Wavelet decomposed dual-time scale crystal plasticity FE model for analyzing cyclic deformation induced crack nucleation in polycrystals

A microstructure sensitive criterion for dwell fatigue crack initiation in polycrystalline alloys is proposed in this paper. Local stress peaks due to load shedding from time dependent plastic deformation fields in neighboring grains are responsible for crack initiation in dwell fatigue. A calibrated and experimentally validated crystal plasticity finite element model (CFEM) is employed for predicting slip system level stresses and strains. Vital microstructural features related to the grain morphology and crystallographic orientations are accounted for in the FEM by construction of microstructures that are statistically equivalent to those observed in OIM scans. The output of the FEM is used to evaluate the crack initiation condition in the post processing stage. The functional form of the criterion is motivated from the similarities in the stress fields and crack evolution criteria ahead of a crack tip and dislocation pile-up. A specific model is developed for estimating the pile-up length necessary for the nucleation criterion using the notion of geometrically necessary dislocations. The crack nucleation criterion is calibrated and validated by using experimental data obtained from ultrasonic crack monitoring techniques. In order to be able to model a large number of cycles to failure initiation, a dual-time scaling algorithm is proposed using wavelet induced decomposition. The algorithm decouples the governing equations into two sets of problems corresponding to two different time scales. One is a long time scale (low frequency) problem characterizing a cycle-averaged solution, while the other is a short time scale (high frequency) problem for a remaining oscillatory portion. The method significantly reduces the computational time till crack initiation.

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