The pursuit of high-performance structural materials that can endure extreme conditions is a formidable challenge in materials science. Such materials must not only exhibit superior strength and toughness, but also maintain these properties under high pressures and strain rates. The emerging concept of multiple principal element alloys, often termed medium- or high-entropy alloys (MEAs/HEAs), provides exciting opportunities to meet this challenge.1,2 In particular, CoCrNi-based MEAs/HEAs have shown remarkable damage tolerance at high strain rates due to continuous strain hardening facilitated by abundant plastic mechanisms.2,3

The mechanical properties of MEAs/HEAs have been reported at a strain rate of ∼10³ s⁻¹. For instance, Zhang et al.3 and Wang et al.4 subjected CoCrFeNi HEA and Fe₄₀Mn₂₀Cr₂₀Ni₂₀ HEA, respectively, to dynamic tension using a split Hopkinson tensile bar (SHTB). A good combination of high strength and ductility was found, originating from the dislocation drag effect, nanotwinning, and short-range order. Wang et al.5 characterized the dynamic tensile properties of CrFeNi MEA at room temperature (298 K) and cryogenic temperature (77 K). As the temperature decreases, a breakthrough with regard to the strength–ductility trade-off is achieved in CrFeNi MEA. At a strain rate of 3000 s⁻¹, the yield strength is increased from 920 MPa at 298 K to 1320 MPa at 77 K, while the uniform elongation increases by 28.5%.

Given the results of these studies on dynamic loading, it is expected that MEAs/HEAs will exhibit superior mechanical performance in extreme impact or shock scenarios. Cui et al.6 recently studied the shock compression and spallation of CoCrNi MEA using light-gas-gun plate impact, suggesting that the material can display high spall strength (around 4 GPa) and impact ductility at a strain rate of ∼10⁵ s⁻¹. Zhao et al.7 reported the deformation and failure behavior of CoCrNi MEA foil under extreme shock loading with strain rates up to 10⁷ s⁻¹. The networks induced by planar defects can confine the geometry and redistribute voids, thereby enhancing spall strength and damage tolerance. Shi et al.8 revealed the outstanding ballistic resistance capabilities of Fe₄₀Mn₂₀Cr₂₀Ni₂₀ HEA through cooperation of nanotwinning and deformation bands under an impact velocity of 500 m/s. However, the mechanical behavior can exhibit disparities under different loading thermodynamic paths.9–11 Previous studies of MEAs/HEAs at high pressures and strain rates have primarily focused on the thermodynamic path of the shock Hugoniot line.2,6,12,13

Recently, a powerful technique called magnetically driven ramp wave compression (RWC), providing ultrafast shockless dynamic compression (with strain rates ∼10⁵ to 10⁶ s⁻¹), has been employed to probe mechanical responses and unravel the plastic mechanisms of materials under compression.9,11,14 RWC experiments offer several advantages over shock compression. First, RWC generates larger compression with a lower temperature rise, owing to its shockless nature, relying solely on mechanical dissipation associated with microstructural evolution. Second, RWC provides a loading thermodynamic pathway that deviates from the shock Hugoniot state, yielding a continuous pressure (P)–specific volume (V/V₀) curve. The method enables substances to reach physical, mechanical, or chemical states unattainable through shock compression.9,15

Since it is difficult to detect in situ phenomena during dynamic experiments, the use of computational methods will allow us to better understand deformation mechanisms. Given that the space and time scales accessible by molecular dynamics (MD) remain limited, the strain rates in MD simulations are significantly higher than those in experiments and under service conditions, and the system and sample sizes are considerably smaller. To address the mechanical response on the macroscale quantitatively, one could adopt the crystal plasticity (CP) model to describe the collective behaviors of microstructure and defect assemblies. A great deal of effort has been undertaken in the last several decades to develop CP models aimed at capturing the mechanical behavior of crystals.16 For example, glide kinetics models describe the mechanical responses of metals for strain rates ranging from 10⁻⁴ to 10³ s⁻¹.17,18 These models are based on the thermally activated mechanism through which dislocations overcome obstacles with the assistance of thermal fluctuations.

Dislocations subjected to high strain rates (>10³ s⁻¹) could overcome the Peierls barrier easily without the aid of thermal fluctuations, with phonon drag controlling their motion.19,20 Mayer et al.21 took account of dislocation drag and microvoid nucleation in the CP model. The model provides a satisfactory description of the elastic precursor, unloading wave, and spall pulse for the shock loading of Al, Cu, and Ni samples. Recently, a model of shock-induced plasticity has been proposed by Yao et al.22,23 The controlling mechanisms of dislocation motion and density under shock compression are considered in this model, and it accurately captures the rate dependence. However, these models do not take adequate account of the evolution of micromechanisms. Therefore, it is crucial to conduct RWC experiments to further understand the underlying material physics of CoCrNi MEA, from which a deformation-mechanism-based CP model can be developed to accurately capture the macro- and mesoscopic mechanical responses under RWC.

This study aims to investigate the mechanical responses that deviate from the shock Hugoniot state of a CoCrNi MEA under RWC using a magnetically driven system. The RWC-induced micromechanisms are systematically revealed and characterized. On the basis of these deformation mechanisms, we propose a modified CP model, incorporating dislocation evolution and twinning information, that faithfully captures and unveils macro- and mesoscopic behavior under RWC.

The rest of the paper is organized as follows. In Sec. II, we present the material preparation, microscopic characterizations, and loading method. In Sec. III, we obtain the P – V/V₀ curves and dynamic yield strength under RWC. Microscopic characterizations reveal the associated micromechanisms, such as dislocation slip, stacking faults (SFs), nanotwin network, and Lomer–Cottrell locks. In Sec. IV, we discuss the dislocation density evolution and stress–strain maps of CoCrNi MEA during RWC on the basis of the modified CP model. Conclusions are summarized in Sec. V.

Equimolar CoCrNi MEA was synthesized by arc-melting Co, Cr, and Ni mixtures with 99.99% purity in a high-purity argon atmosphere. The ingots were remelted more than five times before the drop-casting process to ensure homogeneity. The as-cast CoCrNi MEA ingots were then cold-forged, resulting in a 50% reduction in thickness. Afterward, the alloy was annealed at 1173 K for 1 h to mitigate deformation-induced defects and promote recrystallization.

Electron backscatter diffraction (EBSD) measurements were performed to analyze the microstructural gradient along the direction of ramp wave propagation using a JEOL JSM-7100F field-emission scanning electron microscope (SEM). EBSD samples were prepared through mechanical polishing with Al₂O₃ suspension, followed by electrochemical polishing in a solution of HClO₄ (20%) and CH₃COOH (80%) at a direct current voltage of 15 V at room temperature. An acceleration voltage of 20 kV, a specimen tilt angle of 70°, and a working distance of 15 mm were used in the EBSD observations. A JEM-2100F transmission electron microscope (TEM) was operated at an acceleration voltage of 200 kV to reveal microscopic deformation mechanisms. The TEM samples were first mechanically ground to a thickness of 25 μm and then twin-jet electropolished with a 1:9 solution of HClO₄:C₂H₅OH and a voltage of 12–15 V, followed by Ar-ion milling to an electron-transparent thickness.

The RWC experiments were conducted using the CQ-4 magnetically driven system developed by the Institute of Fluid Physics, China Academy of Engineering Physics.24,25 This system can deliver a pulsed current with a peak value of 4 MA and a rise time of 500 ns.24 The loading configuration primarily consists of two parallel electrode panels (the upper and lower panels). When a large pulsed current J flows through the circuit, a strong pulsed magnetic field B is induced in the gap between the two plates. As a result, a Lorentz force is generated from J × B, leading to the formation of stress waves on the surfaces of the electrode panels. These stress waves propagate into the MEA samples along the thickness direction, ultimately compressing them to high pressures. The loading pressure P and pulsed current J are related by $P=\frac{1}{2}\mu k{\left(J/w\right)}^2$, where μ is the vacuum permeability, k is the structure factor, and w is the electrode panel thickness.

The EBSD inverse pole figure (IPF) indicates a fully recrystallized microstructure with equiaxed grains (grain size ∼160 μm) [Fig. 1(a)]. X-ray diffraction (XRD) confirms a single-phase face-centered cubic (FCC) structure, as presented in Fig. 1(b). Figure 1(c) shows a TEM image of low dislocation density and a grain boundary (GB) in the original CoCrNi MEA sample. Figure 1(d) presents an energy-dispersive spectroscopy (EDS) mapping of the CoCrNi MEA, highlighting the uniform distribution of Co, Cr, and Ni elements. The CoCrNi MEA exhibits a yield strength of ∼270 MPa and an ultimate tensile strength of up to 750 MPa under quasi-static tension [Fig. 1(e)].

RWC, a one-dimensional planar loading method, subjects two samples of varying thicknesses to extremely high stress levels within a few hundred nanoseconds. As shown in Fig. 2(a), the parallel Cu electrode panels ensure a uniform magnetic field distribution across the loading surface, and pressure propagates as a near planar wave through the panel thickness. The Cu electrode panel surface is highly sensitive to variations in the anode–cathode gap distance, owing to the current distribution and pressure loading. Finely machined and well-characterized electrodes are key for high-precision experiments, and the current-carrying surface of each electrode panel was flat to ∼1 mm with a 100 nm surface finish. The pressure applied to the sample results in a ramp wave that increases from zero to a maximum value. The samples are gradually compressed in a quasi-isentropic manner, owing to the ramp nature of the pressure drive. RWC aims to entirely avoid shocks by careful choices of sample thickness, drive pressure, and duration. The experimental conditions of RWC are detailed in Table SI (supplementary material). Pins 1 and 2 measure the free-surface particle velocity histories of the step samples, while pins 3 and 4 measure the loading velocity profiles using dual laser heterodyne velocimetry (DLHV) with accuracies of 1%.14,24

Three shots of RWC experiments with different peak loading pressures were performed. To ensure sample integrity, a sample recovery device was specifically designed for RWC. Figure 2(b) shows the recovered CoCrNi MEA sample. Figures 2(c)–2(e) display the time-resolved free-surface particle velocity histories of samples (RWC-1, RWC-2, and RWC-3). Velocity inflection points, indicative of an elastic–plastic transition process, were noted during the initial loading stage of the velocity profiles. Subsequently, a rapid increase in velocity occurred, reaching a maximum. With increasing charging voltage of the magnetically driven system, the peak velocity for each experiment rose from 0.62 to 0.84 km/s, with a loading rise time of ∼500 ns.

The primary method for analyzing ramp wave propagation is based on the approximation of self-similar motion.10Figure 3(a) illustrates the relationship between the Lagrangian wave speed C_L, measured by the difference in sample thickness and the loading time as Δh/Δt, and the in situ particle velocity u_p for each experiment. All the curves in Fig. 3(a) manifest two characteristic stages, namely, an initial short elastic loading stage and a subsequent longer plastic loading stage. The first kink just following the elastic loading stage signifies the elastic–plastic transition, where elastic waves transform into bulk waves with a sharp drop in wave speed. Following this transition, the relationship of C_L and u_p can be fitted as C_L = 4.408 + 3.306u_p. P is determined as $P={\int }_0^{u_p}{\rho }_0{C}_{L}d{u}_p$, where ρ₀ = 8.4 g/cm³ is the density of the CoCrNi MEA sample. V/V₀ is calculated as $V/V_0=1-{\int }_0^{u_p}d{u}_p/C_L$. The P–V/V₀ relationship for the CoCrNi MEA is obtained as $P=32.638e^{3.306\left(1-V/V_0\right)}+13.860e^{6.612\left(1-V/V_0\right)}-24.72$ and plotted in Fig. 3(b). The macroscopic strain ɛ of CoCrNi MEA samples is calculated as $\epsilon =1-V/V_0={\int }_0^{u_p}d{u}_p/C_L$. From the calculations, the strains are 4.7%, 5.5%, and 6.9% at peak pressures of 11.2, 13.6, and 17.1 GPa, respectively. The strain rate $\dot{\epsilon }$ under RWC is determined as $\dot{\epsilon }=\epsilon /\mathrm{\Delta }t$. The strain rates are calculated as 8.82 × 10⁴, 1.03 × 10⁵, and 1.38 × 10⁵ s⁻¹ at peak pressures of 11.2, 13.6, and 17.1 GPa, respectively. The experimental results, including u_p, P, V/V₀, ɛ, and $\dot{\epsilon }$, are also listed in Table I.

Unlike the shock Hugoniot line, fitted by multiple single points in shock compression, RWC offers a continuous P–V/V₀ curve for each experiment. Our group’s previous study evaluated the RWC’s uncertainty based on the Monte Carlo method, demonstrating that our magnetically driven RWC is a reliable precision physics experiment.26 The existing three-shot experimental P–V/V₀ curves match well with each other at the experimental loading pressures [Fig. 3(b)], effectively validating the accuracy of the P–V/V₀ curves. The sample remains adiabatic during RWC, owing to the loading time scale of only a few hundred nanoseconds. Isentropic compression implies an adiabatic and reversible compression process. Although RWC can meet the adiabatic conditions, the viscous nature and the strength effect of the solid material cause a certain degree of entropy increase.9,27 RWC can only be termed quasi-isentropic compression, and the P–V/V₀ curves measured by RWC serve as a reference for the isentropic line.

Additionally, we compared the P–V/V₀ curves of various materials, including the CoCrFeMnNi HEA,28 Al_0.1CoCrFeNi HEA,29 Fe₄₀Mn₂₀Co₂₀Ni₂₀ MEA,12 NiCoFeCrAl HEA,28 NiTi alloy,14 Ta metal,30 and W metal,31 as shown in Fig. 3(c). Notably, the P–V/V₀ curve of the CoCrNi MEA is comparable to that of Ta metal, known for its excellent blast-resistant properties and widespread application in military settings.32,33 Essentially, the CoCrNi MEA achieves similar compressibility and hardening ability to Ta metal under RWC. Moreover, the CoCrNi MEA also exhibits a high dynamic yield strength Y of 0.72 ± 0.04 GPa, outperforming other reported MEAs/HEAs.12,29,34,35 A detailed comparison of Y values between the CoCrNi MEA and other reported MEAs/HEAs is presented in Table SII (supplementary material). The excellent mechanical properties of the CoCrNi MEA are closely related to its chemical short-range orders (CSROs). CSROs, i.e., a regular arrangements of several atoms, are considered to be nanoscale precipitates that are essentially local compositional fluctuations. CSROs play key roles in dislocation nucleation and multiplication36 and dislocation energetics and dynamics,37 as well as affecting stacking fault energy.38 The existence of CSROs in CoCrNi MEA has been confirmed by atomistic simulations and experiments.39–43 CSROs can limit dislocation slip to a smaller scale and result in deformed subgrains to enhance the dislocation drag effect, especially when dislocation thermal activation gradually fails under RWC.3–5 As short-range thermal obstacles, CSROs may seriously hinder dislocation movement by increasing the energy barrier, thereby improving the hardening ability and yield strength of CoCrNi MEA under RWC.43

The microstructures of the post-deformation samples were characterized using EBSD techniques. Figures 4(a) and 4(d) present IPF maps of the RWC samples under 13.6 and 17.1 GPa, respectively, revealing a significant change in grain orientation. Figures 4(b) and 4(e) present grain boundary (GB) maps illustrating the formation of numerous low-angle grain boundaries (LAGBs, misorientations <10°). This indicates extensive activation of dislocation multiplication, interaction, and trapping within the grains. Figures 4(c) and 4(f) present density maps of geometrically necessary dislocations (GNDs). As the pressure increases from 11.2 to 17.1 GPa, the dislocation density rises from 5.84 × 10¹³ to 6.52 × 10¹³ m⁻². The dislocation density of samples is much lower than that of the severely deformed sample, owing to the lower strain under RWC. Remarkably, the RWC samples exhibit a distinct grain refinement compared with the original sample. Figures 4(g)–4(i) show the grain length distributions of the original and RWC-recovered samples in terms of the area fraction. The average grain length $\bar{L}$ of the original sample is 160 μm, and those of the RWC-recovered samples are 61 and 49 μm under 13.6 and 17.1 GPa, respectively. Grain refinement is an effective approach for enhancing material strength and toughness. Finer-grained alloys require higher stress for dislocation slip, owing to the hindering effect of GBs, thereby strengthening the material.

However, it remains unknown whether the grain refinement is attributable to dynamic recrystallization or microstructural evolution. Dynamic recrystallization necessitates that the temperature during deformation exceed the recrystallization temperature of the metal. The temperature of the CoCrNi MEA during RWC is calculated using the formula14$T=T_0\exp [\gamma \left(1-V/V_0\right)]$, where T₀ = 293 K is room temperature, γ = 2.306 is the Grüneisen parameter, and V/V₀ is the specific volume under RWC [Fig. 3(b)]. The temperature is estimated as 344 K at a loading pressure of 17.1 GPa, which is much less than the metal’s recrystallization temperature. Therefore, grain refinement should be mainly due to dislocation evolution and twinning mechanisms, rather than dynamic recrystallization.

Owing to the limited resolution of EBSD, the characterization of very fine microstructures is challenging. Therefore, transmission electron microscopy (TEM) with higher spatial resolution was employed to further investigate the microdeformation mechanisms of the RWC-recovered samples. Figure 5(a) reveals the occurrence of dislocation planar slips. Numerous stacking faults (SFs) are evident within the planar slip interior because of the ultra-low stacking fault energy (SFE) of the CoCrNi MEA [Fig. 5(b)].44 SFs act as barriers to dislocation motion, leading to the accumulation of dislocations around them. Figure 5(c) displays highly dense dislocation tangles, suggesting that dislocation tangles associated with planar slip serve as the primary mechanisms for dislocation evolution under RWC. The high-resolution TEM (HRTEM) image provided in Fig. 5(d) elucidates the atomic-level deformation mechanisms in the RWC-recovered samples. The image highlights the formation of several Lomer–Cottrell (L-C) locks within the grain interior, as indicated by the orange circles in Fig. 5(d). L-C locks arise from the reaction between leading partial dislocations in extended dislocations of two different slip planes. The effectiveness of L-C locks in strengthening and toughening lies in their capability to accumulate dislocations. Each L-C lock pins four dislocation segments, akin to a pinning point.45

Figure 5(e) demonstrates the high-density deformation twins (DTs) in the CoCrNi MEA under RWC, confirmed by the corresponding selected area electron diffraction (SEAD) pattern along the zone axis Z = [011] of the FCC structure in the inset. The SAED pattern reveals that a set of twin diffraction spots (indicated by the orange dashed line) appear alongside the matrix diffraction spots (indicated by the red dashed line). On the basis of the SAED pattern, we can confirm the activation of nanotwins in the CoCrNi MEA during RWC. The DTs induced by RWC have twofold effects on the toughening and strengthening of the CoCrNi MEA. First, the DTs can introduce new subgrain boundaries, promoting further grain refinement and reducing the mean free path of dislocations (dynamic Hall–Petch effect). This results in a substantial increase in the strength of the material. Second, the grain refinement and DTs hinder localized plasticity and delay the onset of necking, thereby enhancing the toughness of the material.46 Additionally, secondary twinning networks are observed in the RWC-recovered samples [Fig. 5(f)]. The inset in Fig. 5(f) shows two sets of twin diffraction spots along the twin direction in the SEAD pattern. Secondary twinning networks can confer higher strain hardening compared with single DTs. That is, secondary twinning networks can create more obstacles for dislocation motion, thereby contributing to enhanced strength. Moreover, these networks establish pathways that facilitate dislocation slip, enabling significant plastic deformation.47

Quantitative statistics of twinning volume fraction are crucial for understanding the deformation behavior of CoCrNi MEA under RWC. Owing to the limited spatial resolution of the current EBSD setup (the step size was taken as 1 μm), only twin bundles could be detected, rather than individual twins. Therefore, the twin bundles are marked as yellow lines in the EBSD band contrast (BC) maps, as demonstrated in Figs. 6(a) and 6(b). Similar EBSD images were taken from at least three different locations to evaluate the area fractions of the twin bundles, which are concluded to be (11 ± 0.6)% and (13 ± 0.8)% using Image-Pro Plus software at loading pressures of 13.6 and 17.1 GPa under RWC. The twin bundle is shown in the TEM bright field (BF) image [Fig. 6(c)] and dark field (DF) image [Fig. 6(d)]. The twin lamellae constitute an area fraction of about 45% within the twin bundle. Hence, the twinning volume fraction can be estimated by combining the twin-bundle volume fraction from EBSD images with the twin-lamella volume fraction within twin bundles from TEM results. Finally, the twinning volume fractions are estimated to be (5.0 ± 0.6)% and (5.9 ± 0.8)% at loading pressures of 13.6 and 17.1 GPa, respectively, under RWC.

In addition, we did not observe an FCC–hexagonal close packed (HCP) phase transition in RWC-recovered samples. Activation of the FCC–HCP phase transition requires that a critical dislocation density be reached during deformation. We can estimate the critical dislocation density for the phase transition in terms of the SFE as ρ = γ_sf/(ub³), where γ_sf is the SFE, b is the Burgers vector, and u is the shear modulus. Using values for the CoCrNi MEA of b ≈ 0.35 nm, γ_sf ≈ 22 mJ/m², and u ≈ 87 GPa,44 we estimate that the critical dislocation density for the FCC–HCP phase transition would be ρ ≈ 5.9 × 10¹⁵ m⁻². The dislocation density (5.95 × 10¹³ to 6.63 × 10¹³ m⁻²) is much less than the critical dislocation density for the FCC–HCP phase transition. Thus, the FCC-HCP phase transition did not occur in the RWC-recovered sample.

Deformation-induced microbands, marked by the red arrows in Fig. 7, emerge in the RWC-recovered samples. The SEAD pattern in the inset of Fig. 7(a) only shows a set of twin diffraction spots along the transverse direction. Thus, in the longitudinal direction, there are microbands rather than DT bands. Figure 7(a) is a BF TEM image, while Fig. 7(b) is a DF image. Close-up views of the microbands on the RWC-recovered sample are shown in Figs. 7(c) and 7(d). Meng et al.48 and Li et al.49 observed shear bands in CoCrFeMnNi HEA at cryogenic temperature (77 K) and under dynamic compression, respectively. By comparison, the microbands, marked by the red arrows, in Fig. 7, should be shear bands. Shear bands can cause material softening, such as through the shear band localization phenomena known to occur in metallic glasses.50 In the present study, microstructural characterizations exhibit the intense interaction of twins and shear bands. Dense deformation twins and shear bands intersect, forming a weave-like microstructure that can disperse deformation and enhance plasticity.48,49 As the strain increases, the shear bands will eventually expand into cracks, leading to material failure.

We also performed shock compression using a CQ-4 magnetically driven system. The detailed shock compression loading configuration and free-surface velocity profiles of CoCrNi MEA are presented in Fig. S1 (supplementary material). The microdeformation mechanisms of shock-recovered samples have been characterized by TEM, as shown in Fig. S2 (supplementary material). The deformation mechanisms include dislocation slip, SFs, DTs, and secondary twin networks. We did not observe the occurrence of shear bands in shock-recovered samples. To elucidate the differences in deformation mechanisms, we calculated the strain energy under RWC and shock compression using the equation $E={\int }_0^{t}PQdt$, where t is the loading time, P pressure, and Q deformation volume per unit time. The strain energies are calculated to be 69.7 and 106.7 J at pressures of 13.6 and 17.1 GPa, respectively, under RWC. The strain energy is 47.4 J at a pressure of 18.4 GPa under shock compression, as presented in Fig. S3 (supplementary material). Compared with RWC, the strain energy of samples under shock compression is lower and is not sufficient to activate shear bands.

The strain energy initially activates abundant planar defects in CoCrNi MEA under RWC. The continuous strain energy input renders planar defects inadequate to resist high-speed deformation, thereby leading to shear bands. On the whole, the intersections of these planar faults and shear bands produce complex nanointerfaces in three-dimensional space, contributing to the exceptional mechanical performance of CoCrNi MEA under RWC. In addition, CoCrNi MEA has a significant strain rate effect. The yield strength of CoCrNi MEA is 0.72 GPa under RWC, compared with 0.84 GPa under shock compression. This difference in yield strength is mainly attributable to the strain rate. The strain rates are calculated as 8.82 × 10⁴–1.38 × 10⁵ s⁻¹ under RWC and 1.16 × 10⁶ s⁻¹ under shock compression. The higher strain rate under shock compression leads to higher dynamic yield strength, owing to the positive strain rate sensitivity of CoCrNi MEA.3

In this section, we propose a modified CP model that takes into account dislocation motion, dislocation generation, and twinning mechanisms to capture and understand the macro- and mesoscopic mechanical responses of CoCrNi MEA under RWC. The basic framework of the CP model, which is based on crystal flow kinematics, is shown schematically in Fig. 8. The macroscopic responses are established on the basis of a hydrostatic–deviatoric split. The hydrostatic response is mainly controlled by the equation of state (EOS). From the mesoscopic aspect, the CP model adopts dislocation evolution and the twinning effect to establish a framework suitable for metallic material deformation under RWC.

The mechanical responses of a deformed crystal can be characterized by a flow kinematics model. The deformation gradient F = dy/dx is used to describe the deformation process. For a thermoelastic–viscoplastic system, the deformation gradient can be decomposed into three components as follows:51$$F=F^e{F}^t{F}^p,$$(1)where F, F, and F denote the elastic deformation gradient, thermal deformation gradient, and plastic deformation gradient, respectively. The spatial gradient of the total velocity is defined as$$L=\dot{F}{F}^{-1}=\stackrel{\cdot }{F^e}{F}^{e-1}+F^e{\dot{F}}^t{F}^{t-1}{F}^{e-1}+F^e{F}^t{\dot{F}}^p{F}^{p-1}{F}^{t-1}{F}^{e-1},$$(2)where the over dot denotes a time derivative. The spatial velocity gradient of the plastic deformation and thermal deformation can be expressed as follows:$${\dot{L}}^p={\dot{F}}^p{F}^{p-1}=\left(1-\sum _{\beta =1}^{N_{\text{tw}}}{\gamma }_{\text{tw}}^{\beta }\right)\sum _{\alpha =1}^{N_{\text{dis}}}{\dot{\gamma }}_{\text{dis}}^{\alpha }{s}_0^{\alpha }\otimes m_0^{\alpha }+\sum _{\beta =1}^{N_{\text{tw}}}{\dot{\gamma }}_{\text{tw}}^{\beta }{s}_{\text{tw}}^{\beta }\otimes m_{\text{tw}}^{\beta },$$(3)where ${\dot{\gamma }}^{\alpha }$ is the plastic shear rate in slip system α with slip direction $s_0^{\alpha }$ and slip plane normal $m_0^{\alpha }$ in the reference configuration, N_dis is the number of slip systems, N_tw is the number of twinning systems, and ${\dot{\gamma }}_{\text{tw}}^{\beta }$ is the plastic shear rate in twinning system β with twinning direction $s_{\text{tw}}^{\beta }$ and plane normal $m_{\text{tw}}^{\beta }$ in the reference configuration.

Considering the pressure dependence of the elastic constant tensor, which is significant for high strain rates,51 the stress can be defined as$$\sigma =C:{\epsilon }^e+\frac{1}{2}\left[{\epsilon }^e:\frac{\partial C}{\partial P}:{\epsilon }^e\right]\frac{\partial P}{\partial {\epsilon }_V^e}I+\frac{1}{2}\left[{\epsilon }^e:\frac{\partial C}{\partial T}:{\epsilon }^e\right]\frac{\partial T}{\partial {\epsilon }^e}+\frac{\partial T}{\partial {\epsilon }^e}\mathrm{\Delta }\eta ,$$(4)where $C={\left({\partial }^2\epsilon /\partial {\epsilon }^e\partial {\epsilon }^e\right)}_{{\epsilon }^e=0}$ represents the second-order elastic constants, ${\epsilon }_V^e$ is the volumetric component of the elastic strain tensor, and P is the pressure. Using Maxwell’s thermomechanical relation$$\frac{\partial T}{\partial {\epsilon }^e}=\frac{{\partial }^2\epsilon }{\partial {\epsilon }^e\partial \eta }=-T\mathrm{\Gamma },$$(5)the stress can be expressed as$$\sigma =C:{\epsilon }^e+\frac{1}{2}\left[{\epsilon }^e:\frac{\partial C}{\partial P}:{\epsilon }^e\right]\frac{\partial P}{\partial {\epsilon }_V^e}I-\frac{1}{2}\left[{\epsilon }^e:\frac{\partial C}{\partial T}:{\epsilon }^e\right]T\mathrm{\Gamma }I-T\mathrm{\Gamma }I\mathrm{\Delta }\eta ,$$(6)where Γ is the Grüneisen parameter.

The mechanical response is usually decomposed into a spherical part and a deviatoric part. The spherical part is mainly described by the EOS. Here, the stress tensor is split into hydrostatic σ_h and deviatoric S components as follows:$$\begin{array}{ll}\hfill {\sigma }_h& ={\sigma }_{\text{EOS}}+\frac{1}{3}\left({\epsilon }^{\prime e}:\text{C}:I\right)+\left[\frac{1}{2}\left({\epsilon }^{\prime e}:\frac{\partial \text{C}}{\partial P}:{\epsilon }^{\prime e}\right)\right.\hfill \\ \hfill & \left.+\frac{1}{3}\left({\epsilon }^{\prime e}:\frac{\partial C}{\partial P}:I{\epsilon }_V^e\right)\right]\frac{\partial P}{\partial {\epsilon }_V^e}-\frac{1}{2}\left[{\epsilon }^e:\frac{\partial C}{\partial T}:{\epsilon }^e\right]T\mathrm{\Gamma }-T\mathrm{\Gamma }\mathrm{\Delta }\eta \hfill \end{array}$$(7)and$$S=\ell :\text{C}:\left({\dot{\epsilon }}^e\right),$$(8)where ɛ′ is the deviatoric part of the strain tensor, and ℓ denotes a fourth-order operator that extracts the deviatoric part from a second-order tensor. The EOS term is replaced by the Grüneisen EOS$${\sigma }_{\text{EOS}}=\frac{{\rho }_0{C}_0^2\eta }{{\left(1-\lambda \eta \right)}^2}\left(1-\frac{\mathrm{\gamma }\mu }{2}\right)+\mathrm{\gamma }{\rho }_0{E}_m,$$(9)where ρ₀ is the density of CoCrNi MEA, C₀, λ, and γ are EOS parameters determined by the RWC, as listed in Table II, and E_m is the internal energy.

In the plasticity constitutive model, dislocation motion and density together control the plastic strain rate according to the Orowan equation$${\dot{\gamma }}^i=b{\rho }_D^i{V}_D^i,$$(10)where b is the Burgers vector, and ${\rho }_D^i$ and $V_D^i$ are the dislocation density and dislocation velocity, respectively, on slip system i.

Typically, a thermal activation mechanism is employed to describe dislocation motion at low to moderate strain rates. However, at high strain rates, dislocation motion encounters resistance from phonon drag. As a result, we adopt the phonon drag viscosity to govern dislocation motion above the critical shear stress τ_c. The equation governing the dislocation velocity can be written as follows:52$$\frac{d}{dt}\frac{m_0{V}_D}{\sqrt{1-{\left(V_D/C_T\right)}^2}}=\left(\tau -{\tau }_{\text{c}}\right)b-\frac{B_{\text{ph}}}{\sqrt{1-{\left(V_D/C_T\right)}^2}}{V}_D,$$(11)where C_T is the transverse sound speed, τ is the resolved shear stress, V_D is the dislocation velocity, and B_ph is defined as the effective viscosity caused by phonon drag. Under high strain rates, τ is described by the following Taylor hardening model:$$\tau ={\tau }_c+A_{I}Gb\sqrt{{\rho }_D},$$(12)where A_I is the hardening coefficient and G is the shear modulus.

Dislocations glide along the slip plane until they are either annihilated or immobilized by obstacles during deformation. The evolution of the dislocation density can be described by the following equation:53$$\dot{\rho }={\dot{\rho }}_{\text{HN}}+{\dot{\rho }}_{\text{mult}}-{\dot{\rho }}_{\text{anni}},$$(13)where subscripts HN, mult, and anni refer to homogeneous nucleation, multiplication, and annihilation, respectively.

Multiplication: Dislocations can be generated through the multiplication of preexisting dislocation segments. The dislocation multiplication equation can be written as54$${\dot{\rho }}_{\text{mult}}={\alpha }_{\text{mult}}\frac{\tau \dot{\gamma }}{G{b}^2},$$(14)where α_mult is the multiplication coefficient.

Homogeneous nucleation: Massive dislocation homogeneous nucleation, a fast-acting mechanism, becomes more important at high strain rates. Usually, the homogeneous nucleation rate is expressed as55$${\dot{\rho }}_{\text{HN}}={\alpha }_{\text{HN}}\frac{k_{B}T}{G{b}^3}\exp \left(-\frac{\mathrm{\Delta }G-\tau \mathrm{\Omega }}{k_{B}T}\right),$$(15)where α_HN is the homogeneous nucleation coefficient.

Annihilation: Dislocations of opposite signs on parallel slip planes annihilate when they pass within a certain capture distance. The annihilation equation is written as21$${\dot{\rho }}_{\text{anni}}={\alpha }_{\text{anni}}{\rho }_D^2{V}_{D}b,$$(16)where α_anni is the annihilation coefficient.

Considering the occurrence of twinning on CoCrNi MEA under RWC, the governing equation for twinning is used in this model. Marian et al.56 have highlighted the activation of twinning when the applied stress exceeds the critical twinning stress τ_tw. Twinning acts as a key strengthening and toughening mechanism during plastic deformation. The kinetics of twins follows a power-law expression57$${\dot{\gamma }}_{\text{tw}}^{\beta }=\left\{\begin{array}{c}{\dot{\gamma }}_0{\left(\tau /{\tau }_{\text{tw}}\right)}^{1/r},\tau >{\tau }_{\text{tw}},\hfill \\ 0,\tau <{\tau }_{\text{tw}},\hfill \end{array}\right.$$(17)where r is the rate-sensitivity power coefficient.

The developed CP model based on dislocation and twinning mechanisms has been implemented as a VUMAT (user-defined material subroutine) in ABAQUS/Explicit finite element software. Figure 9 shows a multiscale model in crystal plasticity finite element (CPFE) simulations. Three scales are considered: the microscale, representing an individual grain at length scales ranging from nanometers to micrometers; the mesoscale, representing the polycrystal at length scales ranging from micrometers to millimeters; and the macroscale, representing the continuum level at the millimeter scale.

A representative volume element (RVE) is utilized to examine and quantify the mechanical responses (Fig. 9). The planar dimensions of the model are consistent with those of the experimental sample. To obtain a polycrystalline model that has basically the same microstructure and grain size as the as-cast CoCrNi MEA, we performed the establishment and division of the polycrystalline model four times, using the Voronoi tessellation algorithm. The algorithm allocated random morphology, size, and crystalline orientation to simulate the CoCrNi MEA sample. The statistical results (Fig. S4, supplementary material) reveal that when the number of grains is 100, the average grain length of the model, $\bar{L}$ = 156 μm, is closest to that of the CoCrNi MEA, $\bar{L}$ = 160 μm. Loading velocity, as measured by pin 3 and pin 4 (Fig. S5, supplementary material), was imposed in the left face of model along the X direction. The right face of the model remained traction-free, while the upper and lower faces were constrained by periodic boundary conditions. The simulation used a Lagrangian mesh with a mesh size of 10 μm. The mesh-independence analysis is presented in Fig. S6 (supplementary material). The related parameters of the CP model are summarized in Table III, and the parameter determination is described in the supplementary material. The total duration of the calculations ensured that the incident wave traversed the entire sample. A C3D8R element (eight-node linear interpolation brick, reduced integration, hourglass control) was utilized in the present simulation.

Figure 10 presents comparisons between the free-surface velocity histories from simulation and experiment. The calculated results exhibit good agreement with the experimental wave profiles. Notably, the maximum error between the experimental and simulation results is less than 6% in plastic loading (Fig. S8, supplementary material), demonstrating the effectiveness of the proposed CP model in describing the mechanical responses of the CoCrNi MEA under RWC.

In contrast to the evolution of dislocation under quasi-static conditions, dynamic loading induces the generation and rapid evolution of massive dislocations within a very short time. It is important to recognize the dislocation evolution behavior under RWC. The evolution of the dislocation density of CoCrNi MEA, as predicted by the CP model, is presented in Fig. 11(a). This evolutionary process is divided into three stages during RWC. Initially, when the stress exceeds the critical threshold under RWC, dislocations initiate multiplication. However, this mechanism alone may not generate a sufficient number of dislocations to assist deformation under high strain rates and pressures. As a result, homogeneous nucleation of massive dislocation becomes essential. Stage I represents a combination of dislocation multiplication and homogeneous nucleation, significantly increasing the dislocation density.

Upon reaching a critical density, dislocations with opposite Burgers vectors annihilate each other, restoring the perfect lattice structure. This dislocation annihilation process, predominant in stage II, reduces the overall dislocation density. In stage III, the dislocation density becomes stable. The dislocation density values range from 5.95 × 10¹³ to 6.63 × 10¹³ m⁻² as the pressure increases from 11.2 to 17.1 GPa, matching well the results of EBSD analysis (Table SIII, supplementary material). As can be seen from the TEM image in Fig. 11(b), there is significant dislocation pile-up at the GBs, causing substantial stress concentration. Figure 11(c) illustrates that the equivalent stress is higher at GBs, which aligns well with the TEM observation of dislocation pile-up at the GBs in Fig. 11(b). Thus, the current CP model not only predicts the macroscopic free-surface velocity history, but also provides a more accurate depiction of the mesoscopic dislocation density evolution of CoCrNi MEA during RWC.

Local stress and strain significantly influence microstructure formation. Figures 12(a) and 12(b) illustrate the evolution of equivalent stress and strain in the CoCrNi MEA sample at a load pressure of 13.6 GPa. The stress pulse propagates from left to right until it reaches the free surface. The stress and strain distributions exhibit nonplanar characteristics, significantly diverging from the homogeneous geometry in isotropic models.60 This discrepancy can be attributed to the crystal anisotropy, which results in fluctuations and nonuniformities in the stress and strain fields. The maximum values of stress and strain of 9.7 GPa and 54%, respectively, occur at the grain boundaries.

Figure 12(c) presents strain maps for pressures ranging from 11.2 to 17.1 GPa, corresponding to strain rates from 8.82 × 10⁴ to 1.38 × 10⁵ s⁻¹. Increases in loading pressure and strain rate lead to significant localized strain within the sample. Typically, the presence of localized strain is considered a precursor to fracture in most metallic materials. However, owing to the low SFE of CoCrNi MEA,44 the localized strain triggers abundant planar defects, including twin networks, L-C locks, and high-density shear bands, effectively resisting localized deformation under RWC.

We have investigated the mechanical behavior and associated mechanisms of CoCrNi MEA by RWC experiment and simulation. The main conclusions are as follows.1.CoCrNi MEA exhibits outstanding dynamic responses and yield strength under RWC, attributable to grain refinement and multiple deformation mechanisms, including dislocation slip, SFs, twin networks, and L-C locks. High-density shear bands, as unique mechanisms, allow for sustained plasticity. Such a diverse set of deformation mechanisms suggests that CoCrNi MEA can accumulate a remarkably high density of nanointerfaces to promote strengthening and toughening during RWC.2.A modified CP model, incorporating dislocation and twinning mechanisms, has been developed to provide insight into the mechanical responses of CoCrNi MEA during RWC. The calculated results exhibit good agreement with experimental velocity profiles. Moreover, the simulations unveil the dislocation density evolution of multiplication, homogeneous nucleation, and annihilation during RWC, demonstrating the effectiveness of the CP model in describing macro- and mesoscopic mechanical behaviors.3.The inhomogeneous stress distribution and strain localization lead to a multilevel deformation mechanism that effectively resists fracture under RWC. Our comprehensive and systematic study here provides deep insights into the multiscale mechanical responses of CoCrNi MEA under RWC, which will benefit the rational design of MEAs with enhanced performance.

See the supplementary material for details of experimental conditions, dynamic yield strength, schematic diagram of the shock compression, micro-deformation mechanisms, the input strain energy, the average grain length distribution in the polycrystalline model, mesh-independent analysis and parameters determination of model.

Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant Nos. 92166201, 12002327, and 12272391).