The novel single-phase high- and medium-entropy alloys (HEA/MEA) (Cantor et al., 2004; Yeh et al., 2004; Gludovatz et al., 2016; Jo et al., 2017; Yang et al., 2018; Gan et al., 2019; George et al., 2019; Cui et al., 2022), containing three or more elements with equal molar fraction in general, have emerged recently and aroused great interest due to their excellent mechanical properties at ambient and cryogenic temperatures. Previous studies (Otto et al., 2013; Gludovatz et al., 2014; Schuh et al., 2015; Gludovatz et al., 2016; Miao et al., 2017; Yoshida et al., 2017; Zhang et al., 2017; Ma et al., 2018; Yang et al., 2018; Slone et al., 2019; Yang M. et al., 2019) have demonstrated that the random distribution of the atoms lowers the energy penalty for the formation of stacking fault (SF), rendering low stacking fault energy (SFE). The SFE of such alloys can even be negative at cryogenic temperature (Zhang et al., 2017), resulting in high propensity for twinning and phase transformation. The transition of the dominant deformation mechanism from dislocation activities to deformation twins (DTs) then leads to better tensile and fracture properties than that at ambient temperature (Gludovatz et al., 2014; Gludovatz et al., 2016; Yang et al., 2018; Shi et al., 2019; Slone et al., 2019; Yang et al., 2020; Han et al., 2021; Ma et al., 2021). Moreover, recent work suggests that tailoring the local chemical order leads to non-uniform and locally tunable SFE in this sort of alloys (Ding et al., 2018), which may facilitate twinning and phase transformation at positions with lower fluctuated SFE.

Nano-grained (NG) metals and alloys usually have ultra-high strength, but show reduced ductility compared to their coarse grained (CG) counterparts. With increasing grain size, the ductility and strain hardening rate in most homogeneous structured metals are improved while the strength is sacrificed, an effect referred to as the strength–ductility trade-off (Koch et al., 1999; Valiev, 2004; Meyers et al., 2006; Ritchie, 2011; Wei et al., 2014). Materials with gradient nano-grained (GNG) structure, where the grain size increases from NG surface layers to CG core, have drawn widespread interest due to their excellent combination of strength and ductility (Wu X. et al., 2014; Wu X. L. et al., 2014; Wu et al., 2016; Li et al., 2017; Ma et al., 2019; Yang M.-X. et al., 2019; Yuan et al., 2019; Wu and Zhu, 2021). In the GNG structure, the mechanical incompatibility caused by gradient in grain size induces strain gradient, which leads to strong hetero-deformation induced (HDI) hardening and results in better mechanical properties (Yang et al., 2016; Wu and Zhu, 2021). In previous studies on CrCoNi MEA (Wen et al., 2020; Liu et al., 2021), this strategy has also been utilized to enhance the mechanical properties of the material.

Atomistic simulations have been proven to have advantages for investigating the microscopic deformation mechanisms of nanostructured metals, in which the real-time microstructural evolution of the system (snapshots), the atomistic and macroscopic stress and strain, and the stress state can be examined in detail (Yamakov et al., 2002; Schiøtz and Jacobsen, 2003; van Swygenhoven et al., 2004; Li et al., 2010). In previous studies (Widom et al., 2014; Li et al., 2016; Yuan et al., 2020; Ma et al., 2021), molecular dynamics (MD) simulations have been utilized to elucidate the atomistic deformation mechanisms in HEAs and MEAs. For instance, a hybrid Monte Carlo/MD method is applied to investigate the temperature-dependent chemical order in a HEA containing refractory metals Mo-Nb-Ta-W (Widom et al., 2014). The uniaxial tensile behaviors of the AlCrFeCuNi HEA are studied with MD simulation to analyze the evolution of defects (Li et al., 2016). For CrCoNi MEA, MD simulations have helped to study the nano-twinning behaviors (Yuan et al., 2020) and the effects of phase- and interface strengthening on the mechanical properties (Ma et al., 2021). Besides, MD simulations have also helped to investigate the deformation behaviors in hetero-structured materials (Li et al., 2015; Yuan et al., 2020). For example, in GNG structure of BCC Fe, MD method has demonstrated the stress state change and difference of deformation mechanisms in different-sized grains (Li et al., 2015). Using MD method, tensile strain partitioning is observed in CrCoNi MEA with heterogeneous grain structures under uniaxial tensile loadings (Yuan et al., 2020).

MD simulations may provide insights for the atomistic tensile deformation mechanisms either in HEA/MEA or in hetero-structured materials. In this regard, large-scale MD simulations were utilized in this work to investigate the tensile deformation behaviors of CrCoNi MEA with GNG structure and compare them with that of homogeneous NG structures with various grain sizes at cryogenic temperature.

The atomistic simulations were carried out utilizing the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) (Plimpton, 1995) and the force reaction between atoms was simulated by an EAM potential developed by Farkas (Farkas and Caro, 2018).

The stress-strain curves for the five structures are juxtaposed in Figure 2A. At the elastic stage, the NG structure with 12 nm grains demonstrates a slightly lower Young’s modulus, which could be attributed to the higher volume fraction of grain boundary and triple junction (Shen et al., 1995; Zhou et al., 2003). For the GNG structure and homogeneous NG structures with grain size larger than 24 nm, tensile stress was observed to rise with strain to a certain peak stress after elastic stage, where strong strain hardening is showcased, before gradually decreasing to a steady-state value. The higher deformation rate employed in MD simulations, which deviates from the experimental scenarios (Yang et al., 2018; Slone et al., 2019), is considered to account for the stress overshoot phenomenon (Schiøtz and Jacobsen, 2003; Pan et al., 2008; Vo et al., 2009). The peak stress reaches a value over 5 GPa, which was in line with previous computational studies of NG HEA and MEA under cryogenic condition (Yuan et al., 2020; Zhang and Shibuta, 2020). Moreover, the GNG structure exhibits a higher yield stress than homogeneous NG structures. In Figure 2B, the flow stresses for the five structures are computed by the average tensile stress within applied tensile strain of 7%–10%. The average grain size of the GNG structured model is approximated to be 64 nm, calculated as the weighted average of the grain size over the volume occupied by grains of this size in the model. The flow stresses of the homogeneous NG structures agree with the Hall-Petch relation (Hansen, 2004) and the previous MD study on Nanocrystalline Copper (Schiøtz and Jacobsen, 2003), which reports a critical grain size (∼15 nm) of FCC metal which leads to a maximum strength. The flow stress of the GNG structure, marked by the red dot, lies above the interpolated flow stress value of its homogenous NG structured counterpart, implying extra strengthening effects from the GNG structure, which will be discussed later.

In Figures 3A–D, snapshots from GNG structure at applied tensile strain of 2% and 4% of atomic tensile strain contours and on atomistic structures are demonstrated. Similar to previous study (Yuan et al., 2020), shortly after elastic deformation stage, most grains yield successively under the rising tensile load due to the variance in their size and orientation, which indicates an elasto-plastic transition. Therefore, Masing hardening (Skelton et al., 1997) should account for the strong strain hardening at this stage. Moreover, part of the reason for the higher yield stress of GNG structure could be manifest with the help of the snapshot. In the GNG structure, the defect density is higher in small grains during the elasto-plastic transition stage, approximately between 2% and 4% applied tensile strain, which implies that small grains carry more tensile strain at that stage. As a result, the elasticity of the large grains with generally higher Young’s modulus are better preserved so that the hardening decay of them are partially impeded by the small grains at this stage, which helps maintain the high strain hardening rate before 4% applied tensile strain and contribute to the higher yield stress of the GNG structure. After the elasto-plastic transition stage, plastic deformation begins to take place in nearly all grains, so that the large grains start to showcase less strength than the small grains according to Hall-Petch relation (Hansen, 2004), while the generally tougher small grains, on the contrary, begin to bolster the high stress value at applied tensile strain between 4% and 6%, as shown in Figure 2A.

The snapshots from GNG structure at applied tensile strain of 7% and 10% of atomic tensile strain contours and on atomistic structures are displayed in Figures 3E–H. Almost all grains are under plastic deformation with various defects. The low SFE of CrCoNi MEA at cryogenic temperature engenders massive stacking faults that form networks and impede further propagation of defects (Xiao et al., 2021). Besides, as shown in Figure 3G, DTs and HCP transformation are observed, which are reported to improve the strength of the structure (Yuan et al., 2020). In the tensile strain contours, there are noticeably more red areas in large grains, which represent areas with large atomic tensile strain. In this case, a tensile strain partitioning is intuitively demonstrated in the strain contours, which can be further justified by the statistical data in Figure 4.

For the GNG structure, the normalized average tensile strain values demonstrated in Figure 4 are approximated for small grains, (12, 24 nm), median grains, (24, 48 nm), and large grains, (48, 96 nm), separately. The average value of Exx in Green-Lagrangian atomic strain tensor E, corresponding to the elongation in tensile direction, is computed over all atoms for each grain size area, then divided by the applied tensile strain for a clearer comparison. As shown in Figure 4, before the end of elasto-plastic transition stage, the large grains are reported to accommodate less tensile strain than medium and small grains, in line with the previous observation in Figures 3A–D of lower defect density in large grains, which verifies that Masing hardening occurs at this stage and further bolster the view that the elasticity of the large grains are better preserved at this stage so that they might have made critical contribution to the strong strain hardening when the applied tensile strain is smaller than 4%. With the applied tensile strain increasing above 5%, evident partitioning of tensile strain is showcased in the GNG structure. The large grains have accommodated the most tensile strain, while the small grains the least, which could be visually perceived in Figure 3H, corresponding to the previous studies on hetero-structured materials (Cong et al., 2009; Park et al., 2014; Wu et al., 2016; Yuan et al., 2020). The reason is that the small grains are generally harder than large grains during plastic deformation, according to Hall-Petch relation (Hansen, 2004). The observed strain partitioning would result in superior mechanical properties through the following process. As the neighboring zones accommodate different plastic strains due to strain partitioning, strain gradients will come to exist near the zone boundaries to maintain the continuity of plastic strain. To accommodate the strain gradient, geometrically necessary dislocations (GNDs) will be engendered near these interfaces, which will further generate long-range HDI stress near the zone boundaries that lead to higher global strength (Yang et al., 2016; Zhu and Wu, 2019; Wu and Zhu, 2021). Besides, the GNDs lead to higher dislocation density, so that the defects would have a better chance to entangle with each other, which also strengthen the structure (Li et al., 2015). These two mechanisms stemming from the strain partitioning are both believed to account for the higher flow stress of the GNG structure than its interpolated counterpart from homogenous NG structure, as shown in Figure 2B.

Beside strain partitioning, the partitioning of stacking fault factor is also observed in GNG structure and showcased in Figure 5A. The stacking fault factor is also calculated for three grain size area, namely small grains, (12, 24 nm), median grains, (24, 48 nm), and large grains, (48, 96 nm), separately. It is computed by the sum of HCP atoms in the corresponding grain size area, which characterizes the dislocation motion since mobile partial locations leave behind stacking faults, divided by the length of grain boundary, which represents the chance of dislocation formation, and then divided by the applied tensile strain for normalization. As a result, the factor shall reflect the intensity of dislocation motion during the tensile deformation process. As demonstrated in Figure 5A, the stacking fault factor for each grain sizes area in GNG structure generally rises with increasing applied tensile strain, indicating the proliferation of dislocations on the whole model. Besides, the stacking fault factor is reported to be the lowest in small grains and the highest in the large grains, which implies lowest intensity of dislocation motion in small grains and highest in large grains. This result correlates with the observation mentioned above that the large grains have accommodated the most tensile strain while the small grains the least during plastic deformation. Typical snapshots of structure for 24, 48 and 96 nm grains in the GNG structured model at applied tensile strain of 10% are displayed in Figures 5B–D.

In Figure 6A, the stacking fault factors of 24, 48 and 96 nm grains in GNG structure are compared with those in homogeneous NG structures. The factors of 24 and 48 nm grains in GNG structure are generally higher than those in homogeneous NG structure, while the 96 nm case is the opposite, which could be visualized in the snapshots of the relevant typical structure in Figures 6B–E. In other word, the values of stacking fault factor for GNG structure lie closer to each other than that for homogeneous NG counterpart, which further demonstrates the HDI hardening effect within the GNG structure. The reason for closer distribution of stacking fault factor in GNG structure could be attributed to the typical stress state near the zone boundary between the hard zone with smaller grains and soft zone with larger grains. In the soft zone, the GNDs generated by strain partitioning pile up against the zone boundary and induce manifest back stress, so that the resolved shear stress is reduced since the back stress is opposite to the applied shear stress. As a result, higher external stress could be accommodated in the soft zone, which makes the soft zone appear stronger and moderates the dislocation motion. On the other hand, in the hard zone, the forward stress induced by back stress acts in the direction of applied shear stress, which leads to a higher total stress, so that the hard zone appears weaker and more defects are generated. Eventually, the back stress and forward stress together produce the HDI stress that ameliorate the mechanical properties of the material (Wang et al., 2019; Zhu and Wu, 2019; Wu and Zhu, 2021).

In the present study, large-scale MD simulations have been utilized to study the tensile behaviors of a CrCoNi MEA with GNG structure, and the corresponding atomistic deformation mechanisms have also been revealed. The main findings can be summarized as follows.

1) Due to the Masing hardening, strong strain hardening was observed in the GNG structure at the elasto-plastic transition stage.