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Mechanics of Materials
Dependences of Grain Size and Strain-Rate on Deformation Behavior of Commercial Purity Titanium Processed by Multi-Directional Forging
S. YamamotoY. MiyajimaC. WatanabeR. MonzenT. TsuruH. Miura
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2020 Volume 61 Issue 12 Pages 2320-2328

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Abstract

Strain rate dependencies of deformation behavior of commercial purity titanium specimens having different grain sizes were systematically investigated. Ultrafine-grained titanium with an average grain size of 0.07 µm (UFG-Ti) fabricated by multi-directional forging followed by conventional thermo-mechanical processing, and fine-grained (FG-Ti) and coarse-grained (CG-Ti) specimens with an average grain sizes of 0.8 and 12 µm attained by its, respectively, annealing at 773 and 973 K for 1.8 ks were prepared. The FG- and UFG-Ti specimens exhibited strong strain-rate dependence of 0.2% proof stress, while that of CG-Ti ones were almost constant regardless of applied strain-rate. In-situ X-ray diffraction measurements during tensile tests were also conducted at synchrotron radiation facility, SPring-8. Using the modified Williamson-Hall and the modified Warren-Averbach methods, the activated slip systems and change in dislocation density during deformation were estimated. As a result, it was found that ⟨a⟩ and ⟨c + a⟩ slips were activated in FG- and UFG-Ti specimens. On the other hand, the activation of ⟨c + a⟩ slip was never observed in the CG-Ti ones. It can be, thus, concluded that the different strain-rate dependency of deformation behaviors of specimens with different grain sizes were ascribed to the difference in the deformation mechanisms.

 

This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 83 (2019) 465–473.

1. Introduction

Commercially purity titanium (CP-Ti) has been widely used as metallic biomaterials for dentistry and orthopedics due to its high specific strength and excellent biocompatibility.1) Essentially, Ti alloys such as Ti–Al–V alloys are used instead of CP-Ti because of insufficient strength of the latter for the artificial joints and implants.2) However, it is reported that the Ti alloys have problems, i.e., i) worse biocompatibility compared to that of CP-Ti, ii) toxicity due to the alloying elements, and iii) poor machinability.2,3)

It is well-known that grain refinement of metallic materials can induce drastic improvement of mechanical properties without any addition of alloying elements.4,5) One major method to achieve the ultra-fine grained (UFGed) structure is severe plastic deformation (SPD), and various methods for SPDs have been invented. Actually, there are plenty of reports on modification of mechanical properties of metals and alloys to attain superior balance of mechanical properties.57) The CP-Ti is known as its poor plastic deformability since it possesses only two independent slip systems (prismatic ⟨a⟩ slip) activated at room temperature (RT) due to its crystal structure (close-packed hexagonal structure: HCP), which cannot satisfy the von Mises criterion.8) Up to now, several attempts of SPDs of CP-Ti have been conducted to achieve UFGed structure.912) In many of these attempts, the SPDs were applied at elevated temperatures to promote non-prismatic slip deformation.10,11)

On the other hand, Miura and Kobayashi successfully produced UFGed CP-Ti utilizing multi-directional forging (MDFing) at RT.13) The MDFing can precisely and flexibly control the amount of each forging pass strain, whereas the most of the other SPDs represented by equal-channel angular pressing (ECAP) have to introduce a large amount of fixed strain per each processing cycle. Moreover, sharp texture evolution, which makes subsequent plastic deformation difficult, can be effectively suppressed because of change of forging direction, and therefore, MDFing up to high cumulative strain regions becomes possible even at RT. Furthermore, Miura and Kobayashi reported that the MDFing followed by thermomechanical treatment including cold rolling successively produced large plates of UFGed CP-Ti with an average grain size of less than 100 nm.13) The UFGed CP-Ti exhibited extremely high strength/ductility balance with a tensile strength of 930 MPa and an elongation of 14%.13) The mechanical properties of the UFGed CP-Ti surpassed those of the Ti–6Al–4V alloy which is generally used as a high-strength biomaterial.14) However, deformation behaviors and mechanisms of UFGed CP-Ti have not been fully understood yet.

Recently, many researchers have pointed out the characteristic deformation behavior of UFGed metallic materials. For instance, the strain-rate dependence of flow stress of face-centered cubic (FCC) metals is significantly increased with decreasing grain size.1518) It has been widely recognized that the probability of dislocation sources in grain interior became lower with decreasing grain size down to submicron order, and thus, the rate-controlling process of plastic deformation changes over to the emission of dislocations from boundaries.19,20) There are also several reports on characteristic deformation behaviors of UFGed HCP metals. Choi et al. investigated the mechanical properties of a UFGed ZK60Mg alloy fabricated by high-pressure torsion (HPT) processing and reported that the strain-rate-sensitivity of flow stress became larger by grain refinement.21) Watanabe et al. systematically investigated the grain size and strain-rate dependences of ductility of AZ Mg alloys22) and revealed that the elongation to fracture remarkably decreased with increasing the strain rate and/or flow stress when grain size reduced to 1 µm or less. They attributed it to loss of contribution of RT grain-boundary sliding. Saitova et al. demonstrated tensile/compression deformation behaviors at elevated temperatures of Ti–6Al–4V alloys with average grain sizes of 600 nm and 5 µm23) and reported that the strain-rate dependence of flow stress significantly increased by grain refinement. Unfortunately, the causes of the change in strain-rate dependence of flow stress due to grain refinement have not been clarified yet.

In the present study, as the first step for the comprehensive understanding of the deformation mechanisms of UFGed CP-Ti, the strain-rate dependence of the tensile deformation behavior was investigated. The UFGed CP-Ti was produced by combination of MDFing and conventional thermomechanical treatment. Moreover, in-situ X-ray diffraction measurements were performed during tensile tests at the synchrotron radiation facility of the Super Photon Ring – 8 GeV (SPring-8, Hyogo, Japan). The changes in the dislocation density and the ratio of active slip systems were quantitatively evaluated with a maximum time resolution of 1 s. Furthermore, specimens with the different grain sizes were prepared by annealing of the UFGed CP-Ti, and investigations were conducted in the same way. Based on the obtained results, the mechanisms of strain-rate and grain-size dependencies of deformation behavior of CP-Ti was discussed.

2. Experimental Procedure

The JIS grade 2 CP-Ti sheets having dimensions of 50-mm width × of 0.5-mm thickness and 750-mm length provided by Kawamoto Heavy Industries, Ltd. were employed. The sheets are composed of homogeneous UFGed structure developed by combined processes of MDFing at RT and conventional thermomechanical treatment including cold-rolling.13) The chemical composition of the CP-Ti is shown in Table 1. Some of the sheets were annealed at 773 and 973 K for 1.8 ks. Using an Instron-type universal mechanical testing machine (Shimadzu, AG-10kNX plus), tensile tests were conducted under three strain rates $\dot{\varepsilon }$ of 10−5, 10−3 and 10−1 s−1 at RT. Specimen pieces for tensile tests were cut from the sheets using a wire electric discharge machine so that the loading axis was parallel to the rolling direction (R.D.) and perpendicular to the transverse direction (T.D.). The dimensions of the gauge section of the specimen pieces were 5L × 2W × 0.5T mm3.

Table 1 Chemical composition of a CP-Ti used in this study (mass%).

Microstructural observations were performed before and after tensile tests. The surface of the specimens was observed using a scanning electron microscopy (SEM, JEOL JSM-7900F). The substructure observations were conducted using a transmission electron microscopy (TEM, FEI TECNAI G2). Disk-shaped specimens with a diameter of 2.5 mm were cut out so that the incident beam was parallel to normal direction (N.D.). Thin foils for TEM observation were prepared by mechanical polishing using SiC papers and then electrolytic polishing by the twin jet method using a solution of methanol:2-butoxyethanol:perchloric acid = 12:7:1 (volume ratio) under the conditions of the voltage of 21 V and temperature of 243 K.

Furthermore, using a tensile tester equipped on the goniometer of beamline BL-46XU at the SPring-8, tensile tests were performed at RT at $\dot{\varepsilon } = 10^{ - 3}$ s−1. The test pieces were cut out as the tensile axis was parallel to the R.D. The specimen pieces have two shoulders to be irradiated with X-rays on the deformed portion of the specimens as much as possible, as shown in Fig. 1. During the tensile tests, in-situ X-ray diffraction measurements were performed in the transmission arrangement referring the previous report as follows.24) The energy of the incident beam was 30 keV, which corresponds to the wave length λ of 0.041 nm. A one-dimensional semiconductor detector was used to detect the diffracted X-rays. The detector was installed on the plane, including the tensile direction and the incident beam. The camera length was set about 700 mm, and the X-ray beam was incident on the center of the gauge section of specimens. Diffracted X-rays were measured in the range of 2θ = 5°∼35°. The maximum time resolution of the measurement was approximately 1 s. Using the obtained X-ray diffraction profiles, the modified Williamson-Hall method and the modified Warren-Averbach method were utilized to evaluate the change in the ratio of the activated slip systems and dislocation density.25,26)

Fig. 1

Schematic illustration of specimens for in-situ X-ray diffraction measurements during tensile tests.

3. Results

Figure 2 displays a bright-field TEM image of the as-received CP-Ti sheet. In the upper right of Fig. 2, the selected-area-diffraction pattern obtained from the center of the image is shown. The pattern was taken using a selected-area aperture with a diameter of 1.7 µm, and it showed the typical ring feature. Thus, it can be confirmed that many grain boundaries are of high-angle ones. The grain size was measured by the line-intercept method. Over 100 grains were measured, and the average was 0.07 µm, which was almost identical to a previous report.13) Figure 3 displays a typical bright-field TEM image of the specimen annealed at 773 K for 1.8 ks. The grains were coarsened by recrystallization followed by grain growth to have an average size of approximately 0.8 µm. In the specimen annealed at 973 K for 1.8 ks, the grains grew to be about 12 µm in average. Hereafter, the specimens having different grain sizes will be referred to as 0.07-Ti, 0.8-Ti, and 12-Ti, respectively.

Fig. 2

TEM image of an ultrafine-grained CP-Ti specimen fabricated by MDFing and conventional thermo-mechanical treatments. The inset is a selected area diffraction pattern taken using a selected-area aperture of 1.7 µm in diameter.

Fig. 3

TEM image of a coarse-grained CP-Ti specimen obtained by annealing at 773 K for 1.8 ks of the supplied ultrafine-grained CP-Ti plate.

Tensile tests were conducted at RT at various initial strain rates $\dot{\varepsilon }$ of 10−5, 10−3, 10−1 s−1. Figure 4 shows the nominal stress-nominal strain curves attained by tensile tests, and the results of tensile strength σUTS, 0.2% proof stress σ0.2 and elongation to fracture εf are summarized in Table 2. The σUTS of each specimen increased with increase in strain rate. The σ0.2 of the 0.07-Ti and 0.8-Ti also increased in the same way, while almost no distinct change was observed in the 12-Ti. The εf exhibited no strain-rate dependency in all three specimens. Changes in σ0.2 and σUTS as a function of $\dot{\varepsilon }$ plotted in Fig. 5. The result that all the plots are on linear lines indicates clear strain-rate dependence of σ0.2 and σUTS. The strain-rate sensitivity m is expressed by the following equation:   

\begin{equation} m = \frac{\mathrm{d}\ln \sigma}{\mathrm{d}\ln \dot{\varepsilon}} \end{equation} (1)

Fig. 4

Stress–strain curves of the CP-Ti specimens with different grain sizes of 0.07, 0.8 and 12 µm. Tensile tests were conducted at $\dot{\varepsilon } = 10^{ - 5}$, 10−3 and 10−1 s−1 at RT.

Table 2 Ultimate tensile stress σUTS, 0.2% proof stress σ0.2 and fracture strain εf of CP-Ti specimens with different grain sizes of 0.07, 0.8 and 12 µm obtained from tensile tests conducted at $\dot{\varepsilon } = 10^{ - 5}$, 10−3 and 10−1 s−1 at RT.
Fig. 5

Strain-rate dependencies of ultimate tensile stress and 0.2% proof stress at RT of the specimens bearing different grain sizes of 0.07, 0.8 and 12 µm.

Thus, the values of m can be calculated from the slopes of Fig. 5. Although there are only three data points, the values of m for σ0.2 and σUTS were obtained by applying the least-squares method and are listed in Table 3. The value of m for σ0.2 obtained from each specimen became larger as the grain size decreased. Therefore, it can be stated that the strain-rate dependence of σ0.2 becomes more significant by grain refinement. On the other hand, concerning σUTS, the values of m for 0.07-Ti and 0.8-Ti are almost constant while the value for 12-Ti was the largest. It should be noted that the strain-rate dependencies of σUTS exhibits different tendencies from that of σ0.2.

Table 3 Strain-rate sensitivity m of the CP-Ti specimens bearing different grain sizes of 0.07, 0.8 and 12 µm.

Diffraction profiles obtained by the in-situ X-ray diffraction measurements were analyzed, and the changes in the ratio of activated slip systems and dislocation density during tensile test were estimated. The full width at half maximum Δθ of each diffraction peak was determined using the pseudo-Voigt function.24) The obtained values of Δθ were applied to the modified Williamson-Hall method, expressed by the following equations26)   

\begin{equation} [(\Delta K)^{2} - \alpha]/K^{2} \cong \beta \cdot \overline{C_{\text{hk.$\,$l}}} \end{equation} (2)
  
\begin{equation} \overline{C_{\text{hk.$\,$l}}} = \overline{C_{\text{hk.$\,$0}}}(1 + q_{1}x + q_{2}x^{2}) \end{equation} (3)
  
\begin{equation} x = \frac{2}{3}\left(\frac{l}{ga} \right)^{2} \end{equation} (4)
where K = 2 sin θ/λ and ΔK = 2 cos θ(Δθ)/λ. θ and λ are the Bragg angle and the wavelength of X-ray (= 0.041 nm), respectively. β is a constant depending on the dislocation density and the magnitude of the Burger’s vector. $\overline{C_{\text{hk}.\,\text{l}}}$ is the average contrast factor of dislocations corresponding to (hk.l) reflection and is expressed by eq. (3).26) q1 and q2 are parameters based on the elastic constant of the material, and $\overline{C_{\text{hk}.\,0}}$ is the average contrast factor of the dislocations corresponding to the (hk.0) reflection. l in the eq. (4) is the last index of (hk.l) reflection, g is the reflection vector, and a is the lattice constant (= 0.295 nm27)). Utilizing the eqs. (2) and (3), the value of α can be analytically determined so that the relation between [(ΔK)2 − α]/K2 and x became quadratic functions. Figure 6 exemplifies the data for specimens ($\dot{\varepsilon } = 10^{ - 3}$ s−1, plastic strain εp = 0.01) plotted according to eq. (2).

Fig. 6

Modified Williamson-Hall plots of CP-Ti specimens with grain sizes of (a) 0.07, (b) 0.8 and (c) 12 µm tensile deformed to just after yielding (εp = 0.01) at $\dot{\varepsilon } = 10^{ - 3}$ s−1 at RT.

From the obtained α value, the coefficients q1 and q2 in eq. (3) were determined. Using these values, the ratio of slip system activity hi were estimated from the following equation.26)   

\begin{equation} \overline{b^{2}C_{hk.l}} = \sum_{i = 1}^{3}h_{i} \cdot \overline{C_{hk.l}}^{(i)} \cdot b_{i}^{2} \end{equation} (5)

Table 4 lists the typical slip systems of HCP metals.28) The slip systems of HCP metal are roughly classified into three types, they are ⟨a⟩ slip, ⟨c⟩ slip and ⟨c + a⟩ slip. Here in eq. (5), i = a, c or c + a, and bi is the magnitude of the Burger’s vector of each slip system. Moreover, the values of $\overline{C_{hk.0}}^{(i)}$, $q_{1}^{\text{(}i\text{)}}$, and $q_{2}^{\text{(}i\text{)}}$ have been reported in a previous literature,29) and were put to use in eq. (3) in this study. For example, $\overline{C_{hk.0}}^{(\text{a})} = 0.354$, $q_{1}^{\text{(a)}} = - 1.19$, $q_{2}^{\text{(a)}} = 0.356$ for the prismatic ⟨a⟩ slip.

Table 4 The most common slip systems in hexagonal crystals.

Dislocation density ρ was evaluated using the modified Warren-Averbach method expressed as below,26)   

\begin{align} \ln A(L)& \cong \ln A^{\text{s}}(L) - \rho \frac{\pi}{2}L^{2}\ln \left(\frac{R_{\text{e}}}{L} \right)(K^{2}\overline{b^{2}C_{\text{hk.$\,$l}}}) \\ &\quad + Q\left(\frac{\pi}{2} \right)^{2}L^{4}\ln \left(\frac{R_{1}}{L} \right)\ln \left(\frac{R_{2}}{L} \right)(K^{4}\overline{b^{2}C_{\text{hk.$\,$l}}}^{2}). \end{align} (6)
Here, A(L) is the real part of the Fourier coefficient of the measured X-ray profile, As(L) is the Fourier coefficient based on the grain size, and L is the Fourier length. Re is the interaction distance amongst dislocations, and Q, R1 and R2 are all constants.

Figure 7 exemplifies the plots of the real parts A(L) of the Fourier coefficient of the measured X-ray profile against $K^{2}\overline{b^{2}C_{\text{hk}.\,\text{l}}}$. The values of $\overline{b^{2}C_{\text{hk}.\,\text{l}}}$ were obtained from eq. (5). Quadratic functions between ln A(L) and $K^{2}\overline{b^{2}C}$ can be analyzed by the least-squares method. Let Y be the coefficient of the first-order term of the obtained quadratic function, and then the following equation can be obtained by comparing the first-order term of eq. (6).26)   

\begin{equation} \frac{Y}{L^{2}} = \left(\frac{\pi}{2} \right)\rho \ln R_{e} - \left(\frac{\pi}{2} \right)\rho \ln L \end{equation} (7)
According to the eq. (7), Y/L2 were plotted against ln L (Fig. 8). From the slopes in Fig. 8, the values of ρ were estimated.26)

Fig. 7

Modified Warren-Averbach plots of CP-Ti specimens with grain sizes of (a) 0.07, (b) 0.8 and (c) 12 µm tensile deformed to just after yielding (εp = 0.01) at $\dot{\varepsilon } = 10^{ - 3}$ s−1 at RT.

Fig. 8

X/L2 versus ln L plots of CP-Ti specimens with grain sizes of (a) 0.07, (b) 0.8 and (c) 12 µm tensile deformed to just after yielding (εp = 0.01) at $\dot{\varepsilon } = 10^{ - 3}$ s−1 at RT.

Figure 9 shows the changes in the Burger’s vector population against the εpf. The changes in nominal stress are also shown in Fig. 9. The ratio of ⟨a⟩ slip system is high by far in all specimens, indicating that the slip system was activated as the dominant slip system. For the 0.07-Ti and 0.8-Ti, compared with the 12-Ti, the activity ratio of the ⟨c + a⟩ slip system was evidently higher from the early stage of deformation, and it increased further as the εp increased. The activity ratio of the ⟨c⟩ slip system was very low compared with the other slip systems (⟨a⟩ slip, ⟨c + a⟩ slip) and appeared almost constant. On the other hand, in the 12-Ti, no significant changes in the activity ratio of the slip systems were observed whereas εp increased.

Fig. 9

Change in Burgers vector population in CP-Ti specimens with different grain sizes of (a) 0.07, (b) 0.8 and (c) 12 µm against normalized plastic strain εpf. Also shown is a change in nominal-stress against εpf obtained from tensile tests conducted at $\dot{\varepsilon } = 10^{ - 3}$ s−1 at RT.

The changes in ρ of each specimen during the tensile test are plotted in Fig. 10 together with the nominal stress. Here, as same in Fig. 9, the horizontal axis is εpf. The dislocation density in the as-cold worked 0.07-Ti is much higher than those in the annealed 0.8-Ti and 12-Ti. In the 0.07-Ti and 0.8-Ti with submicron grain sizes, the dislocation density increased monotonically with increasing εp. However, the ρ in the 12-Ti increased at the initial stage of deformation and then saturated to a substantially constant value.

Fig. 10

Change in dislocation density in CP-Ti specimens with different grain sizes of (a) 0.07, (b) 0.8 and (c) 12 µm against normalized plastic strain εpf. Also shown is a change in nominal-stress against εpf obtained from tensile tests conducted at $\dot{\varepsilon } = 10^{ - 3}$ s−1 at RT.

The surface of the 12-Ti was observed just after yielding ($\dot{\varepsilon } = 10^{ - 3}$ s−1, εp = 0.01). Figure 11(a) displays the Inverse Pole Figure (IPF) map taken using the Electron Back-Scattered Diffraction (EBSD) camera equipped in the SEM. The observation was performed at an accelerating voltage of 20 kV with a beam step of 0.1 µm. Several twins can be recognized in the IPF map. Since no such twins were detected in the specimen before deformation, the twins were considered to be the mechanical ones formed during deformation. Figure 11(b) presents the boundary map obtained from the identical area of Fig. 11(a). In the boundary maps, the blue lines indicate high-angle boundaries, the light blue lines are low-angle ones, the red lines are $\{ 11\bar{2}2\} \langle 11\bar{2}\bar{3}\rangle $ twins, and the green line are $\{ 10\bar{1}2\} \langle \bar{1}011\rangle $ twins. From Fig. 11(b), it can be understood that the $\{ 11\bar{2}2\} \langle 11\bar{2}\bar{3}\rangle $ twin and the $\{ 10\bar{1}2\} \langle \bar{1}011\rangle $ twin were mainly formed. In the specimens after fracture, mechanical twinning was observed to take place in approximately 90% or more grains. The formation of such mechanical twins was observed in all tensile-tested 12-Ti specimens. On the other hand, for the 0.07-Ti and 0.8-Ti, the mechanical twinning could not be confirmed by the SEM-EBSD or even by TEM.

Fig. 11

(a) IPF map and (b) boundary map of a specimen with a grain size of 12 µm just after yielding (εp = 0.01) at $\dot{\varepsilon } = 10^{ - 3}$ s−1 RT.

4. Discussion

Prismatic ⟨a⟩ slip works as the main deformation mechanism in the HCP α-Ti at RT.8) However, the von Mises condition cannot be satisfied only by activation of the prismatic ⟨a⟩ slip because the ⟨a⟩ slip has only two independent slip systems.8) Therefore, another deformation mechanisms to cause displacement along ⟨c⟩ direction must be activated to continue plastic deformation. As the complementary deformation mechanisms, ⟨c⟩ slip and ⟨c + a⟩ slip can be mentioned.8,30) Furthermore, it is well-known that mechanical twinning is often activated as one of the complementary deformations in the conventional coarse-grained α-Ti.8) In the UFGed 0.07-Ti and 0.8-Ti, the dislocation density increased as the plastic strain increased (Figs. 10(a) and (b)), and the ratio of ⟨c + a⟩ slip also increased (Figs. 9(a), (b)). It can be understood that ⟨c + a⟩ slip was activated as a complementary deformation mechanism, since the mechanical twinning was not observed in the specimens of 0.07-Ti and 0.8-Ti till fracture. On the other hand, the dislocation density saturated at the later stage of deformation in the 12-Ti (Fig. 10(c)). Also, the ratio of activated slips, including the displacements along c-axis (i.e., by ⟨c⟩ slip, ⟨c + a⟩ slip), was almost constant from the initial stage, and these ratios were much smaller than that of the ⟨a⟩ slip (Fig. 9(c)). Therefore, it can be stated that both ⟨c⟩ and ⟨c + a⟩ slips were almost not activated in the 12-Ti. From the above results, it can be concluded that the deformation mechanisms of 12-Ti with large grain size is different from those of the 0.07-Ti and 0.8-Ti.

Mechanical twinning, which was not detected in the 0.07-Ti and 0.8-Ti, took place during deformation in the 12-Ti (Fig. 11). The mechanical twins observed in the 12-Ti were identified as $\{ 11\bar{2}2\} \langle 11\bar{2}\bar{3}\rangle $ and $\{ 10\bar{1}2\} \langle \bar{1}011\rangle $ ones by the EBSD analyses. Thus, it can be understood that the $\{ 11\bar{2}2\} \langle 11\bar{2}\bar{3}\rangle $ and $\{ 10\bar{1}2\} \langle \bar{1}011\rangle $ twins were activated as complementary deformation mechanisms in the 12-Ti. The critical resolved shear stress (CRSS) of ⟨c + a⟩ slips are relatively larger than those of $\{ 11\bar{2}2\} \langle 11\bar{2}\bar{3}\rangle $ and $\{ 10\bar{1}2\} \langle \bar{1}011\rangle $ twins at RT.31) Besides, there are almost no reports that ⟨c + a⟩ slips are activated during plastic deformation of coarse-grained α-Ti. It is generally recognized that the mechanical twinning has a strong grain size dependency. The frequency of mechanical twinning decreases with grain refinement,31) and mechanical twins were hardly formed when the grain size became down to several micrometers.32) Furthermore, the 0.07-Ti and 0.8-Ti exhibited high flow stresses due to the much finer grain sizes (Fig. 4). These factors strongly suggest that mechanical twins were not formed and, instead, ⟨c + a⟩ slips were activated in the 0.07-Ti and 0.8-Ti. In the 0.07-Ti, the grain size was extremely fine, and moreover, the initial dislocation density was quite high. Therefore, the change in the substructure during deformation was not definitely detected even by precise observation using TEM. To confirm the microstructural changes before and after deformation in the 0.8-Ti, analyses by means of a combined technique of SEM-BSE (Back-Scattered Electron: BSE) and EBSD were carried out. Figure 12 represents a substructural image attained by the SEM-BSE observation of the 0.8-Ti specimen tensile deformed to a plastic strain of 5% at $\dot{\varepsilon } = 10^{ - 5}$ s−1 with the crystallographical information from EBSD. The crystallographical orientation and the slip trace analyses in the identical areas were performed. The black lines in Fig. 12 indicate the high-angle boundaries. While formation of mechanical twins was not detected at all, a lot of slip lines were visible. Slip traces of the pyramidal plane ($\{ 10\bar{1}1\} $) as well as prismatic ($\{ 01\bar{1}0\} $) slip traces could be definitely observed. The slip traces of the pyramidal plane ($\{ 10\bar{1}1\} $) are indicated by yellow lines in the grains marked by letters of a–f. It can be confirmed that, therefore, pyramidal slip is activated in the 0.8-Ti, i.e., UFGed Ti. Based on the analytical results of slip trace and activated slip system by the in-situ X-ray diffraction measurements (Fig. 12, and Figs. 9(a) and (b)), it can be concluded that pyramidal ⟨c + a⟩ slip ($\{ 10\bar{1}1\} \langle \bar{2}113\rangle $) was activated as a complementary deformation. As shown in Table 4, the ⟨c + a⟩ slip can also occur along the prismatic plane slip system ($\{ 01\bar{1}0\} \langle \bar{2}113\rangle $). However, the activation could not be confirmed from present trace analyses. The authors are now conducting TEM observations to directly identify the activated slip systems and the dislocation Burger’s vectors in the 0.8-Ti.

Fig. 12

SEM-BSE image of a CP-Ti specimen with an average grain size of 0.8 µm tensile-deformed till 5% at $\dot{\varepsilon } = 10^{ - 5}$ s−1 at RT. The observed traces of pyramidal slips are indicated by yellow lines in the grains marked by a∼h.

It can be understood from above discussion that the different strain-rate dependence of σ0.2 and σUTS among the 0.07-Ti, 0.8-Ti and 12-Ti were ascribed to the deformation mechanisms varying with the grain size (Fig. 5, and Table 3). It is reported that the CRSS of ⟨c + a⟩ slips shows more sensitive temperature and strain-rate dependencies than those of ⟨a⟩ slips.33) On the other hand, the CRSS for the mechanical twinning is almost constant irrespective of temperature.34) The deformation mechanism that exhibits large temperature dependence should also show large strain-rate dependency even under a fixed temperature because of its large activation enthalpy.35) The activity of ⟨c + a⟩ slip in 0.07-Ti and 0.8-Ti is relatively high from the initial stage of plastic deformation (Figs. 9(a), (b)). On the other hand, the formation of mechanical twins was confirmed immediately after yielding in the 12-Ti (Fig. 11) in addition to the activation of ⟨a⟩ slip. Therefore, macroscopic yielding is considered to be caused by the ⟨a⟩ and ⟨c + a⟩ slips in the 0.07-Ti and 0.8-Ti, and ⟨a⟩ slip and mechanical twinning in 12-Ti, respectively. As mentioned above, the strain-rate dependence of the CRSS of mechanical twinning is smaller than that of ⟨c + a⟩ slip. Therefore, it can be concluded that the difference in strain-rate dependence of σ0.2 observed between 0.07-Ti and 0.8-Ti, and 12-Ti is attributed to different yielding mechanisms.

The mechanical twins formed immediately after yielding in the 12-Ti (Fig. 11), the number of twined grains increased with further plastic deformation, and then the mechanical twins were eventually observed in 90% or more of the grains at fracture. The formation of such mechanical twins might cause relatively large ductility due to the twinning-induced plasticity (TWIP) effect.36) In addition, the mechanical twinning is generally enhanced with increasing strain rate.32) It is assumed that, therefore, the strain-rate dependence of σUTS in the 12-Ti appeared due to rapid increase in work-hardening rate by the TWIP effect, which is different deformation mechanisms activated at around the yielding. Of course, the TWIP effect should result in the large uniform elongation (see Fig. 4). However, the mechanisms of strain-rate dependency of σUTS discussed above are just hypotheses at this moment, because the quantitative data analysis such as the change in area fraction of twinned region during deformation and its strain rate-dependence is insufficient. To clarify the strain-rate dependence of σUTS varying with grain size found in this study, more detailed investigations of the microstructural change during deformation are necessary.

The changes in the deformation mechanisms depending on grain size, which affect to the strain-rate dependencies of deformation behavior, are strongly suggested to lead also to the significant temperature dependence of the deformation behavior. The authors are now conducting systematic investigations of the temperature dependence of deformation behavior using the same specimens.

5. Summary

Tensile deformation behavior depending on applied strain rate was systematically investigated using an ultra-fine-grained JIS grade 2 commercial purity Ti plate with an average grain size of d = 0.07 µm (UFG-Ti) fabricated by the combination of multi-directional forging and conventional thermomechanical treatment. In-situ X-ray diffraction measurements during the tensile test revealed changes in the active slip systems and dislocation density. The investigations were also conducted on the other two types of specimens (fine-grained (FG)-Ti: d = 0.8 µm, coarse-grained (CG)-Ti: d = 12 µm) obtained by annealing of the UFG-Ti. The results yielded are summarized as follows.

  1. (1)    The UFG- and FG-Ti exhibited large strain rate dependencies of 0.2% proof stress σ0.2. On the other hand, it in the CG-Ti was relatively small. On the other hand, regarding the strain-rate dependence of tensile strength, the CG-Ti showed largest strain-rate dependence.
  2. (2)    In all three specimens with different grain sizes, ⟨a⟩ slips were predominantly activated during tensile deformation. As the plastic strain increased, the ratio of ⟨c + a⟩ slip increased in the UFG- and FG-Ti. Contrary to this, no activation of the other slip systems excepting ⟨a⟩ one was confirmed in the CG-Ti. However, the $\{ 11\bar{2}2\} \langle 11\bar{2}\bar{3}\rangle $ twin and $\{ 10\bar{1}2\} \langle \bar{1}011\rangle $ twin were formed as the complementary deformation mechanisms in the CG-Ti.
  3. (3)    The dislocation density increased monotonically in the UFG- and FG-Ti with increase of plastic strain. On the other hand, in the CG-Ti, the dislocation density increased at the initial stage of plastic deformation and then leveled off an almost constant value.

The observed strain-rate dependencies of the deformation behavior varying with grain size should be attributed to the changes in the deformation mechanisms described above.

Acknowledgements

This work was partially supported by Grant-in-Aid for Scientific Researchs (B & A), Grant Nos. 17H03409 and 20H00305. Some of authors (C. Watanabe and H. Miura) would also like to acknowledge the financial support of Japan Science and Technology Agency (JST) under Industry-Academia Collaborative R&D Program “Heterogeneous Structure Control: Towards Innovative Development of Metallic Structural Materials” (Grant #: JPMJSK1413). The synchrotron radiation experiments were performed at BL46XU of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI), (Proposal No. 2018B1574 and 2016A1501). The authors would appreciate Dr. M. Sato for the support at SPring-8.

REFERENCES
 
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