Introduction

The recently developed multifunctional β-type titanium alloys exhibit good functional properties of shape memory, superelasticity, zero and/or negative thermal expansion, and low Poisson’s ratio, and excellent mechanical properties being flexible (low elastic modulus), strong (high strength-to-modulus ratio), and ductile [1–6]. The former is crucial for advanced functional applications and the latter is excellent for orthopedic applications to alleviate stress shielding effect by enhancement of stress transfer between implants and their surrounding bone tissues. Furthermore, this combination of properties has enormous potential for the integrated functional and structural applications such as a system for dynamic stabilization of the spine to recover its physiological function.

As a hard tissue replacing material, stronger is desirable to ensure longer service in human body. This can be achieved easily by the precipitation of the α-phase via the aging treatment in the (α + β) phase field. However, this leads to a decrease in ductility and an increase in modulus, which is contrary to the original intention to improve strength and remain low modulus. Most important, the combined functionalities such as superelasticity and shape memory are damaged by the α-phase precipitation.

To optimize the above mechanical and functional properties, the grain refinement would be an ideal way because of its strengthening contribution with little effect on the modulus and its modification on the martensitic transformation (MT) [7, 8]. As to the metallic materials for both industrial and biomedical applications, the microstructure is generally refined by the thermo-mechanical processing (TMP) [9, 10]. This is achieved by two mechanisms, dynamic recrystallization (DRX) and dynamic recovery (DRV). The previous results have shown clearly that, for the materials with low-to-medium stacking-fault energy, the discontinuous DRX (DDRX) contributes greatly to the grain refinement [11, 12]. For the materials with high stacking-fault energy such as the β-type multifunctional titanium alloys, the microstructure evolution is dominated by DRV and continuous DRX (CDRX) [13, 14], leading to the development of abundant sub-grains. However, the DDRX refinement has been reported in several β-type titanium alloys under the condition of high strain rate [15–17]. Therefore, not only primary DRV but also DRX mechanisms of the β-type titanium alloys can be activated via the optimization of the TMP and their microstructure refinement is expected with aid of the above multiple mechanisms during hot forging and rolling.

Ti2448 (abbreviated from its weight percent composition Ti-24Nb-4Zr-8Sn) is a typical example of the multifunction titanium alloys with high strength and low elastic modulus [4]. The alloy is biocompatible because of containing only the non-toxic and non-allergic elements. Typical implants made of the alloy have been finished clinical trials in several qualified hospitals and applied for product licenses to FDA of China. The recent investigations have shown that the multiple warm-processed alloy exhibits much better balanced mechanical and functional properties due to the fabrication of a homogenous ultrafine-grained microstructure [18, 19]. In this study, the microstructure evolution of Ti2448 alloy was investigated during TMP by varying both strain rate and temperature, in hoping of optimizing the microstructure and, correspondingly, the biomechanical properties of the alloy.

Experimental

An ingot of Ti2448 alloy with a diameter of 380 mm was fabricated by vacuum arc melting using a Ti–Sn master alloy and pure Ti, Nb, and Zr as raw materials. The composition determined by chemical and gas analyses is listed in Table 1. The ingot was forged and then rolled at 850 °C to slab with a thickness of 12.5 mm.

Table 1 Chemical composition of Ti2448 alloy (weight percent)
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Cylindrical samples with a diameter of 8 mm and a length of 12 mm were cut from the hot-rolled slab and compressed uniaxially using Gleeble 3800 isothermal thermal simulator. The compression was conducted at strain rates ranged between 0.001 and 70 s−1 and temperatures ranged between 700 and 850 °C in the single β-phase field. Prior to the test, the samples were heated to the targeted temperatures and then held for 2 min to ensure temperature homogeneity. During the compression, the instant temperature was measured by thermocouples welded to the center area of the sample surface. Nickel powder was daubed on the two end surfaces of the sample to alleviate friction. Tantalum foil with a thickness of 0.05 mm was laid between the anvil and the sample to prevent felting. The height reductions are selected to be 18, 50, and 75 %, corresponding to the true strain of 0.2, 0.7, and 1.4, respectively. The compressed samples were cooled in water and then sectioned along the compression axis for microstructure examination.

LEO Supra 35 field emission SEM equipped with a fully automatic electron back-scattering diffraction (EBSD) analysis system was used for the microstructure observation. The EBSD images were acquired using step sizes of 0.8–1.4 μm for the overall deformation microstructure. An area of about 580 × 430 μm in central parts of deformed samples was scanned at each strain level. HKL Channel 5 software was used to perform data acquisition and post-processing. Transmission electron microscopy (TEM) samples were cut from the center of deformed samples and prepared by twin-jet electro-polishing in a solution of 21 % perchloric acid, 50 % methanol, and 29 % n-butyl alcohol at about −23 °C and a voltage of 15 V. The thin foils were examined using a Tecnai G2 20 microscope operated at 100 kV.

Results

Original Microstructure

EBSD image (Fig. 1a) shows that the original hot-rolled alloy has an equiaxed β-phase microstructure with an average grain size of ~65 μm, in which most of these grain boundaries are high-angle boundaries (HABs) with a misorientation angle above 15° (noted by black line) and a few are low-angle boundaries (LABs) (noted by white line). TEM observation found that these coarse grains contain many sub-grains with small misorientation angle less than 2° in general (Fig. 1b), beyond the detectable limitation of the EBSD analysis. The above results are consistent with the previous report [18].

Fig. 1
figure 1

EBSD (a) and TEM (b) images of the original microstructure of Ti2448 alloy. In a, crystal orientation is marked by the inset color code, and high angle (>15°) and low angle (<15°) grain boundaries are noted by black and white lines, respectively

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Strain Rate Sensitivity

The typical true stress–strain curves measured at 750 °C under different strain rates are shown in Fig. 2a, showing clearly a strain rate sensitivity of flow behavior. At the strain rate of 70 s−1, the flow stress rises to a peak at the beginning of loading and then reaches a multi-peak stage before the final steady state, a typical behavior of the DDRV process [20]. At the strain rates of 10 s−1 and 1 s−1, strain hardening stage exist until the steady state. As the strain rate is less than 0.1 s−1, the initial stress peak is followed by a strain softening and subsequent steady state. Such initial stress peak, which is considered generally as discontinuous yielding, is common for the β-type titanium alloys, which can be explained by a sudden generation of gliding dislocations [16]. Such strain rate sensitivity behavior is also observed at other temperatures, as exampled by the selected stress–strain curves shown in Fig. 2b.

Fig. 2
figure 2

True stress–strain curves (a, b) and the relationship between flow stress and strain rate (c, d)

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The relation between the true stress and the strain rate is shown in Fig. 2c. To estimate the strain rate sensitivity factor m, the above measured flow stresses and the corresponding strain rates are plotted in Fig. 2d. It is clear that there exists a critical strain rate of ~1 s−1. Below the value, the factor m is ~0.265, which is located at the normal range of the conventional β-type titanium alloys being 0.2–0.3 [21–23]. Above the value, however, the factor m is ultra-low ~0.032. Thus, the flow stress and strain rate of the alloy follows a bilinear relation [21], which is in sharp contrast with other metallic materials obeying the monotonic linearity [22, 23]. Additionally, Fig. 2d shows that the factor m in both strain rate regions decrease slightly as the temperature decreased. As a result, the temperature decrease leads also to a slight decrease of the critical strain.

The above bilinear relation cannot be explained by the temperature increase caused by the compression because the data were corrected by the common method proposed by Dadras and Thomas [24]. To alleviate the effect of temperature increase, the data measured at a small strain of 0.2 were used to estimate the factor m above the critical strain. The additional results confirmed also the extremely low value of m. Thus, the bilinear relation should be an intrinsic behavior of the alloy. In the following, we try to reveal the origin via the measured processing map, misorientation accumulation, sub-grain evolution, and localized grain refinement.

Processing Maps

To estimate the processing map of Ti2448 alloy, dynamic material model (DMM) was adopted in the study [25–27]. Since the alloy has variable factor m (Fig. 2d), the Murty’s criterion was applied to determine the power dissipation of the DMM and the plastic instability [28]. Thus, the power dissipated by viscoplastic heat (G) is shown as Eq. (1), the power dissipation efficiency (η) is expressed as Eq. (2) and the criterion for instable flow is deduced as Eq. (3).

$$G = \int_{0}^{{\dot{\varepsilon }_{\hbox{min} } }} {\sigma {\text{d}}\dot{\varepsilon } + \int_{{\dot{\varepsilon }_{\hbox{min} } }}^{{\dot{\varepsilon }}} {\sigma {\text{d}}\dot{\varepsilon } = \left[ {\frac{{\sigma \dot{\varepsilon }}}{m + 1}} \right]_{{\dot{\varepsilon } = \dot{\varepsilon }_{\hbox{min} } }} } } + \int_{{\dot{\varepsilon }_{\hbox{min} } }}^{{\dot{\varepsilon }}} {\sigma {\text{d}}\dot{\varepsilon }}$$
(1)
$$\eta = 2\left[ {1 - \frac{1}{{\sigma \dot{\varepsilon }}}\left( {\left[ {\frac{{\sigma \dot{\varepsilon }}}{m + 1}} \right]_{{\dot{\varepsilon } = \dot{\varepsilon }_{\hbox{min} } }} + \int_{{\dot{\varepsilon }_{\hbox{min} } }}^{{\dot{\varepsilon }}} {\sigma {\text{d}}\dot{\varepsilon }} } \right)} \right]$$
(2)
$$2m < \eta {\text{ or }}\eta \le 0.$$
(3)

The power dissipation efficiency maps at strain of 0.2, 0.7, and 1.2 are shown in Fig. 3a–c. It is clear that the power dissipation exhibits a similar variation tendency as the strain increased and the η is more sensitive to strain rate than temperature. In the high η domain, the microstructure evolution dominates the plastic flow, while, in the low η domain, the total power is dissipated mainly by the viscoplastic heat. All the η values were kept between zero and 2m, suggesting stable plastic flow of Ti2448 alloy.

Fig. 3
figure 3

The processing maps of Ti2448 alloy at the strain of 0.2 (a), 0.7 (b), and 1.2 (c)

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Microstructure Evolution

To evaluate the microstructure evolution, the samples deformed at 750 °C under the strain rate of 0.01 and 10 s−1 were selected to present EBSD images (Fig. 4). At the strain rate of 0.01 s−1, a small strain of 0.2 can induce the LABs and accommodated lattice distortion especially near to grain boundaries and triple junctions (Fig. 4a). As the strain rate increased to 0.7 (Fig. 4b), they are visible more clearly and spread from grain boundaries to the grain interiors. Several micron-scale grains appear in the original boundaries, in accordance with the CDRX process characterized by the transformation from LABs into HABs [29]. Both the strain accommodation and CDRX process are enhanced as the strain increased to 1.4 (Fig. 4c). The lattice distortion indicated by color gradient evolves into regular sub-grain boundaries, implying the primary DRV process operated at low strain rate of 0.01 s−1. Additionally, micron-scale grains with HABs can also be induced by dislocation rearrangement.

Fig. 4
figure 4

EBSD micrographs of Ti2448 alloy compressed at 750 °C under the strain rate of 0.01 s−1 (a–c) and 10 s−1 (d–f). The strain from the upper to below is 0.2, 0.7, and 1.4. Elongation direction and normal direction are noted by ED and ND, respectively

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At the strain rate of 10 s−1, a small strain of 0.2 leads to more strain-induced LABs and accommodated lattice distortion than that of the low strain rate of 0.01 s−1 (Fig. 4d). The newly developed HABs at the original boundary regions (arrows noted) demonstrate that the CDRX process is operative to change the LABs into HABs [29, 30]. As the strain rate increased to 0.7 (Fig. 4e), the original grains become pancake-shaped and contain more LABs and lattice distortion, and their boundaries are decorated by a few grain inter-layers. At 1.4 strain (Fig. 4f), micron-scale grains congregate at the triple junctions, suggesting the concentrated strain promotes the formation of LABs and accelerates the transformation from LABs into HABs [31, 32]. Thus, the DRX process including CDRX and DDRX is activated at high strain rate of 10 s−1.

The other compressed samples under different temperatures and strain rates were also observed by EBSD and several examples with the strain rate of 1.4 are given in Fig. 5. The results showed clearly that the DRV is more significant at higher temperature and lower strain rate. On the contrary, the DRX is stronger.

Fig. 5
figure 5

EBSD micrographs of Ti2448 alloy compressed to a strain of 1.4: a 700 °C, 0.001 s−1; b 850 °C, 0.001 s−1; c 700 °C, 70 s−1; d 750 °C, 70 s−1

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Misorientation Distributions

To trace the microstructure evolution quantitatively, the crystal misorientations of the compressed samples were measured and the results are presented in Fig. 6. From these data, the fraction of LABs (FLABs) and the averaged misorientation angles of LABs (θLABs) and HABs (θHABs) were estimated (Fig. 6).

Fig. 6
figure 6

Misorientation distributions of the original microstructure (a) and the deformed microstructure (b–r), in which the random distribution of cubic crystal noted by blue curve (Color figure online)

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The original alloy follows roughly a random distribution of cubic crystal with small FLABs of 4.6 % and θLABs of 8.5º (Fig. 6a). After the hot compression, the crystal misorientations become nearly unimodal distribution (Fig. 6b–r). The microstructure deformed at high strain rate of 1–70 s−1 has more FLABs and θHABs but fewer θLABs than that of low strain rate of 0.001–0.1 s−1. The increased sub-grain and transformation from LABs into HABs are in agreement with the enhanced CDRX and DDRX process. Additionally, the HABs tend to be distributed randomly (as the blue lines indicated).

Strain-Induced Sub-Micron Crystallites

Strain-induced sub-micron crystallites and the localized grain refinement are two important features of the deformed microstructures because both are associated with the substructure development [33–36]. Three typical orientation accumulations, which were detected along L1, L2, and L3 directions in Figs. 4 and 5, are shown in Fig. 7. The first is a continuous orientation accumulation (Fig. 7a) that the cumulative orientation displayed by point-to-origin profile increases continuously up to about 16°, indicating a long-range continuous lattice distortion but the step is small, less than 2° in general. The second is orientation jump (Fig. 7b), which is also called orientation band. It is clear that four sub-grains display four orientation jumps along 80 μm distance (Fig. 7b). Moreover, LABs with small misorientation and lattice distortion were not observed in these sub-grains, which can be explained by a strong DRV process. The third is multi-peak orientation distribution (Fig. 7c). The point-to-origin profile exhibits multiple waves, which indicates that the lattice distortion is multidirectional rather than a long-range continuous. Furthermore, the point-to-point profile shows LABs with high density.

Fig. 7
figure 7

Three typical misorientation accumulation patterns of continuous accumulation (a), orientation jump (b), and multi-peak orientation distribution (c), corresponding to L1 in Fig. 4b, L2 in Fig. 5a, and L3 in Fig. 5d, respectively

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The three types of accumulation patterns were observed in all microstructures deformed at different strain rates and temperatures. Statistically, the first continuous accumulation is more prevalent at lower strain rate, the second orientation jump favors to low strain rate and large strains while the multi-peak orientation distribution tends to be stronger at higher strain rate.

Localized Grain Refinement

The experimental results showed that the localized grain refinement is favored by both high strain rate and large deformation strain. In the localized region (Fig. 4e), the DRX grain layers align along the original boundaries and develop in the region with large strain. The localized grain refinement becomes more obvious (Fig. 4f), where the DRX layers expand into the grain interior and incline to consume the original grains. Simultaneously, the LABs with high density subdivide the elongated grains into several fragments, and then evolve into HABs by misorientation accumulation as the deformation increased.

This localized refinement is favorable to the center region of sample as deformed at 850 °C and high strain rate of 70 s−1 (Fig. 8). Figure 8a gives an example of the refined grains with HABs, containing abundant sub-grains with LABs. Statistical analysis shows that these grains with size less than 1 μm are about 80 %. Additionally, the misorientation angles of these refined grains display a random distribution of cubic crystal (Fig. 8b), being similar with that of the original coarse grains (Fig. 6a). The reconstructed pole figures also exhibit a random orientation in this localized refinement region (Fig. 8c).

Fig. 8
figure 8

Grain-refined region of the sample deformation at 850 °C under a strain rate of 70 s−1 (a) and its misorientation distributions (b) and reconstructed texture pole figures (c)

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Discussions

The Low m Value

The strain-hardening behavior of Ti2448 alloy can be described by a bilinear relation (Fig. 2d), which is in sharp contrast with other metallic materials obeying the monotonic linearity [22, 23]. At the low-strain rate region, the sensitivity factor m is ~0.265, which is identical with other materials. However, as the strain rate over ~1 s−1, it decreases sharply to an ultra-low value of ~0.03 (Fig. 2d). This novel behavior can’t be explained by the transition of microstructure evolution mechanisms from DRV to DRX, although the DRX is a softening mechanism which is stronger at larger strain (Figs. 3 and 4). This is confirmed further by additional data of the factor m being independent of deformation strain.

The ultra-low m at high temperature in single β-phase field would relate with the ultra-weak work hardening rate of the alloy at room temperature and its induced plastic instability. The previous study found that its coarse-grained microstructure can be refined easily by cold deformation and, compared with the coarse-grained alloy, the nanostructured alloy has strength higher only ~5 % [37, 38]. Since these novel behaviors are unexpected from other materials including shape memory alloys, it was termed as soft nanostructured alloy [37]. The lack of work hardening and the plastic instability at room temperature are in agreement with the alloy exhibiting an extreme high strength-to-modulus ratio reaching ~2 % [4], which is as high as that of these brittle amorphous materials. The in situ high-resolution TEM analyses found several novel strengthening and reversible mechanisms such as the nano-scale disturbance of BCC crystal and the homogeneously nucleated dislocation loops in advance of the formation of nano-sized martensite with equiaxed morphology [39]. These reversible mechanisms should be much sluggish because their movement can be easily detected by high-resolution TEM analysis. Furthermore, the nano-sized equiaxed martensite, unlike the micron-scale internally twinned martensitic plates commonly observed in shape memory alloys, reveals the MT in the alloy is confined by unknown factors.

Under the assumption that these sluggish deformation mechanisms are operative at high temperature, the alloy should behave like other metallic materials at extreme high strain rate. This can explain the origin of its ultra-low critical strain of ~1 s−1, which is lower about several orders of magnitude than other crystal materials. Since both DRV and DRX are available at high temperature, the alloy is plastic stable (Fig. 3). Thus, the microstructure evolution of the alloy can be described as the dislocation movements (Fig. 9a), cell structure formation (Fig. 9b), and then the DRX to cause the localized grain refinement at high strain rate.

Fig. 9
figure 9

Abundant dislocations (a) and cell structure (b)

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Localized Grain Refinement

As the alloy compressed at the single β-phase field, the localized refinement is produced by DRX, including CDRX and DDRX. Generally, the DDRX is observed commonly in metallic materials with face-centered cubic (FCC) crystal structure, such as pure Cu [40], Ni-20 %Cr alloy [12], and Nimonic 80a alloy [41], in which the grain boundary especially triple junction serve as the preferential sites for nucleation. These boundaries bugle out and prone to form new nucleation to satisfy the decrease in interfacial energy. For the studied alloy with BCC structure, the DDRX nucleation is enhanced by boundary bugling intensified by the concentration strain, leading to the formation of the micron-scale grains with regular boundaries and fewer dislocations (Fig. 10a). Another grain refinement mechanism is CDRX, which is considered as a continuous process started from dislocations, cell structures, and sub-grains to produce the refined grains with HABs [12]. The transformation from cell boundaries to LABs, and then HABs shows a continuous dislocation accumulation process (Fig. 10b). This is similar with that of FCC metals [42, 43]. This behavior was also observed in some BCC metals under the condition of high-speed deformation [44].

Fig. 10
figure 10

TEM images of the grain-refined regions showing the DDRX grains (a) noted by white arrows and the CDRX process from LABs to HABs (b)

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Although the localized grain refinement is unusual for the studied alloy, the homogenous ultrafine-grained microstructure cannot be obtained by the single-step compression at high temperature. However, the repeated deformation such as hot forging would be possible. This was confirmed by multi-step warm deformation that the coarse grains were refined to ~0.2 μm [18, 19]. Compared with the nanostructured Ti2448 alloy, which was obtained by cold deformation [37, 38], the warm-processed alloy exhibits much better balance among strength, ductility, and superelasticity.

Conclusions

Microstructure evolution and strain rate sensitivity of Ti2448 alloy were studied by the uniaixal compression deformation at temperature of 700–850 °C and strain rate of 0.001–70 s−1. Following conclusions are drawn:

  1. (1)

    The alloy has two linear strain-hardening regions separated by a critical strain of 1 s−1. The strain rate sensitivity factor is similar with other metallic materials at the low-strain region (below 1 s−1) but decreases about one order of magnitude to 0.03 at the high-strain region (above 1 s−1).

  2. (2)

    The dynamic recovery (DRV) is dominant at all deformation conditions in the single β-phase field, while both high strain rate and large deformation strain favor to the discontinuous and continuous dynamic recrystallization (DDRX and CDRX).

  3. (3)

    Both microstructure characterization and processing map show that the alloy is plastic stable at high temperature.