Precipitation-assisted heterostructure in a FeMnCoCrCuC high entropy alloy enables superior mechanical property

Material preparation

In this work, Fe₅₀Mn_27-xCo₁₀Cr₁₀Cu₃C_x HEAs with x ranging from 0 to 3 at.% were studied. The Fe₅₀Mn₂₇Co₁₀Cr₁₀Cu₃ alloy was derived from the Fe₅₀Mn₃₀Co₁₀Cr₁₀ HEA by replacing an equivalent amount of Mn with 3 at.% Cu. This modification aims to increase the SF energy (SFE) of the alloy system, resulting in the absence of martensite both before and after deformation, which will be shown in the X-ray diffraction (XRD) and transmission electron microscope (TEM) analysis. Initially, high-purity metals (> 99.95 wt.%) were selected as raw materials, and alloys were melted in a vacuum arc melting furnace under an argon protective atmosphere. The melting process was repeated at least five times with continuous electromagnetic stirring. The as-cast alloys were subjected to a solution treatment at 1,200 °C for 4 h followed by air cooling to ensure uniform composition and microstructure. It should be noted that the alloys were not hot rolled, but were directly cold-rolled to avoid cracking of the copper-containing alloys during hot deformation^[34,35]. Subsequently, the alloys were cut into plates with dimensions of 40 mm in length, 25 mm in width, and 4.5 mm in thickness using an electrical discharge wire-cutting machine. These plates were then cold rolled at room temperature with five passes to reach a total reduction of 40%. The cold-rolled plates were encapsulated in vacuum quartz tubes, followed by annealing at 1,200 °C for two hours and air cooling. Afterward, the alloys underwent multiple passes of cold rolling at room temperature with a total reduction of 60%. Finally, these cold-rolled plates were annealed in a salt bath at 1,000 °C for three minutes. The detailed process of sample preparation is illustrated in Figure 1. In the following text, the alloys obtained through the above thermo-mechanical processing route are sequentially named C0, C0.5, C1, C2, and C3 alloys, according to their different C contents (0-3 at.%).

Figure 1. Schematic illustration of the preparation route.

Microstructure characterization

The phase composition of the alloy was characterized using a Smartlab XRD instrument equipped with CuKα1 radiation (λ = 0.154056 nm). The scanning range was 40-100°, with a scanning rate of 5°/min. Microstructures before and after tensile deformation were characterized using a JSM-7001F scanning electron microscope (SEM), a ZEISS Crossbeam 550 SEM equipped with an electron backscatter diffraction (EBSD) probe, and a JEM 2100F TEM. Compositions of the matrix and precipitates were also analyzed using high-precision Gemini SEM 560 equipment. For SEM and EBSD analysis, samples were initially mechanically polished with sandpaper to remove surface oxides. Subsequently, electrolytic polishing was performed using a mixed solution of HClO₄: C₂H₅OH=1:15 (vol.%) at a polishing voltage of 20 V for 20 s, maintaining the solution temperature at -20 °C. EBSD mapping was conducted with a step size of 80 nm, and the obtained data were processed and analyzed using the Channel 5 software. TEM samples were first mechanically polished to a thickness of 50 μm. They were then thinned using a TenuPol-5 twin-jet electropolisher at -25 °C and 25 V, using an electrolyte solution of HClO₄:C₂H₅OH=1:10 (vol.%). The sample coordinate system was defined by three orthogonal directions, i.e., rolling direction (RD), transverse direction (TD), and normal direction (ND). SEM and EBSD samples were taken from the longitudinal section (RD-ND plane) of the rolled plate, while TEM samples were taken from the rolling surface (RD-TD plane). The size and volume fraction of grains and precipitates for each material were statistically obtained from microstructure images using Image J software. To ensure the accuracy of the experimental results, these data were based on the average values obtained by characterizing five or more different regions.

Mechanical property testing

Uniaxial tensile tests and loading-unloading-reloading (LUR) cyclic tensile tests were conducted using an AG-XPLUS 100 kN universal testing machine at room temperature. The tests were performed along the RD of the plate with a strain rate of 1 × 10^-3 s^-1. It should be noted that both the rolled and annealed samples exhibit weak texture components (see Supplementary Figures 1 and 2). Accordingly, mechanical properties in the RD and TD directions show insignificant changes (see Supplementary Figure 3), indicating isotropic mechanical properties of the alloys. The more detailed information can be found in the Supplementary Note “Texture Analysis”. In the LUR tests, the specimens were first stretched to 1% engineering strain, and then unloaded to 30 MPa. Subsequently, the LUR process was repeated at every 4% engineering strain interval until the sample fractured. An extensometer was used to accurately measure and control the displacement during testing. The gauge length of the specimens was 24 × 3 × 1 mm³. To ensure the repeatability of the results, both tensile and LUR tests were conducted three times. Microhardness test was performed with a load of 50 g and a dwell time of 10 s. The hardness measurements were taken at 20 different locations for each sample, and the average value was reported.

Tensile properties

Figure 2A depicts the room-temperature tensile stress-strain curves of the C0, C0.5, C1, C2, and C3 alloys. As the C content increases, yield strength of the alloys gradually grows, while uniform elongation only decreases slightly. Specifically, yield strength (σ_s) and tensile strength (σ_b) of C0 alloy are 223 MPa and 535 MPa, respectively, with a uniform elongation of 57.1%. The C0.5 and C1 alloys show slight improvements in yield and tensile strengths, with yield strengths of 240 MPa and 265 MPa, tensile strengths of 566 MPa and 626 MPa, respectively. Both alloys maintain relatively high uniform elongations of 47.6% and 49.7%. In contrast, the C2 and C3 alloys exhibit a significant increase in yield and tensile strength. The yield strengths for the C2 and C3 alloys are 417 MPa and 500 MPa, with tensile strengths of 856 MPa and 979 MPa, respectively. The uniform elongations decrease slightly to 38.1% and 42.0%, respectively (detailed tensile properties are summarized in Supplementary Table 1). The corresponding tensile true stress-true strain curves and strain hardening rate curves are shown in Figure 2B and C. The strain hardening rate curves of the alloys consist of three stages. Taking the C3 alloy as an example, firstly, the strain hardening rate rapidly decreases with increasing true strain (Stage I, true strain < 0.03). Then, the rate of decrease slows down (Stage II, true strain is between 0.03 and 0.34). Finally, as deformation continues, the strain hardening rate rapidly decreases until the sample fractures (Stage III, true strain > 0.34). Notably, the strain hardening capability monotonically increases with the C content. Specifically, at a true strain of 0.2, the strain hardening rate for the C0 alloy is 1,351 MPa. This rate increases to 1,441 MPa and 1,560 MPa for the C0.5 and C1 alloys, respectively. Interestingly, starting from the C2 alloy, the work hardening rate of the alloy significantly increases, with the work hardening rates of C2 and C3 reaching 2,053 and 2,155 MPa, respectively.

Figure 2. Tensile properties and strain hardening curves of the C0, C0.5, C1, C2 and C3 alloys: (A) engineering stress-strain curves, (B) true stress-strain curves and (C) strain-hardening rate curves.

Initial microstructure

As mentioned earlier, the C2 and C3 alloys exhibited significantly enhanced mechanical properties compared to the C1 alloy, with notable increase in yield and tensile strengths, slight decrease in uniform elongation, and substantial improvement in work hardening rates. Based on these findings, we selected the carbon-free base alloy C0 as well as the C1 and C3 alloys as the subjects for further investigation. Figure 3 shows the microstructures and corresponding grain size distributions of the C0 and C1 alloys obtained by SEM. Both alloys exhibit completely recrystallized microstructures with similar average grain sizes of 19.9 μm and 18.8 μm, respectively. However, with increased C content, the C3 alloy presents a laminated structure characterized by the alternation of two distinct regions with different contrasts, as shown in Figure 4A. A magnified view of the interface within the red boxed region reveals that this laminated structure consists of CG and FG regions with significantly different grain sizes, both in a completely recrystallized state [Figure 4B]. The maximum grain size can reach up to 54.6 μm, while the minimum grain size is only 2.5 μm. By defining coarse and fine grains with a threshold of 10 μm, we conducted a statistical analysis of the grain sizes in these two regions at more than three sample locations. The results indicate that CG regions account for 43.4% of the alloy, while FG regions constitute 56.6%. The average grain sizes are 21.6 μm for the CG regions and 5.9 μm for the FG regions [Figure 4C and D]. Additionally, numerous spherical precipitates are observed at the grain boundaries, with a higher concentration along the grain boundaries of the FG regions compared to the CG regions. A few precipitates are distributed in bands within or across the grains (indicated by yellow arrows in Figure 4). The volume fraction of intergranular precipitates is 1.5%.

Figure 3. Microstructures of (A) C0 and (B) C1 alloys; (C) and (D) show grain size distributions corresponding to (A) and (B), respectively.

Figure 4. Microstructure of the C3 alloy: (A) macroscopic morphology; (B) enlarged view within the blue box in (A); (C) and (D) grain size distributions within the FG and the CG regions corresponding to (A). The yellow arrows in (B) indicate the band-like distribution of precipitates within or traversing grains. FG: Fine-grained; CG: coarse-grained.

To determine the type and structure of the precipitates, XRD measurements were conducted for the alloys. Unfortunately, only austenite was identified in the XRD pattern, and no precipitates were found [Figure 5A]. This may be due to the small size and low volume fraction of the precipitates (with a minimum size of tens of nanometers; see the text below), which prevents detection of the peaks from M₂₃C₆ precipitates. Linear fitting of the relationship between the lattice constant and C content indicates that an increase of 1 at.% C leads to a rise of 0.003 Å in lattice constant [Figure 5B]. Figure 6A shows the morphology of intergranular and intragranular precipitates in the FG regions of the C3 alloy obtained by TEM. Statistical analysis of precipitate sizes at multiple locations (including Figure 7) indicates that intragranular precipitates are smaller, with an average size of 73.1 nm [Figure 6B]. In contrast, intergranular precipitates are relatively large, with an average size of 182.4 nm [Figure 6C]. Selected area electron diffraction (SAED) patterns along the [0$$ \overline{1} $$1], [1$$ \overline{2} $$3], [111] and [112] zone axes confirm that the intergranular precipitates at location “1” are M₂₃C₆ [Figure 6D1-D4]. Similarly, SAED patterns along the [010], [1$$ \overline{5} $$0], [$$ \overline{1} $$30] and [$$ \overline{1} $$32] zone axes identify that the intragranular precipitates at location “2” are also M₂₃C₆[Figure 6E1-E4]. To further determine the composition of the precipitates, scanning TEM (STEM) combined with energy dispersive X-ray spectroscopy (EDS) was employed, as shown in Figure 7. Analysis of the CG regions reveals that the precipitates mainly exhibit a band distribution, accounting for only 3.4% in CG regions [Figure 7A]. The elemental mapping results indicate that these precipitates are rich in Cr and C, while the contents of Fe, Mn, Co, and Cu are relatively low. In the FG regions, the precipitates are uniformly distributed within grains, with a volume fraction of 10.7% in FG regions. Some large precipitates (with a diameter of ~94 nm) are also present at grain boundaries, presenting a similar chemical composition to those in the CG regions. Namely, the precipitates found in both CG and FG regions, as well as within and between grains, are intermetallic compounds rich in Cr and C. Another set of results obtained by using high-precision SEM for the region with triple junctions are presented in Supplementary Figure 4, with the compositions of the precipitates and matrix listed in Supplementary Table 2. The elemental segregation deduced here is consistent with that obtained by TEM. In summary, the C3 alloy exhibits a dual-heterostructure. This structure comprises CG and FG regions with significant differences in grain size, as well as non-uniformly distributed precipitates ranging from tens to over a hundred nanometers.

Figure 5. XRD patterns of the Fe₅₀Mn_27-xCo₁₀Cr₁₀Cu₃C_x alloys and the evolution of lattice parameter with increasing carbon content. XRD: X-ray diffraction.

Figure 6. Microstructure of intragranular and intergranular M₂₃C₆ precipitates in the C3 Alloy: (A) typical TEM image of M₂₃C₆ precipitates; (B and C) precipitate size distribution of intragranular and intergranular precipitates; (D₁-D₄) the SAED patterns of the intergranular precipitates taken from the [0$$ \overline{1} $$1], [1$$ \overline{2} $$3], [111] and [112] zone axes, (E₁-E₄) the SAED patterns of the intergranular precipitates taken from the [010], [1$$ \overline{5} $$0], [$$ \overline{1} $$30] and [132] zone axes.

Figure 7. Microstructure and elemental distribution of M₂₃C₆ precipitates in the C3 Alloy: (A) STEM image showing the band-like distribution of M₂₃C₆ precipitates in the CG region; (B) STEM image displaying M₂₃C₆ precipitates in the FG region, (A₁-A₆) and (B₁-B₆) the corresponding EDS mapping of Fe, Mn, Co, Cr, Cu and C elements. STEM: Scanning transmission electron microscope; CG: coarse-grained; FG: fine-grained; EDS: energy dispersive X-ray spectroscopy.

Microhardness

Vickers hardness measurements at different positions for each alloy are shown in Figure 8. The average hardness of the C0 alloy is 1.6 GPa. Due to the solid solution strengthening effect of C, the average hardness of the C1 alloy increases to 1.9 GPa. Additionally, because the grain size distribution in these two alloys is uniform, the hardness values fluctuate very little across different positions. In contrast, the average hardness in the CG regions of the C3 alloy reaches 2.5 GPa, while the FG regions exhibit a higher average hardness of 3.2 GPa. The difference in hardness between the CG and FG regions is not only attributed to grain size but also to the non-uniform distribution of precipitates. Furthermore, due to the highly inhomogeneous microstructure in this alloy, the hardness values in both CG and FG regions exhibit significant fluctuations.

Figure 8. Microhardness measurements for 20 randomly selected locations in C0 and C1 alloys, as well as FG and CG regions of the C3 alloy. FG: Fine-grained; CG: coarse-grained.

Microstructure after tensile deformation

To reveal the mechanisms underlying the significant enhancements in strength and work hardening rate of the C3 alloy compared to the C0 and C1 alloys, we first performed EBSD characterization on the three alloys with a tensile strain of 42% (fracture strain of C3 alloy, corresponding to 0.35 true strain). Figure 9A-C shows the orientation distribution maps, indicating that the grains in all three alloys are elongated along the tensile direction. The corresponding strain distribution is expressed by the Kernel average misorientation (KAM) maps, as shown in Figure 9D-F. Due to the relatively uniform grain distributions in the C0 and C1 alloys, high KAM values are identified only at large-angle grain boundaries [Figure 9D and E]. In contrast, the C3 alloy, with its heterogeneous intergranular and intragranular structure, exhibits generally higher KAM values within the microstructure [Figure 9F]. Detailed KAM value distributions are presented in Figure 9G-I. The C0 and C1 alloys exhibit relatively low average KAM values of 0.95° and 0.86°, respectively. In contrast, the C3 alloy demonstrates a significantly higher average KAM value of 1.79°.

Figure 9. EBSD maps of C0, C1, and C3 alloys after 42% tensile strain: (A-C) orientation distribution maps; (D-F) KAM maps and (G-I) misorientation distribution maps. High-angle grain boundaries, defined as those with misorientation angles above 10°, are indicated by thin black solid lines in (A-C). EBSD: Electron backscatter diffraction; KAM: kernel average misorientation.

Subsequently, we perform TEM analysis on the three alloys with a tensile strain of 42%, as shown in Figure 10. After tensile deformation, fine intersecting twins are observed in the C0 alloy with an average thickness of 19 nm and an average spacing of 29 nm [Figure 10A]. The corresponding SAED pattern is shown in Figure 10A1. The C0 alloy also contains a significant amount of dislocation cell structures [Figure 10B], which are observed near the [110] zone axis under g = (002) condition [Figure 10B1]. The deformation microstructure of the C1 alloy closely resembles that of the C0 alloy [Figure 10C and D], with the deformed twins having average thickness and spacing of 16 nm and 39 nm, respectively, along with high-density dislocation cell structures. For the C3 alloy, twinning activation is also observed, with the deformed twins exhibiting average width and spacing of 12 nm and 44 nm, respectively [Figure 10E and E1]. High-density dislocation cell structures are similarly present [Figure 10F and F1]. Additionally, extensive dislocation-precipitate interactions are identified within the C3 alloy. Representative uniform and band-like distributions of precipitates are depicted in Figure 10G and H, respectively, with the corresponding dislocation g vectors shown in Figure 10G1 and H1. Regardless of the precipitate distribution type, a significant amount of dislocation entanglement is observed around the precipitates, indicating strong dislocation hindrance effects by the precipitates. The precipitates maintain a prominent spherical morphology, suggesting that they are not sheared by dislocations.

Figure 10. TEM images of the C0, C1 and C3 alloys after 42% tensile deformation: (A-A₁), (C-C₁) and (E-E₁) deformation twins observed in C0, C1 and C3 alloys and the corresponding SAED patterns; (B-B₁), (D-D₁) and (F-F₁) dislocations within the alloys and the corresponding SAED patterns; (G-G₁) interaction between the uniformly distributed M₂₃C₆ precipitates and dislocations; (H-H₁) interaction between the M₂₃C₆ precipitates within a band-like region and dislocations. Dislocations are observed near the [110] zone axis with g = (002). TEM: Transmission electron microscop; SAED: selected area electron diffraction.

Construction of the dual-heterostructure

The dual-heterostructure in the C3 alloy, characterized by bimodal grain sizes and the non-uniform distribution of precipitates, contributes to high strength and excellent work hardening capacity [Figure 2]. It is crucial to have a deep understanding of the formation mechanism of these non-uniform structures, in which the M₂₃C₆ precipitates play a key role. We then first analyze the formation of precipitates in the C3 alloy. Microstructural observations of the C3 alloy after solid solution treatment reveal that grain diameter reaches several hundred micrometers [Supplementary Figure 5A]. Further TEM characterization confirms that even with an addition of 3 at.% Cu, no Cu precipitation or other intermetallic compounds formed in the alloy [Supplementary Figure 5B and C]. This indicates that M₂₃C₆ precipitates only form during the subsequent short-term annealing process. Subsequently, SEM observations are conducted on the samples annealed at 1,000 °C for 1 min and 2 min. The sample annealed for 1 min has already formed CG and FG regions inside. At this stage, the average grain size of the CG region was smaller (~13.8 μm) compared to the sample annealed for 3 min, but the difference in distribution of M₂₃C₆ precipitates has already appeared [Figure 11A]. Specifically, the FG regions contain numerous fine precipitates within the grains, whereas the CG regions have a lower density of precipitates. Additionally, precipitates with a size of ~90 nm are present at the grain boundaries [Figure 11B]. As the annealing time extends to 2 min, grains in the CG regions significantly grow, while the grain size in the FG regions remains almost unchanged [Figure 11C]. At this point, the precipitates inside the FG regions slightly increase in size, while their density decreases [Figure 11D]. This suggests that the precipitates exert a strong pinning effect on the grain boundaries.

Figure 11. SEM images of the C3 alloy annealed at 1,000 °C for different time durations: (A) 1 min and (C) 2 min; (B) and (D) are the enlarged view of the red dashed rectangles in (A)and (C), respectively. SEM: Scanning electron microscope.

The formation of the dual-heterostructure in the C3 alloy can be illustrated by a schematic diagram, as depicted in Figure 12. The homogenized alloy exhibits a uniform, equiaxed CG structure. During the subsequent room-temperature rolling process, the degree of deformation of individual grains varies due to their different initial orientations. The regions with a high degree of deformation can provide numerous sites and sufficient energy for the nucleation of new grains and precipitates. Conversely, the regions with less deformation have the lower energy stored, resulting in fewer nucleation sites for precipitates and recrystallization. During deformation, a high density of dislocations and deformation twins is formed. In the following annealing process, in that area with the higher deformation energy, a high density of precipitates and a greater number of recrystallized grains are developed. Twins can serve as fast diffusion pathways for C atoms, allowing some M₂₃C₆ precipitates to nucleate along the twin boundaries^[36]. As the annealing time increases, the recrystallized grains grow. When the moving grain boundaries encounter M₂₃C₆ precipitates, they interact with the precipitates via the well-known Zener pinning effect^[37,38]. Then, the high interfacial energy and relatively weak bonding in grain boundaries leads to precipitation coarsening. However, since the thermal stability temperature of twin boundaries is only around 625 °C for the Fe-Mn-based HEAs^[39], twins tend to decompose as the recrystallized grains grow, ultimately leaving behind the band-like M₂₃C₆ precipitates distributed within grains or across grain boundaries. These band-like precipitates that nucleate along the original deformation twin boundaries not only enhance strength but also weaken the precipitation of M₂₃C₆ along grain boundaries. Furthermore, the presence of precipitates significantly inhibits grain boundary migration^[30,35]. In FG regions, with a high density of precipitates, grain growth is restricted, resulting in the smaller grains. In contrast, in CG regions, the nucleation rate of recrystallization and precipitates is low, which has a weak hindering effect on grain boundary migration, resulting in rapid grain growth and formation of CG regions. Interestingly, as annealing time is further extended, the high-density precipitates in the FG regions continue to pin the grain boundaries effectively, while the lower-density precipitates in the CG regions allow further grain growth, thereby increasing the grain size difference between the CG and the FG regions.

Figure 12. Schematic illustration showing the formation of the dual-heterostructure in the C3 alloy during thermomechanical processing.

Strengthening mechanisms

The C3 alloy exhibits an excellent combination of strength and ductility, with the significantly improved yield and tensile strengths compared to the C0 and C1 alloys. Subsequently, we analyze the sources of strengthening in the C0, C1, and C3 alloys at their yielding point and an engineering strain of 42%. Since all three alloys are in the fully recrystallized state, the strength contribution from dislocations should be minor and close to each other^[40], so the dislocation-induced strengthening was ignored in the calculation. Their yield strength contributions include solid solution strengthening from atoms other than carbon (σ₀), interstitial solid solution strengthening from C atoms (σ_C), grain boundary strengthening (σ_G), and precipitation strengthening (σ_P).

For the C0 alloy, the strength comprises only σ₀ and σ_G. According to the classical Hall-Petch formula^[29], yield strength of the alloy can be expressed as:

where σ_G is the yield strength, d is the average diameter of the recrystallized grains, and k is the Hall-Petch coefficient. By fitting the relationship between grain size and yield strength for the C0 alloy with various grain sizes (as shown in Supplementary Figure 6, with tensile properties and Hall-Petch coefficient fitting illustrated in Supplementary Figure 7), σ₀ and k_C1 were determined to be 134 MPa and 416 MPa/μm^1/2, respectively.

Similarly, the Hall-Petch coefficient for the C1 alloy was determined as 423 MPa/μm^1/2. Due to the presence of precipitates in the C3 alloy, it is difficult to determine its Hall-Petch coefficient directly. The Hall-Petch coefficients for the C0 and C1 alloys are similar, thus we assume that the coefficient for the C3 alloy is ~420 MPa/μm^1/2, which is taken to be an average value of C0 and C1 alloys.

For the C0 alloy, with an average grain size of 19.9 μm, its grain boundary strengthening is 93 MPa. For the C1 alloy, with an average grain size of 18.8 μm, the grain boundary strengthening is 98 MPa. The C3 alloy can be subdivided into a CG region which occupies 56.6% of the area and has an average grain size of 21.6 μm, and a FG region which occupies 43.4% of the area and has an average grain size of 5.9 μm. Thus, its strength contribution can be evaluated using the rule of mixtures:

here, f_CG and f_FG are the area fractions of the CG and FG regions, and d_CG and d_FG are the average grain sizes of the regions, respectively. The grain boundary-induced strengthening for the C3 alloy was then determined as 126 MPa.

Next, we calculated σ_C for the C1 alloy through interpolation. Yield strength of the C1 alloy is composed of σ₀, σ_C, and σ_G, resulting in σ₀ = 33 MPa for the C1 alloy. To estimate the strength contribution from 1 at.% C, σ_C for the C0.5 alloy was also calculated as 8 MPa using the same method. Specifically, the grain boundary strengthening of the C0.5 alloy, with an average grain size of 18.4 μm [Supplementary Figure 8], is 98 MPa. By performing linear fitting on σ_C for the C0, C0.5, and C1 alloys [Supplementary Figure 9], we determined that each 1 at.% C contributed ~33 MPa of solid solution strengthening. The measured C content of the C3 alloy was 2.29 at.% [Supplementary Table 2], leading to an estimated σ_C of 76 MPa.

Finally, the C3 alloy contains a significant amount of M₂₃C₆ precipitates. Due to the minimum size of the precipitates being tens of nanometers, dislocations primarily move by bypassing these precipitates through the Orowan mechanism (as illustrated in Figure 10G and H). The strengthening contribution of precipitation can be calculated using^[41,42]:

where λ is the interparticle spacing, r is the radius of the precipitate, and b is the magnitude of the Burgers vector $$ (b=\sqrt{2} a / 2) $$. The value of λ can be approximately evaluated as follows^[41,43]:

here, d_P represents the diameter of precipitates, and V_P denotes the volume fraction of precipitates. As previously mentioned, the average diameter of the small precipitates within grains is 73.1 nm. The precipitate fraction in the CG region is 3.4%, while in the FG region, the volume fraction of precipitates is 10.7%. The average diameter of the larger intergranular precipitates is 182.4 nm, with a volume fraction of 1.5%. Therefore, the strength contributions from precipitates in the CG region, FG region, and intergranular areas are 56 MPa, 90 MPa, and 23 MPa, respectively. The total σ_P of the alloy is 169 MPa. Consequently, the calculated total yield strength of the C3 alloy is 505 MPa, which is consistent with the measured yield strength of 500 MPa.

At an engineering strain of 42%, the flow stress originates from σ₀, σ_C, σ_G, σ_P, dislocation strengthening (σ_D), and deformation twinning-induced strengthening (σ_T). Firstly, after tensile deformation, high-density dislocations are generated in the alloy, which plays an important role in increasing the flow stress. The dislocation density (σ_P) is calculated using^[14,29]:

where θ is the misorientation angle, evaluated by the average KAM value obtained from EBSD, and μ is the step size of EBSD mapping (0.08 μm). The calculated dislocation densities for the C0, C1, and C3 alloys are 2.80 × 10¹⁵, 2.54 × 10¹⁵ and 5.28 × 10¹⁵ m^-2, respectively. The strengthening contributions due to dislocations (σ_D) for the three alloys are calculated according to^[44]:

where M is the Taylor factor (3.06) and α is a constant (0.2)^[45]. Therefore, the contributions from dislocations in the C0, C1, and C3 alloys are 364 MPa, 347 MPa, and 500 MPa, respectively.

Additionally, deformation twining occurs in the alloys during tensile deformation [Figure 10]. The continuous activation of these twinning significantly refines the microstructure, thereby enhancing the flow stress of the material. By subtracting σ₀, σ_C, σ_G, σ_P and σ_D from the measured yield strength, the σ_T values for the three alloys are calculated to be 137 MPa, 258 MPa, and 382 MPa, respectively. The results indicate that the contribution of twin boundaries to strength of the C3 alloy is the largest, which may be attributed to the limited carbon content of only 2.29 at.% in the alloy matrix. This means that the practical increase in SFE induced by interstitial carbon is not high enough to substantially change the deformation mode. Additionally, grain size is another important factor affecting the activation of mechanical twins^[16,46]. The presence of coarse grains in the C3 alloy tends to promote extensive twining, leading to the more significant strengthening induced by the twin boundaries. The strength contribution for each alloy is illustrated in Figure 13. Compared to the C0 alloy, the yield strength increment of C3 alloy mainly comes from precipitation strengthening (145 MPa) and interstitial solid solution induced strengthening (76 MPa). This explains why both CG and FG regions of the C3 alloy exhibit significantly higher microhardness than the C0 alloy. After tensile deformation, the primary source of flow stress in the alloys is dislocation strengthening, which is attributed to the complex interactions between precipitates and dislocations [Figure 10G and H]. Additionally, the dynamic Hall-Petch effect induced by deformation twinning also contributes to the high flow stress in the C3 alloy. It is important to note that the total strength discussed above is considered as the sum of contributions from individual strengthening mechanisms^[4,47]. However, in the context of multiphase alloys, this assumption may not be entirely accurate, as the matrix of these alloys is essentially in a state of “overall solute”, lacking clear solute boundaries, and the various strengthening mechanisms are not completely independent of one another^[48,49].

Figure 13. Strength contributions in the C0, C1 and C3 alloys at: (A) the yielding point and (B) 42% tensile strain.

HDI strengthening and plastic deformation mechanisms

The C3 alloy demonstrates an excellent strength-plasticity combination, which can be attributed to its unique dual heterostructure. In this case, the CG region acts as the soft domain, while the FG region is the hard domain. The uneven distribution of precipitates in the CG and FG regions further enhances the differences in mechanical properties between the different regions. Specifically, the Vickers hardness of the CG region in the C3 alloy is measured to be 2.5 GPa, while that of the FG region can reach 3.4 GPa. Similarly, the micron-sized recrystallized grains are viewed as the soft domain, whereas the nanosized M₂₃C₆ precipitates are regarded as the hard domain. At the onset of deformation, both soft and hard regions undergo elastic deformation simultaneously. As deformation proceeds, the soft region begins to undergo plastic deformation, while the hard region remains in the elastic state. To facilitate the coordinated deformation between the different regions, GNDs are generated at the interface between the soft and hard regions. Results from EBSD analysis indicate that under the same strain, the dual heterostructure of the C3 alloy exhibits approximately double the dislocation density compared to the equiaxed C0 and C1 alloys. Specifically, the dislocation densities for C0, C1, and C3 alloys are 2.80 × 10¹⁵, 2.54 × 10¹⁵, and 5.28 × 10¹⁵ m^-2, respectively [Figure 9D-F].

To evaluate the HDI strengthening and hardening resulting from the heterostructure, we conducted LUR cyclic tensile experiments on the C0, C1, and C3 alloys. The engineering stress-strain and true stress-strain curves for each alloy are presented in Figure 14A and B, with an enlarged view of the individual hysteresis loops depicted in Figure 14C. The HDI stress is calculated as the average of the unloading stress (σ_u) and the reloading stress (σ_r)^[50,51], as follows:

Figure 14. (A) Engineering stress-strain curves of the C0, C1 and C3 alloys obtained by LUR tests; (B) the corresponding true stress-strain curves; (C) an enlarged view of typical hysteresis loops in the shadow area in (B); (D) HDI stress as a function of true stress. LUR: Loading-unloading-reloading; HDI: hetero-deformation-induced.

As shown in Figure 14D, both C0 and C1 alloys exhibit relatively small hysteresis loops at all stages of deformation, indicating low HDI stress for both, with a similar rate of stress increase with straining. In contrast, the C3 alloy displays larger hysteresis loops, demonstrating significantly higher HDI stress than C0 and C1 alloys at all strains, with the highest ratio of HDI stress to true strain. This indicates that the C3 alloy, due to its dual heterogeneous structure, has a greater HDI strengthening and hardening effect compared to the C0 and C1 alloys with uniform microstructures.

Furthermore, the C3 alloy exhibits optimal strain hardening ability while the strength is elevated, which can be ascribed to the following. Firstly, similar to the C0 and C1 alloys, the C3 alloy still shows significant twinning activation during tensile deformation [Figure 10]. The continuous activation of twinning refines the microstructure, thus providing the capacity for sustained plastic deformation and good work hardening^[52]. The activation of twinning is closely related to the SFE, which for the solid solution-treated C3 alloy is 37.2 mJ/m² [Supplementary Note and Supplementary Figure 10]. For the cold-rolled and short-time annealed alloy, the SFE should be lower than this value due to a certain amount of C element precipitating from the matrix as precipitates, thereby promoting the activation of twins^[53,54]. Secondly, the multiscale M₂₃C₆ precipitates which are unevenly distributed both within grains and between the neighboring grains also hinder dislocation motion, thereby increasing the work hardening rate of the alloy^[55,56]. Finally, the difference in mechanical properties between the coarse and fine grains in the C3 alloy is a significant source of the HDI stress, and the higher density of precipitates within the FG regions increases the strength difference between coarse and fine grains. Additionally, another heterostructure forms between the precipitates and the matrix. This dual-heterostructure ultimately leads to pronounced HDI strengthening and hardening in the C3 alloy.