2024 Volume 64 Issue 6 Pages 1067-1077
Fe50Mn30Co10Cr10 dual-phase metastable high-entropy alloys (HEAS) have gained significant attention for their outstanding mechanical properties. However, limited research has explored the relationship between grain size and strain rate sensitivity (SRS) in dual-phase HEAS. Current investigations primarily focus on pure metals and single-phase FCC HEAS. To address this gap, this study examines the impact of grain size on the deformation behavior and SRS of TRIP-(Fe50Mn30Co10Cr10)97Al3 dual-phase HEAS. Two variants of dual-phase HEAS were prepared, distinguished by their grain sizes (2.86 µm, labeled Fine Grain or FG, and 5.25 µm, termed Coarse Grain or CG), via the vacuum melting method. Subsequent tensile tests were conducted at varying strain rates, ranging from 0.001/s to 0.02/s. The findings unveil a robust grain size dependency in the phase transformation and deformation twinning of the (Fe50Mn30Co10Cr10)97Al3 dual-phase HEA during tensile deformation. Within the FeMnCoCrAl HEA system, characterized by a dual-phase structure, both TRIP (Transformation-Induced Plasticity) and TWIP (Twinning-Induced Plasticity) effects intensify with increasing grain size. Additionally, as the strain rate increases, the TRIP effect gradually diminishes while the TWIP effect strengthens. Notably, the strain rate sensitivity index ‘m’ exhibits a downward trend with an increase in grain size, distinguishing it from the behavior observed in single-phase FCC HEAS. This study conducts an in-depth analysis of grain size’s impact on the SRS of (Fe50Mn30Co10Cr10)97Al3 dual-phase HEA, scrutinizing micro-level aspects encompassing phase transformation, deformation twinning, and grain boundary slip. The findings provide essential theoretical insights for designing HEAS tailored for applications requiring high strain rates.
High-entropy alloys (HEAs) have garnered significant attention due to their exceptional mechanical properties, including high strength, substantial strain hardening capacity, favorable radiation resistance, superior toughness, excellent high-temperature softening resistance, and notable temperature-dependent behavior, among other advantageous attributes.1,2,3,4) For instance, Li et al.5) recently designed a high-performance metastable dual-phase high-entropy alloy by adjusting the atomic ratios of Fe, Mn, Co, and Cr in the Fe80-xMnxCo10Cr10 high-entropy alloy. This alloy demonstrates a single-phase FCC structure at elevated temperatures and partially undergoes martensitic transformation during cooling, resulting in the formation of both FCC and HCP phases with identical chemical compositions. This dual-phase heterogeneous layered structure not only enhances the solid solution strengthening effect of the alloy but also reduces the stacking fault energy, thanks to the variation in manganese content. As a consequence, two distinct effects, transformation-induced plasticity (TRIP) and twinning-induced plasticity (TWIP), are observed. These effects serve to augment the dislocation strengthening and strain hardening capabilities of the alloy, leading to improvements in both yield strength and plasticity.
The TRIP effect is a phenomenon observed in materials where plasticity is augmented through martensitic phase transformation under stress. In FeMnCoCr-based high-entropy alloys, the incorporation of aluminum (Al) atoms can be strategically employed to fine-tune the stacking fault energy of the alloy system, placing it within an optimal range. This adjustment facilitates the activation of both TRIP and TWIP effects, consequently enhancing the alloy’s work-hardening capability and overall mechanical performance.6,7,8,9,10)
Since the advent of TRIP-dual-phase High-Entropy Alloys (HEAs), extensive research has been conducted within this system, including investigations into the mechanical behavior of HEAs under various grain sizes,11,12) different strains,13) and mechanical responses related to strain rates.14) In their analysis, Meyers et al. explored the impact of grain size on the properties and deformation behavior of the alloy under high strain rates. They observed that deformation twinning exhibited sensitivity to grain size, with a delayed onset of twinning as grain size decreased.15) However, it is worth noting that smaller grain sizes generate higher driving forces for phase transformation, favoring the formation of HCP phases.15) This underscores the significant influence of grain size on the deformation behavior of the alloy.
Furthermore, the presence of multiple elements with differing atomic radius in HEAs can induce strain fields, leading to atomic displacements and consequent alterations in the SRS of the alloy.16) SRS is a parameter that is highly sensitive to the microstructure,17) with a close correlation to grain size. For instance, the strain rate sensitivity index (m) of single-phase FCC high-entropy alloys tends to decrease as the grain size decreases.18) Nevertheless, research on the relationship between strain rate sensitivity and grain size in HEAs containing aluminum, particularly in the context of TRIP-FeMnCoCrAl dual-phase high-entropy alloys, remains somewhat limited. In contrast to conventional single-phase high-entropy alloys, this category of alloy, characterized by a dual-phase structure and the combined influence of phase transformation, twinning, and dislocation mechanisms, may exhibit distinctive and unique behaviors concerning grain size and strain rate sensitivity.
This study aims to bridge the existing research gap and achieve a comprehensive understanding of the distinctive behavior of FeMnCoCrAl high-entropy alloys. Various heat treatment methods were employed to successfully fabricate TRIP-FeMnCoCrAl dual-phase high-entropy alloys with varying grain sizes. A systematic investigation was then conducted to examine their mechanical properties and deformation behavior under different strain rates. Through these comprehensive examinations, the study intends to unveil the impact of grain size and strain rate on the deformation behavior of the TRIP-FeMnCoCrAl dual-phase high-entropy alloy while also exploring the patterns of variation in its strain rate sensitivity.
The outcomes of this research endeavor are poised to furnish both innovative theoretical foundations and valuable experimental insights for the high-entropy alloys domain. Furthermore, they hold significant implications for guiding the optimization of high-entropy alloy designs and their practical applications. Additionally, by elucidating the intricate relationship between grain size and strain rate sensitivity in FeMnCoCrAl high-entropy alloys, this study offers fresh perspectives and approaches for fine-tuning performance and expanding the range of applications for this emerging class of alloys.
The experimental materials utilized in this study comprised high-purity Fe, Al, Cr, Co, and Mn metal elements, all possessing a purity exceeding 99.9%. The proportions of these elements were calculated based on the nominal composition of the high-entropy alloy (Fe50Mn30Co10Cr10)97Al3. To compensate for the potential volatilization of Mn during the melting process, adjustments were made to the Mn content. The cast alloy was meticulously prepared using a ZDF-5227A vacuum arc melting furnace under an argon atmosphere. The resulting ingot underwent multiple remelting cycles, ranging from 4 to 6 repetitions, ensuring the uniformity of the alloy composition. Subsequently, the cast alloy was subjected to homogenization at 1100°C for 6 hours, followed by hot-rolling at 1200°C to attain a 4 mm-thick hot-rolled plate.
In the subsequent step, a cold-rolling experiment was conducted, achieving a reduction rate of 75%. The cold-rolled samples were then subjected to annealing processes at temperatures of 800°C and 900°C, each for a duration of 1 hour.
For microstructural analysis, a FEI Quanta 650 FEG field emission scanning electron microscope (SEM) and electron backscatter diffraction (EBSD) were employed. Before EBSD observation, the alloy samples underwent mechanical polishing and electrochemical etching using a solution composed of a 9:1 volume ratio of anhydrous ethanol and perchloric acid. The electrolytic voltage was maintained at 28 V, and the temperature was set to −30°C.
Furthermore, X-ray diffraction (XRD) analysis of the samples was conducted using a Bruker D8 X-ray diffractometer, scanning within the range of 30° to 100° at a speed of 5°/min. Quasi-static tensile tests were performed at room temperature utilizing an Instron 3382 double-column floor-type electronic universal testing machine, employing two different strain rates, specifically, 1×10−3s−1 and 2×10−2s−1. The tensile samples were dog-bone-shaped along the length and rolling direction, with a gauge length of 10 mm×3 mm×1 mm.
To characterize the phases present in the annealed ((Fe50Mn30Co10Cr10)97Al3 high-entropy alloy, X-ray diffraction analysis was carried out on materials annealed at 800°C and 900°C for 1 hour, as depicted in Fig. 1. These analyses revealed that all alloys comprised both FCC and HCP phases. With an increase in annealing temperature, there was a decrease in the intensity of the γ (111) and ε (1011) diffraction peaks, whereas the intensity of the γ (200) diffraction peak exhibited an increase. These findings suggest that the alloy underwent preferred orientation.
Figure 2 presents the EBSD diagrams for the (Fe50Mn30Co10Cr10)97Al3 high-entropy alloy after annealing. The IPF (Inverse Pole Fig) and grain boundary (GB) maps of the annealed samples at 800°C and 900°C exhibit a limited number of low-angle grain boundaries, primarily consisting of equiaxed grains. This observation suggests that the alloy underwent complete recrystallization. The average grain sizes of the annealed samples were statistically analyzed and determined to be 2.86 μm (FG) and 5.25 μm (CG), respectively. As illustrated in Figs. 2(c1) and 2(c2), the HCP phase content decreased from 0.6% to 0.1% with an increase in annealing temperature. Additionally, annealing twinning was detected, with twinning contents of 35% and 30% in the respective samples.
The engineering stress-strain curves and work hardening rate curves of (Fe50Mn30Co10Cr10)97Al3 alloy with two different grain sizes are shown in Fig. 3. The Fig. 3 reveals a strong dependence of the mechanical properties on the grain size, as the alloys’ tensile strength decreases from 643 MPa to 585 MPa and its plasticity decreases from 62.5% to 54% with increasing grain size. The FG sample shows better overall mechanical performance. Figure 3(b) shows that the work hardening curves of both FG and CG samples exhibit three stages. In the first stage, both samples show a similar trend, with a rapid decrease in work hardening rate due to elastic-plastic transition. In the second stage, the two samples exhibit different behaviors. During the early stage of plastic deformation, both FG and CG samples show saw-tooth-like fluctuations, indicating the occurrence of FCC-HCP phase transformation and deformation twinning.19) In the later stage of plastic deformation, the work hardening rate of the CG sample is higher than that of the FG sample. In the third stage, the work hardening rate drops rapidly, indicating sample instability and fracture.
Figure 4 depicts stress-strain curves and work hardening rate curves for the (Fe50Mn30Co10Cr10)97Al3 alloy with varying grain sizes subjected to two distinct tensile rates. Observing Figs. 4(a) and 4(c), it becomes evident that both alloys exhibit noteworthy enhancements in tensile strength and total elongation at elevated tensile rates. The FG sample displays an increase in tensile strength from 643 MPa to 678 MPa, along with a modest elongation improvement from 62.5% to 62.8%. In contrast, the CG sample experiences a more substantial enhancement in both tensile strength and total elongation, elevating from 585 MPa and 54% to 622 MPa and 69.9%, respectively. This notable improvement in comprehensive performance for the CG sample at high strain rates can be attributed mainly to the occurrence of increased twinning and HCP phases, thereby enhancing plasticity through the TWIP and TRIP effects. A detailed explanation of the HCP phase and twinning content will be provided in section 3.3.
Furthermore, at high strain rates, the swift dislocation motion and higher accumulation rate at grain boundaries contribute to dislocation entanglement, consequently strengthening the alloy.20,21) Figures 4(b) and 4(d) illustrate the work hardening curves for both grain sizes under different strain rates. Remarkably, the trend of work hardening rate changes at high strain rates aligns with that observed at low strain rates.
3.3. Microstructure Evolution and Deformation Mechanism 3.3.1. Microstructure Evolution under Different Grain SizesTo investigate the evolution of deformation substructures during tensile deformation of the (Fe50Mn30Co10Cr10)97Al3 High Entropy Alloy, Electron Backscatter Diffraction (EBSD) characterization was employed on the deformed samples. In Fig. 5, we present the Inverse Pole Fig (IPF), phase, Grain Boundary (GB), and Kernel Average Misorientation (KAM) maps following deformation.
As shown in Fig. 5(a1), the IPF map reveals that the grains underwent elongated deformation along the tensile direction. Furthermore, the HCP phase grains predominantly exhibited orientation distributions close to the <101> and <001> directions. This observation implies that the FCC phase grains with similar orientations were more susceptible to martensitic phase transformation during tensile deformation, resulting in the generation of the HCP phase. Consequently, it can be inferred that the orientation of the FCC phase grains played a pivotal role in the formation of the HCP phase.
The phase maps in Fig. 5 indicate that, as the grain size increased during deformation, the alloy experienced a substantial transformation towards the TRIP-HCP phase. This transformation led to a notable increase in the HCP phase content, rising from 4.5% to 13.6%. The HCP phase predominantly manifested in a plate-like and block-like morphology on the FCC phase grains.
In Fig. 5, the GB map (a3–d3) reveals a notable tendency for newly formed Low-Angle Grain Boundaries (LAGB) to cluster around the grain boundaries (GB) and Twin Boundaries (TBS), with few LAGBs detected within the grain interiors. Additionally, there is a decrease in the proportion of annealing twins following tensile deformation, with a small number of deformation twins observed in the deformed grain microstructure. These deformed twins exhibit a distinct distribution, resembling lenses within the alloy grains. Specifically, the content of deformed twins in the FG and CG samples is measured at 0.4% and 2%, respectively, highlighting the influence of grain size on deformed twin formation. Furthermore, the low-angle grain boundaries corresponding to the FG and CG samples after tensile deformation are measured at 68.3% and 64.7%, respectively. This phenomenon can be attributed to the reduced number of grain boundaries in the CG sample, resulting in weakened dislocation barriers on low-angle grain boundaries. Consequently, there is a decrease in dislocation density, with dislocations relocating to high-angle grain boundaries, leading to a reduction in low-angle grain boundaries.
The KAM maps serve to qualitatively reflect the degree of plastic deformation uniformity within the material, where higher KAM values signify increased deformation or higher defect density. In Figs. 5(a4) and 5(c4), it becomes apparent that the distribution of KAM values gradually becomes more uniform. The formation of TRIP-HCP phases induces a notable shift in the distribution of KAM values within the alloy structure. Notably, the newly formed HCP phase lacks low-angle grain boundaries and exhibits lower KAM values, indicative of stress concentration relief in the alloy due to TRIP-HCP phase formation. At the interface between the HCP and FCC phases, applied stress drives dislocations to slip, resulting in the creation of numerous stress concentration regions in the alloy structure. As depicted in Figs. 5(a4) and 5(c4), these stress concentration regions are primarily concentrated at the grain boundaries between large and small grains.
In order to further analyze the characteristics of plastic deformation in alloy, the Taylor factor (TF) distribution of the deformed structure was statistically analyzed. The TF represents the resistance of the alloy grain to plastic deformation. The TF is defined as follows:
| (1) |
where σy represents the yield stress, τ0 represents the critical resolved shear stress, i.e., the minimum activated stress of slip systems in a single grain. The activation of slip systems within grains is proportional to the TF value. Therefore, the deformation energy of the material is positively correlated with the resistance of the grain to plastic deformation. In addition, the grains in the alloy structure are classified into three types according to their TF values: grains that can rotate at low stress (M ≤ 3), grains that can slide through suitable slip systems (3 < M < 4), and grains that are difficult to deform (M ≥ 4).
The TF value is calculated using the {111} <1-10> slip system in FCCmetals and the uniaxial tensile gradient formula. The gradient formula F is expressed as:22)
| (2) |
As evident from Figs. 5(a) and 5(c) and 6(a) and 6(c), the tensile deformation of the (Fe50Mn30Co10Cr10)97Al3 high entropy alloy primarily triggers the TRIP and TWIP effects within the hard-oriented grains where slip is inherently challenging. Additionally, the TF values associated with deformation twins and HCP phases are relatively small, signifying that these deformation twins and TRIP-HCP phases promote grain plastic deformation and facilitate the coordinated deformation of the alloy.
Furthermore, it’s evident from the Taylor factor distribution diagram that the average Taylor factor, denoted as M, decreases as grain size increases. However, this reduction in M still places the alloy in an intermediate state where the slip system activation is relatively straightforward. Interestingly, an increase in strain rate leads to a higher density of grain boundaries and twin boundaries. When combined with the interphase and twin boundary effects, this phenomenon contributes to an increase in the average M value.
3.3.2. Microstructure Evolution under Different Strain RatesThe elevation in strain rate exerts a heightened impact on the fracture occurrence within post-deformation grain boundaries, concurrently fostering a notable augmentation in small-angle grain boundaries, as visually evident in Figs. 5(b3), 5(b4), 5(d3), and 5(d4). It is worth noting that the HCP phase content in the deformed samples subjected to high strain rates registers a decrease when compared to that observed at low strain rates. Specifically, this decrease is quantified at 0.9% (FG) and 3.6% (CG) for the respective cases.
Furthermore, upon comparing Figs. 5(a3) and 5(b3’), as well as Figs. 5(c3) and 5(d3’), a substantial emergence of deformation twins is discernible during high strain rate deformation. These deformation twins exhibit significant enlargement, with both their thickness and length exhibiting increases. During this period, the twin content stands at 2% and 1.8%, respectively. It’s noteworthy that due to the twin deflection (with specific details provided in section 4.1.2), the actual deformation twinning fractions for the FG and CG samples, after adjusting for twin boundaries within a 5° deviation range, are measured at 12.2% and 17.3%, respectively. This amplification in deformation twins results in the release of strain energy, while the increase in twin boundaries serves to refine the grains and disperse internal stresses. Consequently, the KAM values decrease concomitantly with the increase in strain rate.
Additionally, the analysis delved into slip grains possessing moderate TF values within two distinct grain sizes under varying strain conditions. Figures 6(a3)–6(d3) depict the point-to-point and point-to-origin maps of these slip grains, labeled as ①, ③, ②, and ④ in Fig. 6, with their respective locations indicated in Figs. 6(a1)–6(d1).
With an increase in grain size, the orientation difference between the point-to-origin pairs diminishes from the range of 0–17° to 0–11°. This observation signifies that the FG sample boasts a high dislocation density, consequently bestowing it with a robust work hardening capability.
Conversely, as the strain rate escalates, the orientation difference between the point-to-origin pairs expands, transitioning from the range of 0–17° and 0–11° to 0–22° and 0–12°, respectively. This phenomenon points to heightened dislocation motion and interaction within grains at higher strain rates, leading to greater deviations in grain orientation and an upswing in the point-to-point orientation difference. This, in turn, underscores the alloy’s enhanced capacity for plastic deformation at higher strain rates.
Furthermore, the acceleration of the deformation rate contributes to an increase in the number of small-angle grain boundaries, rendering slip more challenging. This, in turn, promotes the occurrence of the deformation twin mechanism, which effectively facilitates the coordinated plastic deformation of the alloy.
The aforementioned experiments shed light on the predominant deformation mechanisms at play in the (Fe50Mn30Co10Cr10)97Al3 dual-phase high entropy alloy, which are primarily governed by dislocation slip, FCC-HCP phase transformation, and deformation twinning. Moreover, it’s evident that the grain size significantly impacts the alteration of these deformation mechanisms. Notably, dislocation slip is profoundly influenced by the numerous grain boundaries present within the alloy. Consequently, the influence of grain boundaries on dislocation slip is paramount in understanding the material’s plastic deformation behavior.
The Hall-Petch relationship, which stipulates that the yield strength of materials is inversely proportional to the square root of the average grain size,23) underscores this relationship. In simpler terms, more grain boundaries per unit volume of the material lead to enhanced material strength and greater difficulty for lattice dislocations to traverse grain boundaries. Consequently, for the FG sample, dislocation slip is challenging. Figure 7 presents the orientation difference distribution for both FG and CG samples before and after deformation. It’s evident that the CG sample possesses a higher number of low-angle grain boundaries before deformation, with an average orientation difference of 43.39, facilitating easier dislocation motion across adjacent grains during deformation.24)
Additionally, the average Taylor factor (M) decreases with increasing grain size, as demonstrated in Fig. 6. This decrease reinforces the notion that dislocation slip is more arduous in the FG sample. The average orientation differences of the two samples after tensile deformation measure 17.46 and 20.42 (Fig. 7), respectively, rising to 18.22 and 20.61 with increasing strain rate. Notably, the FG sample exhibits a larger average orientation difference before and after deformation, indicating more pronounced plastic deformation and a higher dislocation density within this sample.
In the context of the FCC-HCP phase transformation, stress and strain emerge as pivotal factors that exert significant influence over this transition.25,26) High levels of strain lead to an elevated dislocation density, providing crucial nucleation sites for the phase transformation, while stress acts as the driving force propelling this transition. Notably, alloys with smaller grain sizes, as illustrated in Fig. 3(a), experience more pronounced stress and strain during deformation, thus resulting in heightened driving forces facilitating the formation of the HCP phase.
Interestingly, as documented in Figs. 2 and 5, there is an observed increase in the HCP phase content within the CG samples during tensile deformation. This observation challenges traditional theory and warrants further investigation. Previous studies27,28,29,30,31,32) have proposed that the augmented volume fraction of the HCP phase can be attributed to the decreased stability of the parent FCC phase and the heightened susceptibility of larger grains to martensitic phase transformation. Initially, grain refinement leads to an increase in grain boundary density within the alloy’s microstructure. Typically, the formation and growth of the TRIP-HCP phase closely involve the motion of dislocations and stacking faults. The presence of grain boundaries, in this context, serves to pin dislocations, impeding their mobility. Consequently, grain refinement acts as an inhibitor for the growth of the HCP phase within the alloy’s microstructure.
Furthermore, in FG samples, the ratio of large to small grains stands at 1:1, while in CG samples, it is 3:7 in terms of grain size distribution. Therefore, within FG samples, the higher concentration of grain boundaries at the interfaces between large and small grains often leads to elevated interface back stresses. The presence of these back stresses obstructs the propagation of stacking faults, thereby suppressing HCP nucleation.33)
The grain size in alloys can also affect the formation of deformation twins. When the maximum flow stress of the alloy is greater than the critical twinning stress, deformation twins can be activated. It should be noted that both FG and CG samples have undergone the TWIP effect (Table 1), and the CG sample has a relatively higher content of deformation twins. The maximum flow stress required during necking is marked in Fig. 3(b). The relationship between the critical twinning stress and grain size can be expressed as Eq. (3):34)
| (3) |
| Type | HCP/% | Deformation twin/% | ||
|---|---|---|---|---|
| έ=0.001 | έ=0.02 | έ=0.001 | έ=0.02 | |
| FG | 4.4 | 0.9 | 0.4 | 0.07 |
| 12.2 | ||||
| CG | 13.6 | 3.6 | 2 | 1.8 |
| 17.3 | ||||
Where σT is the critical resolved shear stress for deformation twinning(MPa), M is the Taylor factor (M is 3.01 for FG samples and 3.04 for CG samples before deformation), γ—is the stacking fault energy35) (mJ/m2), bρ is the Burgers vector of a partial dislocation (m),36) kT is the Hall-Petch coefficient for twinning,37) d is the grain size (μm). The calculated results of σT and the maximum flow stress required during necking are shown in Table 2. It was found that the twinning stress increases sharply with decreasing grain size, and that deformation twinning is more likely to occur during deformation as the grain size increases.
| Type | σT/MPa | Maxiumum flow stress at necking/MPa |
|---|---|---|
| FG | 600 | 994 |
| CG | 449 | 890 |
The experimental findings reveal significant disparities in the effects of different FCC-HCP phase transformation and deformation twinning contents under varying strain rates for the two samples. Figure 5(a2)–5(d2) illustrate that the FCC phase content increases with the strain rate, indicating a weaker TRIP effect. This phenomenon is closely linked to the facile nucleation of martensitic transformation at defects and the presence of specific habit planes for this transformation process. Under high strain rates, the nucleation of martensitic transformation predominantly occurs on a single habit plane aligned parallel to the primary slip plane of the original FCC phase. Conversely, at lower strain rates, the nucleation of the HCP phase transpires on multiple habit planes.38) Additionally, lower strain rates are more conducive to defect generation, and defects play a promoting role in the martensitic transformation.39)
The GB maps (Figs. 5(b3), 5(d3)) illustrate an increase in twinning content with the strain rate. Nevertheless, it’s important to note that the formation of deformation twins not only contributes to the plastic deformation of the coordinated microstructure but also induces a certain degree of rotation within the deformation twins and the matrix grains.40) Moreover, within the alloy microstructure, deformation twin boundaries tend to interact with dislocations during high strain rate deformation, resulting in alterations in the twinning orientation.41) Consequently, the orientation difference of deformation twin boundaries in the microstructure deviates from the standard Σ3=60° <111> configuration. Consequently, some deformation twin boundaries may not be clearly discernible, which can lead to a lower recorded twinning value at high strain rates, as reflected in Table 1.
Figure 8 provides a point-to-point illustration of the selected area from Fig. 5(d). It is evident that the deviation of the deformation twin orientation from the standard twin orientation remains within 5°. Given that the use of EBSD to detect deformation twins relies on the standard twin orientation, it may not adequately capture the full extent of deformation twin content in the deformed microstructure. Consequently, in this analysis, all parallel grain boundaries in the grain boundary map in Figs. 5(b3’) and 5(d3’) are considered to represent deformation twin boundaries.
As illustrated in Figs. 5(a) and 5(c), the occurrence of deformation twins in the alloy microstructure remains relatively low at low strain rates. This observation can be attributed to the sluggish dislocation velocity characteristic of low strain rates, resulting in weak interactions between deformation twins and dislocations. Consequently, the orientation of deformation twins within the alloy microstructure closely aligns with the standard twin orientation.
Conversely, under high strain rate conditions, as depicted in Figs. 5(b3’) and 5(d3’), there is a substantial increase in the prevalence of deformation twins within the alloy microstructure. This can be attributed to the heightened dislocation velocity associated with high strain rates, leading to an elevation in the shear stress linked to dislocation motion. Consequently, dislocation slip within the grains encounters greater hindrance, resulting in elevated internal stress and enhanced deformation resistance of the alloy. When the stress attains the critical twinning shear stress threshold, it promotes the formation of deformation twins. This augmentation accentuates the Twinning-Induced Plasticity (TWIP) effect within the alloy, thereby enhancing both its strength and ductility.
4.2. Effect of Grain Size on Strain Rate Sensitivity (SRS)The strain rate sensitivity index, denoted as “m,” exhibits a distinctive behavior in the context of FeMnCoCrNi single-phase FCC High entropy alloys, where it tends to increase with the augmentation of grain size during room temperature tensile tests.18) However, in the present study, a contrary trend is observed in the dual-phase (Fe50Mn30Co10Cr10)97Al3 high entropy alloy, where the strain rate sensitivity index, “m,” diminishes with an increase in grain size. This stands in contrast to the behavior typically witnessed in single-phase High entropy alloys.
To gain deeper insights into the relationship between grain size and strain rate sensitivity within the (Fe50Mn30Co10Cr10)97Al3 dual-phase high entropy alloy, Formula (4) can be employed to calculate the strain rate sensitivity of the alloy at two distinct grain sizes.42)
| (4) |
Where σ is yield stress (MPa),
Within the (Fe50Mn30Co10Cr10)97Al3 dual-phase high entropy alloy, it is observed that the stress necessary for dislocation nucleation increases as the grain size decreases. This shift in dislocation nucleation sites, from within the bulk of the grain to the grain boundaries, is attributed to the relatively uneven stress distribution at grain boundaries. Importantly, the driving force required for nucleation is lower at the grain boundary compared to the intra-grain. Consequently, once dislocation nucleation primarily occurs at grain boundaries, the interaction between dislocations and grain boundaries takes precedence in the plastic deformation process. This effectively results in an increase in the value of the strain rate sensitivity index, “m”.43)
Furthermore, the inverse correlation between strain rate sensitivity and grain size may be attributed to the strengthening effect of solid solution strengthening within the (Fe50Mn30Co10Cr10)97Al3 alloy. The relationship between solid solution strengthening and strain rate can be described using the following formula.:44)
| (5) |
Where σss is solid solution strengthening, σ0 is the stress contribution at K0 temperature, R is gas constant, T is absolute temperature, ΔE is activation energy barrier,
The contribution of solid solution strengthening to the overall strength is clearly correlated with the strain rate. Previous studies have demonstrated that the flow stress in CrMnFeCoNi High entropy alloys comprises two primary components: solid solution strengthening and fine-grain strengthening. Notably, at room temperature, the effect of grain boundary strengthening is diminished, with solid solution strengthening emerging as the predominant mechanism responsible for the rheological stress.44) While the grain boundary strengthening effect is more pronounced in the FG sample compared to the CG sample, the disparity in total strength between the two samples at high strain rates is not substantial. Consequently, the solid solution strengthening effect within the CG samples becomes more pronounced, leading to a higher strain rate sensitivity.
The relationship between strain rate and strain rate sensitivity is mathematically described by the following equation.45)
| (6) |
Where σ denotes stress, ε represents strain,
In summary, grain boundaries can be regarded as long-range obstacles to dislocation motion, whereas deformation twins and TRIP-HCP phases can be considered as short-range impediments to dislocation motion.42) When dislocations nucleate and commence sliding, these boundaries act as barriers, thereby consequently, causing the SRS value in CG materials to be lower than that in FG materials. Consequently, in dual-phase high-entropy alloys featuring TRIP effects, the intricate interplay between grain boundaries and dislocations, solid solution strengthening mechanisms, and the combined effects of twinning and phase transformations collectively lead to a negative correlation between grain size and strain rate sensitivity.
4.3. Strain Hardening BehaviorsThe observations above indicate that grain size not only influences the formation of deformation twins in High Entropy Alloys but also impacts the FCC-HCP phase transformation, resulting in varying strain hardening capabilities. To comprehend the effect of grain size on strain hardening behavior, we must first elucidate the primary micro-mechanisms involved in different stages of hardening.
As depicted in Fig. 3, both grain sizes exhibit a two-stage strain hardening behavior, providing an explanation for the alterations in mechanical properties. In the first stage, known as the linear descent stage corresponding to elastic deformation, the work hardening rate linearly decreases with increasing true strain until it reaches its nadir. This marks the conclusion of elastic deformation, and plastic deformation commences in the second stage.
During the initial stage of deformation, dislocations undergo slip under stress, with multiple slip systems concurrently acting under grain coordination. Dislocations become intertwined and entangled with one another. As they approach grain boundaries, the motion of dislocations is impeded, leading to the formation of numerous dislocation pile-ups. In the later stages of deformation, these dislocation pile-ups trigger additional deformation mechanisms, including the TWIP and TRIP mechanisms.
Due to the relatively higher occurrence of deformation twinning (2%) and the presence of the TRIP-HCP phase (13.6%) in the CG sample, these coordinated plastic deformation mechanisms result in a steeper work hardening curve when compared to the FG sample. Prior studies by Asghari-Rad46) and Sun34) have also established that the phenomenon of work hardening in CG samples with a grain size of 82 μm during the tensile deformation process is primarily driven by deformation twins. Simultaneously, phase transformation occurs during the deformation process in the later stages of low-strain second-stage CG samples, leading to a high accumulation rate of geometrically necessary dislocations (GNDs), thereby exhibiting a robust strain hardening capability.47)
To investigate the differences in strain hardening behavior between two distinct grain sizes at various strain rates, we measured the strain hardening index “n” (where n = lnσ/lnε) as a function of true strain for both FG and CG samples at different strain rates, as depicted in Fig. 9. Notably, an increase in grain size resulted in a decrease in the “n” value for both FG and CG samples, primarily attributed to the higher presence of the HCP phase in the CG sample.
During martensite nucleation, a significant strain disparity emerges at the interface with the parent phase. To minimize this strain energy, the FCC phase auxiliary deformation, leading to the formation of a high-density GND network around the HCP phase, primarily accumulating at the grain boundaries. In the initial stages of plastic deformation, the “n” value for the FG sample surpassed that of the CG sample, closely linked to the mode of dislocation slip.
In scenarios with larger grain sizes, dislocation slip predominantly follows a wavy pattern, where dislocations bypass or climb over obstacles on the slip plane. In this mode, there is a reduced accumulation and entanglement of dislocations, resulting in a lower strain hardening rate. Conversely, in cases with smaller grain sizes, dislocation slip mainly occurs in a planar pattern, with dislocations halting or annihilating upon encountering obstacles on the slip plane. In this mode, a greater accumulation and entanglement of dislocations occur, resulting in a higher strain hardening rate.48)
As the strain rate increases, the “n” value also notably rises. The work hardening index characterizes the extent of hardening exhibited by the material during plastic deformation, with higher “n” values indicating enhanced uniform plastic deformation capability. The work hardening ability is closely related to dislocation density, with a higher dislocation density leading to a more pronounced work hardening effect, consequently increasing the “n” value.46)
When increasing the strain rate, the dislocation density significantly increases, as evidenced by the proliferation of low-angle grain boundaries (as shown in Fig. 7), which to some extent enhances the material’s n-value. Furthermore, at higher strain rates, the increased presence of deformation twins has a more pronounced effect on dislocation pinning, further elevating the n-value.49)
The engineering stress-strain curves and work hardening rate curves of two different grain sizes under varying strain rates are depicted in Fig. 4. It is evident from the work hardening curves of the alloys that the work hardening value increases with an escalation in the tensile rate, particularly during the initial stages of plastic deformation. This can be analyzed using Eq. (7):50)
| (7) |
Where v is dislocation velocity, A is the constant, m is the constant, τ is the shear stress for dislocation motion. At high strain rates, the velocity of dislocations in the alloy will increase. Furthermore, according to Eq. (7), it can be inferred that higher dislocation velocities result in the generation of larger shear stresses, leading to a positive correlation between the work hardening rate of the alloy and the strain rate. Additionally, it is observed that in specimens with larger grain sizes, the enhancement in the alloy’s performance and deformation strengthening capability due to high strain rates is more pronounced. This is attributed to the larger grain size of the alloy specimen, which promotes the formation of a significant number of deformation twins during high strain rate deformation. Subsequently, the thickness of these twins increases after deformation, thereby enhancing the uniform plastic deformation capability of the alloy and manifesting a higher work hardening ability.
The present study investigates the microstructure evolution and mechanical properties of two samples with different grain sizes, obtained through different heat treatments of TRIP-(Fe50Mn30Co10Cr10)97Al3 dual-phase high entropy alloy. The following conclusions are drawn from the analysis of the experimental results:
(1) The nucleation of the HCP phase and the formation of twins exhibit a pronounced dependence on grain size. As the grain size increases from 2.86 μm to 5.25 μm, the HCP phase content increases from 4.4% to 13.6%, and the presence of deformed twins rises from 0.4% to 2%. This indicates an enhancement of both the TRIP and TWIP effects with increasing grain size. Concurrently, as the grain size enlarges, the alloy’s yield strength decreases from 256 MPa to 219 MPa, and the elongation decreases from 62% to 54%.
(2) Strain rate is closely associated with martensitic phase transformation and twinning as well. As the strain rate increases from 0.001/s to 0.02/s, the HCP phase content in FG and CG samples decreases from 4.4% and 13.6% to 0.9% and 3.6%, respectively, indicating a weakening of the TRIP effect. This can be attributed to the ease of martensitic phase nucleation at defects, as well as the association of phase transformation with specific habit planes. However, the TWIP effect intensifies, leading to an increase in the content of deformed twins from 0.07% and 2% to 12.2% and 17.3% in FG and CG samples, respectively.
(3) With increasing strain rate, the alloy’s overall mechanical performance improves. In the FG sample, the tensile strength and total elongation increase from 643 MPa and 62.8% to 678 MPa and 62.5%, respectively. Similarly, the CG sample’s tensile strength and total elongation increase from 585 MPa and 54% to 622 MPa and 69.9%, respectively. Notably, at higher strain rates, the CG sample exhibits optimal mechanical properties due to the significant occurrence of deformation twinning.
(4) In the dual-phase (Fe50Mn30Co10Cr10)97Al3 high-entropy alloy, as the grain size increases, the strain rate sensitivity parameter (m) decreases from 0.0435 to 0.0121. This inverse relationship between grain size and the strain rate sensitivity index (m) is primarily attributed to the complex interplay of grain boundary interactions with dislocations, solid solution strengthening mechanisms, and the effects of twinning and phase transformation processes. This behavior is notably distinct from that observed in single-phase FCC (face-centered cubic) high-entropy alloys.
CRediT Authorship Contribution StatementBo Zhang: Investigation, Data curation, Formal analysis, Writing - original draft. Jie Li: Investigation, Writing-review & editing. Lichong - Niu: Investigation, Data curation, Formal analysis. Minghe Zhang: Conceptualization, Methodology, Visualization, Supervision, Writing – review & editing. Yunli Feng: Conceptualization, Supervision, Funding acquisition.
Declaration of Competing InterestThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
This work was financially supported by the General Program of National Nature Science Foundation of China (No. 51974134); Major Science and Technology Special Project of Hebei Province (21281008Z); Applied Basic Research Project of Tangshan City (21130237C).
