In recent years, phase-field method (PFM) has attracted a lot of attention as an advanced numerical simulation technique in fracture mechanics. However, few PFM models adequately account for the effects of multi-axial stress states during crack initiation and propagation. This paper proposes a new phase-field model by integrating the critical plane method, multi-axial fatigue life models, and PFM, to simulate crack initiation and propagation under multi-axial stress states. We integrate the critical plane approach and multi-axial fatigue life models (SWT, MWHS, MGSE) and S-N curve into the phase-field framework, proposing modified models (E-MWHS, E-MGSE) to enhance prediction accuracy, six kinds of PFMs are thus obtained. The proposed PFM was applied to investigate how the multi-axial fatigue life models, critical plane search step size, cycle skipping increment, and strain energy density decomposition methods affect crack initiation and propagation, compact tension (CT) specimen was also used to quantify these parameters’ influence on da/dN-ΔK and a-N curves. The fatigue life of Titanium alloy: TC4 and Nickel base superalloy: GH4169 predicted by the proposed PFM is mostly within the triple scatter band, and the multi-axial fatigue life models and strain energy decomposition method have a significant effect on crack growth rate and path. The proposed phase-field model can provides an analytical method for fatigue life prediction and reliability design of aero-engine components.
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