- Email: [email protected]
Texture and shape memory behavior of Ti–22Nb–6Ta alloy
Acta Materialia 54 (2006) 423–433 www.actamat-journals.com
Texture and shape memory behavior of Ti–22Nb–6Ta alloy H.Y. Kim
a,*
, T. Sasaki a, K. Okutsu a, J.I. Kim a, T. Inamura b, H. Hosoda b, S. Miyazaki a
a,*
Institute of Materials Science, University of Tsukuba, Ten-nodai, Tsukuba, Ibaraki 305-8573, Japan Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan
b
Received 23 June 2005; received in revised form 23 August 2005; accepted 19 September 2005 Available online 3 November 2005
Abstract Textures of cold-rolled and heat treated plates of Ti–22Nb–6Ta alloy were investigated by X-ray diffraction measurements. A welldeveloped f0 0 1gh1 1 0i texture was obtained in the as-rolled specimen and after heat treatment at 873 K for 600 s. A recrystallization texture of f1 1 2gh1 1 0i was developed after heat treatment at 1173 K for 1.8 ks. Anisotropy in the shape recovery strain and YoungÕs modulus was observed in both specimens heat treated at 873 and 1173 K. For the specimen heat treated at 873 K, a large recovery strain of 3.4% was observed when the loading axis is along the rolling direction (RD) and the transverse direction (TD). On the other hand, recovery strain took the largest value along the RD and the lowest value along the TD for the specimen heat treated at 1173 K. The experimental results on orientation dependence of transformation strain were in good agreement with calculated results utilizing the texture information and lattice correspondence between martensite and parent phases. 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Titanium alloys; Shape memory alloys; Texture; Thermomechanical processing
1. Introduction Recently, b-type Ti alloys composed of non-toxic elements have attracted attention as biomedical shape memory and superelastic materials [1–7]. The shape memory effect and superelastic behavior are associated with a reversible, thermoelastic transformation between the bphase and the a00 martensite phase in the b-type Ti alloys. It has been reported by Baker that a revision from a00 to b results in the shape memory effect in the Ti–35 wt.%Nb (Ti–21.7 at.%Nb) alloy [8]. The shape memory effect was also observed in b-type Ti alloys including Ti–10V–2Fe– 3Al(wt.%) [9], Ti–15.4V–4Al(wt.%) [10] and Ti–Mo–Al [11] alloys. Recently, it has been reported that superelasticity can be obtained in b-type Ti alloys such as b-Cez [12], Ti–(8–10)Mo–4Nb–2V–3Al(wt.%) [13], Ti–Nb–Sn [1], Ti– Nb–Al [4–6] and Ti–Mo–Ga [3] alloys.
*
Corresponding authors. Tel.: +81 298 53 5488; fax: +81 298 55 7440. E-mail addresses: [email protected] (H.Y. Kim), miyazaki@ ims.tsukuba.ac.jp (S. Miyazaki).
Systematic research on mechanical properties, martensitic transformation temperature and shape memory effect conducted on binary Ti–Nb alloys by Kim et al. [7] showed that Ti–(22–27)at.%Nb alloys exhibited shape memory effect and/or superelasticity. However, the low critical stress for slip deformation resulted in only a small superelastic strain. Various attempts have been made to improve the shape memory and superelastic properties. The addition of alloying elements such as Zr [14], Ta [15], Al [4–6] and O [16] stabilizes these properties. The heat treatment condition also affects the shape memory and superelastic properties. For example, aging at low temperature is effective for increasing the critical stress for permanent deformation in Ti–Nb-based alloys [7]. Typically the b-type Ti alloys are prepared by casting followed by hot working and/or cold working and heat treatment. The texture developed during the thermomechanical process affects the shape memory and superelastic behavior. In particular, the transformation strain is dependent on the texture [17,18]. Therefore, it is very important to carry out texture studies in order to obtain the maximum transformation strain in a desired direction in shape
1359-6454/$30.00 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2005.09.014
424
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
memory alloys. So far very few results have been reported on the texture of Ti-based shape memory alloys. In this study, textures of cold-rolled and heat treated plates of Ti–22Nb–6Ta alloy were investigated by X-ray diffraction (XRD) measurements. The effect of cold rolling on deformation and recrystallization textures was investigated. The effect of heat treatment temperature on evolution of texture and shape memory property was also investigated. The orientation dependence of transformation strain and YoungÕs modulus is also discussed on the basis of the experimental results obtained. 2. Experimental procedures The Ti–22Nb–6Ta(at.%) alloy was prepared by the Ar arc melting method. The ingot was sealed in vacuum into a quartz tube and homogenized at 1273 K for 7.2 ks, and then cold-rolled with the reductions of 90%, 95% and 99% in thickness. The cold-rolled plates were cleaned with ethanol, wrapped in Ti foils and encapsulated in quartz tubes under a 25 Torr partial pressure of high-purity Ar, and then heat treated at 873 K for 600 s and at 1173 K for 1.8 ks, respectively. The plates were quenched into water by breaking the quartz tubes. Specimens for the mechanical tests were cut by an electro-discharge machine. The oxidized or damaged surface was removed by mechanical polishing followed by chemical polishing. Tensile tests were carried out at a strain rate of 1.67 · 104 s1 at room temperature. The gage length of the specimens was 20 mm. X-ray diffraction (XRD) measurements were conducted at room temperature with Cu Ka radiation. The distribution of diffraction intensities from three crystal planes {0 1 1}, {0 0 2} and {1 1 2} of the b-phase was measured and three corresponding pole figures were obtained. Orientation distribution functions (ODFs) were derived using the three pole figures. Specimens for transmission electron microscope (TEM) observation were prepared by a conventional twin-jet polishing technique. The TEM observation was conducted using a JEOL2010F operated at 200 kV.
3. Results and discussion 3.1. Deformation texture in cold-rolled plates Fig. 1 shows {0 1 1}, {0 0 2} and {1 1 2} pole figures obtained from a 99% cold-rolled specimen. The center of the pole figures corresponds to the direction normal to the specimen surface (ND). The top and the right of the pole figures correspond to the rolling direction (RD) and transverse direction (TD), respectively. A well developed rolling-texture is confirmed in the 99% as-rolled specimen as shown in Fig. 1. The {0 1 1} pole figure shows four peaks symmetrically located around 45 from the center. The four peaks are located at 45 from both RD and TD. This means that the rolling direction is parallel to h1 1 0i crystal directions. The {0 0 2} pole figure shows a strong texture with a maximum peak density of 44 at the center of pole figure, which indicates that the {0 0 2} planes align preferentially to the rolling plane. These results indicate that a well developed f0 0 1gh1 1 0i texture is formed in the coldrolled specimen. Pole figures obtained in the other specimens with the cold rolling reductions of 90% and 95% also show similar deformation textures, though they are not shown in the present paper. Using the three pole figures, the corresponding ODFs were obtained. Fig. 2 shows u2 = 45 sections of the ODFs for the specimens with the cold rolling reductions of 99%, 95% and 90%. The ODFs confirm the f0 0 1gh1 1 0i texture in the as-rolled specimens. The f0 0 1gh1 1 0i texture is a major rolling texture component observed in body-centered cubic (bcc) metals such as a-Fe, Ta, Mo and W [19]. The maximum orientation density Imax of the f0 0 1gh1 1 0i texture decreased with decreasing cold rolling reduction. 3.2. Texture and microstructure in heat treated plates Fig. 3 shows u2 = 45 sections of ODFs obtained from specimens heat treated at 873 K for 600 s. The ODFs revealed the similar f0 0 1gh1 1 0i texture observed in the
Fig. 1. {0 1 1}, {0 0 2} and {1 1 2} pole figures of the 99% cold-rolled specimen.
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
425
Fig. 2. Sections (u2 = 45) of the orientation distribution functions for the cold-rolled specimens with cold rolling reductions of 99%, 95% and 90%.
Fig. 3. Sections (u2 = 45) of the orientation distribution functions for the specimens heat treated at 873 K for 600 s with cold rolling reductions of 99%, 95% and 90%.
as-rolled specimens. This indicates that recrystallization did not occur by annealing at 873 K. This can be confirmed using the TEM, as shown in Fig. 4. Fig. 4 reveals a recov-
Fig. 4. A bright field TEM micrograph of the specimen heat treated at 873 K for 600 s with cold rolling reduction of 99%.
ery structure with a high density of thermally rearranged dislocations. The maximum orientation density of each specimen is higher than that of the as-rolled specimen. This means that the deformation texture is intensified by recovery. The maximum orientation density of the deformation texture also increased with increasing cold rolling reduction. Fig. 5 shows the {0 1 1}, {0 0 2} and {1 1 2} pole figures obtained from the 99% cold-rolled specimen subjected to heat treatment at 1173 K for 1.8 ks. The {0 1 1} pole figure shows two strong axis density peaks at around 30 from the ND to RD and two other intermediate peaks at around 55 to the TD. The {0 0 2} pole figure shows two peaks at around 35 from the ND to TD and the {1 1 2} pole figure shows a strong peak with a maximum peak density of 46 at the center of the pole figure, which indicates the {1 1 2} planes locating preferentially on the rolling plane. According to the three pole figures, it is concluded that the recrystallization texture is a f1 1 2gh1 1 0i type. This can be confirmed by the ODFs as shown in Fig. 6. As can be seen in Fig. 6, the maximum orientation distribution density of the f1 1 2gh1 1 0i recrystallization texture decreases with decreasing cold rolling reduction. The same f1 1 2gh1 1 0i
426
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
Fig. 5. {0 1 1}, {0 0 2} and {1 1 2} pole figures of the specimen heat treated at 1173 K for 1.8 ks with cold rolling reduction of 99%.
Fig. 6. Sections (u2 = 45) of the orientation distribution functions for the specimens heat treated at 1173 K for 1.8 ks with cold rolling reductions of 99%, 95% and 90%.
recrystallization texture was also reported in the Ti–24Nb– 3Al alloy [6]. In addition to the f1 1 2gh1 1 0i texture, a weak c-fiber component which represents grains with Æ1 1 1æ directions perpendicular to the rolling plane, is observed for the 99% and 95% cold-rolled specimens heat treated at 1173 K. The f0 0 1gh1 1 0i texture still remains and a very weak recrystallization texture is observed in the 90% cold-rolled specimen subjected to the heat treatment at 1173 K. 3.3. Shape memory behavior Fig. 7 shows stress–strain curves of the 99% cold-rolled specimens subjected to the heat treatment at 1173 K for 1.8 ks, tensile axes being along RD, and 45 from RD and TD, respectively. In the first cycle, the tensile stress was applied until strain reached about 1.5%, and then the stress was removed. The measurement was repeated by increasing the maximum strain by 0.5% upon loading using the same specimen. After unloading, specimens which did not exhibit complete superelastic recovery were heated up to about 500 K: lines with an arrow indicate the shape
recovery by heating. The starting points of the stress–strain curves are shifted in order to separate each curve. Perfect superelasticity occurred in the first cycle when the tensile direction was parallel to the RD. With increasing tensile strain, the superelastic behavior became incomplete. The residual strain was almost completely recovered by heating at the third cycle. On the other hand, shape recovery was hardly observed when the tensile direction was parallel to the TD even at the first cycle. In order to characterize the shape memory behavior of the alloy, three types of strains are defined as follows: (1) the strain, eel, recovered elastically upon unloading; (2) the recovered strain etr due to the reverse transformation (which is equal to sum of the transformation strain recovered superelastically upon unloading (eSE) and the strain recovered by heating (eSME)); (3) the total recovered strain er consisting of eel and etr. The magnitudes of er and etr were plotted as a function of tensile strain in Fig. 8. Almost perfect recovery was exhibited up to about 2.5% tensile strain when the tensile direction is parallel to the RD. The data points deviate from the diagonal line beyond 2.5% tensile strain. The residual permanent strain indicated by the deviation from the diagonal
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
427
Fig. 9. Stress–strain curves obtained by cyclic loading–unloading tensile tests for the specimen heat treated at 873 K for 600 s. Fig. 7. Stress–strain curves obtained by cyclic loading–unloading tensile tests for the specimen heat treated at 1173 K for 1.8 ks.
Fig. 8. Total recovered strain and transformation strain as a function of tensile strain obtained by cyclic loading–unloading tensile tests for the specimen heat treated at 1173 K for 1.8 ks as shown in Fig. 7.
line increased with increasing tensile strain. When the tensile direction is 45 from the RD, the recovery strain starts to deviate from the diagonal line at 2% tensile strain. On the other hand, the residual permanent strain appeared at the first cycle for the specimen loaded along the TD. It
can be also seen that the etr at each cycle decreased with increasing the angle between the tensile direction and the RD. As a result, the maximum recovery strain decreased with the increase in angle between the tensile direction and the RD for the specimen heat treated at 1173 K for 1.8 ks. Similar cyclic tensile tests were carried out for the 99% cold-rolled specimen subjected to the heat treatment at 873 K for 600 s, and the results are shown in Fig. 9. Both the er and etr values were plotted as a function of tensile strain in Fig. 10. Contrary to the specimen heat treated at 1173 K for 1.8 ks, both specimens loaded along the RD and TD exhibited similar stress–strain curves. This is reasonable because the specimen heat treated at 873 K has the strong f0 0 1gh1 1 0i texture. The f0 0 1gh1 1 0i texture indicates that the h1 1 0i directions of many grains are parallel to both the RD and TD. Although the permanent strain increased with increasing tensile strain, almost perfect shape recovery was exhibited up to the 4th cycle, i.e. 3% tensile strain, when the tensile direction is parallel to the RD and TD. The etr increased up to approximately 2.2% with increasing tensile strain for the specimens loaded along the RD and TD. When the tensile direction is 45 from the RD, the recovery strain starts to deviate from the diagonal line at 3% tensile strain. A permanent strain of 0.3% remained at the 4th cycle when the tensile direction is 45 from the RD. The maximum etr was 1.6% for the specimen loaded along 45 from the RD. It is interesting to note that er of the specimen loaded along 45 from the RD exhibited an equivalent value to those of the specimens loaded along the RD and TD up to the 3rd cycle, although etr is smaller. This is due to a large elastic strain of the specimen loaded along 45 from the RD. As a result, this indicates that the anisotropy of the shape recovery strain is
428
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
where R is the coordinate transformation matrix from the martensite to the parent phase and Rt is the transpose of R. As can be seen in Fig. 11, the lattice correspondence between a00 and b can be expressed as follows: ½1 0 0 00 ½1 0 0 ; ½0 1 0 00 ½0 1 1 ; ½0 0 1 00 ½0 1 1 . a
b
a
b
a
b
According to the above lattice correspondence, R corresponding to the most favorable martensite variant is expressed as follows: 2 3 1 0 0 pffiffiffi pffiffiffi 7 6 R ¼ 4 0 1= 2 1= 2 5. ð3Þ pffiffiffi pffiffiffi 0 1= 2 1= 2 By substituting Eqs. (1) and (3) into Eq. (2), the lattice distortion matrix T is obtained. If we assume that a given vector x in the coordinates of the parent phase is transformed to x 0 due to the martensite transformation, the maximum transformation strain eiM in each orientation can be calculated as follows: eiM ¼ Fig. 10. Total recovered strain and transformation strain as a function of tensile strain obtained by cyclic loading–unloading tensile tests for the specimen heat treated at 873 K for 600 s.
weaker for the specimen heat treated at 873 K than the specimen heat treated at 1173 K.
jx0 j jxj ; jxj
ð4Þ
where x 0 = Tx. Fig. 12 shows the calculated results of the transformation strain eiM expressed by contour lines for each orientation in a ½0 0 1 ½0 1 1 ½1 1 1 standard stereographic triangle. The maximum transformation strain of 2.46%
3.4. Transformation strain In order to elucidate the anisotropy of the recovery strain, the orientation dependence of the transformation strain due to the martensitic transformation has been calculated. It is convenient to assume that the most favorable martensite variant grows to induce the maximum transformation strain in each grain. The transformation strain produced by the lattice distortion due to the martensitic transformation in a single crystal can be calculated using the lattice constants of the parent b-phase (a0) and the orthorhombic a00 martensite phase (a 0 , b 0 , c 0 ). A schematic illustration of crystal structures of the b and a00 is shown in Fig. 11. The lattice distortion matrix T 0 is written as follows in the coordinates of the martensite: 2 0 3 0 0 a =a0 p ffiffi ffi 6 7 ð1Þ b0 = 2a 0 0 T0 ¼ 4 0 5. p ffiffi ffi 0 0 0 c = 2a0
Fig. 11. A schematic illustration exhibiting a lattice correspondence between b and a00 phases.
The lattice constants of the b and a00 in the Ti–22Nb–6Ta alloy were determined to be as follows: a0 ¼ 0:3289 nm;
a0 ¼ 0:3221 nm;
b0 ¼ 0:4766 nm;
c0 ¼ 0:4631 nm. The lattice distortion matrix T with respect to the coordinates of the parent b-phase can be expressed as follows: T ¼ RT 0 Rt ;
ð2Þ
Fig. 12. Orientation dependence of the calculated transformation strain associated with the martensitic transformation from the b to a00 .
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
was obtained along the [0 1 1] direction. The transformation strain decreases with changing direction from [0 1 1] towards the directions of [0 0 1] and ½ 1 1 1, respectively. The transformation strains along [0 0 1] and ½ 1 1 1 were calculated to be 1.02% and 0.97%, respectively. This indicates that the maximum transformation strain can be obtained when the loading axis is parallel to the [0 1 1] direction. It is noted that the maximum recoverable strain of 2.46% is much smaller than that for the B2–B19 0 transformation in Ti–Ni alloys. From the result of Fig. 12, the transformation strain anisotropy can be expected for b-Ti alloys which have preferential orientation distribution. For simplicity, the standard stereographic triangle was divided into 36 representative orientations. Then the transformation strain eM for a polycrystal with randomly distributed grains can be estimated by averaging eiM for the representative 36 orientations which are located in the ½0 0 1 ½0 1 1 ½ 1 1 1 standard stereographic triangle. However, if there is a texture, it is necessary to consider the orientation density Ii, so that the transformation strain can be estimated as follows: !, 36 X i i eM ¼ eM I 36. ð5Þ i¼1
The orientation density is dependent on the loading axis. Thus, in order to clarify the anisotropy of the transformation strain, it is necessary to know the orientation density distribution for a specific tensile direction quantitatively. An inverse pole figure reveals the crystalline axis density
429
distribution along a specific direction in a rolled plate. Figs. 13 and 14 show the inverse pole figures corresponding to three directions in the rolling plane, i.e. 0, 45 and 90 from RD, in 99% cold-rolled plates subjected to heat treatment at 873 K for 600 s and 1173 K for 1.8 ks, respectively. The orientation distributions of the specimens subjected to the two different heat treatments are quite different. The inverse pole figures for the RD and TD of the specimen heat treated at 873 K show that the [0 1 1] axis density presents a maximum peak. The inverse pole figure corresponding to 45 from the RD shows that the [0 0 1] axis density presents a maximum peak. As for the specimen heat treated at 1173 K, the inverse pole figures corresponding to 0, 45 and 90 from the RD show high axis densities at [0 1 1], [0 1 2] and ½1 1 1, respectively. The transformation strain was calculated as a function of the angle from the RD using the orientation distribution in Figs. 13 and 14, and the results are shown in Fig. 15. For the specimen heat treated at 873 K, the maximum strain is obtained at the RD as shown in Fig. 15(a). The strain decreases with increasing angle from the RD until showing a minimum strain at 45, and then the strain increases as the angle to the TD increases. It is noted that the transformation strains at the RD and TD are almost same for the specimen heat treated at 873 K. On the other hand, the strain tends to decrease monotonically from the RD to TD for the specimen heat treated at 1173 K as shown in Fig. 15(b), though the strain slightly increases from 30 to 45.
Fig. 13. Inverse pole figures showing axis density distribution along different directions in the rolling plane for the specimen heat treated at 873 K for 600 s.
Fig. 14. Inverse pole figures showing axis density distribution along different directions in the rolling plane for the specimen heat treated at 1173 K for 1.8 ks.
430
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
It is concluded that the low temperature annealing is effective for improving the shape memory and superelastic properties due to increasing critical stress for permanent deformation. 3.5. YoungÕs modulus
Fig. 15. Orientation dependence of the calculated transformation strain and the experimentally obtained maximum recovery strain for the specimens heat treated at: (a) 873 K for 600 s and (b) 1173 K for 1.8 ks.
The maximum transformation strains emax obtained by tr the cyclic tensile tests are also plotted in Fig. 15 to compare between the calculated and the experimentally measured transformation strains. The transformation strain etr was obtained by subtracting the elastic strain from the recovery strain er as shown in Fig. 7. Thus, the emax indicates the maxtr imum recovery strain which is experimentally obtainable. For the specimen heat treated at 873 K, the orientation dependence of transformation strain exhibited reasonably good agreement with the calculated results qualitatively. On the other hand, the difference between the measured and the calculated strains was larger in the specimens heat treated at 1173 K. It is supposed that this is due to the permanent deformation easily introduced prior to inducing the martensitic transformation completely in the recrystallized specimen heat treated at 1173 K. It is suggested that the fine subgrain structure as shown in Fig. 4 stabilized the shape memory property for the specimen heat treated at 873 K.
The well developed f0 0 1gh1 1 0i texture in the specimen heat treated at 873 K and the f1 1 2gh1 1 0i texture in the specimen heat treated at 1173 K also resulted in anisotropy of the YoungÕs modulus. Fig. 16(a) and (b) show the orientation dependence of the YoungÕs modulus for the specimens heat treated at 873 and 1173 K, respectively, clearly showing the anisotropy in the YoungÕs modulus for both specimens. For the specimen heat treated at 873 K, the YoungÕs modulus exhibits a minimum when the tensile direction is 45 from the RD. The YoungÕs moduli along the RD and TD exhibit similar values. On the other hand, for the specimen heat treated at 1173 K, the YoungÕs modulus exhibits the highest value along the TD and takes a minimum along 45 from the RD. As can be seen in Fig. 13, the inverse pole figures corresponding to 0, 45 and 90 from the RD exhibit high axis densities at [0 1 1], [0 0 1] and [0 1 1], respectively, for the specimen heat treated at 873 K. For the specimen heat treated 1173 K, the inverse pole figures corresponding to 0, 45 and 90 from the RD exhibit high axis densities at [0 1 1], [0 1 2] and ½1 1 1, respectively, as shown in Fig. 14. As a result, Fig. 16 implies that the YoungÕs modulus of this alloy is lowest along the Æ1 0 0æ and is highest along the Æ1 1 1æ. It is interesting to note that the er of the specimen loaded along 45 from the RD exhibited an equivalent value to that of the specimen loaded along the RD up to the 3rd cycle although the etr is smaller than that of the specimens loaded along the RD as shown in Fig. 10. It is supposed that this is due to a large elastic strain which is attributed to the low modulus and high strength of the specimen loaded along 45 from the RD. The YoungÕs modulus along a certain direction Æuvwæ in the cubic crystals can be expressed as: 1=Ehuvwi ¼ s11 2½ðs11 s12 Þ s44 =2ðl2 m2 þ m2 n2 þ n2 l2 Þ; ð6Þ where s11, s12 and s44 are characteristic compliances, EÆuvwæ is the YoungÕs modulus along Æuvwæ, and l, m and n are the direction cosines of the Æuvwæ direction and the three directions [1 0 0], [0 1 0] and [0 0 1], respectively. The above equation can be expressed by the following formula using EÆ1 0 0æ and EÆ1 1 1æ. 1=Ehuvwi ¼ 1=Eh1 0 0i 3ð1=Eh1 0 0i 1=Eh1 1 1i Þ ðl2 m2 þ m2 n2 þ n2 l2 Þ;
ð7Þ
EÆ1 0 0æ and EÆ1 1 1æ of this alloy can be estimated to be 24 and 64 GPa, respectively, on the assumption that the textures of the specimens are sufficiently strong to be treated as single crystals. EÆ1 1 0æ and EÆ1 2 0æ were obtained as 45 and
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
431
R of the Ti–22Nb–6Ta all the values of EÆ1 0 0æ, EÆ1 1 1æ and E alloy are quite low compared with those of bcc and facecentered cubic transition metals. The low YoungÕs modulus in the range of 45–50 GPa was also observed in b-Ti alloys such as Ti–24Nb–2Ta–5Zr(at.%) [21], Ti–19.9Nb–4.6Ta– 1.1Sn(at.%) [22] and Ti–20.1Nb–4.6Ta–3.3Zr(at.%) [22] alloys. It is also noted that the Ti–22Nb–6Ta alloy exhibits a large anisotropy in the elastic constants compared with those of the bcc transition metals. The following relationships can be obtained from Eqs. (6) and (7). s11 ¼
1 ; Eh0 0 1i
ð9Þ
h s44 i ðs11 s12 Þ ¼ 2
1 1 c11 c12 2c44 3 1 1 ¼ ; 2 Eh1 0 0i Eh1 1 1i
ð10Þ
where cij is the inverse matrix of sij with the relations c44 ¼ s1 c11 c12 = (s11 s12)1, c11 + 2c12 = (s11 + 2s12)1. 44 , The anisotropy ratio, A = 2c44/(c11 c12), is roughly the same as EÆ1 1 1æ/EÆ1 0 0æ in cubic metals, as can be seen in Table 1. Thus, the anisotropy ratio of the Ti–22Nb–6Ta alloy was estimated using the following assumption, Eh1 1 1i 2ðs11 s12 Þ 2c44 ¼ ¼ . s44 ðc11 c12 Þ Eh1 0 0i
Fig. 16. Orientation dependence of YoungÕs modulus for the specimens heat treated at: (a) 873 K for 600 s and (b) 1173 K for 1.8 ks.
34 GPa, respectively, from Eq. (7), which are well consistent with the results obtained from tensile tests as shown in Fig. 16. The average of YoungÕs modulus (Reuss average) for a randomly oriented cubic symmetry polycrystal is given by 1 1 3 1 1 ð8Þ R ¼ Eh1 0 0i 5 Eh1 0 0i Eh1 1 1i ; E R is the Reuss average, which is the lower limit of where E the YoungÕs modulus for polycrystalline materials. Table 1 R for a number of lists the values of EÆ1 0 0æ, EÆ1 1 1æ and E R were calculated metals. The values of EÆ1 0 0æ, EÆ1 1 1æ and E using c11, c12 and c44 of the metals [20]. It can be seen that
ð11Þ
The anisotropy ratio of the Ti–22Nb–6Ta alloy was obtained to be 2.7; i.e. 2c44/(c11 c12) = 2.7. By substituting the measured EÆ1 0 0æ, EÆ1 1 1æ and the anisotropy ratio into Eq. (10), c44 and (c11 c12)/2 were obtained as 21.3 and 8 GPa. The anomalously low value of (c11 c12)/2 was also reported in b-Ti alloys with the electron/atom ratio of 4.24. Saito et al. [23] claimed that c11 c12 approaches zero at the electron/atom ratio of 4.2 in Ti–X (X=Nb, Ta, V, Mo) binary alloys by a theoretical calculation. This result supports the low value of (c11 c12)/2 in the Ti–22Nb– 6Ta alloy, because the electron/atom ratio of the alloy is 4.28. It has been well known that many shape memory alloys with ordered bcc structures exhibit an anomalously low value of (c11 c12)/2 near the martensite start (Ms) temperature. The (c11 c12)/2, c44 and anisotropy ratio in alloys exhibiting the martensitic transformation are listed in Table 2. By definition, (c11 c12)/2 and c44 correspond to the stiffnesses associated with a shear along Æ1 1 0æ direction and Æ0 0 1æ direction, respectively, i.e. G1 1 0 = (c11 c12)/2 and G0 0 1 = c44. Note that the values of (c11 c12)/2 in the alloys listed in Table 2 are quite low compared with those in the transition metals listed in Table 1. In particular, the (c11 c12)/2 of the Ti–22Nb–6Ta alloy is very close to those of Cu–Al–Ni, Cu–Zn and Cu–Zn–Al. From this point of view, it is suggested that the low modulus of bTi alloys is a common property observed in bcc metals exhibiting the martensitic transformation. We can also see another interesting fact in Table 2, the value of c44 in the Ti–22Nb–6Ta is lower than those in other alloys.
432
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
Table 1 Moduli and stiffness coefficients for selected cubic metals
Ti–22Nb–6Ta Ni Au Cu Fe Ta Nb Mo
EÆ1 0 0æ (GPa)
EÆ1 1 1æ (GPa)
R (GPa) E
Eh1 1 1i Eh1 0 0i
c11 c12 2
24 136 42 67 132 146 151 357
64 304 116 191 278 217 82 290
38 203 68 110 193 182 100 311
2.7 2.2 2.8 2.9 2.1 1.5 0.5 0.8
8 49.6 14.5 23.5 47.8 53 56 142
Table 2 Comparison of stiffness coefficients of the Ti–22Nb–6Ta with those of other bcc-based shape memory alloys [24] c11 c12 2
Ti–22Nb–6Ta Ti–Ni [25–27] Cu–Al–Ni [28] Cu–Zn [29] Cu–Zn–Al [30] Au–Cu–Zn [31] Au–Cd [32] Ni–Al [33]
8 17–19 7–8 8 5.8 3–5 3–3.8 14.6
(GPa)
c44 (GPa)
44 A ¼ c112cc 12
21.3 35–39 100 90 86 60 42 132
2.7 2 13 11 15 20–12 14–11 9
As a result, it is suggested that the low YoungÕs modulus in b-Ti alloys are due to the low values of not only (c11 c12)/ 2 but also c44.
(GPa)
c44 (GPa)
44 A ¼ c112cc 12
21.3 124.7 42 75.4 112 82.5 28.7 110
2.7 2.5 2.9 3.2 2.3 1.6 0.5 0.8
tion strain decreases with changing direction from [0 1 1] toward the directions of [0 0 1] and ½ 1 1 1, respectively. 4) The experimental results on orientation dependence of transformation strain were in good agreement with the results calculated utilizing the lattice constants, the texture information and lattice correspondence between martensite and parent phases for the specimens heat treated at 873 K. 5) The minimum YoungÕs modulus was obtained in the specimen heat treated at 873 K loaded along 45 from the RD and the maximum value in the specimen heat treated at 1173 K loaded along the TD, suggesting that YoungÕs modulus is lowest along the Æ1 0 0æ and is highest along the Æ1 1 1æ.
Acknowledgments 4. Conclusions 1) A well developed f0 0 1gh1 1 0i texture was obtained in as-rolled specimens with reductions of 90%, 95% and 99% in thickness. A similar f0 0 1gh1 1 0i texture was observed in the specimen heat treated at 873 K for 600 s. The maximum orientation density of the texture increased with increasing cold rolling reduction. A f1 1 2gh1 1 0i recrystallization texture was developed after the heat treatment at 1173 K for 1.8 ks only for the 95% and 99% cold-rolled specimens. 2) Anisotropy in shape recovery strain was observed in the specimens heat treated at 873 K for 600 s and 1173 K for 1.8 ks. For the specimen heat treated at 873 K, a large recovery strain was observed when the loading axes are RD and TD. On the other hand, the maximum recovery strain was obtained when the loading axis was RD, and then decreased nearly monotonically with the increase in the angle between the tensile direction and the RD for the specimen heat treated at 1173 K for 1.8 ks. 3) Transformation strains for single crystals were calculated using the lattice constants and the lattice correspondence between the b and a00 phases. The maximum transformation strain of 2.46% was obtained along the [0 1 1] direction. The transforma-
This work was partially supported by the 21 Century Center of Excellence Program and the Grants-in-Aid for Fundamental Scientific Research (Kiban A(1999–2001), Kiban A(2002–2004)) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. The authors are grateful to Prof. P.G. McCormick for his valuable comments. References [1] Takahashi E, Sakurai T, Watanabe S, Masahashi N, Hanada S. Mater Trans 2002;43:2978–83. [2] Maeshima T, Nishida M. Mater Trans 2004;45:1096–100. [3] Kim HY, Ohmatsu Y, Kim JI, Hosoda H, Miyazaki S. Mater Trans 2004;45:1090–5. [4] Hosoda H, Fukui Y, Inamura T, Wakashima K, Miyazaki S, Inoue K. Mater Sci Forum 2003;426–432:3121–5. [5] Fukui Y, Inamura T, Hosoda H, Wakashima K, Miyazaki S. Mater Trans 2004;45:1077–82. [6] Inamura T, Fukui Y, Hosoda H, Wakashima K, Miyazaki S. Mater Trans 2004;45:1083–9. [7] Kim HY, Satoru H, Kim JI, Hosoda H, Miyazaki S. Mater Trans 2004;45:2443–8. [8] Baker C. Metal Sci J 1971;5:92–100. [9] Duerig TW, Albrecht J, Richter D, Fischer P. Acta Metall 1982;30:2161–72. [10] Lei CY, Pak JSL, Inoue HRP, Wayman CM. In: Proceedings of the international conference on martensitic transformations. Monterey (CA): Monterey Institute for Advanced Studies; 1992. p. 539.
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433 [11] Sasano H, Suzuki T. In: Proceedings of the 5th international conference on titanium. Frankfurt: Deutsche Gesellschaft fur Metallkunde; 1985. p. 1667. [12] Grosdidier T, Philippe MJ. Mater Sci Eng 2000;A291:218–23. [13] Zhou T, Aindow M, Alpay SP, Blackburn MJ, Wu MH. Scripta Mater 2004;50:343–8. [14] Kim JI, Kim HY, Inamura T, Hosoda H, Miyazaki S. Mater Sci Eng A 2005;403:334–9. [15] Kim HY, Hashimoto S, Kim JI, Inamura T, Hosoda H, Miyazaki S. Mater Sci Eng A 2005 [submitted for publication]. [16] Kim JI, Kim HY, Hosoda H, Miyazaki S. Mater Trans 2005;46:852–7. [17] Shu YC, Bhattacharya K. Acta Mater 1998;46:5457–73. [18] Miyazaki S, No VH, Kitamura K, Khantachawana A, Hosoda H. Int J Plast 2000;16:1135–54. [19] Park YB, Lee DN, Gottstein G. Acta Mater 1998;46:3371–9. [20] Hirth JP, Lothe J. Theory of dislocations. 2nd ed. New York (NY): McGraw-Hill; 1968. p. 837. [21] Tang X, Ahmed T, Rack HJ. J Mater Sci 2000;35:1805–11.
433
[22] Kuroda D, Niinomi M, Morinaga M, Kato Y, Yashiro T. Mater Sci Eng A 1998;A243:244–9. [23] Saito T, Furuta T, Hwang JH, Kuramoto S, Nishio K, Suzuki N, et al. Science 2003;300:464–7. [24] Ren X, Otsuka K. Scripta Mater 1998;38:1669–75. [25] Mercier O, Melton KN, Gremaud G, Hagi J. J Appl Phys 1980;51:1833–4. [26] Khachin VN, Muslov SA, Pushin VG, Chumlyakov YI. Sov Phys Dokl 1987;32:606–9. [27] Brill TM, Mittelbach S, Assmus W, Mullner M, Luthi B. J Phys Condens Matter 1991;3:9621–7. [28] Suezawa M, Sumino K. Scripta Metall 1976;10:789–92. [29] Prasetyo A, Reynaud F, Warlimont H. Acta Metall 1976;24:1009–16. [30] Guenin G, Morin M, Gobin PF, Dijonghe W, Delaey L. Scripta Metall 1977;11:1071–5. [31] Nakanishi N, Murakami Y, Kachi S. Scripta Metall 1971;5:433–8. [32] Zirinsky S. Acta Metall 1956;4:164–71. [33] Enami K, Hasunuma J, Nagasawa A, Nenno S. Scripta Metall 1976;10:879–84.
Texture and shape memory behavior of Ti–22Nb–6Ta alloy H.Y. Kim
a,*
, T. Sasaki a, K. Okutsu a, J.I. Kim a, T. Inamura b, H. Hosoda b, S. Miyazaki a
a,*
Institute of Materials Science, University of Tsukuba, Ten-nodai, Tsukuba, Ibaraki 305-8573, Japan Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan
b
Received 23 June 2005; received in revised form 23 August 2005; accepted 19 September 2005 Available online 3 November 2005
Abstract Textures of cold-rolled and heat treated plates of Ti–22Nb–6Ta alloy were investigated by X-ray diffraction measurements. A welldeveloped f0 0 1gh1 1 0i texture was obtained in the as-rolled specimen and after heat treatment at 873 K for 600 s. A recrystallization texture of f1 1 2gh1 1 0i was developed after heat treatment at 1173 K for 1.8 ks. Anisotropy in the shape recovery strain and YoungÕs modulus was observed in both specimens heat treated at 873 and 1173 K. For the specimen heat treated at 873 K, a large recovery strain of 3.4% was observed when the loading axis is along the rolling direction (RD) and the transverse direction (TD). On the other hand, recovery strain took the largest value along the RD and the lowest value along the TD for the specimen heat treated at 1173 K. The experimental results on orientation dependence of transformation strain were in good agreement with calculated results utilizing the texture information and lattice correspondence between martensite and parent phases. 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Titanium alloys; Shape memory alloys; Texture; Thermomechanical processing
1. Introduction Recently, b-type Ti alloys composed of non-toxic elements have attracted attention as biomedical shape memory and superelastic materials [1–7]. The shape memory effect and superelastic behavior are associated with a reversible, thermoelastic transformation between the bphase and the a00 martensite phase in the b-type Ti alloys. It has been reported by Baker that a revision from a00 to b results in the shape memory effect in the Ti–35 wt.%Nb (Ti–21.7 at.%Nb) alloy [8]. The shape memory effect was also observed in b-type Ti alloys including Ti–10V–2Fe– 3Al(wt.%) [9], Ti–15.4V–4Al(wt.%) [10] and Ti–Mo–Al [11] alloys. Recently, it has been reported that superelasticity can be obtained in b-type Ti alloys such as b-Cez [12], Ti–(8–10)Mo–4Nb–2V–3Al(wt.%) [13], Ti–Nb–Sn [1], Ti– Nb–Al [4–6] and Ti–Mo–Ga [3] alloys.
*
Corresponding authors. Tel.: +81 298 53 5488; fax: +81 298 55 7440. E-mail addresses: [email protected] (H.Y. Kim), miyazaki@ ims.tsukuba.ac.jp (S. Miyazaki).
Systematic research on mechanical properties, martensitic transformation temperature and shape memory effect conducted on binary Ti–Nb alloys by Kim et al. [7] showed that Ti–(22–27)at.%Nb alloys exhibited shape memory effect and/or superelasticity. However, the low critical stress for slip deformation resulted in only a small superelastic strain. Various attempts have been made to improve the shape memory and superelastic properties. The addition of alloying elements such as Zr [14], Ta [15], Al [4–6] and O [16] stabilizes these properties. The heat treatment condition also affects the shape memory and superelastic properties. For example, aging at low temperature is effective for increasing the critical stress for permanent deformation in Ti–Nb-based alloys [7]. Typically the b-type Ti alloys are prepared by casting followed by hot working and/or cold working and heat treatment. The texture developed during the thermomechanical process affects the shape memory and superelastic behavior. In particular, the transformation strain is dependent on the texture [17,18]. Therefore, it is very important to carry out texture studies in order to obtain the maximum transformation strain in a desired direction in shape
1359-6454/$30.00 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2005.09.014
424
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
memory alloys. So far very few results have been reported on the texture of Ti-based shape memory alloys. In this study, textures of cold-rolled and heat treated plates of Ti–22Nb–6Ta alloy were investigated by X-ray diffraction (XRD) measurements. The effect of cold rolling on deformation and recrystallization textures was investigated. The effect of heat treatment temperature on evolution of texture and shape memory property was also investigated. The orientation dependence of transformation strain and YoungÕs modulus is also discussed on the basis of the experimental results obtained. 2. Experimental procedures The Ti–22Nb–6Ta(at.%) alloy was prepared by the Ar arc melting method. The ingot was sealed in vacuum into a quartz tube and homogenized at 1273 K for 7.2 ks, and then cold-rolled with the reductions of 90%, 95% and 99% in thickness. The cold-rolled plates were cleaned with ethanol, wrapped in Ti foils and encapsulated in quartz tubes under a 25 Torr partial pressure of high-purity Ar, and then heat treated at 873 K for 600 s and at 1173 K for 1.8 ks, respectively. The plates were quenched into water by breaking the quartz tubes. Specimens for the mechanical tests were cut by an electro-discharge machine. The oxidized or damaged surface was removed by mechanical polishing followed by chemical polishing. Tensile tests were carried out at a strain rate of 1.67 · 104 s1 at room temperature. The gage length of the specimens was 20 mm. X-ray diffraction (XRD) measurements were conducted at room temperature with Cu Ka radiation. The distribution of diffraction intensities from three crystal planes {0 1 1}, {0 0 2} and {1 1 2} of the b-phase was measured and three corresponding pole figures were obtained. Orientation distribution functions (ODFs) were derived using the three pole figures. Specimens for transmission electron microscope (TEM) observation were prepared by a conventional twin-jet polishing technique. The TEM observation was conducted using a JEOL2010F operated at 200 kV.
3. Results and discussion 3.1. Deformation texture in cold-rolled plates Fig. 1 shows {0 1 1}, {0 0 2} and {1 1 2} pole figures obtained from a 99% cold-rolled specimen. The center of the pole figures corresponds to the direction normal to the specimen surface (ND). The top and the right of the pole figures correspond to the rolling direction (RD) and transverse direction (TD), respectively. A well developed rolling-texture is confirmed in the 99% as-rolled specimen as shown in Fig. 1. The {0 1 1} pole figure shows four peaks symmetrically located around 45 from the center. The four peaks are located at 45 from both RD and TD. This means that the rolling direction is parallel to h1 1 0i crystal directions. The {0 0 2} pole figure shows a strong texture with a maximum peak density of 44 at the center of pole figure, which indicates that the {0 0 2} planes align preferentially to the rolling plane. These results indicate that a well developed f0 0 1gh1 1 0i texture is formed in the coldrolled specimen. Pole figures obtained in the other specimens with the cold rolling reductions of 90% and 95% also show similar deformation textures, though they are not shown in the present paper. Using the three pole figures, the corresponding ODFs were obtained. Fig. 2 shows u2 = 45 sections of the ODFs for the specimens with the cold rolling reductions of 99%, 95% and 90%. The ODFs confirm the f0 0 1gh1 1 0i texture in the as-rolled specimens. The f0 0 1gh1 1 0i texture is a major rolling texture component observed in body-centered cubic (bcc) metals such as a-Fe, Ta, Mo and W [19]. The maximum orientation density Imax of the f0 0 1gh1 1 0i texture decreased with decreasing cold rolling reduction. 3.2. Texture and microstructure in heat treated plates Fig. 3 shows u2 = 45 sections of ODFs obtained from specimens heat treated at 873 K for 600 s. The ODFs revealed the similar f0 0 1gh1 1 0i texture observed in the
Fig. 1. {0 1 1}, {0 0 2} and {1 1 2} pole figures of the 99% cold-rolled specimen.
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
425
Fig. 2. Sections (u2 = 45) of the orientation distribution functions for the cold-rolled specimens with cold rolling reductions of 99%, 95% and 90%.
Fig. 3. Sections (u2 = 45) of the orientation distribution functions for the specimens heat treated at 873 K for 600 s with cold rolling reductions of 99%, 95% and 90%.
as-rolled specimens. This indicates that recrystallization did not occur by annealing at 873 K. This can be confirmed using the TEM, as shown in Fig. 4. Fig. 4 reveals a recov-
Fig. 4. A bright field TEM micrograph of the specimen heat treated at 873 K for 600 s with cold rolling reduction of 99%.
ery structure with a high density of thermally rearranged dislocations. The maximum orientation density of each specimen is higher than that of the as-rolled specimen. This means that the deformation texture is intensified by recovery. The maximum orientation density of the deformation texture also increased with increasing cold rolling reduction. Fig. 5 shows the {0 1 1}, {0 0 2} and {1 1 2} pole figures obtained from the 99% cold-rolled specimen subjected to heat treatment at 1173 K for 1.8 ks. The {0 1 1} pole figure shows two strong axis density peaks at around 30 from the ND to RD and two other intermediate peaks at around 55 to the TD. The {0 0 2} pole figure shows two peaks at around 35 from the ND to TD and the {1 1 2} pole figure shows a strong peak with a maximum peak density of 46 at the center of the pole figure, which indicates the {1 1 2} planes locating preferentially on the rolling plane. According to the three pole figures, it is concluded that the recrystallization texture is a f1 1 2gh1 1 0i type. This can be confirmed by the ODFs as shown in Fig. 6. As can be seen in Fig. 6, the maximum orientation distribution density of the f1 1 2gh1 1 0i recrystallization texture decreases with decreasing cold rolling reduction. The same f1 1 2gh1 1 0i
426
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
Fig. 5. {0 1 1}, {0 0 2} and {1 1 2} pole figures of the specimen heat treated at 1173 K for 1.8 ks with cold rolling reduction of 99%.
Fig. 6. Sections (u2 = 45) of the orientation distribution functions for the specimens heat treated at 1173 K for 1.8 ks with cold rolling reductions of 99%, 95% and 90%.
recrystallization texture was also reported in the Ti–24Nb– 3Al alloy [6]. In addition to the f1 1 2gh1 1 0i texture, a weak c-fiber component which represents grains with Æ1 1 1æ directions perpendicular to the rolling plane, is observed for the 99% and 95% cold-rolled specimens heat treated at 1173 K. The f0 0 1gh1 1 0i texture still remains and a very weak recrystallization texture is observed in the 90% cold-rolled specimen subjected to the heat treatment at 1173 K. 3.3. Shape memory behavior Fig. 7 shows stress–strain curves of the 99% cold-rolled specimens subjected to the heat treatment at 1173 K for 1.8 ks, tensile axes being along RD, and 45 from RD and TD, respectively. In the first cycle, the tensile stress was applied until strain reached about 1.5%, and then the stress was removed. The measurement was repeated by increasing the maximum strain by 0.5% upon loading using the same specimen. After unloading, specimens which did not exhibit complete superelastic recovery were heated up to about 500 K: lines with an arrow indicate the shape
recovery by heating. The starting points of the stress–strain curves are shifted in order to separate each curve. Perfect superelasticity occurred in the first cycle when the tensile direction was parallel to the RD. With increasing tensile strain, the superelastic behavior became incomplete. The residual strain was almost completely recovered by heating at the third cycle. On the other hand, shape recovery was hardly observed when the tensile direction was parallel to the TD even at the first cycle. In order to characterize the shape memory behavior of the alloy, three types of strains are defined as follows: (1) the strain, eel, recovered elastically upon unloading; (2) the recovered strain etr due to the reverse transformation (which is equal to sum of the transformation strain recovered superelastically upon unloading (eSE) and the strain recovered by heating (eSME)); (3) the total recovered strain er consisting of eel and etr. The magnitudes of er and etr were plotted as a function of tensile strain in Fig. 8. Almost perfect recovery was exhibited up to about 2.5% tensile strain when the tensile direction is parallel to the RD. The data points deviate from the diagonal line beyond 2.5% tensile strain. The residual permanent strain indicated by the deviation from the diagonal
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
427
Fig. 9. Stress–strain curves obtained by cyclic loading–unloading tensile tests for the specimen heat treated at 873 K for 600 s. Fig. 7. Stress–strain curves obtained by cyclic loading–unloading tensile tests for the specimen heat treated at 1173 K for 1.8 ks.
Fig. 8. Total recovered strain and transformation strain as a function of tensile strain obtained by cyclic loading–unloading tensile tests for the specimen heat treated at 1173 K for 1.8 ks as shown in Fig. 7.
line increased with increasing tensile strain. When the tensile direction is 45 from the RD, the recovery strain starts to deviate from the diagonal line at 2% tensile strain. On the other hand, the residual permanent strain appeared at the first cycle for the specimen loaded along the TD. It
can be also seen that the etr at each cycle decreased with increasing the angle between the tensile direction and the RD. As a result, the maximum recovery strain decreased with the increase in angle between the tensile direction and the RD for the specimen heat treated at 1173 K for 1.8 ks. Similar cyclic tensile tests were carried out for the 99% cold-rolled specimen subjected to the heat treatment at 873 K for 600 s, and the results are shown in Fig. 9. Both the er and etr values were plotted as a function of tensile strain in Fig. 10. Contrary to the specimen heat treated at 1173 K for 1.8 ks, both specimens loaded along the RD and TD exhibited similar stress–strain curves. This is reasonable because the specimen heat treated at 873 K has the strong f0 0 1gh1 1 0i texture. The f0 0 1gh1 1 0i texture indicates that the h1 1 0i directions of many grains are parallel to both the RD and TD. Although the permanent strain increased with increasing tensile strain, almost perfect shape recovery was exhibited up to the 4th cycle, i.e. 3% tensile strain, when the tensile direction is parallel to the RD and TD. The etr increased up to approximately 2.2% with increasing tensile strain for the specimens loaded along the RD and TD. When the tensile direction is 45 from the RD, the recovery strain starts to deviate from the diagonal line at 3% tensile strain. A permanent strain of 0.3% remained at the 4th cycle when the tensile direction is 45 from the RD. The maximum etr was 1.6% for the specimen loaded along 45 from the RD. It is interesting to note that er of the specimen loaded along 45 from the RD exhibited an equivalent value to those of the specimens loaded along the RD and TD up to the 3rd cycle, although etr is smaller. This is due to a large elastic strain of the specimen loaded along 45 from the RD. As a result, this indicates that the anisotropy of the shape recovery strain is
428
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
where R is the coordinate transformation matrix from the martensite to the parent phase and Rt is the transpose of R. As can be seen in Fig. 11, the lattice correspondence between a00 and b can be expressed as follows: ½1 0 0 00 ½1 0 0 ; ½0 1 0 00 ½0 1 1 ; ½0 0 1 00 ½0 1 1 . a
b
a
b
a
b
According to the above lattice correspondence, R corresponding to the most favorable martensite variant is expressed as follows: 2 3 1 0 0 pffiffiffi pffiffiffi 7 6 R ¼ 4 0 1= 2 1= 2 5. ð3Þ pffiffiffi pffiffiffi 0 1= 2 1= 2 By substituting Eqs. (1) and (3) into Eq. (2), the lattice distortion matrix T is obtained. If we assume that a given vector x in the coordinates of the parent phase is transformed to x 0 due to the martensite transformation, the maximum transformation strain eiM in each orientation can be calculated as follows: eiM ¼ Fig. 10. Total recovered strain and transformation strain as a function of tensile strain obtained by cyclic loading–unloading tensile tests for the specimen heat treated at 873 K for 600 s.
weaker for the specimen heat treated at 873 K than the specimen heat treated at 1173 K.
jx0 j jxj ; jxj
ð4Þ
where x 0 = Tx. Fig. 12 shows the calculated results of the transformation strain eiM expressed by contour lines for each orientation in a ½0 0 1 ½0 1 1 ½1 1 1 standard stereographic triangle. The maximum transformation strain of 2.46%
3.4. Transformation strain In order to elucidate the anisotropy of the recovery strain, the orientation dependence of the transformation strain due to the martensitic transformation has been calculated. It is convenient to assume that the most favorable martensite variant grows to induce the maximum transformation strain in each grain. The transformation strain produced by the lattice distortion due to the martensitic transformation in a single crystal can be calculated using the lattice constants of the parent b-phase (a0) and the orthorhombic a00 martensite phase (a 0 , b 0 , c 0 ). A schematic illustration of crystal structures of the b and a00 is shown in Fig. 11. The lattice distortion matrix T 0 is written as follows in the coordinates of the martensite: 2 0 3 0 0 a =a0 p ffiffi ffi 6 7 ð1Þ b0 = 2a 0 0 T0 ¼ 4 0 5. p ffiffi ffi 0 0 0 c = 2a0
Fig. 11. A schematic illustration exhibiting a lattice correspondence between b and a00 phases.
The lattice constants of the b and a00 in the Ti–22Nb–6Ta alloy were determined to be as follows: a0 ¼ 0:3289 nm;
a0 ¼ 0:3221 nm;
b0 ¼ 0:4766 nm;
c0 ¼ 0:4631 nm. The lattice distortion matrix T with respect to the coordinates of the parent b-phase can be expressed as follows: T ¼ RT 0 Rt ;
ð2Þ
Fig. 12. Orientation dependence of the calculated transformation strain associated with the martensitic transformation from the b to a00 .
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
was obtained along the [0 1 1] direction. The transformation strain decreases with changing direction from [0 1 1] towards the directions of [0 0 1] and ½ 1 1 1, respectively. The transformation strains along [0 0 1] and ½ 1 1 1 were calculated to be 1.02% and 0.97%, respectively. This indicates that the maximum transformation strain can be obtained when the loading axis is parallel to the [0 1 1] direction. It is noted that the maximum recoverable strain of 2.46% is much smaller than that for the B2–B19 0 transformation in Ti–Ni alloys. From the result of Fig. 12, the transformation strain anisotropy can be expected for b-Ti alloys which have preferential orientation distribution. For simplicity, the standard stereographic triangle was divided into 36 representative orientations. Then the transformation strain eM for a polycrystal with randomly distributed grains can be estimated by averaging eiM for the representative 36 orientations which are located in the ½0 0 1 ½0 1 1 ½ 1 1 1 standard stereographic triangle. However, if there is a texture, it is necessary to consider the orientation density Ii, so that the transformation strain can be estimated as follows: !, 36 X i i eM ¼ eM I 36. ð5Þ i¼1
The orientation density is dependent on the loading axis. Thus, in order to clarify the anisotropy of the transformation strain, it is necessary to know the orientation density distribution for a specific tensile direction quantitatively. An inverse pole figure reveals the crystalline axis density
429
distribution along a specific direction in a rolled plate. Figs. 13 and 14 show the inverse pole figures corresponding to three directions in the rolling plane, i.e. 0, 45 and 90 from RD, in 99% cold-rolled plates subjected to heat treatment at 873 K for 600 s and 1173 K for 1.8 ks, respectively. The orientation distributions of the specimens subjected to the two different heat treatments are quite different. The inverse pole figures for the RD and TD of the specimen heat treated at 873 K show that the [0 1 1] axis density presents a maximum peak. The inverse pole figure corresponding to 45 from the RD shows that the [0 0 1] axis density presents a maximum peak. As for the specimen heat treated at 1173 K, the inverse pole figures corresponding to 0, 45 and 90 from the RD show high axis densities at [0 1 1], [0 1 2] and ½1 1 1, respectively. The transformation strain was calculated as a function of the angle from the RD using the orientation distribution in Figs. 13 and 14, and the results are shown in Fig. 15. For the specimen heat treated at 873 K, the maximum strain is obtained at the RD as shown in Fig. 15(a). The strain decreases with increasing angle from the RD until showing a minimum strain at 45, and then the strain increases as the angle to the TD increases. It is noted that the transformation strains at the RD and TD are almost same for the specimen heat treated at 873 K. On the other hand, the strain tends to decrease monotonically from the RD to TD for the specimen heat treated at 1173 K as shown in Fig. 15(b), though the strain slightly increases from 30 to 45.
Fig. 13. Inverse pole figures showing axis density distribution along different directions in the rolling plane for the specimen heat treated at 873 K for 600 s.
Fig. 14. Inverse pole figures showing axis density distribution along different directions in the rolling plane for the specimen heat treated at 1173 K for 1.8 ks.
430
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
It is concluded that the low temperature annealing is effective for improving the shape memory and superelastic properties due to increasing critical stress for permanent deformation. 3.5. YoungÕs modulus
Fig. 15. Orientation dependence of the calculated transformation strain and the experimentally obtained maximum recovery strain for the specimens heat treated at: (a) 873 K for 600 s and (b) 1173 K for 1.8 ks.
The maximum transformation strains emax obtained by tr the cyclic tensile tests are also plotted in Fig. 15 to compare between the calculated and the experimentally measured transformation strains. The transformation strain etr was obtained by subtracting the elastic strain from the recovery strain er as shown in Fig. 7. Thus, the emax indicates the maxtr imum recovery strain which is experimentally obtainable. For the specimen heat treated at 873 K, the orientation dependence of transformation strain exhibited reasonably good agreement with the calculated results qualitatively. On the other hand, the difference between the measured and the calculated strains was larger in the specimens heat treated at 1173 K. It is supposed that this is due to the permanent deformation easily introduced prior to inducing the martensitic transformation completely in the recrystallized specimen heat treated at 1173 K. It is suggested that the fine subgrain structure as shown in Fig. 4 stabilized the shape memory property for the specimen heat treated at 873 K.
The well developed f0 0 1gh1 1 0i texture in the specimen heat treated at 873 K and the f1 1 2gh1 1 0i texture in the specimen heat treated at 1173 K also resulted in anisotropy of the YoungÕs modulus. Fig. 16(a) and (b) show the orientation dependence of the YoungÕs modulus for the specimens heat treated at 873 and 1173 K, respectively, clearly showing the anisotropy in the YoungÕs modulus for both specimens. For the specimen heat treated at 873 K, the YoungÕs modulus exhibits a minimum when the tensile direction is 45 from the RD. The YoungÕs moduli along the RD and TD exhibit similar values. On the other hand, for the specimen heat treated at 1173 K, the YoungÕs modulus exhibits the highest value along the TD and takes a minimum along 45 from the RD. As can be seen in Fig. 13, the inverse pole figures corresponding to 0, 45 and 90 from the RD exhibit high axis densities at [0 1 1], [0 0 1] and [0 1 1], respectively, for the specimen heat treated at 873 K. For the specimen heat treated 1173 K, the inverse pole figures corresponding to 0, 45 and 90 from the RD exhibit high axis densities at [0 1 1], [0 1 2] and ½1 1 1, respectively, as shown in Fig. 14. As a result, Fig. 16 implies that the YoungÕs modulus of this alloy is lowest along the Æ1 0 0æ and is highest along the Æ1 1 1æ. It is interesting to note that the er of the specimen loaded along 45 from the RD exhibited an equivalent value to that of the specimen loaded along the RD up to the 3rd cycle although the etr is smaller than that of the specimens loaded along the RD as shown in Fig. 10. It is supposed that this is due to a large elastic strain which is attributed to the low modulus and high strength of the specimen loaded along 45 from the RD. The YoungÕs modulus along a certain direction Æuvwæ in the cubic crystals can be expressed as: 1=Ehuvwi ¼ s11 2½ðs11 s12 Þ s44 =2ðl2 m2 þ m2 n2 þ n2 l2 Þ; ð6Þ where s11, s12 and s44 are characteristic compliances, EÆuvwæ is the YoungÕs modulus along Æuvwæ, and l, m and n are the direction cosines of the Æuvwæ direction and the three directions [1 0 0], [0 1 0] and [0 0 1], respectively. The above equation can be expressed by the following formula using EÆ1 0 0æ and EÆ1 1 1æ. 1=Ehuvwi ¼ 1=Eh1 0 0i 3ð1=Eh1 0 0i 1=Eh1 1 1i Þ ðl2 m2 þ m2 n2 þ n2 l2 Þ;
ð7Þ
EÆ1 0 0æ and EÆ1 1 1æ of this alloy can be estimated to be 24 and 64 GPa, respectively, on the assumption that the textures of the specimens are sufficiently strong to be treated as single crystals. EÆ1 1 0æ and EÆ1 2 0æ were obtained as 45 and
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
431
R of the Ti–22Nb–6Ta all the values of EÆ1 0 0æ, EÆ1 1 1æ and E alloy are quite low compared with those of bcc and facecentered cubic transition metals. The low YoungÕs modulus in the range of 45–50 GPa was also observed in b-Ti alloys such as Ti–24Nb–2Ta–5Zr(at.%) [21], Ti–19.9Nb–4.6Ta– 1.1Sn(at.%) [22] and Ti–20.1Nb–4.6Ta–3.3Zr(at.%) [22] alloys. It is also noted that the Ti–22Nb–6Ta alloy exhibits a large anisotropy in the elastic constants compared with those of the bcc transition metals. The following relationships can be obtained from Eqs. (6) and (7). s11 ¼
1 ; Eh0 0 1i
ð9Þ
h s44 i ðs11 s12 Þ ¼ 2
1 1 c11 c12 2c44 3 1 1 ¼ ; 2 Eh1 0 0i Eh1 1 1i
ð10Þ
where cij is the inverse matrix of sij with the relations c44 ¼ s1 c11 c12 = (s11 s12)1, c11 + 2c12 = (s11 + 2s12)1. 44 , The anisotropy ratio, A = 2c44/(c11 c12), is roughly the same as EÆ1 1 1æ/EÆ1 0 0æ in cubic metals, as can be seen in Table 1. Thus, the anisotropy ratio of the Ti–22Nb–6Ta alloy was estimated using the following assumption, Eh1 1 1i 2ðs11 s12 Þ 2c44 ¼ ¼ . s44 ðc11 c12 Þ Eh1 0 0i
Fig. 16. Orientation dependence of YoungÕs modulus for the specimens heat treated at: (a) 873 K for 600 s and (b) 1173 K for 1.8 ks.
34 GPa, respectively, from Eq. (7), which are well consistent with the results obtained from tensile tests as shown in Fig. 16. The average of YoungÕs modulus (Reuss average) for a randomly oriented cubic symmetry polycrystal is given by 1 1 3 1 1 ð8Þ R ¼ Eh1 0 0i 5 Eh1 0 0i Eh1 1 1i ; E R is the Reuss average, which is the lower limit of where E the YoungÕs modulus for polycrystalline materials. Table 1 R for a number of lists the values of EÆ1 0 0æ, EÆ1 1 1æ and E R were calculated metals. The values of EÆ1 0 0æ, EÆ1 1 1æ and E using c11, c12 and c44 of the metals [20]. It can be seen that
ð11Þ
The anisotropy ratio of the Ti–22Nb–6Ta alloy was obtained to be 2.7; i.e. 2c44/(c11 c12) = 2.7. By substituting the measured EÆ1 0 0æ, EÆ1 1 1æ and the anisotropy ratio into Eq. (10), c44 and (c11 c12)/2 were obtained as 21.3 and 8 GPa. The anomalously low value of (c11 c12)/2 was also reported in b-Ti alloys with the electron/atom ratio of 4.24. Saito et al. [23] claimed that c11 c12 approaches zero at the electron/atom ratio of 4.2 in Ti–X (X=Nb, Ta, V, Mo) binary alloys by a theoretical calculation. This result supports the low value of (c11 c12)/2 in the Ti–22Nb– 6Ta alloy, because the electron/atom ratio of the alloy is 4.28. It has been well known that many shape memory alloys with ordered bcc structures exhibit an anomalously low value of (c11 c12)/2 near the martensite start (Ms) temperature. The (c11 c12)/2, c44 and anisotropy ratio in alloys exhibiting the martensitic transformation are listed in Table 2. By definition, (c11 c12)/2 and c44 correspond to the stiffnesses associated with a shear along Æ1 1 0æ direction and Æ0 0 1æ direction, respectively, i.e. G1 1 0 = (c11 c12)/2 and G0 0 1 = c44. Note that the values of (c11 c12)/2 in the alloys listed in Table 2 are quite low compared with those in the transition metals listed in Table 1. In particular, the (c11 c12)/2 of the Ti–22Nb–6Ta alloy is very close to those of Cu–Al–Ni, Cu–Zn and Cu–Zn–Al. From this point of view, it is suggested that the low modulus of bTi alloys is a common property observed in bcc metals exhibiting the martensitic transformation. We can also see another interesting fact in Table 2, the value of c44 in the Ti–22Nb–6Ta is lower than those in other alloys.
432
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433
Table 1 Moduli and stiffness coefficients for selected cubic metals
Ti–22Nb–6Ta Ni Au Cu Fe Ta Nb Mo
EÆ1 0 0æ (GPa)
EÆ1 1 1æ (GPa)
R (GPa) E
Eh1 1 1i Eh1 0 0i
c11 c12 2
24 136 42 67 132 146 151 357
64 304 116 191 278 217 82 290
38 203 68 110 193 182 100 311
2.7 2.2 2.8 2.9 2.1 1.5 0.5 0.8
8 49.6 14.5 23.5 47.8 53 56 142
Table 2 Comparison of stiffness coefficients of the Ti–22Nb–6Ta with those of other bcc-based shape memory alloys [24] c11 c12 2
Ti–22Nb–6Ta Ti–Ni [25–27] Cu–Al–Ni [28] Cu–Zn [29] Cu–Zn–Al [30] Au–Cu–Zn [31] Au–Cd [32] Ni–Al [33]
8 17–19 7–8 8 5.8 3–5 3–3.8 14.6
(GPa)
c44 (GPa)
44 A ¼ c112cc 12
21.3 35–39 100 90 86 60 42 132
2.7 2 13 11 15 20–12 14–11 9
As a result, it is suggested that the low YoungÕs modulus in b-Ti alloys are due to the low values of not only (c11 c12)/ 2 but also c44.
(GPa)
c44 (GPa)
44 A ¼ c112cc 12
21.3 124.7 42 75.4 112 82.5 28.7 110
2.7 2.5 2.9 3.2 2.3 1.6 0.5 0.8
tion strain decreases with changing direction from [0 1 1] toward the directions of [0 0 1] and ½ 1 1 1, respectively. 4) The experimental results on orientation dependence of transformation strain were in good agreement with the results calculated utilizing the lattice constants, the texture information and lattice correspondence between martensite and parent phases for the specimens heat treated at 873 K. 5) The minimum YoungÕs modulus was obtained in the specimen heat treated at 873 K loaded along 45 from the RD and the maximum value in the specimen heat treated at 1173 K loaded along the TD, suggesting that YoungÕs modulus is lowest along the Æ1 0 0æ and is highest along the Æ1 1 1æ.
Acknowledgments 4. Conclusions 1) A well developed f0 0 1gh1 1 0i texture was obtained in as-rolled specimens with reductions of 90%, 95% and 99% in thickness. A similar f0 0 1gh1 1 0i texture was observed in the specimen heat treated at 873 K for 600 s. The maximum orientation density of the texture increased with increasing cold rolling reduction. A f1 1 2gh1 1 0i recrystallization texture was developed after the heat treatment at 1173 K for 1.8 ks only for the 95% and 99% cold-rolled specimens. 2) Anisotropy in shape recovery strain was observed in the specimens heat treated at 873 K for 600 s and 1173 K for 1.8 ks. For the specimen heat treated at 873 K, a large recovery strain was observed when the loading axes are RD and TD. On the other hand, the maximum recovery strain was obtained when the loading axis was RD, and then decreased nearly monotonically with the increase in the angle between the tensile direction and the RD for the specimen heat treated at 1173 K for 1.8 ks. 3) Transformation strains for single crystals were calculated using the lattice constants and the lattice correspondence between the b and a00 phases. The maximum transformation strain of 2.46% was obtained along the [0 1 1] direction. The transforma-
This work was partially supported by the 21 Century Center of Excellence Program and the Grants-in-Aid for Fundamental Scientific Research (Kiban A(1999–2001), Kiban A(2002–2004)) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. The authors are grateful to Prof. P.G. McCormick for his valuable comments. References [1] Takahashi E, Sakurai T, Watanabe S, Masahashi N, Hanada S. Mater Trans 2002;43:2978–83. [2] Maeshima T, Nishida M. Mater Trans 2004;45:1096–100. [3] Kim HY, Ohmatsu Y, Kim JI, Hosoda H, Miyazaki S. Mater Trans 2004;45:1090–5. [4] Hosoda H, Fukui Y, Inamura T, Wakashima K, Miyazaki S, Inoue K. Mater Sci Forum 2003;426–432:3121–5. [5] Fukui Y, Inamura T, Hosoda H, Wakashima K, Miyazaki S. Mater Trans 2004;45:1077–82. [6] Inamura T, Fukui Y, Hosoda H, Wakashima K, Miyazaki S. Mater Trans 2004;45:1083–9. [7] Kim HY, Satoru H, Kim JI, Hosoda H, Miyazaki S. Mater Trans 2004;45:2443–8. [8] Baker C. Metal Sci J 1971;5:92–100. [9] Duerig TW, Albrecht J, Richter D, Fischer P. Acta Metall 1982;30:2161–72. [10] Lei CY, Pak JSL, Inoue HRP, Wayman CM. In: Proceedings of the international conference on martensitic transformations. Monterey (CA): Monterey Institute for Advanced Studies; 1992. p. 539.
H.Y. Kim et al. / Acta Materialia 54 (2006) 423–433 [11] Sasano H, Suzuki T. In: Proceedings of the 5th international conference on titanium. Frankfurt: Deutsche Gesellschaft fur Metallkunde; 1985. p. 1667. [12] Grosdidier T, Philippe MJ. Mater Sci Eng 2000;A291:218–23. [13] Zhou T, Aindow M, Alpay SP, Blackburn MJ, Wu MH. Scripta Mater 2004;50:343–8. [14] Kim JI, Kim HY, Inamura T, Hosoda H, Miyazaki S. Mater Sci Eng A 2005;403:334–9. [15] Kim HY, Hashimoto S, Kim JI, Inamura T, Hosoda H, Miyazaki S. Mater Sci Eng A 2005 [submitted for publication]. [16] Kim JI, Kim HY, Hosoda H, Miyazaki S. Mater Trans 2005;46:852–7. [17] Shu YC, Bhattacharya K. Acta Mater 1998;46:5457–73. [18] Miyazaki S, No VH, Kitamura K, Khantachawana A, Hosoda H. Int J Plast 2000;16:1135–54. [19] Park YB, Lee DN, Gottstein G. Acta Mater 1998;46:3371–9. [20] Hirth JP, Lothe J. Theory of dislocations. 2nd ed. New York (NY): McGraw-Hill; 1968. p. 837. [21] Tang X, Ahmed T, Rack HJ. J Mater Sci 2000;35:1805–11.
433
[22] Kuroda D, Niinomi M, Morinaga M, Kato Y, Yashiro T. Mater Sci Eng A 1998;A243:244–9. [23] Saito T, Furuta T, Hwang JH, Kuramoto S, Nishio K, Suzuki N, et al. Science 2003;300:464–7. [24] Ren X, Otsuka K. Scripta Mater 1998;38:1669–75. [25] Mercier O, Melton KN, Gremaud G, Hagi J. J Appl Phys 1980;51:1833–4. [26] Khachin VN, Muslov SA, Pushin VG, Chumlyakov YI. Sov Phys Dokl 1987;32:606–9. [27] Brill TM, Mittelbach S, Assmus W, Mullner M, Luthi B. J Phys Condens Matter 1991;3:9621–7. [28] Suezawa M, Sumino K. Scripta Metall 1976;10:789–92. [29] Prasetyo A, Reynaud F, Warlimont H. Acta Metall 1976;24:1009–16. [30] Guenin G, Morin M, Gobin PF, Dijonghe W, Delaey L. Scripta Metall 1977;11:1071–5. [31] Nakanishi N, Murakami Y, Kachi S. Scripta Metall 1971;5:433–8. [32] Zirinsky S. Acta Metall 1956;4:164–71. [33] Enami K, Hasunuma J, Nagasawa A, Nenno S. Scripta Metall 1976;10:879–84.