-time scale method for fatigue crack initiation in polycrystalline alloys

Fatigue crack nucleation in polycrystalline alloys is strongly influenced by the crystallographical and morphological features of the underlying microstructure. This necessitates the incorporation of microstructural effects in the fatigue crack nucleation models developed for these alloys. Crystal plasticity based finite element (CPFE) simulations of statistically equivalent microstructures coupled with a physically motivated crack nucleation law captures the microstructural effects and can accurately predict fatigue life of polycrystalline alloys. However, fatigue analysis for large number of cycles by single time scale CPFE simulations is computationally exhaustive. To alleviate this problem, a wavelet transformation based multi-time scale (WATMUS) method is developed in the present work. In the WATMUS method, the wavelet based transformation of variables decouples the slow monotonic evolution from the fast oscillatory behavior and permits integration in time steps of cycles to provide significant computational benefit. This method has no assumption of periodicity in the evolution of variables and hence can be used to decouple the strongly non-linear crystal plasticity equations. The accuracy and efficiency of the WATMUS method is compared with conventional single time scale integration scheme through cyclic CPFE simulations of Ti-6242.;The load and microstructure sensitive fatigue behavior of Ti-6242 is investigated using a physically motivated non-local crack initiation law and the proposed WATMUS method based CPFE simulations. The crack nucleation model is based on dislocation pile up and stress concentration at grain interfaces, caused by inhomogeneous plastic deformation in the microstructure. The dislocation pile up length and stress concentration increases with load cycles, causing macroscopic crack nucleation. The number of cycles to nucleate a crack and the microstructural feature characteristics at the initiation site, predicted by the model shows good agreement with experimentally observed values.;A variable is defined based on experimentally observed crystallographical feature characteristics at the crack initiation site to relate the sensitivity of fatigue crack nucleation to the underlying microstructure. From cyclic CPFE simulations on different statistically equivalent microstructures of Ti-6242, a correlation between this local microstructural variable and number of cycles to nucleate a crack is observed. Additionally, the sensitivity of crack nucleation to the characteristics of the applied load is studied by performing WATMUS based CPFE simulations on a statistically equivalent microstructure. The predicted number of cycles to nucleate a crack agrees with experimentally observed trends.