Wavelet transformation based multi-time scaling method for crystal plasticity FE simulations under cyclic loading

Microstructure based mechanistic calculations, coupled with physically motivated crack initiation criterion, can provide effective means to predict fatigue cracking in polycrystalline materials. However the accommodation of large number of cycles to failure, as observed in the experiments, could be computationally exhaustive to simulate using conventional single time scale finite element analysis. To meet this challenging requirement, a novel wavelet transformation based multi-time scaling algorithm is proposed for accelerated crystal plasticity finite element simulations in this paper. An advantage over other conventional methods that fail because of assumptions of periodicity etc., is that no assumption of scale separation is needed with this method. The wavelet decomposition naturally retains the high frequency response through the wavelet basis functions and transforms the low frequency material response into a “cycle scale” problem with monotonic evolution. The method significantly enhances the computational efficiency in comparison with conventional single time scale integration methods. Adaptivity conditions are also developed for this algorithm to improve accuracy and efficiency. Numerical examples for validating the multi-scaling algorithm are executed for a one dimensional viscoplastic problem and a 3D crystal plasticity model of polycrystalline Ti alloy under the cyclic loading conditions.