Dynamic response of high-entropy alloys to ballistic impact.

High-entropy alloys (HEAs) are promising to provide effective antiballistic capability because of their superior mechanical properties. However, the twinning-active Cantor alloy is found less ballistic resistant, compared with its Mn-free companion. It is unclear how the HEAs resist ballistic impact and why Mn does not benefit the ballistic resistance. Here, we used molecular dynamics simulations to investigate the ballistic resistances of CrMnFeCoNi and CrFeCoNi and elucidate underlying mechanisms. It is shown that the alloys' ballistic resistances dominantly benefit from active dislocations generated at higher strain rates. Stronger atomic bonding and higher dislocation densities make the CrFeCoNi easier to be strain hardened with elevated toughness to resist high-speed deformation, while weaker atomic bonding and easier occurrence of dislocation tangling make CrMnFeCoNi less resistant to failure under ballistic impact. This work helps better understand the antiballistic behavior of HEAs and guide the design of armor and energy-absorption materials.

INTRODUCTION

High-entropy alloys (HEAs) have received substantial interest because of their nonconventional design strategy (), unique physical mechanism (–), superior mechanical properties (–), and others that are of significance to industrial or technological applications. For instance, AlCrFe2Ni2W0.2Mo0.75 coating provides excellent wear protection for ocean engineering equipment because of its good corrosion resistance, high hardness, and reaction products formed on the worn surface (). Addition of Nb in Fe0.25Co0.25Ni0.25(B0.7Si0.3)0.25 coating greatly benefits the wear resistance of the alloy with enhanced glass formation ability (). The mechanism for plastic deformation of HEAs is considered to be between those for conventional alloys and amorphous metals or involves both (, ). The Cantor alloy (), CrMnFeCoNi, is a representative HEA (, –). This HEA has unusual dependence of its mechanical properties on temperature, showing that its strength and ductility increase simultaneously with decreasing temperature (, , ). The high strength of CrMnFeCoNi at cryogenic temperature is considered to benefit from active deformation nano–twinning (TW), while the planar-slip dislocations contribute more to its plastic deformation at room temperature. Cantor alloy’s fracture toughness exceeds 200 MPa·m1/2 at both cryogenic and room temperatures, which is exceptionally superior to those of conventional alloys. The fracture strain of Cantor alloy is strongly affected by the strain rate within the range 10−3 to 10 s−1 at high temperatures (), while its yield strength is insensitive to the strain rate at different temperatures (, ). Low temperature is found beneficial to the strain hardening of CrMnFeCoNi (), and annealing-induced abnormal hardening is observed after cold work, which is attributed to the long-range ordered structure ().

Because of their superior mechanical properties, especially the excellent strain hardening ability, the HEAs have great potential to be used for ballistic protection. However, there are very limited reports regarding the application or potential application of HEAs in ballistic protection (–). Both dislocations and deformation TW were observed near bullet holes on HEAs and were considered responsible for their antiballistic performance (, ). However, in situ observations of dynamic response of the HEAs to ballistic impact are in lack or very limited for further fundamental understanding, and the influence of chemical composition to the alloys’ ballistic performance is not included in the experimental studies. Combining with finite element simulations to investigate the dynamic response of a HEA, AlCrFeCoNi, to bullet impact, Geantă et al. () performed bullet impact tests and showed that the ballistic resistance of the HEA was largely influenced by its chemical composition. However, this simulation method is ineffective to well reveal the dynamic behavior of HEA, since the numerical method is based on given mechanical properties. The mechanism for the dynamic mechanical behavior of materials at various high strain rates cannot be properly described by finite element simulation. Experimental results suggest that the strain hardening ability of HEAs can be enhanced at high strain rates because of a combination of multiple strengthening mechanisms including solid solution hardening, forest dislocation hardening, and TW hardening (–). The Cantor alloy, CrMnFeCoNi, is considered to have a high ballistic resistance because of its high resistance to shear localization () and the cooperation of dislocations and deformation TW as well (). The amorphization is noticed to be an additional deformation mechanism that also benefits strengthening and/or toughening of the alloy (, ). Currently, there is no suitable information reported in the literature for direct comparison between ballistic resistances of CrMnFeCoNi and those of other practical materials. However, compared with conventional alloys for armor protection and many commercial structural materials (), the Cantor alloy exhibits considerably higher capability of strain energy absorption, which is of importance to the ballistic resistance. For instance, the absorbed strain energy of Cantor alloy can be 6 to 10 times as large as that of 4340 steel (), which is used for military vehicles, structural units with high protection, armaments, and other protective parts ().

The Mn-free HEA, CrFeCoNi, which has static tensile properties comparable to those of CrMnFeCoNi (, , ), shows even higher strength and ductility when deformed at high strain rates (). At the Future Tech Expo in Taipei (December 2018), a team led by J. R. Yang at the National Taiwan University reported their ballistic impact tests, directly showing that the Mn-free HEA had better ballistic resistance than the Mn-containing HEA (see Fig. 1A). Thus, on the basis of the above-mentioned ballistic impact tests and the high strain energy absorption capability of CrMnFeCoNi in contrast with many commercial structural materials, the Mn-free HEA with higher ballistic resistance is more promising for armor and relevant applications than many other practical materials. However, the response of HEAs to ballistic impact is poorly understood, and it is unclear why Mn in CrMnFeCoNi weakened the ballistic resistance of this HEA. Understanding of the deformation mechanisms of Mn-containing and Mn-free HEAs under the ballistic impact condition for developing high-performance antiballistic HEAs is the driving force for the present study.

Fig. 1.

Ballistic impact on CrFeCoNi and CrMnFeCoNi HEA plates.

(A) Photos of CrFeCoNiMn plates after bullet impact tests (by courtesy of J. R. Yang at the National Taiwan University): bullet velocity, ~840 m/s; sample thickness, 1 cm. (B) Schematic diagram of the system for ballistic impact simulation; the initial speed of the rigid sphere (simulated bullet) is 25 nm/ps. (C) Two HEA plates with thickness of 2.29 nm after the ballistic impact. (D) Atomic snapshots of sectional views of HEA plates with thickness of 6.04 nm at different moments (0.5, 2, and 10 ps) during the ballistic impact (scale bar, 2 nm). Green atoms are in the FCC structure, red atoms are in the stacking faults (HCP structure), blue atoms are in the BCC structure, and white atoms are in the disordered structure. (E) Penetration depth of the rigid sphere into the two HEA plates with 6.04-nm thickness versus time. (F) Distributions of stacking faults and TW boundaries (TB) in the two HEA plates at 10 ps. (G) Distributions of dislocations in the two HEA plates at 10 ps. Dislocation line lengths for Mn-free and Mn-containing HEAs are 1669.9 and 984.101 nm, respectively.

RESULTS

Ballistic impact tests on HEA plates

J. R. Yang’s team performed ballistic impact tests to show the antiballistic performance of CrFeCoNiMn (x = 0, 0.3, 0.6) plates (see experimental details in the Supplementary Materials). It was observed that the bullet was stuck on the Mn-free HEA plate, while the two Mn-containing HEA plates were penetrated (Fig. 1A), demonstrating that the Mn-free HEA was more ballistic resistant than the Mn-containing ones. The ballistic resistance was further reduced as more Mn was added, indicating that adding Mn has a negative effect on the ballistic resistance. To get an insight into this issue, we performed molecular dynamics (MD) simulation to reproduce the ballistic impact tests and investigate performances of Mn-containing and Mn-free HEA plates in resisting ballistic impact. As shown in Fig. 1B, a high speed normal to the surface of HEA plate was given to a rigid sphere to simulate the ballistic impact process at room temperature (300 K).

Figure 1C presents results of the ballistic impact tests on the HEA plates having their thicknesses equal to 2.29 nm. As shown, after the impact by the sphere, there is more damage to the Mn-containing HEA plate, showing a larger perforation hole, compared with that on the Mn-free HEA plate, which is in agreement with the experimental observations shown in Fig. 1A. The bulge on the backplate is more pronounced for the Mn-containing HEA plate, suggesting that the structural integrity of the CrMnFeCoNi HEA plate is damaged more severely.

For more details about the dynamic responses of the HEA plates to ballistic impact, thicker HEA plates with 6.04-nm thickness were used to resist impact by the rigid sphere. Structural variations of the plates during ballistic impact are illustrated in Fig. 1D and movie S1. At the very beginning after contact occurred between the sphere and the HEA plate, recorded 0.5 ps after the simulation began, atomic bonds near the contacting zone were completely broken, leaving near-contact regions of the two HEA plates in disordered structures with forming the amorphous phase. The occurrence of amorphization rather than stacking faults is ascribed to the initial huge kinetic energy of the sphere associated with initial ultrahigh strain rate, which is consistent with experimental observations that amorphization occurred in deformed CrMnFeCoNi. Amorphization can be induced when subjected to deformation at high strain rates or under extreme conditions (, , ), e.g., amorphization was in boron carbide caused by ballistic impact (). The occurrence of amorphization in the two HEAs during the impact test implies that the HEAs have good ballistic resistances, since the strain-induced structural change or amorphization rather than cracking helps enhance the toughness of HEAs (, ), and this also demonstrates that strain-induced amorphization is an important mechanism for HEAs’ toughening.

Some unstable body-centered cubic (BCC) phases were found in the surrounding disordered regions in early stages of impact, especially in the Mn-containing HEA, which is consistent with observations in reported simulations of tension and compression tests for the Cantor alloy (). In the early stage, the depth the sphere penetrated into the Mn-containing HEA plate was slightly larger than that into the Mn-free one (Fig. 1E), implying that the Mn-containing HEA is less resistant to the impact deformation caused by the high-speed ejected sphere. This should be ascribed to weaker interatomic bonding in CrMnFeCoNi, since Mn has a lower electron work function (4.1 eV) than Cr (4.5 eV), Fe (4.5 eV), Co (5.0 eV), and Ni (5.15 eV) (), which weakens the overall metallic bonding of CrMnFeCoNi, in contrast with CrFeCoNi, leading to lowered elastic moduli and ultimate stress (, ). The correlation between the electron work function and metallic bonding strength has been well proven for alloy systems (, ). The weaker interatomic bonding in CrMnFeCoNi can also be reflected by its less negative cohesive energy (−4.01 eV per atom), compared with that of CrFeCoNi (−4.25 eV per atom). Atomic potential energy distributions of the two HEAs (fig. S4A) show that the potential energy in CrMnFeCoNi is higher (less negative) than that in the Mn-free one, and the distributions of Mn atoms (fig. S4B) and regions with less negative potential energy (fig. S4A) are highly overlapped in CrMnFeCoNi, indicating that Mn has less contribution to the overall bonding, compared with other elements, Cr, Fe, Co, and Ni.

The penetration of the sphere into the plate of the Mn-free alloy was well blocked after 2 ps, indicating the kinetic energy of the sphere was completely absorbed by the plate within about 2 ps. While for the Mn-containing alloy, this process took a longer time of about 2.5 ps, and the sphere finally stopped at a deeper depth in the plate. Figure 1 (D, F, and G) shows that in the Mn-free HEA plate, more stacking faults appeared along the moving path of the ejected sphere at 2 ps, and a series of stacking faults and a large amount of dislocation bands developed at 10 ps, while fewer stacking faults and dislocations were found in the Mn-containing HEA plate. For the Mn-free HEA plate, kinetic energy from the ejected sphere was absorbed to activate dislocations, which benefited hardness and toughness of the HEA, thus leading to a higher resistance to the impact deformation with reduced damage to the structural integrity of the plate. For the Mn-containing HEA plate, because of its weaker interatomic bonding, the kinetic energy from the sphere was absorbed more by atomic bond breaking instead of generation and movement of dislocations in the crystalline lattice, resulting in the disordered regions throughout the HEA plate. As a result, the structural integrity of the HEA plate was severely damaged. Thus, the higher resistance of CrFeCoNi to ballistic impact, compared with CrMnFeCoNi, should benefit from its stronger interatomic bonding and generation of more active dislocations during the ballistic impact. In addition to the intrinsic antiballistic capabilities of the two HEAs, their resistance to ballistic impact is influenced by the crystallographic orientation, grain size, and present or residual dislocations. To see how the three parameters influence the ballistic resistances of the HEAs, additional simulations of ballistic attacks to the HEA plates with different crystallographic orientations, grain sizes, and dislocation densities were performed. Results of the simulations are given in the Supplementary Materials (see figs. S1 to S3). It is demonstrated that the differences in crystal orientation, grain size, and dislocation density do not influence the observed phenomena. The Mn-free HEA always shows a higher ballistic resistance than the Mn-containing one, with smaller penetration depth and damaged region in the former.

Influences of temperature and strain rate on the resistances of the HEAs to deformation

The Cantor alloy is well known because of its superior mechanical properties benefiting from the deformation TW (). However, as shown in Fig. 1 (D and F), only minor deformation TW was observed during the impact process, and most of the observed stacking faults are intrinsic stacking faults (ISF) and extrinsic stacking faults (ESF). Therefore, the deformation TW in the HEAs should not be a dominant factor affecting their resistance to ballistic impact. Here, the simulated ballistic impact tests were performed under the condition that the HEAs were deformed at high strain rates and at room temperature. However, as reported (, ), highly activated deformation TW was observed at cryogenic temperature under the quasi-static tension condition. Thus, the influences of both temperature and strain rate need to be considered to understand the ballistic resistance of the HEAs and underlying mechanisms.

In general, during the plastic deformation, ISFs are first generated and react with dislocations to form ESFs, which are the precursor of deformation nano-TW and could be considered as a two-layer nano-TW embryo (, ). We calculated SFEs of ISF, ESF, and three-layer TW in the MD simulation for CrMnFeCoNi and CrFeCoNi at cryogenic (70 K), room, and high (1000 K) temperatures, respectively. The lower (more negative) the stacking fault energy, the more stable the stacking fault relative to the face-centered cubic (FCC) lattice. The MD-calculated SFEs shown in Fig. 2A are comparable to values obtained from density functional theory calculations (), in which the negative SFEs are considered to result from the thermodynamic metastability of FCC stacking sequence of HEA, which is related to the local atomic environment ().

Fig. 2.

Influences of temperature and strain rate on deformation resistances of CrMnFeCoNi and CrFeCoNi.

(A) SFEs of different stacking faults in the two HEAs at cryogenic, room, and higher temperatures. (B) Cryogenic temperature stress-strain curves of the two HEAs at different strain rates. The moments when deformation TW initially appears are marked by blue circles on the stress-strain curves.

In Fig. 2, one may see that for each HEA, as temperature increases, a higher energy barrier needs to be overcome to generate deformation TW from the stacking faults. The energy barrier is calculated as the difference between the lowest stacking fault energy (ISF for the Mn-containing HEA and ESF for the Mn-free HEA) and the TW stacking fault energy, which is illustrated in fig. S5. For each of the two HEAs, the higher the temperature, the higher is its energy barrier to the formation of deformation TW. The reason why the energy barrier to the formation of TW is higher at elevated temperatures is ascribed to the fact that the hexagonal close-packed (HCP)–FCC structural energy difference increases with the lattice expansion caused by temperature rise, so that the magnitude of stacking fault energy would increase with increasing temperature (, ), leading to an increase in the energy barrier to the formation of deformation TW. Therefore, the deformation TW is harder to be activated at room temperature than that at cryogenic temperature, which is consistent with experimental observations (, ). The results indicate that the contribution of deformation TW to the deformation resistances of the two HEAs decreases at elevated temperatures, which also implies that the role that dislocations play would be more important for their room temperature deformation resistance. According to Fig. 2A, the lowest SFE of the Mn-free HEA is lower than that of the Mn-containing one. Since a lower SFE (more negative) favors the dissociation of full dislocations into partial dislocations, dislocations should be more active or easier to be generated in CrFeCoNi once initial dislocations are generated. This also means that the constituent Mn suppresses the activation/introduction of dislocations and stacking faults. This hypothesis is validated in the following analysis corresponding to the presentations in Fig. 3 (B and C).

Fig. 3.

Stress-strain relationships and dislocation processes in CrMnFeCoNi and CrFeCoNi during simulated uniaxial tension tests at strain rates of 5 × 107, 5 × 108, and 5 × 109s−1, respectively, at room temperature.

(A) Stress-strain curves of the two HEAs at different strain rates. (B) Changes in dislocation densities in the HEAs with increasing strain. (C) Distributions of dislocations in the HEAs strained by 0.1 at different strain rates. Dislocations in green: 1/6<112> (Shockley), and in purple: 1/6<110> (Stair-rod). (D and E) Numbers of different types of dislocations in CrFeCoNi and CrMnFeCoNi, respectively, strained by 0.1. (F) Atomic snapshots of sectional views of CrMnFeCoNi and CrFeCoNi strained by 0.1 at different strain rates.

To estimate the influence of strain rate on resistances of the HEAs to deformation, MD uniaxial tension simulations were performed for CrMnFeCoNi and CrFeCoNi at different strain rates and cryogenic temperature. From the stress-strain curves shown in Fig. 2B, the Mn-free HEA has slopes of its stress-strain curves larger than those of the Mn-containing one in the elastic stage, indicating that the Mn-free HEA has higher elastic modulus with stronger atomic bonding, which is consistent with experimental measurements (). The Mn-free HEA is also tougher than the Mn-containing one at higher strain rates, reflected by its larger area under the stress-strain curve. The Mn-free HEA shows a higher ultimate strength than the Mn-containing one at higher strain rates as well, reflecting its higher strain hardening capability than that of the Mn-containing alloy. These results are in agreement with results of reported experimental tension tests (). It is also noticed that the deformation TW showed up later when higher strain rates were applied to the HEAs, indicating that the deformation TW is also harder to be activated at higher strain rates even at cryogenic temperature. Thus, the larger energy barrier to the occurrence of deformation TW at higher temperatures and higher strain rates should be the cause regarding why less activated deformation TW was observed in the simulated ballistic impact at room temperature. Thus, dislocations should have more contributions to the room temperature ballistic resistances of the HEAs.

Considering the heat generation during ballistic impact deformation, tension tests at different high strain rates in the range of 107 to 109s−1 at room and higher temperatures (300 and 1000 K) were also simulated for the two HEAs. Results of the simulation are given in the Supplementary Materials (see fig. S6 for comparison), which show that the stress-strain curves at each strain rate at different temperatures are similar, suggesting that the failure mechanisms of the two HEAs at the high strain rates do not change with increasing temperature, although the HEAs are softened at elevated temperatures.

Resistances of the HEAs to high-speed deformation at room temperature

For more detailed information, dynamic responses of CrMnFeCoNi and CrFeCoNi to uniaxial tension at 300 K were analyzed in MD simulations at high strain rates of 5 × 107, 5 × 108, and 5 × 109 s−1, respectively. From the stress-strain curves shown in Fig. 3A, one may see that the elastic modulus and ultimate tensile strength of the Mn-free HEA are higher than those of the Mn-containing HEA, which is similar to the cases at cryogenic temperature (Fig. 2B). The ultimate tensile strengths of both the two HEAs were increased when higher strain rates were applied, indicating that both the alloys were more strain hardened at higher strain rates. Figure 3 (B and C) shows that more dislocations were activated at higher strain rates for the two HEAs, especially when the strain rate was increased to 5 × 109 s−1. The higher strain hardening ability results from faster increase in the dislocation density as the strain rate is increased, leading to enhanced dislocation interactions and thus higher hardness and greater toughness as well. The increased dislocation density and enhanced strain hardening along with the increase in strain rate were also observed in experimental tension tests (). Such a behavior is different from those of conventional alloys, in which dislocation processes are suppressed while microcracking is promoted when deformed at such high strain rates (). Besides, less deformation TW was observed, compared with the situation at cryogenic temperature, implying that planar-slip dislocations played a predominant role in plastic deformation of the two HEAs (Fig. 3F). This is consistent with our theoretical analysis and the reported experimental observations (, ). Figure 3 (C to F) shows that the 1/6<112> partial dislocation is highly active in the Mn-containing HEA, which is in agreement with experimental measurements (, ), and the 1/6<112> partial dislocation is also the primary type of dislocation in the Mn-free HEA. With increasing the strain rate, in addition to more activated 1/6 <112> dislocations, 1/6 <110> dislocations were involved as well, especially for the Mn-free HEA deformed at the strain rate of 5 × 109 s−1, in which a much larger number of these two types of dislocations were activated, rendering the Mn-free HEAs to have more enhanced strain hardening ability and toughness, compared with the Mn-containing one. Thus, in the ballistic impact simulations shown in Fig. 1, one may see that more dislocations are present in the CrFeCoNi plate and the high-speed rigid sphere is blocked at a smaller penetration depth.

According to Fig. 3A, after passing the yielding point, there are many sharp peaks on the stress-strain curves of the two HEAs at the strain rate of 5 × 107 s−1, corresponding to dislocation generation and interactions. Such peaks are less apparent at the strain rate of 5 × 108 s−1 and even disappear at the strain rate of 5 × 109 s−1, indicating that dislocation processes become smooth at the higher strain rates. From Fig. 3B, it can be seen that at higher strain rates, initial dislocations showed up at larger strains, and more dislocations were activated once the initial dislocations appeared, leading to enhanced strain hardening as Fig. 3A illustrates. However, when the strain rate increased to 5 × 109 s−1, the huge number of rapidly activated dislocations would tangle up quickly and suppress further dislocation process, especially for the Mn-containing HEA (see in movie S2) in which the dislocation tangling occurs more easily. Mn has a larger atomic radius than other four elements, Cr, Fe, Co, and Ni (), which increases the lattice distortion and thus enhances pinning dislocations () and further promotes dislocation tangling in the Mn-containing HEA (). As a result of the dislocation tangling, the absorbed deformation energy would be consumed more by dislocation interactions and less by generation and movement of new dislocations. Since the Mn-containing HEA has weaker interatomic bonding, atom bonds in the tangled dislocations are easier to be broken to form disordered regions. Thus, taking the weakened bonding and lattice distortion into consideration, it becomes understandable why more disordered regions instead of the activation of planar slips were observed in the Mn-containing alloy (see Fig. 3F and movie S2). The earlier occurrence of dislocation tangling in the Mn-containing HEA at higher strain rates was responsible for the larger defected poor regions throughout the entire CrMnFeCoNi plate after the ballistic impact as shown in Fig. 1 and movie S1.

DISCUSSION

In summary, MD simulations were performed to investigate the ballistic resistances of the Cantor alloy (CrMnFeCoNi) and its Mn-free companion (CrFeCoNi) and elucidate corresponding underlying mechanisms. The ballistic impact simulation reproduced the reported experimental ballistic impact tests, which showed that Mn-free HEA was more ballistic resistant than the Mn-containing HEA. Compared with the Mn-containing HEA, the Mn-free HEA blocks the high-speed ejected sphere at a smaller penetration depth and maintains better structural integrity. The structural analysis shows that planar-slip dislocations are more active in the Mn-free HEA plate than in the Mn-containing one, in which structurally damaged zones are found throughout the Mn-containing plate. In addition, for the two HEAs, the amorphization also contributes to the impact energy absorption when the sphere strikes the HEA plates. Uniaxial tension tests were simulated to understand the mechanisms for the resistances of the two HEAs to high-speed deformation. It was observed that unlike the reported occurrence of highly activated deformation TW at low strain rates and cryogenic temperature, dislocations played a predominant role in the two HEAs to resist deformation at high strain rates. Ballistic resistances of both the two HEAs benefit from their more active dislocations generated at higher strain rates. The Mn-free HEA shows a better strain hardening ability and higher toughness during high-speed deformation, attributed to its stronger interatomic bonding and lower stacking fault energy that helps induce more active dislocations, leading to enhanced ballistic resistance, while dislocation tangling is found to occur earlier in the Mn-containing HEA when higher strain rates are applied, but its weaker atomic bonding due to the presence of Mn makes the structural integrity of CrMnFeCoNi easier to be damaged by ballistic impact. Other than the mechanisms such as deformation TW, amorphization, dislocation, and solid-solution strengthening, the atomic bonding strength is a fundamental parameter affecting the toughness of HEAs, e.g., adding a low EWF element (Mn) to an alloy system (CrFeCoNi) weakens the overall metallic bonding strength, leading to a lowered ability of the alloy to absorb strain deformation energy. On the basis of the obtained results, CrFeCoNi exhibits a higher capability of energy absorption and is thus more promising for ballistic protection, compared with CrMnFeCoNi. Sufficient attention needs to be given to the modification of the atomic bonding strength in addition to the plastic deformation mechanism when designing armor and energy-absorption HEAs and related materials.

MATERIALS AND METHODS

MD simulations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code (), with an integration time step of 1 fs. Interatomic interactions in the HEAs were described using the second nearest-neighbor modified embedded-atom method (2NN MEAM) potential (). The models with different orientations, polycrystalline structures, and dislocation densities were built using Atomsk (). Visual structural analysis was completed using the Open Visualization Tool (OVITO) (), in which stacking faults were identified by the adaptive common neighbor analysis (CNA) and dislocation distribution analysis was conducted by the dislocation extraction algorithm (DXA) (, ). Structures with two adjacent planes of atoms in local HCP arrangement are ISFs, those containing two planes of atoms in local HCP arrangement with an inserted plane of atoms in local FCC arrangement are ESFs, and a single plane of atoms in local HCP arrangement is identified as a twin boundary. Before the simulated ballistic impact and uniaxial tension tests were performed, bulk models of CrMnFeCoNi and CrFeCoNi were built, with elements initially positioned at FCC crystal lattice sites equally and randomly. The systems were heated from 300 to 1000 K for 200 ps and then cooled down to 300 K for another 200 ps to obtain equilibrium structures. The holding times in different stages were all 200 ps. The optimized structures of CrMnFeCoNi and CrFeCoNi have average lattice constants of 3.605 and 3.585 Å at 300 K, respectively, which are close to experimentally measured values (). Models with ISF, ESF, and three-layer nano-twin, as shown in Fig. 2B, were constructed by shifting atom layers with index of <111> along the <> direction based on a pristine FCC supercell. The stacking fault energy for a specific kind of stacking fault was calculated as the energy difference per unit area between the pristine FCC supercell and the supercell containing the stacking fault at 70, 300, and 1000 K, respectively.

For the ballistic impact simulation, single-crystal bulk HEAs were cleaved along the <111> direction to obtain HEA plates (15.98 nm × 15.88 nm) with thicknesses of 2.29 and 6.04 nm, respectively. The boundary in the <111> direction was nonperiodic, while boundaries in the surface plan were periodic and restricted in all directions. As shown in Fig. 1B, an iron rigid sphere (diameter, 3 nm) with an initial speed of 25 nm/ps was used as the simulated bullet to shoot the surface of HEA plates. The ballistic impact simulations were performed at room temperature (300 K). Interactions between atoms in the rigid sphere and atoms in the HEA plate, including Cr-Fe, Mn-Fe, Fe-Fe, Co-Fe, and Ni-Fe interactions, were described using the Lennard-Jones (L-J) 12-6 potential ()where r is the distance between atoms i and j, V(r) is the potential between atoms i and j, and ε and σ are depth of the potential well and equilibrium position between atoms i and j, which were calculated using the following equationswhere ε and σ are L-J potential parameters for interactions between the same kind of atoms, namely, Cr-Cr, Mn-Mn, Fe-Fe, Co-Co, and Ni-Ni (, ). Parameters for different atom pairs are shown in Table 1.

Table 1.

L-J parameters for interactions between different atom pairs.

Atom pair	ε/eV	σ/Å
Cr-Fe	0.514	2.329
Mn-Fe	0.518	2.325
Fe-Fe	0.527	2.321
Co-Fe	0.521	2.303
Ni-Fe	0.523	2.302

For uniaxial tension simulations, nonperiodic boundaries were applied to the single-crystal sample to construct tensile samples along the <111> direction with the sample size of 4.89 nm × 4.84 nm × 20.52 nm. Two layers of atoms at one side of the sample were restricted in all directions as the fixed end of the sample, and two layers of atoms at the other side of the sample were restricted in directions normal to the <111> direction as the loading end of the sample. Rigid displacement with different speeds along the <111> direction was applied to the loading end of the sample for tension tests at different strain rates (5 × 107, 5 × 108, and 5 × 109 s−1). The tension simulations were performed at 70, 300, and 1000 K, respectively.

The strain rates for the simulated tension tests were chosen on the basis of the consideration of the balance between the experimental ballistic strain rate (, ) and the computational resource. The ballistic strain rate is usually in the range of 106 s−1 but can be higher up to 109 s−1 (, ). The lowest strain rate (5 × 107 s−1) could be close to or a little higher than the strain rate according to the reported bullet speed-strain rate relationship (). However, the simulation showed that the increase in strain rate mainly influenced the strain hardening rate but not the failure mode. Thus, the higher strain rate or speed used in this study should not influence the conclusion regarding how the atomic structure is damaged by ballistic impact.

It should be mentioned that the real bullet and HEA plates are in the range of millimeters to centimeters, while the dimensions of MD simulation are in nanometers. However, the dimensional difference between the real ballistic tests and the MD simulation should not affect the elucidation of the mechanism for the damage caused by the bullet as revealed by the MD simulation. The main potential deviation due to the nanoscale effect is related to the space for the development of dislocations or stacking faults, which is smaller compared with that of the real-world experiment. The difference in scale, however, should not affect the calculated influence of Mn on the bonding strength and stacking fault energy, so that the MD simulation can capture key points for understanding and explaining the experimental observations.