Fig. 1. Schematic illustration of the geometry and boundary conditions defined in the simulations for global model and submodel.

Fig. 2. Finite element model of cracked geometry. (a) Global model, (b) Sub-scale model.

Fig. 3. Local support domains used in RBF-FD method for construction of shape function.

Fig. 4. Flow stress behavior of RR1000 showing model predictions (solid lines) and measured data points (symbols).

Fig. 5. Simulated kinetics of oxide length growth along the grain boundary with different values of stress factor, κp.

Fig. 6. Simulated oxide length ahead of the crack tip against the stress factor at a time of 5 h. Calibrated stress factor was chosen based on the experimental measurement in Ref. [12] which is 9.7 µm.

Fig. 7. (a) The EDX mapping obtained by Kitaguchi et al. [12] from a region near the oxide tip is provided for comparison. (b) Contour of the simulated oxide intrusion around the oxide tip (Crack tip is on the left and not included in both images).

Fig. 8. Comparison between the predicted concentration profiles of Ni, Al, Cr and O across the oxide thickness (the right half) and the corresponding experimental measurement (data shown on the left half of the figure is extracted from Ref. [12]).

Fig. 9. Evolution of crack opening stress ahead of the crack tip during oxide formation.

Fig 10. Simulated kinetics of oxide growth ahead of the crack tip under different applied load.

Fig. 11. Evolution of crack opening stress near the crack tip during oxide formation under applied stress of (a) 100 MPa, (b) 200 MPa, (c) 300 MPa. t = 0 s represents the time when uploading is just finished and no oxide exists.

Fig. 12. Evolution of crack opening stress near the crack tip during oxide formation when ${{K}_{\text{max}}}=22.0\;\text{MPa}\sqrt{m}$ and crack length a = 2 mm and the local fracture stress curve of the oxide ahead of the crack tip (dashed line). The red line indicates the extent of oxide growth at a given time. As shown, fracture is predicted at a time of approximately 100 s (the text states the precise value as 126 s).

Fig. 13. Calculation of the time when crack growth is activated, i.e., when the normal stress at the oxide tip reaches the fracture stress curve, for different Kmax.

Fig. 14. Comparison between predicted crack growth rates under different Kmax for the as-received and aged microstructures and experimental data of dwell fatigue test with (1-3600-1-1) and without (1-1-1-1) 1 h dwell period at the maximum load. Results are normalised based on the predicted values of the as-received microstructure under Kmax = 32.65. (a) da/dt (mm/s). (b) da/dN (mm/cycle).