Multiscale crystal-plasticity phase field and extended finite element methods for fatigue crack initiation and propagation modeling

This paper presents a physics-based prediction of crack initiation at the microstructure level using the phase field (PF) model without finite element discretization, coupled with an efficient and accurate modeling of crack propagation at macro-scale based on extended finite element method (XFEM). Although the macro-scale model assumes linear elastic material behavior, at micro-scale the behavior of plastically deforming heterogeneous polycrystals is taken into account by coupling the PF model and a crystal plasticity model in the fast Fourier transform computational framework. A sequential coupling has been established for the multiscale modeling where the macro-scale finite element (FE) model determines the hot spots at each cyclic loading increment and passes the associated stress/strain values to the unit-cell phase-field model for accurate physics-based microstructure characterization and prediction of plasticity induced crack initiation. The PF model predicts the number of cycles for the crack initiation and the phenomenological crack growth models are employed to propagate the initiated crack by the appropriate length to be inserted in the FE mesh. Finally, the XFEM solution module is activated to perform mesh independent crack propagation from its initial crack size to the final size for the total life prediction. The effectiveness of the proposed multiscale method is demonstrated through numerical examples.