In this work, the mechanical behaviors and cooperative deformation mechanisms for FCC/B2 composites with lamellar and core-shell structures in AlCoCrFeNi_2.1, Fe₂₀Co₂₀Ni₄₁Al_19, and Ni + NiAl alloys were studied. Furthermore, the universality of the relevant deformation mechanisms was explored by comparing the composites with different configurational entropies. Experimental studies show that the compositions of the FCC and B2 phases in the AlCoCrFeNi_2.1 alloy are Al_9.04Co_19.41Cr_20.77Fe_18.53Ni_32.23 and Al_27.56Co_13.24Cr_5.55Fe_10.21Ni_43.42 (at.%), respectively (All alloy compositions studied in this paper are in atomic percent except AlCoCrFeNi_2.1 and Ni + NiAl)^[34]. According to the energy dispersive spectroscopy results obtained from the B2 and FCC phase microregions of the FeCoNiAl alloy after approximately 83% cold rolling and short-time annealing at 660 °C, the compositions of the FCC phase and BCC phase are roughly Fe₂₇Ni₄₁Co₂₇Al₅ and Fe₁₉Ni₄₃Co₁₉Al₁₉, respectively^[26]. These values do not represent the overall alloy composition. To match experimental measurements, the FCC-phase compositions of the two alloys were set as Al_9.04Co_19.41Cr_20.77Fe_18.53Ni_32.23 and Fe₂₇Ni₄₁Co₂₇Al₅. In the Ni + NiAl model, the FCC phase was pure Ni. To simplify the ordered B2 phase, the B2 phase composition was uniformly set to NiAl. The primary contributing factors are summarized as follows. First, Fe, Co, and Cr exhibit low contents in the B2 phase of the two eutectic high entropy alloys (EHEAs)^[26,34]. Second, inadequate experimental evidence for the atomic site occupation of these elements prevents accurate atomic-scale modeling of the B2 phase. Third, this study mainly investigates the coordinated deformation mechanisms of the FCC/B2 composite. Although the B2 phase is simplified to pure NiAl, dislocation slip remains the dominant deformation mechanism in the B2 phase. This is consistent with experimental investigations on AlCoCrFeNi_2.1 and Fe₂₀Co₂₀Ni₄₁Al₁₉ (at.%) alloys^[25,26]. Accordingly, the B2-phase composition was temporarily simplified to NiAl.

To reveal the influence of phase distribution variations in core-shell structures on mechanical behavior, B2-core/(FCC-shell) and FCC-core/(B2-shell) models were also constructed for comparison. The atomic and dislocation structures of the different structural models represented by the AlCoCrFeNi_2.1 alloy are shown in Figure 1. Compared with the lamellar model, core-shell models contain more unknown atoms at the heterogeneous interface, indicating a rougher interface structure. Dislocation analysis reveals a small number of dislocations at the heterogeneous interfaces of each model. Only the FCC phase was varied to introduce entropy differences, while the B2-phase composition remained unchanged. The dimensions of all models are 20(X) × 20(Y) × 20(Z) nm³. The core region in the core-shell structure model is spherical. The volume fraction ratio of FCC to B2 phase in all models is fixed at V_FCC:V_B2 = 1:1, with a total number of atoms ranging from 675,000 to 695,000. The diameter of the core sphere calculated from the volume is slightly smaller than the total length of the model. Therefore, adjacent core structures appear relatively close to each other under periodic boundary conditions. Studies have shown that the FCC and B2 phases in EHEAs follow the K-S orientation relationship, namely $$ (11\bar{2})_\mathrm{FCC} $$//$$ (11\bar{2})_\mathrm{B2} $$, $$ (\bar{1}10)_\mathrm{FCC} $$//(111)_B2 and (111)_FCC//$$ (\bar{1}10)_\mathrm{B2} $$^[35,36,41]. Therefore, the crystal orientations of FCC and B2 along the X, Y, and Z directions are $$ [11\bar{2}] $$, $$ [\bar{1}10] $$, [111] and $$ [11\bar{2}] $$, [111], $$ [\bar{1}10] $$, respectively. Uniaxial tensile deformation simulations were performed along the Z-direction.

The atomic-scale simulations in this work were performed using the large-scale atomic/molecular massively parallel simulator software^[42]. The embedded atom method (EAM) potential function developed by Farkas et al.^[43] was used to describe the interactions between different atoms. Based on this potential, the calculated lattice parameter and single-crystal elastic constants (C₁₁, C₁₂, C₄₄) of B2-phase NiAl are 0.3 nm, 183.7, 112.6, and 93.3 GPa, respectively. For the FCC phase in AlCoCrFeNi_2.1, the corresponding lattice parameter and elastic constants (C₁₁, C₁₂, C₄₄) are 0.359 nm, 255, 213, and 173 GPa. All these calculated results exhibit good consistency with experimental measurements^[24]. Besides, the EAM potential has been widely used to study the mechanical behaviors and micro-deformation mechanisms of AlCoCrFeNi alloys^[44-47]. The time step was 5 fs. Before deformation, each model was first fully relaxed in an isobaric-isothermal ensemble to reach an equilibrium state at 300 K. A periodic boundary condition was applied along the three orthogonal directions. Previous MD studies on FCC and B2 structured alloy models have shown that strain rates ranging from 10⁷ to 10⁹ s^-1 generate no significant effect on the deformation mechanism^[39,48]. To improve computational efficiency, the strain rate was set to 10⁸ s^-1. The total engineering strain was set to 50% in order to obtain the evolution laws of different deformation systems under large plastic deformation. Simulation results were visualized using the Open Visualization Tool software^[49]. Dislocation types and atomic structures were analyzed using the dislocation analysis (DXA)^[50] and common neighbor analysis (CNA)^[51], respectively. The voids were quantitatively analyzed using the Gaussian density method built into the Construct Surface Mesh modifier^[52].

The stress-strain curves of three metal models with different non-uniform structures, as well as the strain values at different deformation stages, are shown in Figure 2. The whole deformation process was divided into four stages: elastic deformation stage, work-hardening stage (flow stress > 4 GPa), stress-stabilized stage (2.5 GPa < flow stress < 4 GPa), and fracture stage (flow stress < 2.5 GPa). For all models, stress increases approximately linearly with increasing strain during the elastic deformation stage, and the slopes of all stress-strain curves are nearly identical, indicating similar elastic moduli. At the elastic-plastic transition point (maximum stress also defined as the yield stress), the lamellar structure in all three alloy systems exhibits a significantly higher yield stress and corresponding yield strain than the core-shell structure [Figure 2A₂-C₂]. This result is consistent with experimental observations that the yield stress of lamella-structured AlCoCrFeNi_2.1 is higher than that of its core-shell structure^[25,29]. The yield stress of the lamellar model increases with decreasing elemental species, whereas that of the core-shell model is less sensitive to the number of alloying elements. For metal models with identical composition, yield strength varies among different core-shell structures. For the FCC-core models of AlCoCrFeNi_2.1 and Fe₂₀Co₂₀Ni₄₁Al₁₉ alloys, the yield stress is higher than that of the B2-core models, whereas the opposite trend is observed in the Ni + NiAl model.

After yielding, the stress of lamellar models decreases rapidly with increasing strain, then rebounds noticeably after reaching a minimum. For core-shell models, stress also fluctuates with increasing strain but with milder amplitude and maintains a high flow stress (> 4 GPa) [Figure 2A₁-C₁]. This regime is defined as the work-hardening stage due to pronounced work hardening in all models. During this stage, the corresponding strains in the AlCoCrFeNi_2.1 alloy models follow the order: lamella > B2-core > FCC-core. In the Fe₂₀Co₂₀Ni₄₁Al₁₉ models, the FCC-core model exhibits the smallest strain. For Ni + NiAl, the B2-core model exhibits the largest strain, followed by the FCC-core, and the lamella has the smallest strain. With decreasing element species, the strains of the work-hardening stage decrease significantly in lamellar models but show no obvious change in core-shell models [Figure 2A₂-C₂].

With further deformation, the flow stress of the lamellar Ni + NiAl model decreases rapidly to zero. However, the flow stresses for the other models slowly stabilize above 2.5 GPa at relatively large strains. Meanwhile, stress fluctuation amplitude diminishes with increasing strain [Figure 2A₁-C₁]. This regime is designated the stress-stabilization stage. During this stage, the strain of lamellar models decreases with reducing element species, and core-shell models display larger strains than lamellar models. Among all models, the lamellar Ni + NiAl model exhibits the lowest strain [Figure 2C₂]. This indicates that at the nanoscale, the plastic deformation capability of the lamellar structure decreases with the reducing element species, whereas the core-shell structure maintains favorable plastic deformation capability. In the late deformation stage (fracture stage), the lamellar Fe₂₀Co₂₀Ni₄₁Al₁₉ model, as well as the lamellar and FCC-core Ni + NiAl models, exhibit a sharp drop in stress compared with other models, indicating poor uniform deformation capability.

As described in Section 3.1, lamellar and core-shell models exhibit significant differences in mechanical behaviors during plastic deformation [Figure 2], and are strongly influenced by alloy composition. In this section, the yield strengths of all models are compared in detail. The main factors governing the yield strength are intrinsic physical characteristics at heterogeneous interfaces and the mechanical properties of single phases^[38,39]. The yield strengths of three metallic models with different non-uniform structures, the atomic potential energy analysis at heterogeneous interfaces in lamellar models with different compositions, the engineering stress-strain curves of FCC and B2 single crystals under uniaxial tension, and the stacking fault energies of FCC single crystals with different compositions are shown in Figure 12A-D, respectively.

For models with identical composition but different structures, the yield strength of the lamellar model is significantly higher than that of the core-shell structure [Figure 12A]. The initial dislocation densities of the three models for AlCoCrFeNi_2.1 alloy are 13.58 × 10¹⁴, 111.5 × 10¹⁴, and 95.6 × 10¹⁴ m^-2, respectively. This indicates that the initial DD at the heterogeneous interface is much lower than that of the core-shell model. In other words, a higher stress is required to activate dislocation slip, resulting in a higher yield strength.

As the number of alloying elements decreases, the yield strength of the lamellar model increases significantly [Figure 12A]. Detailed analysis of atomic potential energy at heterogeneous interfaces in lamellar models reveals that the number of low-potential-energy atoms increases with decreasing elemental diversity [Figure 12B], indicating that reduced interfacial potential energy strengthens interfacial stability. In addition, comparison of single-crystal mechanical behaviors shows that the yield strength of single phases follows the order: Ni > Fe₂₇Ni₄₁Co₂₇Al₅ > NiAl > Al_9.04Co_19.41Cr_20.77Fe_18.53Ni_32.23 [Figure 12C]. That is, the yield strength of FCC single crystals increases with decreasing alloying element species. Since the activated dislocations in the model are mainly SPDs, whose activation is closely related to unstable SFE, the SFEs of the three FCC single crystals were analyzed. The results show that the unstable SFE and the intrinsic SFE of Ni are the highest [Figure 12D], meaning the highest stress is required to activate SPD slip. The activation of dislocations leads to a decrease in stress. Thus, pure Ni exhibits the most significant stress fluctuations during deformation among all investigated single crystals. Fe₂₇Ni₄₁Co₂₇Al₅ and Al_9.04Co_19.41Cr_20.77Fe_18.53Ni_32.23 exhibit similar stacking fault energies, leading to small differences in yield strength. In summary, as the number of alloying elements decreases, the stability of heterogeneous interfaces, the yield strength of single crystals, and the SFE all increase, collectively enhancing the yield strength of lamellar models.

After entering plastic deformation, the characteristic mechanical behaviors of the composites depend on the activation of deformation systems and the dynamic evolution of micro-defects^[36,41]. In this section, the dynamic evolutions of micro-deformation mechanisms were analyzed in detail. Since both twins and stacking faults are characterized by HCP atoms, and their formation both generates coherent interfaces that dynamically refine grains and hinder dislocation slip^[55,56], the dynamic evolution of the HCP volume fraction was used to represent these two deformation configurations. The evolutions of micro-deformation configurations in the three-component alloy models with different non-uniform structures during deformation are shown in Figure 13. In the models with different compositions, a higher DD corresponds to a higher volume fraction of the HCP phase. However, the volume fraction of the HCP phase in all models is below 10%, indicating that the number of stacking faults and twins is limited and insufficient to induce significant work hardening in the later deformation stages. The B2-core models exhibit the highest DD, corresponding to the highest volume fraction of HCP atoms and a relatively low VSA [Fe₂₀Co₂₀Ni₄₁Al₁₉ (at.%) and Ni + NiAl]. This indicates that the activation of twinning and stacking faults is closely related to dislocation slip, and the coordinated deformation of dislocations, twins, and stacking faults inhibits void propagation, thereby promoting uniform deformation. In addition, the rapid propagation of voids in the lamellar and FCC-core models of Fe₂₀Co₂₀Ni₄₁Al₁₉ and Ni + NiAl is the main factor responsible for fracture. In summary, the limited number of activated twins and stacking faults in lamellar models readily leads to the concentration and rapid propagation of defects at heterogeneous interfaces, thereby deteriorating plasticity. For the core-shell models, when the phase with fewer deformation systems is located in the core, the plastic deformation capability of the metal can be optimized.

As shown in Figure 13, the density of activated dislocations decreases significantly with decreasing alloying element species. To reveal the physical mechanism, the effects of lattice distortion (LD, induced by configurational entropy) and SFE on dislocation slip are thoroughly discussed in this section. According to the classical formula for configurational entropy: $$ \Delta S_{\operatorname{mix}}=-\mathrm{R} \sum_{i}^{n} c_{i} \ln c_{i} $$. In this equation, c_i stands for the atomic percentage of the i-th element, R and n represent the gas constant and the total number of components, respectively^[57,58]. Due to differences in the atomic radii of alloying elements, Al_9.04Co_19.41Cr_20.77Fe_18.53Ni_32.23, Fe₂₇Ni₄₁Co₂₇Al_5, and pure Ni exhibit different degrees of LD. LD is usually quantified by the difference in atomic size δ, which is expressed as^[58-60]:

(1) $$ \delta=100 \sqrt{\sum_{i}^{n} c_{i}\left(1-\frac{r_{i}}{\bar{r}}\right)^{2}} $$

(2) $$ \bar{r}=\sum_{i}^{n} c_{i} r_{i} $$

Here, n denotes the element species, $$ \bar{r} $$ represents the average atomic radius, and c_i and r_i correspond to the atomic percentage and atomic radius of the i-th element, respectively. Accordingly, the configurational entropies of Al_9.04Co_19.41Cr_20.77Fe_18.53Ni_32.23, Fe₂₇Ni₄₁Co₂₇Al₅, and Ni are 1.54, 1.22, and 0 R, respectively. The LDs are 4.24, 3.28, and 0, respectively. Figure 14 shows the atomic structures of the FCC phases with different compositions. Their atomic arrangement further indicates that the degree of disorder decreases as the number of alloying elements decreases, i.e., both the configurational entropy and LD decrease. Therefore, lower configurational entropy leads to lower LD, which further reduces DD. This is consistent with MD simulation results of the deformation behaviors for CoCrNi-based medium-entropy alloys (MEAs)^[61-63]. Furthermore, compared with Al_9.04Co_19.41Cr_20.77Fe_18.53Ni_32.23 and Fe₂₇Ni₄₁Co₂₇Al₅, pure Ni exhibits a significantly higher SFE [Figure 12D], making SPDs more difficult to activate, which is another key factor responsible for the poor plastic deformation capability of the Ni + NiAl model. In summary, Chemical composition exerts direct impacts on configurational entropy, LD, and SFE. Notably, configurational entropy shows a positive correlation with LD. LD and SFE jointly dominate the activation of SPDs. While the nucleation of twins and SFs depends primarily on SFE, the dislocation storage capacity of the alloy is predominantly governed by LD.