A hybrid XFEM-calibrated analytical framework for efficient fatigue crack growth prediction

• A hybrid XFEM-calibrated analytical framework for fatigue crack growth (FCG) prediction is proposed. • Periodic geometric factor β ( z ) calibration enables efficient analytical integration while retaining 3D fidelity. • Spatially varying 3D constraint factor α ( z ) improves load retardation prediction. • Accurate FCG life prediction under both constant-amplitude and overload loading is achieved. • Computational cost is reduced by more than an order of magnitude compared to XFEM. Accurate fatigue crack growth (FCG) prediction in finite-thickness components requires representation of three-dimensional (3D) crack-front evolution and out-of-plane constraint effects that conventional two-dimensional solutions cannot capture. Crack propagation simulations using 3D extended finite element method (XFEM) can resolve these effects but remain computationally prohibitive for high-cycle fatigue applications. This paper proposes a hybrid XFEM-calibrated analytical framework for efficient FCG prediction under constant- and variable-amplitude cyclic loading. Stationary 3D XFEM analyses are performed at discrete crack configurations to determine the through-thickness stress intensity factor and the corresponding geometric factor β ( z ). Crack growth between calibration steps is then integrated analytically using established crack growth laws. A spatially varying constraint factor α ( z ) is introduced to account for the thickness-dependent variation in plastic zone size and to enable overload retardation modeling. The framework is experimentally validated using compact-tension specimens of Grade E cast steel and R400HT rail steel under stress ratios R = 0.1–0.5 and single-overload conditions (OLR = 1.5–2.0). Predicted crack growth lives agree with experiments within 7%, and the predicted crack-front evolution matches experimentally observed marker bands. Compared with full XFEM crack propagation, the proposed framework reduces computational time by more than an order of magnitude while retaining 3D crack-front representation. The proposed framework provides an efficient and physically consistent strategy for FCG prediction in configurations where closed-form solutions are unavailable or where load interaction effects are significant.