Fig. 1. (a) Synchrotron XRD diffraction pattern of the as-annealed HfNbTaTiZr HEA, indicating a body-cubic-centered (bcc) crystal structure with a lattice constant of $a=3.408\overset{\circ }{\mathop{\text{A}}}\,$. (b) TEM micrograph of the as-annealed HEA at a randomly selected area revealing pre-existing dislocations. The selected area diffraction pattern (SADP) in the inset reaffirms a bcc structure.

Fig. 2. (a) EBSD map of randomly oriented equiaxed grains with an average grain size of 45±7 μm. (b) EDX mapping of all five constituent elements in a typical microstructure domain (the first sub-figure), ruling out the possibility of elemental segregation and formation of additional phases.

Fig. 3. (a) A representative engineering stress-strain curve and the corresponding true stress-strain curve of the HfNbTaTiZr HEA at room temperature and a strain rate of 1×10-3 s-1. The average yield strength (σy), ultimate tensile strength (σUTS), uniform elongation (eu) and fracture elongation (ef) obtained from three different tests are superimposed as circular markers. (b) The Considere's construction in the strain hardening rate and true stress versus true strain for determining the onset of necking.

Fig. 4. (a) Illustration of the Neuber method for correcting an overestimated elastic stress to a realistic elastoplastic stress. (b) Experimentally recorded stress amplitude (σa) against the number of cycles to failure (Nf) along with the Weibull probabilistic modeling (lines).

Fig. 5. (a) SEM image of a representative fatigue-failed half sample, failed at σmax=1137 MPa and Nf=120,547, showing crack deflection on the primary crack and a secondary crack initiating also from the tensile side of the bending sample. The long arrows are indicative of crack-propagation directions. (b) Magnified micrograph of the crack tip of a crack branched from the primary crack, indicating hierarchical crack branching. (c) Magnified micrograph of the tip of the secondary crack, exhibiting crack interlocking resulting from frequent crack deflection.

Fig. 6. Adjoined SEM images of the sample failed at σmax=1149 MPa and Nf=275792, showing the full propagation trajectory of another secondary crack, from which crack deflection, crack interlocking, crack branching, and crack closure (indicated by the pile-ups) are noticed. The long arrows are indicative of crack-propagation directions.

Fig. 7. SEM images of the secondary crack segments of the sample failed at σmax=1123 MPa and Nf=148868, showing (a) pronounced serrations on the crack surfaces by transgranular crack deflection and crack interlocking by the action of the mode-II shear, (b) extensive crack branching near the crack tip with some branched cracks exhibiting hierarchical characteristics, (c) debris wedging behind the crack tip.

Fig. 8. (a) SEM image of a crack derived from the primary crack (location marked), manifesting serrated fracture surfaces formed from the intergranular fracture, the sample failed at σmax=1179 MPa and Nf=23395. (b) Enlarged view of (a) confirming the intergranular fracture. Note that the primary crack is not perpendicular to the global maximum tensile stress. Therefore, the derived crack is experiencing a mixed-mode fracture.

Fig. 9. Fracture surface morphologies of the sample fatigue-failed at σmax=1123 MPa and Nf=148868. (a) Overall view. Magnified views of (b) region b in stage II, (c) stage I, and (d) region d in stage III.

Fig. 10. Magnified fracture-surface morphologies in stage II, showing (a) fine striations with secondary cracks across striations and (b) coarse striations with secondary cracks between striations. The sample failed at σmax=1179 MPa and Nf=23395.

Fig. 11. SEM images of plastic deformation in the vicinity of the main fatigue crack, the sample failed at σmax=1119 MPa and Nf=107553. (a) Overview. (b) Highly strained grains with a high density of slip lines. (c) Grains with extrusions from persistent slip bands. (d) The region somewhat away from the crack, still showing dense slip lines in grains.

Fig. 12. Bright-field STEM/TEM images in the vicinity of the main fatigue crack, showing various dislocation substructures. (a) Dislocation tangles. (b) Dislocation cells separated by walls. (c) Dislocation loops. (d) Dislocation arrays. (e) Dislocation network composed predominantly of hexagonal cells. (f) The dislocation network consisted predominantly of parallelogrammatic cells. The TEM image in (b) was taken with g = {110} and zone axis ≈〈001〉, whereas the STEM images in the remaining sub-graphs were obtained with g = $\left\{ 10\bar{1} \right\}$ and zone axis ≈〈111〉, all under a two-beam condition. The sample for (b) failed at σmax=1149 MPa and Nf=275729, while the rest at σmax=1139 MPa and Nf=34041.

Fig. 13. SEM images of plastic deformation in the vicinity of the main fatigue crack, the sample failed at σmax=1114 MPa and Nf=2200000. (a) Overview. (b) Highly strained grains with extrusions from persistent slip bands. (c) Secondary cracks with dense slip lines.

Fig. 14. Comparison of the fatigue properties of the HfNbTaTiZr alloy with other high-entropy and conventional alloys. (a) Fatigue strength and (b) fatigue ratio versus ultimate tensile strength. All fatigue data are converted to be at R=-1 with the Smith-Watson-Topper relation [61]. (c) Fracture elongation versus ultimate tensile strength. The data for all other alloys are taken from Refs. [60,62,80,81]. Note that steels with tensile strength greater than 2000 MPa are not included in (a) and (b), greater than 1600 MPa not in (c).

Fig. 15. Schematic depicting the intrinsic and extrinsic toughening mechanisms observed in the HfNbTaTiZr alloy.