Nanoscale origins of the damage tolerance of the high-entropy alloy CrMnFeCoNi

Damage tolerance can be an elusive characteristic of structural materials requiring both high strength and ductility, properties that are often mutually exclusive. High-entropy alloys are of interest in this regard. Specifically, the single-phase CrMnFeCoNi alloy displays tensile strength levels of ∼1 GPa, excellent ductility (∼60–70%) and exceptional fracture toughness (KJIc>200 MPa√m). Here through the use of in situ straining in an aberration-corrected transmission electron microscope, we report on the salient atomistic to micro-scale mechanisms underlying the origin of these properties. We identify a synergy of multiple deformation mechanisms, rarely achieved in metallic alloys, which generates high strength, work hardening and ductility, including the easy motion of Shockley partials, their interactions to form stacking-fault parallelepipeds, and arrest at planar slip bands of undissociated dislocations. We further show that crack propagation is impeded by twinned, nanoscale bridges that form between the near-tip crack faces and delay fracture by shielding the crack tip.

marked as "1" and "2", are ~20 nm away from the crack tip. a,d. HRTEM images of areas "1" and "2". b,c. Local lattice strain maps of normal strain along x-axis (<111> direction) and shear strain in area "1" in c. In the strain maps, colors for positive values represent tensile strain and those for negative values represent compressive strain. e,f. Srain maps of area 2 in c. g,j. HRTEM images taken from area "1" and "2"

Supplementary Note 1. Strain analysis of the crack-tip region
Local lattice strain distribution maps were obtained from time-resolved HRTEM images (shown in Fig. 1c,d in the main text of the paper) using geometric phase analysis (GPA), as shown in Supplementary Figure 1. The x-axis is along the normal direction of the {111} plane on which Shockley partials glide during the opening of the crack. With the propagation of the crack tip, the strain (and therefore stress) states were clearly discernible with the different colors. Before the nucleation of Shockley partials, the local normal stresses along the <111> direction in region 1 are the most compressive ( Supplementary Fig. 1b). It seems reasonable to assume that the area of enhanced stress concentration (the blue area) is where partial dislocations nucleated.
After the nucleation of partials, the local lattice normal distortion became less severe ( Supplementary Fig. 1h). The pronounced variation in shear strain also indicates the nucleation of partials ( Supplementary Fig. 1c,i). In region "2", which is ~20 nm away from the crack tip, the strain state is complex due to the high density of dislocations ( Supplementary Fig. 1e,f,k,l), in particular in the vicinity of the undissociated dislocations ( Supplementary Fig. 1k).

Supplementary Note 2. Calculation of the energy dissipation achievable by twin and slip
The effectiveness of twinning in the nano-bridging ligaments can be estimated by the following considerations. The Taylor factor (M) links the single crystal shear strain () to the polycrystalline tensile strain () as follows: γ = • ε. Considering the fcc twinning shear of  =1/2, and assuming an average Taylor factor of M = 3.06 for a randomly textured material, twinning can account for a maximum tensile strain of 0.23 (ε = γ/ ), provided that the twinned volume is 100% of the total material; in reality, the strain that can be accommodated by deformation twinning will likely be well below this value. 1 In the current experiment where nano-twinned bridges are formed in the wake of the crack tip ( Supplementary Fig. 2), if a twin of thickness 10 nm is formed in a bridging ligament, the volume fraction of the nano-twin will be ~10％, so the shear strain produced by the twin will be on the order of   2.3 × 10 −2 .
By comparison, the shear strain produced by the motion of a full dislocation In summary, the plastic strain produced by nano-twins in the crack-tip bridging ligaments is much larger than the strain induced by the motion of a full dislocation or partial dislocation through the nano-bridge. As the strain energy is a function of  2 and the elastic modulus, assuming that the modulus remains constant, the energy dissipation achieved by twinning would be much larger. Of course, the above comparison is confined to twinning and dislocation activity within the nano-bridges.
Considerably more energy would be dissipated by dislocation activity in the plastic zone ahead of the crack tip than by nano-twinning within the fiber-like bridges.

Supplementary Note 3. Factors controlling the synergy of deformation mechanisms
As shown in the Supplementary Movie 1 and 2, there is a marked activation of fast-moving partial dislocations at the early stage of deformation. However, since the full dislocations move slowly, forming localized bands of planar slip, the fast motion of partial dislocations is blocked at higher strains. In relatively simple terms, these observations may be rationalized as follows. distribution of elements appears to be random and disordered in high-entropy alloys, 3,4 it is conceivable that the local stacking fault energy may vary from point to point.
Indeed, recent HAADF/MAADF observations of dislocation core structures in this alloy seem to support this notion. 5 These local variations in stacking fault energy could account for the observed coexistence of full and partial dislocations.
Additionally, since the Peierls stress varies exponentially as (-w/b), where w is the dislocation width and b is the Burgers vector, it would be higher for a full dislocation than for its shorter partials. In other words, local chemical fluctuations could result in local regions of undissociated and dissociated dislocations with different mobilities.
Their subsequent synergistic interactions could then produce the sequence of events shown in the movies discussed above. Systematic theoretical calculations, if possible, would certainly be helpful to understand local differences in the stacking fault energy and the stress to move different dislocations, but because of the complex nature of high