Ultrafine-grained pure metals and their alloys have high strength and low ductility. In this study, cryorolling under different strains followed by low-temperature short-time annealing was used to fabricate pure nickel sheets combining high strength with good ductility. The results show that, for different cryorolling strains, the uniform elongation was greatly increased without sacrificing the strength after annealing. A yield strength of 607 MPa and a uniform elongation of 11.7% were obtained after annealing at a small cryorolling strain (ε = 0.22), while annealing at a large cryorolling strain (ε = 1.6) resulted in a yield strength of 990 MPa and a uniform elongation of 6.4%. X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), and electron backscattered diffraction (EBSD) were used to characterize the microstructure of the specimens and showed that the high strength could be attributed to strain hardening during cryorolling, with an additional contribution from grain refinement and the formation of dislocation walls. The high ductility could be attributed to annealing twins and micro-shear bands during stretching, which improved the strain hardening capacity. The results show that the synergistic effect of strength and ductility can be regulated through low-temperature short-time annealing with different cryorolling strains, which provides a new reference for the design of future thermo-mechanical processes.
Zhide Li, Hao Gu, Kaiguang Luo, Charlie Kong, Hailiang Yu.
Achieving High Strength and Tensile Ductility in Pure Nickel by Cryorolling with Subsequent Low-Temperature Short-Time Annealing.
Engineering, 2024, 33(2): 208-221 DOI:10.1016/j.eng.2023.01.019
High strength and high ductility are the main pursuits in the design and development of new structural materials. For a long time, alloying has been indispensable for improving the performance of materials; however, it is very unfavorable to the sustainability and recycling/reuse of materials [1]. Li and Lu [2], [3] proposed the use of simpler alloys to create tailored microstructures without changing the chemical composition and thereby achieve high-performance alloyed materials, which can be used to improve sustainability. One way to enhance the strength of a pure metal is strain hardening through plastic deformation [4]. Increasing the strain at cryogenic temperatures leads to increased strength due to grain refinement [5], [6] and the inhibition of dislocation sliding by the formation of microstructures such as forest dislocation and low- and high-angle grain boundaries. However, an increase in strength usually leads to a decrease in ductility [7], [8], [9]. Many studies have shown that this effect can be mitigated by annealing after severe plastic deformation (SPD) [10], [11], [12]. Annealing at different temperatures and times following SPD results in different combinations of strengths and ductility [13], [14], [15], [16], [17], [18], [19]. While the high strength is chiefly due to strain hardening and grain refinement, the increase in elongation is attributed to the formation of bimodal or lamellar heterostructures by abnormally grown grains during annealing. However, the yield strengths of these kinds of materials are generally sacrificed to obtain enhanced ductility, because precipitation strengthening is not possible in pure metals during heat treatment [10], [11]. Wu et al. [20] reported that asymmetric rolling with 87.5% reduction and subsequent annealing at 748 K for 5 min created pure titanium with both high strength and high ductility—enhanced properties that were attributed to back stress hardening and dislocation hardening of the heterostructure. Increasing attention has been paid to developing ultrafine-grained metals with high ductility through new methods without sacrificing the metals’ ultrahigh strength.
The influence of the annealing parameters on a metal’s thermo-mechanical properties has been the focus of many studies [21], [22]. Regulating the annealing temperature and time can control the characteristics of the microstructure, such as grain size [13], [23], [24]. Liu et al. [25] reported that processing pure nickel by means of equal-channel angular pressing and cryorolling followed by annealing resulted in a combination of high strength and high ductility. While many studies have examined the microstructure evolution of materials subjected to SPD [26] or small pre-deformation [27] and subsequent annealing, few studies have investigated incipient and moderate strain (i.e., a reduction of less than 50%) and subsequent low-temperature short-time annealing in thermo-mechanical processing. Immanuel and Panigrahi [28] investigated the microstructural evolution mechanism of casted Al–Si alloys at cryorolling reductions of 50% and 87%, which enhanced the alloys’ strength and ductility. The strain was considered to be too small to exert the advantage of work hardening to improve the material performance. The distribution of dislocations generated by deformation is different at different strain stages [29]. The microstructure evolves differently when going from coarse grains to ultrafine grains under SPD and from ultrafine grains to coarse grains during annealing. A study of the evolution of the microstructure of materials via different strains and low-temperature short-time annealing will add greatly to knowledge in this area.
Cryorolling can rapidly accumulate dislocations with increasing strain because dynamic recovery is inhibited at cryogenic temperatures [30]. The aim of this study was to investigate the microstructure and mechanical properties of nickel subjected to different strains during cryorolling and subsequent low-temperature short-time annealing. The annealed pure nickels exhibited higher uniform elongations, while their yield strengths were maintained or even improved compared with the cryorolled samples. The strain hardening of nickel sheets after cryorolling and annealing was analyzed, revealing that the increase in elongation after annealing was associated with the formation of dislocation wall distributions. The results of this study show that the synergy of strength and ductility can be enhanced by annealing after cryorolling, offering the possibility of applying pure metallic materials as structural materials.
2. Materials and methods
The raw material for this study was a fully annealed commercial pure nickel (N4) sheet with a thickness of 2 mm. The elemental assay is given in Table 1. Cryorolling was done on a four-high rolling mill with a work roll diameter of 80 mm and a roll speed of 1 m·min−1. The experimental process flow is shown in Fig. 1(a) and the microstructure of the raw material is shown in Fig. 1(b). Before each cryorolling pass, the specimens were submerged in liquid nitrogen for 8 min. The target reduction ratio per pass was set as 10%. Specimens with reduction ratios of 20%, 40%, 60%, and 80% were retained and subsequently annealed at 623 K (0.24 of the melting temperature of nickel using Celsius system) in a tubular vacuum furnace with a vacuum degree of 1 × 10−3 Pa, a heating rate of 10 K·min−1, and a holding time of 5 min. The original sheet was designated as “CR0,” the specimen with a cryorolling reduction ratio of 20% was designated as “CR2,” and the annealed CR2 specimen was designated “CRA2,” and so forth.
A static uniaxial tensile test was performed using a Shimadzu AGS-X 10 kN tensile testing machine and a strain rate of 1 × 10−3 s−1. A video extensometer was used to record the strain during tensile testing. The tensile sample cut from the rolled and annealed sheets had a gauge length of 13.0 mm and a width of 2.5 mm (Fig. 1(c)). To ensure the accuracy of the tensile results, the tensile tests were repeated three times for each sample, and the results were averaged. The samples for transmission electron microscopy (TEM), scanning electron microscopy (SEM), electron backscattered diffraction (EBSD), and transmission Kikuchi diffraction (TKD) analysis were first thinned by mechanical grinding and then polished using twin-jet electropolishing in a nitric acid and methanol solution (3:7 by volume) at 243 K. TEM observations were performed on a 200 kV transmission electron microscope (FEI Tecnai G2 F20, FEI Company, USA). EBSD and TKD were performed on a dual-beam electron microscope (FEI Scios 2 HiVac, FEI Company) with an operating voltage of 30 kV and step sizes of 1.5 µm and 2 nm, respectively. X-ray diffraction (XRD) was performed on an Advance D8 Automatic X-ray diffractometer with a Cu Kα radiation of 0.154060 nm, a scan rate of 2(° )∙min−1, and a scan step size of 0.02°. TEM, SEM, EBSD, TKD, and XRD analyses were performed on the plane normal to the thickness direction for all specimens.
The crystallite size was estimated by XRD results from the width of the strongest peak using the Debye–Scherrer method [31]:
where D is the crystallite size, k (k = 0.9) is the shape factor [31], λ (λ = 0.154060 nm) is the wavelength of the radiation, is the full width at half maximum (FWHM), and θ is the diffraction angle. The degree of microstrain was estimated using the Stokes and Wilson relationship [32]:
where ε is the microstrain and is the integral breadth due to the strain effect. The dislocation density can be calculated from D and ε using Eq. 3 [32]:
where is the dislocation density due to domain size, is the dislocation density due to strain broadening, and
where K= 6π, and b is the Burgers vector with a value of 0.249 nm [25].
3. Results
3.1. Microstructure evolution
Fig. 2(a) and (b) show the SEM images of the microstructure of the specimens after cryorolling with different reductions. In the CR4 specimen (Fig. 2(a)), the local grains were refined, and obvious substructures can be seen in the grains. In the CR8 specimen (Fig. 2(b)), there were abundant and obvious macroscopic shear bands. Fig. 2(c)–(f) show the microstructure of the cryorolled specimens following low-temperature short-time annealing with different reductions. As shown in the figure, the microstructure of the CRA2 specimen (Fig. 2(c)) is slightly deformed, and the grains are locally smaller when compared with the microstructure of the CR0 specimen (Fig. 1(b)). With a 40% reduction (CRA4; Fig. 2(d)), more grain refinement is visible, and some grain boundaries have begun to blur, indicating that the deformation has become serious. With a 60% reduction (CRA6; Fig. 2(e)), the grains have become elongated, and the grain boundaries are more difficult to distinguish. By the time the reduction reaches 80% (CRA8; Fig. 2(f)), the grains are elongated and the grain boundaries have blurred further, indicating that the grains have been seriously deformed, and a large number of low-angle grain boundaries and other substructures have appeared in the grains. Compared with the CR8 specimen, the CRA8 specimen has more subgrain boundaries and substructures.
As Fig. 3(a) shows, before cryorolling, there were only scattered dislocations, and the dislocation density was quite small (CR0). Fig. 3(b)–(d) show the scanning TEM (STEM) and high-resolution TEM (HRTEM) images of the microstructures of the cryorolled nickel with an 80% reduction (CR8). The lower (Fig. 3(b)) and higher (Fig. 3(c)) magnification STEM results indicate that cryorolling gave the CR8 specimen uniform and abundant dislocations and other substructures. The HRTEM image (Fig. 3(d)) also shows that the cryorolled specimen had a high density of dislocations. Fig. 3(e)–(h) show the TEM images of the microstructures of the cryorolled and annealed specimens. With only a 20% reduction (CRA2; Fig. 3(e)), there were many more dislocations, random storage dislocations had increased, a dislocation cell (DC) structure had begun to form, and the slidable dislocations had become entangled to form uncondensed dislocation walls (UDWs). With increasing cryorolling reduction, the number of dislocations continued to increase, a mature DC structure appeared, and the number of dislocations accumulated on the UDW structure continued to increase (CRA4; Fig. 3(f)). For CRA6, when the number of dislocations on the dislocation wall structure reached a certain level, a dense-dislocation wall (DDW) structure formed, as shown in Fig. 3(g); these DDWs were composed of a dislocation-tangle zone (DTZ) of high dislocation density (Fig. 3(h)). With further cryorolling reduction, these DDWs continued to widen (Fig. 3(i)). The difference between UDW and DDW was not in the width of the dislocation wall but the degree of dislocation density. Compared with the CR8 specimen, the TEM results of the CRA8 specimen show that the dislocations recovered in some regions, forming substructures such as dislocation walls and subgrain boundaries.
Fig. 4(a) and (b) show the XRD patterns of the cryorolled and annealed specimens. As shown in Fig. 4, as the cryorolling reduction increased, there was an increase in the intensity of the peak corresponding to the (220) plane, which can be attributed to the accumulation of strain during cryorolling, resulting in the rolling texture. Table 2 shows the values of the crystallite size and microstrain for the cryorolled and annealed samples. The crystallite size according to the XRD result is small, because XRD measures the coherent diffraction domain size—that is, the subgrain or DC size [21]. Fig. 5 shows the variation in dislocation density across the cryorolled and annealed specimens.
3.2. Mechanical properties
The engineering stress–strain curves of the cryorolled specimens (CR0–CR8) and of the specimens after subsequent annealing at 623 K for 5 min (CRA2–CRA8, compared with CR0) are shown in Fig. 6(a) and (b), respectively. As shown in the figure, the elongation of the specimens improved after annealing, while the strength decreased only slightly or even improved. The true stress–strain curves of the specimens after cryorolling alone and after both cryorolling and annealing are shown in Fig. 6(c) and (d), respectively; the curves intuitively show the increase in uniform elongation caused by annealing. The yield strength, tensile strength, uniform elongation, and fracture elongation of the specimens after both cryorolling and annealing are shown in Fig. 7. As shown in the figure, annealing after cryorolling resulted in a slight lowering of the yield strength but improved the strain hardening ability and increased the tensile strength and elongation. For the CR2 specimens, the yield strength increased significantly compared with that of CR0 (614 MPa compared with 203 MPa), while the elongation decreased significantly, and the ratio of yield strength to tensile strength changed from 0.4 to nearly 1.0. For the CRA2 specimens, the yield strength was slightly lower compared with the CR2 specimens (607 MPa compared with 614 MPa), but the uniform elongation was significantly improved (from 3.3% to 11.7%). As the cryorolling reduction ratio further increased, there was a slow increase in the yield strength, while the ductility began to flatten out. The annealed specimens exhibited a similar slow increase in yield strength, with a fairly constant rate of increase, as the cryorolling reduction increased. The uniform elongation of the annealed specimens gradually decreased to 6.4% with increasing cryorolling reduction before stabilizing, while the fracture elongation decreased to 8.7% before stabilizing.
Fig. 8 shows fracture photographs of the tensile-tested specimens. The failure modes of the cryorolled specimens showed a mixed fracture, the coexistence of dimples and cleavage planes, and a gradual trend toward cleavage fracture. In contrast, the annealed specimens showed a characteristic ductility fracture with many dimples. The number of large and deep dimples in the CRA2 specimen was greater than that in the CR2 specimen. In contrast, the dimples in the CRA4 specimen were smaller and denser than those in the CR4 specimen. Specimens CRA6 and CRA8 showed no obvious cleavage plane, unlike CR6 and CR8. From these results, it is clear that the short annealing improved the ductility of the cryorolled specimens, which confirms the tensile properties shown in Fig. 6, Fig. 7.
4. Discussion
4.1. Origins of the high strength and ductility of cryorolled nickel after short-time annealing
The results of the tensile tests show that nickel increases in both strength and ductility after cryorolling and subsequent short-time annealing at low temperatures. Fig. 9 [7], [21], [25], [33], [34], [35], [36], [37], [38] provides a comparison between the yield strength and uniform elongation results reported here and those reported in the literature. The light grey area stretching from the top left to the bottom right represents the zone in which strength and ductility are mutually exclusive. The dark-grey shaded area on the left encloses the properties of some severely plastically deformed [7], [39] and electrodeposited [33], [34], [35] nickel samples with high strength and low ductility. The properties of nickel with different types of heterostructures, such as gradient [36], bimodal [25], [37], and multimodal [38] structures, are shown in green, orange, and blue. Any metals with properties near the boundary of the mutual-exclusion zone have a degree of synergy in strength and ductility.
It is very difficult to simultaneously increase strength and ductility, as the ductility usually decreases rapidly with increasing strength, as shown by the CR0 and CR2 specimens in Fig. 7(a). All the main approaches to strengthening, which include dislocation strengthening, grain refinement strengthening, solid solution strengthening, and precipitation strengthening (although solid solution strengthening and precipitation strengthening are not suitable for pure metals), reduce ductility to varying degrees. A recently introduced approach of generating a heterogeneous structure has been reported to achieve simultaneous optimization of strength and ductility [40], [41]. One of the main methods for fabricating heterostructured materials is through SPD and subsequent annealing [42]. The results presented in this study show that annealing after a small strain is another promising approach for breaking the mutual exclusivity of strength and ductility. As shown in Fig. 7(b), the performance of the CR2 specimens after low-temperature short-time annealing is similar to that of a bimodal-structure nickel [25] produced via equal-channel angular pressing and a cryorolling reduction of 84% plus annealing at 748 K for 5 min. With a small strain, dislocation strengthening is the main approach for achieving high strength. The increase in elongation is similar to that of hetero-deformation-induced strengthening [41], which is due to the long-term internal stress generated by a hard region composed of a soft region of low dislocation density and a dislocation wall [43].
The specimens in present study achieved high strength due to strain hardening during cryorolling with a large strain. Estrin et al. [44] proposed a dislocation-based model for all hardening stages in large-strain deformation based on a composite model considering two dislocation structures: the cell wall and the dislocation density inside the cell, with the cell wall volume fraction being a function of strain. Nes [45] concluded that work hardening was the result of strain-induced refinement of the cell structure during deformation after the intracellular dislocation density reached a saturated level. Dislocations during deformation are accommodated in three main ways: random storage of the dislocation in cells or subgrains, storage in “old” dislocation walls, and storage through the formation of new dislocation walls. Fig. 10(a) shows the TKD inverse pole figure (IPF) of the CRA8 specimen, with local misorientations of each grain boundary marked. Fig. 10(b)–(e) show the cumulative misorientation of the lines a1–a4 in Fig. 10(a). Fig. 10(b) shows a continuous increase in misorientation due to the presence of a large number of random dislocations in the grain caused by deformation. The strike-line corresponding to Fig. 10(c) does not cross the low-angle grain boundary, but rises strongly at the position of 70 nm, indicating that the dislocation wall was formed due to the accumulation of dislocation and that there was a trend of transition to the low-angle grain boundary. The lineation corresponding to Fig. 10(d) crosses the low-angle grain boundary, indicating that the local misorientation at this location was 4°. Fig. 10(e) corresponds to another part of the same low-angle grain boundary, but with a misorientation of 6°. The formation of this grain boundary indicates that three processes may occur simultaneously: the increase of random dislocation in the grain, the aggregation of dislocation to form a dislocation wall or sub-boundary, and the increase of the existing sub-boundary misorientation. Fig. 10(f)–(h) show the HRTEM of the partially microscopic defects in the CRA6 specimen. These images show a full dislocation (Fig. 10(f)), a stacking fault (SF) structure and the corresponding Fourier transformation (Fig. 10(g) and (i)), and the subgrain boundary structure and its corresponding Fourier transformation, showing that the local misorientation of the two grains is 12° (Fig. 10(h) and (j)).
Fig. 10(k)–(n) provide schematic diagrams of the evolution of the dislocation structure with increasing strain. Before cryorolling, the material displays only scattered random mobile dislocations (Fig. 10(k)). However, these random dislocations rapidly increase with the reduction (Fig. 10(l)). As the strain increases further, dislocation walls are formed due to the trapping of random dislocations (Fig. 10(m)). Continuing to increase the strain will not only form a new dislocation wall but also increase the dislocation density of the existing dislocation wall, resulting in an increase in the local misorientation between the two sides of the dislocation wall (Fig. 10(n)). Hughes and Hansen [46], [47] described the relationship between strength and structure in terms of low-angle boundaries being dislocation strengthening, while medium and high-angle boundaries are fine-grain strengthening. Thus, with increasing strain, the main strengthening mode will change from dislocation to grain refinement strengthening.
Annealing at a low temperature for a short time results in good ductility without reducing the strength of the cryorolled nickel. The improved ductility may be the result of a reduction in lattice distortion during annealing [12]. Annealing twins may also contribute to increased elongation. As Fig. 11 shows, twins were discovered in specimens with different reductions and subsequent annealing. Cryorolling will generate residual elastic strain energy both near the grain boundary and within the grain, and annealing provides thermal energy, which becomes the driving force for grain boundary migration. The low annealing twin boundary energy may lead to the formation of coherent twin boundaries at the migration grain boundaries through the generation of SFs. Bair et al. [48] showed that higher twinning densities could be achieved at lower temperatures and slower heating rates. In the same time, Jin et al. [49] reported twin formation when the boundary migrated to the deformed region, with increasing annealing twin density during recrystallization and decreasing annealing twin density during grain growth. In the present study, the twin widths were 1.50 µm in the CR0 specimen (Fig. 11(a)), 1.45 µm in the CRA2 specimen (Fig. 11(b)), 1.31 µm in the CRA6 specimen (Fig. 11(c)), and 185 nm in the CRA8 specimen (Fig. 11(d)). The length reached 15.4 µm in the CRA6 specimen and 8.5 µm in the CRA8 specimen. Thus, the twins exhibited decreasing width with increasing reduction, and nano-twins also exist in the CRA8 specimen (Fig. 10(a)) [50]. Twins were observed in the specimens after cryorolling and subsequent annealing. Low-temperature short-time annealing does not result in such large annealing twins, so the twins are more likely to be annealing twins in CR0 specimen (Fig. 11(a)). The width of the twins gradually decreases with an increase in the cryorolling reduction. However, twin boundaries are not easily observed due to the high dislocation density in the specimens after cryorolling. After short-time annealing, the dislocations in the region near the twin boundaries recover, making the twin boundaries easier to observe. These dislocations recover without causing a significant reduction in strength; moreover, the twins might contribute to the strength of the materials being retained after annealing. The decreasing dislocation density in the region near the twin boundary also contributes to the enhanced dislocation accumulation capability during deformation, thereby improving the strain hardening ability and promoting the improvement of ductility.
As shown in Fig. 8, there are deep and large dimples on the fracture surface of the annealed specimens. Fig. 12 shows the surface topography of the lateral fracture of the CR0, CRA4, and CRA8 specimens. The CR0 specimen has excellent plasticity; the fractures shown in Fig. 12(a)–(c) have obvious necking and abundant shear bands. The shear band is at a 58° angle to the roll direction (RD). CRA4 and CRA8 are both cryorolled and annealed specimens with similar shear band morphologies. However, the CRA4 specimen (Fig. 12(f)) has more shear bands than the CRA8 specimen (Fig. 12(h)) and fewer than the CR0 specimen (Fig. 12(c)). Shear bands are visible in two directions in the expanded view (Fig. 12(f) and (h)): a micro-shear band at a 26° angle to the RD and a macro-shear band at a 64° angle to the RD (stretch). Macroscopic shear bands resemble conventional adiabatic shear bands, which often occur at high metal strain rates [51] and in the final necking stage of deformation [52]. The formation of micro-shear bands can delay the formation of macro-shear bands, thereby delaying the onset of necking and increasing the uniform elongation. Such bands are thought to form due to synergistic grain boundary sliding [53]. Zhao et al. [54] reported that the ductility enhancement of the annealed specimen was related to the activation of numerous homogeneous micro-shear bands and considered that these shear bands were controlled by cooperative grain boundary sliding. They proposed that the dislocation walls formed during recovery promote the formation of micro-shear bands and cooperative grain boundary sliding and thereby enhance the tensile ductility. Large plastic deformation and annealing will increase the number of subgrain boundaries in the material. Thus, the good ductility of the cryorolled and annealed specimens may also result from synergistic grain boundary sliding of the formed dislocation walls and subgrain boundaries due to annealing.
4.2. Strain hardening behavior of cryorolled and annealed nickel
The strain hardening behavior of cryorolled nickel and annealed nickel reflects the changes in the material’s strength and uniform elongation. The theory of the strain hardening of materials requires an understanding of dislocations. The core problem of strain hardening is to establish the relationship between the flow stress τ and dislocation [45]:
where is the frictional stress of the material.
Nes [45] concluded that the parameter is related to the elementary dislocation density, the unit cell size, and the unit cell or sub-boundary misorientation. However, Hughes and Hansen [46] argued that deformed microstructures can be described in terms of misorientation, volume fraction, and distribution of the incidental dislocation boundary and the geometrically necessary dislocation boundary. Mughrabi [43] described deformed metallic materials as composites formed of a combination of hard regions of dislocation walls composed of local high-density dislocations and soft regions composed of low-density dislocations between the walls. Changela et al. [55] modified the Kocks–Mecking–Estrin model to consider the contributions of grain size, solutes, and precipitates to dislocation density evolution during straining. In this paper, since the study material was pure nickel, which differs from alloys, it was considered that the influence of the evolution of the relative dislocation density of the solute and precipitation can be ignored.
All the studies described above concluded that strain hardening is caused by the formation of complex dislocation structures during deformation. The “frictional stress” in Eq. 6 is the total contribution to the flow stress arising from both the short-range interactions experienced by the mobile dislocations (i.e., the lattice contribution (Peierls stress), interactions of solute atoms in solid solutions, and cutting of dislocation forests) and the contribution from the hindrance of second-phase particles. The flow stress arising from the dislocations () has a classical Taylor relationship with the dislocation density ρ [3]:
where G is the shear modulus, and α is the material and temperature-dependent constant. Due to thermal activation, α decreases with increasing temperature and decreasing strain, varying by 10% [45]. α is also dependent on how precisely ρ is measured. The reason why the deformation leads to strain hardening is that the dislocation ρ changes with the strain γ [45]:
This relation reflects the fact that the dislocations are stored at a rate determined by the balance between deformation-induced dislocations and dislocations lost due to dynamic recovery , where can be written as follows [56]:
where refers to the length of dislocation stored per area swept ; and can be called a “mean free path” [56]. The term is considered to be mainly affected by temperature and strain rate.
Another important parameter is the strain hardening rate, Θ, which describes the intensity of strain hardening [57]:
where is the strengthening term brought about by dislocation storage, and is the softening term brought about by dynamic recovery. Strain hardening is classified according to the different types of hardening behavior observed with increasing strain, being divided as follows: almost zero hardening (stage I), steep linear hardening (stage II), parabolic hardening (stage III), and finally lower linear hardening (stage IV) [47]. Some scholars separate the late stage of continuous decline in stage IV into stage V [44].
In this study, there are two strain hardening processes at work: deformation during cryorolling and strain hardening during the tensile test. The former increases the yield strength of the material, and the latter increases the tensile strength and affects the ductility of the material. The two processes differ in temperature and deformation methods, but they can be connected through the strain hardening rate (Fig. 13(a)). This may be due to one of two reasons: the fact that the strain hardening rate of cryorolling is calculated through tensile measurement of the specimens and the fact that the dislocation recovery will be slightly reduced under the influence of temperature during cryorolling, reducing the difference caused by different deformation modes. The relationship between the strain hardening effect and the flow stress is [44]
Substituting Eq. 7 into Eq. 11 gives the following:
where M is the Taylor factor with a value of 3.1, and the values of α, G, and b are 0.24, 79 GPa, and 0.249 nm, respectively [25]. The ρ value determined from the XRD measurements is substituted into Eqs. 12, 10 to obtain the change in strain hardening rate caused by the change in dislocation density during cryorolling, as shown by the dotted red line in Fig. 13(a).
The Taylor factor changes with strain due to the change in texture that results from cryorolling at different reductions. Estrin et al. [44] analyzed the influence of the constant M and concluded that it might be important to correct the value under large strain due to texture change. In the fitting of the strain hardening rate calculated by dislocation density in Fig. 13(a), there is a large deviation between strains of 0.22 and 0.92 and a small deviation between strains of 0.92 and 1.60. However, when the strain increases, the difference between the obtained by dislocation density and the measured value becomes larger and larger due to integration, as shown in Fig. 13(b). This difference arises from a combination of the generalized “frictional stress” (Eq. 6) and the fact that only dislocation density is used in estimating strain hardening due to dislocation, not the effect of the uneven distribution of dislocation. The difference increases with the increase of strain, indicating that the strengthening effect caused by uneven dislocation distribution becomes more prevalent with increasing strain. Mughrabi [43] and Estrin et al. [44] both developed a composite model based on uneven dislocation distribution under large strain conditions, pointing out that dislocation walls formed by dislocation aggregation strongly influence strain hardening. With increasing strain, the internal dislocation density will reach saturation, and the subsequent strain hardening is dependent on both the random movable dislocation density and the dislocation wall network with high dislocation density. Nes [45] predicted through modeling that the dislocation density would reach saturation at the end of the parabolic hardening (stage III) transition. Thus, the strain hardening rate decreases with increasing strain, and the dislocation density of the cryorolled nickel begins to saturate when the strain reaches 1.6.
Dynamic recovery occurs during deformation, while static recovery occurs during annealing. Both types of recovery are driven by forces resulting from changes in free energy associated with the local reduction of stored energy. The difference is that the driving force during deformation arises from applied stress, while the driving force during annealing arises from defect interactions under thermal activation. Kocks and Mecking [56] suggested that dynamic recovery is a function of temperature and strain rate. As dynamic recovery is related to dislocation annihilation, Nes [45] suggested that the dislocation annihilation frequency would be a function of temperature and dislocation density at a constant strain rate. The higher the dislocation density, the more the stored dislocations are exposed to moving dislocations during annealing, which increases the dislocation annihilation frequency. As the dislocation density increases, dynamic recovery may increase by several orders of magnitude [57]. Whatever the cause, the degree of dynamic recovery diminishes with decreasing temperatures. Because of the low deformation temperature, cryorolling can effectively reduce the degree of dynamic recovery during deformation and can accumulate more dislocations than conventional (i.e., room-temperature or high-temperature) rolling with the same strain. Thus, the strain hardening efficiency can be improved by lowering the temperature; however, as Fig. 14(a) shows, the strain hardening capacity of the deformed material decreases sharply after yielding. Tsuji et al. [15] reported that work hardening after yielding is difficult to achieve, and that the reason for the sudden decline of uniform elongation can be understood in terms of plastic instability. After annealing at 623 K for 5 min, the strain hardening capacity of the nickel was effectively improved, mainly due to improvements in the strain hardening rate of stage IV, as shown in Fig. 14(b).
Fig. 15 shows the true stress–strain curves of the CR0, CR2, and CRA2 specimens. As shown in the figure, the true stress–strain curve of CR2 (true strain: 0.22) intersects with that of CR0 in the plastic deformation stage after moving 0.22 to the right, which is consistent with the strain hardening rate results in Fig. 13. Cryorolling results in high yield strength but low ductility. By annealing at a low temperature for a short time after cryorolling, the ductility was improved with almost no reduction in yield strength, as shown in the CRA2 curve in Fig. 15. Sergueeva et al. [58] reported that ultrafine titanium after SPD displayed increased ultimate tensile strength and ductility after annealing at 523 and 573 K for 10 min. Annealing reduces the lattice distortion significantly; the grain boundary becomes closer to the equilibrium state, the defects of the grain boundary become orderly, and the grains do not grow. Thus, low-temperature and short-duration static recovery can improve the ductility of the material without reducing its yield strength.
Lee et al. [12] reported that, after annealing at low temperature, the size of the dislocation substructure in the cryorolled specimens did not change significantly, and rearrangement of the dislocations during the recovery processing led to a rapid increase in uniform elongation. Fig. 16 shows the relationship between strain hardening rate and stress—usually referred to as the Kocks–Mecking diagram [45]—for the specimens before and after annealing. It can be seen that the original specimen before cryorolling displays a gentle linear downward trend in stage IV, indicating that it has a good strain hardening ability. After cryorolling, the specimens have very limited strain hardening ability after yielding. In contrast, after annealing, the specimens have distinct characteristics at stage III, with the strain hardening dropping steeply at first and then rising steeply, which is a typical manifestation of discontinuous yield [20]. This is due to the lack of movable dislocations at the onset of plastic deformation, so the dislocations must slide at a faster rate to accommodate the constant strain rate applied, as more stress is required to move the dislocation faster. At yield, dislocations rapidly multiply, resulting in a rapid increase in the strain hardening rate due to dislocation interaction and entanglement [20]. The lack of movable dislocations may be due to the preferential rearrangement of these movable dislocations during annealing. With an increase in the reduction, the linear phase of the annealed specimens in stage IV is steeper and the duration is shorter, which reflects the changing trend of the uniform elongation.
According to strain hardening theories [4], [56], there are two basic mechanisms related to strain hardening. One is the existence of an athermal hardening rate, which corresponds to the first term of Eq. 10, indicating that the strain is a process of dislocation accumulation; another is the phenomenon of dynamic recovery, which corresponds to the second term of Eqs. 8, 10. These two mechanisms may predominate at different strain stages, but they coexist at all stages. The first mechanism dominates at strain stage II, with a high strain hardening rate on the order of G/200; this stage is athermal and somewhat insensitive to variables [56]. The second mechanism dominates at the lower linear hardening stage (stage IV), which is highly dependent on the temperature and strain rate [56]. For the CR2 specimens in Fig. 16, the strain hardening rate at the end of stage II is very small, with only weak strain hardening ability, while the CR4, CR6, and CR8 specimens have almost no strain hardening. The metals after SPD can no longer go through several strain hardening stages and are hence susceptible to plastic instabilities such as necking in tension and without uniform elongation [59]. In Fig. 16, the strain hardening rate values at the end of stage II for the CR0, CRA2, CRA4, CRA6, and CRA8 specimens are marked on the ordinate, and gradually decrease from G/250 (CR0; 3150) to G/350 (CRA8; 2250) with increasing cryorolling reduction. The magnitude of this value may affect whether the material has the capability for strain hardening. The ability to strain harden is important for stabilizing uniform tensile deformation, and increasing the strain hardening ability can result in large uniform tensile strains [59]. The transition points from the end of stage II to the beginning of stage III are thought to be possibly related to the occurrence of cross-slip when the local pile-up stress becomes high enough or to the climb of the thermal activation of vacancies due to stress enhancement [45]. In Fig. 16, the slopes of the CR0, CRA2, CRA4, CRA6, and CRA8 specimens at stage IV are marked, and the slope gradually changes from −5.4 to −23.5 with the increase in the cryorolling reduction. The change in the strain hardening rate at stage IV is mainly affected by the dynamic recovery, which is a function of temperature and strain rate [56]. In Fig. 15, the strain hardening stage of the CR2 specimen is shortened, but the change in the strain hardening rate in the linear hardening stage (stage IV) is similar to that of the CR0 at the later strain stage. However, in Fig. 16, the strain hardening rate of the CRA2 specimen in the linear hardening stage (stage IV) decreases more rapidly than that of the CR0 specimen, indicating a stronger dynamic recovery. The slope of the decrease in the strain hardening rate at stage IV is different between CRA2 and CR0 samples, indicating that the dynamic recovery of different specimens has significant differences; this finding supports Nes’s [45], [57] viewpoint that the dynamic recovery is also a function of dislocation density. Wang and Ma [59] pointed out that the suppression of dynamic recovery will cause a material to have better strain hardening ability and thus better uniform elongation. With the increase in the cryorolling reduction for the annealed specimens in Fig. 16, the dislocation structure is gradually enriched and the dynamic recovery is stronger, resulting in a decrease in the strain hardening ability and uniform elongation.
5. Conclusions
In this work, we used cryorolling under different strains followed by brief low-temperature annealing to fabricate pure nickel sheets that combined high strength with good ductility. Based on the results of this study, we draw the following conclusions:
(1)The technique of cryorolling followed by low-temperature short-time annealing is expected to lead to the development of structural materials with high strength and ductility. The results show that a large strain followed by annealing results in high-strength pure nickel with a yield strength of 990 MPa and a uniform elongation of 6.4%. A small strain followed by annealing yields pure nickel with good ductility, with a uniform elongation of 11.7% and a yield strength of 607 MPa.
(2) Cryorolling followed by annealing at low temperatures for a short time can cause a material to regain its strain hardening ability, resulting in higher tensile strength and elongation. With an increase in the reduction, the strain hardening rate of the annealed specimens exhibited a steeper linear decreasing trend in stage IV of the hardening process, while the uniform elongation showed a decreasing trend, with the lowest elongation ratio being 6.4%.
(3) The twin width gradually decreased as the cryorolling reduction increased. The dislocation walls and subgrain boundaries that formed during low-temperature short-time annealing promoted the formation of micro-shear bands during tensile processing, contributing to enhanced ductility.
Acknowledgments
The authors are grateful for the financial support from the High-Tech Industry Technology Innovation Leading Plan of Hunan Province, China (2020GK2032), the Innovation Driven Program of Central South University (CSU) (2019CX006), and the Research Fund of the Key Laboratory of High Performance Complex Manufacturing at CSU.
Compliance with ethics guidelines
Zhide Li, Hao Gu, Kaiguang Luo, Charlie Kong, and Hailiang Yu declare that they have no conflict of interest or financial conflicts to disclose.
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