Nanoindentation into FeCoNiCrCu high-entropy alloy: An atomistic study

Mechanical properties of HEAs

Figure 2(a) shows the typical load-displacement curves of HEAs during the nanoindentation process. It can be found clearly that all the HEAs undergo an elastic deformation first, and then followed by plastic deformation. This is similar to the in-situ micro/nano compression induced deformation behaviour of this kind of HEA [32]. Also, it can be observed that the curves exhibit displacement burst. According to the Hertzian elastic theory [33,34], the relation of the indentation load along the z-direction, F_z, and the indentation depth h during the elastic deformation can be expressed as follows (2) where R is the radius of the virtual indenter, and is the reduced Young's modulus derived from the equation of (3) where and are the Poisson's ratio and Young's modulus of the indenter, respectively. and represent the Poisson's ratio and Young's modulus of HEA. Because of the value of the constant, K in Equation (1) was set large enough, the indenter used in the current MD simulation can be approximately regarded as an ideal rigid body with an infinite elastic modulus of , Equation (3) can be simplified as (4)

OPEN IN VIEWER

Figure 2

(a) Evolution of the normal force with indentation depth; Snapshots showing the dislocation network in the (b) HEA without Cu segregation, (c) HEA with coherent interface Cu segregation, and (d) HEA with incoherent interface Cu segregation at full indentation. Dislocations are coloured according to their Burgers vectors b . green: Shockley partials 1/6〈112〉; pink: stair-rod 1/6〈110〉; red: others; yellow: Hirth 1/3〈100〉 and blue: perfect 1/2〈110〉.

The Hertzian fitting curves of the three simulation models from Equation (3) were shown (solid lines) in Figure 2(a). According to the fitting results, the corresponding reduced Young's modulus of HEAs with no Cu segregation (NS), coherent Cu precipitation (CP), and incoherent precipitation (IP) were 73.01, 82.18, and 79.95 GPa with a standard deviation of about 0.5 GPa, respectively. It was reported that, the values of Poisson's ratio were 0.25 for CrFeCoNi, 0.31 for CrCoNi, 0.20 for CrFeNi, 0.28 for FeCoNi [35], 0.22∼0.26 for CoCrFeMnNi [36,37]. Here the Poisson's ratio for all simulated alloys was set as 0.25. So, based on Equation (4), Young's modulus of HEA models can be obtained as 68.45, 77.04, and 79.95 GPa, respectively. The results were qualitatively in agreement with about 56.5∼82.5 GPa from the in situ mechanical experiments of the HEA [32]. It can be found that the values of Young's modulus of the alloys with Cu precipitation are higher than that of HEA without Cu segregation. This can be explained by the rule of mixtures and the value of elastic modulus for Cu is much lower than the others [32].

The evolution of defect structures

It also can be found in Figure 2(a) that, these three kinds of alloys showed different behaviours during the period of plastic deformation (h > 0.5 nm), which can be explained by the propagation features of dislocations. The states and distributions of dislocations in the NS, CP, and IP alloys at the full indentation were shown in Figure 2(b–d), respectively. The dislocation-filled region in the vicinity of – and adherent to – the indent pit could be denoted as a plastic zone. Comparing to the homogenous HEA, the reaction volume for dislocation interactions in the segregated alloy was confined by the interfaces to the upper half of the simulation box, which can be seen in Figure 2(b–d). Figure S2 shows a comparison in the evolution of defect structures in all simulated models during nanoindentation. The atoms were colour-coded according to the value of the centrosymmetric parameter. The defect structures were generated due to the penetration of indenter into the samples or the mismatch of the lattice constants, including dislocation, stacking fault, or interface.

For the NS alloy, plastic deformation initiates at the indentation depth of 5.2 Å when a burst of dislocations occurs under the indenter, which can be seen in Figure S2 (a). Several dislocations nucleate under the tip of indenter on {1 1 1} slip planes, which results in an obvious force drop on the load-displacement curve (Figure 2(a)). The dislocation loops nucleate and emit from the indentation region (Figure S2(b–d)). As can be seen in Figure S3, two Shockley partial dislocations of Burgers vectors b₁  = 1/6[2-1-1] and b₂  = 1/6[-121] were activated and slipped on the planes of (111) and (-1-11), respectively, until they met and reacted with each other. A stair-rod dislocation of Burgers vector b₃ = 1/6[110] was formed then, and the slip in the two slip planes was locked by this Lomer–Cottrell lock. With the indenter penetrating, the Hirth lock, dislocations of Burgers vector b₄  = 1/3[110] were also formed by the reaction of dislocations of Burgers vectors of 1/6[112] and 1/6[-11-2]. These two kinds of dislocations cannot slip on the slip system. The formation of these two kinds of locks can explain the high deformation resistance of uniform HEA during further plastic deformation.

For the CP alloy, it can be found in Figure 2(c) that dislocations were confined in the upper half of the simulation box by the coherent interface. More dislocation reactions are to be expected in this smaller volume. As can be seen in Figure S2(e), dislocations bounding the stacking faults were already formed before the indentation. This can be explained by the mismatch between the lattice constants of alloy and precipitated Cu. The atomistic configuration corresponding to point A, which is the end of the first drop on the load-displacement curve in Figure 2(a), was shown in Figure S2(f). It can be seen that the entangled dislocation structure initially formed at point A did not substantially change until point B. The load increased from 0.085 to 0.232 μN, which corresponds to a considerable strain-hardening of the alloy. The hardening can be attributed to the presence of the coherent interface. The deformation features during the process of nano-indentation and the contribution of the interface of this bilayer system is similar to the results reported in the previous research [38].

For the IP HEA, intrinsic dislocations were also found before indentation, as is shown in Figure S2(i). The atomistic configurations corresponding to different indentation depths were shown in Figure. S2(j–l). In this kind of alloy, entangled dislocation structure cannot be found in the different stages of indentation. Instead, stacking faults are either widened or narrowed during the process of plastic deformation. The evolutions of two specific stacking faults (marked as ‘1’ and ‘2’ in Figure S4(d)) are shown in Figure S4(a–f). Stacking fault 1 is widened because of the propagation of Shockley partial dislocations with Burgers vector of b₁  = 1/6[-12-1] and b₂  = 1/6[-211] in different directions, during the indentation process. Stacking fault 2, as shown in Figure S4(a–f), was narrowed through the propagation of Shockley partial dislocations with Burgers vector of b₃  = 1/6[-211] and b₄  = 1/6[-1-12] in opposite directions. A perfect dislocation, b  = 1/2[-101] was formed on the incoherent interface by the reaction of b₃  +  b₄  =  b . The formation of this perfect dislocation may lead to the strain concentration on the interface. The accumulation of arriving dislocations from the indenter tip results in server shear strain shown in Figure 4(d) and finally leads to the formation of new dislocations in the precipitated Cu (Figure 2(d)).

The effects of Cu concentration and temperature

Recent experiments clearly showed that elemental segregation can take place in HEAs to minimise the total Gibb's free energy. Elements, such as Cu and Fe, in a HEA, have positive mixing enthalpy, hence leading to elemental segregation [2,3,15,39]. To investigate the effect of the concentration of element Cu on the mechanical properties of HEA, the corresponding models with different Cu concentrations were employed in the simulations, and the concentrations of the other four elements were changed in equal proportion to normalise the total concentration. The effect of temperature on the mechanical properties of NS HEA was also studied, and the results were shown in Figure 3. The load-displacement curves at various temperatures were shown in Figure 3(a). In order to smooth the fluctuations in Figure 3(a) plotted using instantaneous values of F_z, a regression analysis using Locally Weighted Scatterplot Smoothing (LOWESS) is performed. The smoothed load-displacement curves were shown in Figure S8. With the increase of the indentation temperature, the stiffness of uniform HEA decreased. Besides, for the same load, the indentation depth increases with the increasing temperature. It also could be found that at a higher temperature, the curve showed more violent fluctuations, which was caused by the vibration of atoms and fading of the bonding strength between atoms. This phenomenon was also found in the experiments [13,40]. The nanoindentation load-displacement curves of HEAs with different Cu concentrations were shown in Figure 3(b). With the increase of the Cu concentration, the repulsive force that the indenter subjects to decreased, revealing the softening in HEA because of the low Young's modulus of Cu. It means that, if the Cu segregated to the grain boundary or the Cu-rich phase precipitated from HEA, the stiffness of the Cu-poor phase would be increased, but the Cu-rich phase and the newly formed interfaces between the different phases would decrease the stiffness of HEA.

OPEN IN VIEWER

Figure 3

Load vs. indentation displacement curves of the HEA during nanoindentation at various temperatures (a) and that of HEAs with different Cu contents at 300 K (b).

The evolution of shear strain

The shear strain distributions of HEAs underneath the indenter at full indentation depths were shown in Figure 4(a,c,e), while the shear strain distributions on the surfaces of HEAs were shown in Figure 4(b,d,f). All atoms were coloured according to the value of local atomic shear strain, where the blue atoms mean the lowest shear strain, and the red atoms represent the highest shear strain. The shear strain distributions of HEAs at different indentation depths were shown in Figures S5–S7. The distributions both underneath the indenter and on the surface show the shear strain anisotropy of all these three kinds of HEAs. It also can be found that the shear strain zone nucleated from the contact region between the indenter and HEA workpiece, and grew up towards the inner of the workpiece along the direction of the indentation and the directions which were about 45 degrees to the indentation force. The extending directions of the shear strain zone were inconsistent with the distributions of stacking faults discussed above. For the uniform HEA, the shear strain regions could extend further without any barrier, while the shear strain regions in the HEAs with Cu precipitation were blocked by the interfaces, both coherent and incoherent. At the coherent interface, almost no atomic shear strain was found, which could be explained by the formation of Lomer-Cottrell locks and Hirth locks. Strain concentration at the incoherent interface shown in Figure 4(e) was mainly caused by the lattice distortion induced by the server lattice mismatch and the formation of perfect dislocations (Figure S4(d)). Most partial dislocations react on the interface to form perfect dislocations and no such dislocations or shear strain region can migrate across the incoherent grain boundary. The migration and reaction of these Shockley partial dislocations can explain the lowest working strengthening rate shown by the HEA with incoherent Cu precipitation.

OPEN IN VIEWER

Figure 4

The shear strain distributions underneath the indenter at full indentation depths in HEAs of (a) no Cu segregation, (b) coherent interface Cu precipitation, and (d) incoherent interface Cu precipitation. The shear strain distributions on the surface of different workpieces were shown in (b), (d), and (f), respectively.