Fig. 1. Focused-ion-beam cross-section (FIB-CS) characterization method. (a) Crack-initiation region showing the α facet and the β facet. (b) FIB section across faceted grains suitable for the subsequent EBSD tests. (c) Higher magnification of the area marked by the rectangular box in (b) showing the microstructure features beneath the fracture surface.

Fig. 2. SEM/SE and TEM micrographs showing the bimodal microstructures of Ti-7333A (a-c) and Ti-7333B (d-f) before fatigue tests. SEM/SE images (a, b and d) showing equiaxed and elongated αp particles, multiple adjacent αp particles within β+αs matrix. TEM bright-field images showing fine αs precipitates inside the retained β phase (c and f) and locally continuous grain boundary α (GB α) layer at β GB (e). The cross-sections parallel to the loading direction (LD) were used for SEM microstructure observations.

Fig. 3. EBSD-derived inverse pole figure (IPF) map (a) and phase map (b) of the initial microstructure of Ti-7333B, showing the presence of the αp particles, GB αp particles and GB α layers.

Fig. 4. EBSD-derived IPF map (a) and phase map (b) of the initial microstructure of Ti-7333A. (c) Pole figures of selected αp particles and two adjacent β grains, showing an obedience or not of Burgers orientation relationship (BOR) of β1 and α1-α7, β2 and α3-α12. The cross-section perpendicular to the LD was used for EBSD testing.

Fig. 5. S-N diagrams of Ti-7333A (a) and Ti-7333B (b), showing the maximum applied stress and the resulting cycles to failure. Unbroken specimens after 107 cycles are represented by symbols with arrows.

Fig. 6. SEM images of fatigue fracture surface of Ti-7333A. (a) S1; (b) S2; (c) S3. The detailed information is illustrated in Table 3. Fatigue crack-initiation with the presence of elongated αp facet (a and b) or multiple contiguous αp facets (c1). (b1) Low magnification image of internal crack-initiation showing β facet. (c2) Fine striations and secondary cracks on crack-growth region near the crack origin. (c3) Equiaxed dimples and tear ridges on crack-growth region away from the crack origin. The distances between the crack-initiation site and the nearest free surfaces of fatigued specimens are attached in figures.

Fig. 7. SEM images of fatigue fracture surface of Ti-7333B. (a) S4; (b) S5; (c) S6; (d) S7; (e) S8; (f) S9 and (g) S10. The detailed information is illustrated in Table 3. Fatigue crack-initiation with the presence of elongated αp facet (a, b, d1 and g), multiple isolated αp facets (e) and multiple contiguous αp facets (c and f). (d2) Fine striations and secondary cracks on crack-growth region near the crack origin. (d3) Equiaxed dimples and tear ridges on crack-growth region away from the crack origin. The distances between the crack-initiation site and the nearest free surfaces of fatigued specimens are attached in figures.

Fig. 8. FIB-CS characterization of a selected Ti-7333B failed specimen (S10) that produced elongated αp facet sit on a β facet. (a) FIB section across faceted αpparticles and FIB milling direction along LD. (b and c) Faceted αp particles and β+αs matrix shown on the FIB-CS. (d) EBSD-derived IPF//LD map of the EBSD area. (e) {0001} and {10-10} slip trace maps and corresponding Schmid factor values for each slip system in faceted αp particles, slip trace maps are superimposed on IPF map. (f) {110} and {112} slip trace maps and corresponding Schmid factor values for each slip system in faceted β grain. (g) EBSD-derived pole figure showing a near BOR relation between faceted αp particles and faceted β grain. 3D-view of crystal are superimposed on IPF map.

Fig. 9. FIB-CS characterization of a selected Ti-7333A failed specimen (S1) that produced elongated αp facet sit on a β facet. (a) Faceted αp particle and β+αs matrix shown on the FIB-CS. (b) The enlarged view of the crack-initiation site. (c-e) EBSD-derived IPF//LD maps of the EBSD area 1, EBSD area 2 and EBSD area 3. (f) Slip trace maps and corresponding Schmid factor values for each slip system in faceted αp particle, faceted β grain and the first-nearest-neighbor β grains, {0001} and {10-10} slip trace map are superimposed on IPF map. (g) EBSD-derived pole figure showing a near BOR relation between faceted αp particle and faceted β grain. 3D-view of crystal are superimposed on IPF map.

Fig. 10. FIB-CS characterization of a selected Ti-7333B failed specimen (S9) that produced multiple contiguous αp facets sit on a β facet. (a) FIB section across contiguous faceted αp particles and FIB milling direction along LD. (b) SEM/SE image of FIB section at a tilt angle of 52°. (c) Faceted αp particles and β+αs matrix shown on the FIB-CS. (d) EBSD-derived IPF//LD map of the crack-initiation region in (c). (e) {0001} and {10-10} slip trace maps and corresponding Schmid factor values for each slip system in faceted αp particles. (f) {110} and {112} slip trace maps and corresponding Schmid factor values for each slip system in faceted β grain. (g) EBSD-derived pole figure showing no BOR relation between faceted αp particles and faceted β grain. 3D-view of crystal are superimposed on IPF map.

Fig. 11. Schematic depiction of the fatigue-critical microstructural configurations: (a) elongated αp particle oriented for basal slip; (b) elongated αpparticle oriented for prismatic slip; (c) multiple adjacent αp particles oriented for basal slip. (d) Schematic for phenomenological model for facet formation in bimodal microstructure: the dislocation pileup is formed at αp and αs particles boundaries. With increasing number of cycles, a sufficient stress is reached to active the basal slip in αp particles until a basal dislocation through the phase boundary, leaving a residual boundary dislocation. Once the residual dislocations accumulate to a critical value, a fatigue crack is formed that propagates along the slip band.