Fig. 1 Relationship between the fatigue life and the strain range of experimental alloy at 980 °C: a total strain range versus fatigue life of various oriented alloy, b-d total, elastic and plastic strain ranges versus the number of cycles to failure of the alloy with the [001], [011] and [111] orientations, respectively

Fig. 2 Relationship between the fatigue life and the strain range of the experimental [001], [011] and [111] alloy at 980 °C: a normalized elastic strain range versus the number of cycles, b inelastic strain range versus the number of cycles

Fig. 3 SEM images of fatigue fracture of the [001] specimens after LCF at 980 °C: a-d ?εt/2 = 0.8%, e-h ?εt/2 = 0.45%: a, e macroscopical fracture morphology, b, f high magnification of the yellow boxes in a and e indicating the crack initiation site, c, g surface oxidation cracks, d, h high magnification of the blue dashed boxes in a and e showing striations in the area of crack propagation

Fig. 4 Schematic of the octahedral slip planes of the [001] specimens

Fig. 5 SEM images of fatigue fracture of the [011] specimens after LCF at 980 °C: a-d ?εt/2 = 0.8%, e-h ?εt/2 = 0.25%: a, e macroscopical fracture morphology, b, f, g surface slip morphologies, c the microporosity crack, d high magnification of the blue dashed box in a showing striations and secondary cracks, h surface oxidation crack

Fig. 6 Schematic of the octahedral slip planes of the [011] specimens

Fig. 7 SEM images of fatigue fracture of the [111] specimens after LCF at 980 °C: a-c ?εt/2 = 1.0%, d-f ?εt/2 = 0.2%: a, d macroscopical fracture morphology, b, e crack initiation site, c surface oxidation crack, f slip bands

Fig. 8 Schematic of the octahedral slip planes of the [111] specimens

Fig. 9 Morphologies of secondary cracks on the longitudinal sections of the [001] specimens after LCF at 980 °C: a forked and kinked cracks, b crystallographic secondary crack, c slip bands and partial crack closure of the crack tip (high magnification of the yellow dashed box in b), d slip bands of the crack tip (high magnification of the green dashed box in b)

Fig. 10 Morphologies of secondary cracks on the longitudinal sections of the [011] specimens after LCF at 980 °C: a secondary crack deflection at interdendritic carbides and eutectics, b the secondary crack accompanied by γ and γ′ phases distortion and slip bands, c different directions of slip bands (high magnification of the yellow dashed box in b)

Fig. 11 Morphologies of secondary cracks on the longitudinal sections of the [111] specimens after LCF at 980 °C: a secondary crack generated at the junction of different slip planes, b crack propagation path altered by carbides (high magnification of the blue dashed box in a), c crack-penetrating carbides (high magnification of the purple box in a)

Fig. 12 Schematic illustration of the crack initiation and propagation