Fig.1

Curve of material Gc variation with temperature and phase-field dispersion integral results

Table 1

Material parameters for Ti6Al4V［31］

Fig.2

Comparison of numerical and analytical solutions of thermo-mechanically coupled phase-field models

Fig.3

Comparison of two fatigue degradation functions

Fig.4

Comparison of mesh refinement between unassigned and assigned manifold

Fig.5

Schematic of hanging nodes

Fig.6

Convergence plot of overall iterative method and alternate minimization algorithm

Fig.7

Flowchart of solution program

Fig.8

Schematic of constant load accumulation method

Fig.9

Geometric dimensions and loading conditions of dog-bone specimen

Fig.10

Simulated results based on manifold adaptive mesh refinement

Fig.11

Comparison of calculation time about global mesh refinement method， manifold adaptive method， constant load accumulation method + manifold adaptive method

Fig.12

Influence of fatigue threshold parameters on model calibration of S-N curves

Fig.13

Influence of material parameter κ onmodel calibration of S-N curves

Fig.14

Calibration of S-N curves parameters for Ti6Al4V

Fig.15

Temperature-dependent S-N curves

Fig.16

Geometric dimensions and loading conditions of a plate with a central hole

Fig.17

Calculation results of plate with a central hole

Table 2

Crack initiation life of a center-holed plate under thermal-mechanical fatigue loading with different phase differences

Fig.18

Geometric dimensions and loading conditions of microstructures with defects

Table 3

Material parameters of microstructures with defects［31］

Fig.19

Fatigue crack at complete fracture of microstructure with defects

Table 4

Crack initiation life of microstructures containing defects under different stress states

Table 5

Crack initiation life of microstructures containing defects under different mesh sizes

Fig.20

Comparison of calculation time between global mesh refinement method and manifold adaptive method under triaxial stress loading