Effect of Annealing Temperature on Microstructure and Superelastic ...

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Jan 30, 2015 - Effect of annealing temperature on microstructure and superelasticity of Ti-4Au-5Cr-8Zr (mol%) was investigated. Only ¢ phase was observed ...
Materials Transactions, Vol. 56, No. 3 (2015) pp. 404 to 409 © 2015 The Japan Institute of Metals and Materials

EXPRESS REGULAR ARTICLE

Effect of Annealing Temperature on Microstructure and Superelastic Properties of Ti-Au-Cr-Zr Alloy Yuri Shinohara1,+, Masaki Tahara1, Tomonari Inamura1, Shuichi Miyazaki2 and Hideki Hosoda1 1

Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan Division of Materials Science, University of Tsukuba, Tsukuba 305-8573, Japan

2

Effect of annealing temperature on microstructure and superelasticity of Ti-4Au-5Cr-8Zr (mol%) was investigated. Only ¢ phase was observed in the specimen annealed at 1173 K, whereas the precipitation of Ti3Au, Zr33Ti40Au27 (Laves phase) and ¡ phase occurred in the specimens annealed below 1073 K. Superelasticity was clearly observed in the specimens annealed at 1073 K and 1173 K, though it was absent in the specimens annealed at 873 K and 973 K. The maximum superelastic recovery strain was increased by the precipitation of Ti3Au in the specimen annealed at 1073 K. This is due to the increase in the critical stress for slip by the precipitation strengthening effect of Ti3Au. [doi:10.2320/matertrans.M2014439] (Received December 5, 2014; Accepted December 15, 2014; Published January 30, 2015) Keywords: shape memory alloys, superelasticity, biomaterials, titanium based alloy

1.

Introduction

Superelasticity of Ti-Ni shape memory alloys (SMAs) has been successfully used for biomedical applications such as dental arch wires and bone plates at present.1,2) Recently, the development of Ni-free ¢-Ti SMAs has been strongly required because the risk of Ni-hypersensitivity in human body has been pointed out. Superelasticity of ¢-Ti alloys originates from the thermoelastic martensitic transformation from parent ¢ phase (bcc) to ¡AA martensite phase (orthorhombic)3,4) and its reversion. A number of ¢-Ti SMAs have been developed such as Ti­Nb base alloys (e.g. Ti-Nb,5) Ti­Nb­ Al,6) Ti-Nb-Zr,7) Ti­Nb­Ta­Zr8) and Ti-Nb-Mo9)), Ti-Mo base alloys (e.g. Ti-Mo-Al,10) Ti-Mo-Sn11) and Ti-Mo-SnZr12)) and Ti-Ta base alloys (e.g. Ti-Ta13) and Ti-Ta-Sn14)). However, the total shape recovery strain of these alloys is smaller than that of Ti-Ni alloys: 3.5% for Ti-26Nb alloy,5) 7% for Ti-24Zr-10Nb-2Sn alloy15) and more than 10% for Ti50.2Ni alloy.16) Table 1 summarizes the maximum tensile component of the lattice deformation and the critical stress for slip deformation for some alloys. The small total shape recovery strain of ¢-Ti alloys is due to the small lattice deformation strain and low critical stress for slip deformation compared with Ti-Ni alloys.5,17,18) Ti-Au-Cr-Zr biomedical shape memory alloys have, therefore, been developed to solve these problems.19) These alloys consist of the biocompatible elements which have been used for the biomaterials such as Ti-Nb-Ta-Zr8) alloys, Co-Cr-Mo alloys20) and gold base dental alloys.21) The Ti-Au-Cr-Zr alloys exhibited superelasticity and 9% in maximum tensile component of the lattice deformation strain.22) However, only the 3.0% of total shape recovery strain was obtained in TiAu-Cr-Zr alloys because of the lower critical stress for slip.22) Strengthening of ¢-Ti SMAs have been attempted by precipitation hardening using ¡ and ½ phases,23,24) solid solution hardening,25,26) grain size refinement27) and work +

Graduate Student, Tokyo Institute of Technology. Corresponding author, E-mail: [email protected]

Table 1 Lattice deformation strain and critical stress for slip of Ti-Ni and Ti-Nb superelastic alloys. Lattice deformation strain, (%)

Critical stress for slip, /MPa

10.517)

800³18)

Ti-50.6Ni Ti-26Nb Ti-24Nb-1Mo

5)

400³5505)

9)

4209)

2.6 2.8

hardening.28) In this study, intermediate temperature annealing after cold-rolling was made for Ti-Au-Cr-Zr alloy to increase the critical stress for slip by using the precipitation hardening. The eutectoid reaction exists in Ti-Au and Ti-Cr alloys; the eutectoid reaction (decomposition of ¢ phase) has been reported in Ti-4 mol%Au alloy29) and Ti-13.5 mol%Cr alloy30) at 1105 K and 940 K, respectively. In the Ti-Au-Cr-Zr alloys, therefore, various types of precipitates such as Ti3Au and TiCr2 are expected to be formed by heat treatments at intermediate temperatures in addition to ¡ and ½ phases. Though the precipitation of Ti3Au has been reported in the Ti-4Au-5Cr-8Zr (mol%) alloy,31) there is no report on the effect of Ti3Au precipitates on superelasticity in Ti-Au-Cr-Zr alloys. The objective of this study is to investigate effects of annealing temperature on phase constitution, microstructure and superelasticity of Ti-4Au-5Cr-8Zr alloy. 2.

Experimental

The alloy used was Ti-4Au-5Cr-8Zr (mol%). The ingot was made by Ar arc melting, homogenized at 1273 K for 7.2 ks and cold-rolled with a reduction in thickness of 98%. The specimens were cut from the cold-rolled sheet, annealed at 873 K, 973 K, 1073 K or 1173 K for 1.8 ks in an Ar atmosphere and quenched into water. Each specimen is denoted by the annealing temperature, i.e., the specimen annealed at 1173 K is termed as AT1173. The phase constitution was identified by ª-2ª X-ray diffraction (XRD) analysis at room temperature (RT).

Effect of Annealing Temperature on Microstructure and Superelastic Properties of Ti-Au-Cr-Zr Alloy

405

Microstructure was characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM) observations. TEM specimens of AT873 and AT973 were prepared by a twin-jet polishing technique using an electrolyte solution of 5 vol% sulphuric acid + 2 vol% hydrofluoric acid + 93 vol% methanol at about 210 K. TEM specimens of AT1073 and AT1173 were prepared by a dimple grinder and Ar-ion milling. The ion milling was carried out on a liquid nitrogen-cooled specimen holder at 4 keV/2 mA with an incident angle of 12° and at 2 keV/2 mA with an incident angle of 6° for finish. TEM observation was made using a JEOL JEM-2100 microscope operated at 200 kV. Electron backscattering diffraction (EBSD) mapping and SEM energy dispersive X-ray spectrometry (EDX) were carried out to estimate the grain size and the chemical composition of each phase, respectively. A field-emission gun-type scanning electron microscopy (HITACHI S4300SE) operated at 20 kV was used for the SEM observation. Mechanical properties were evaluated by cyclic loading-unloading tensile tests at RT with a strain rate of ¾_ ¼ 8:3  104 /s. The tensile direction was set to be parallel to the rolling direction (RD). 3. 3.1

Results and Discussion

Effect of annealing temperature on phase constitution and microstructure of Ti-4Au-5Cr-8Zr alloy Figure 1 shows XRD profiles obtained at RT for (a) AT1173, (b) AT1073, (c) AT973 and (d) AT873. Phase constitutions of each specimen are summarized in Table 2. Only parent ¢ phase was detected in AT1173, whereas Ti3Au (A15), Zr33Ti40Au27 (C14) and ¡ phase were detected in the specimens annealed below 1073 K. Zr33Ti40Au27 (C14) is a hexagonal Laves phase reported by Waterstrat.32) The annealing temperature dependence of microstructure was analyzed by TEM. A bright field (BF) image and a  dark field (DF) image using 1011 ½ of ½-phase of AT1173 are shown in Fig. 2(a) and (b), respectively. The inset in Fig. 2(b) is a selected area diffraction pattern (SADP) with zone axis of ½110¢ . Fine ellipsoidal ½-phase was observed entire the fully recrystallized parent ¢-phase. In general, ½-phase is formed by quenching (athermal-½ phase) or aging (isothermal-½ phase)33) and the latter one in Ti-Cr alloy is cuboidal.34,35) The ellipsoidal ½-phase in this study is, therefore, athermal-½ phase formed by quenching. In addition, it is reported that isothermal ½-phase particles in Ti-Cr alloy are cubes34,35) and this morphology is different from ½-phase observed in this study. The formation of the athermal-½ phase is unavoidable in metastable ¢-Ti alloys and was confirmed in the ¢ matrix of all the specimens in this study. The effect of the fine athermal-½ phase on the difference of mechanical properties among the specimens is, therefore, ignored hereafter. Figure 3(a) shows a BF image of the AT1073. The Ti3Au precipitates with dark contrast were observed as indicated by a white arrow in the BF image. A SADP taken from the encircled region in the BF image is shown in the inset of Fig. 3(a). The zone axis of the SADP was parallel to ½001Ti3 Au . The specimen was fully recrystallized and there were few dislocations in the matrix. SEM-EDX observation

Fig. 1 XRD profiles of the Ti-4Au-5Cr-8Zr alloy for the (a) AT1173, (b) AT1073, (c) AT973 and (d) AT873. Phase “L” indicates Zr33Ti40Au27 Laves phase.

Table 2

Annealing temperature dependence of phase constitutions. Phase constitution

AT1173

¢

AT1073 AT973

¢ + Ti3Au ¢ + Ti3Au + Zr33Ti40Au27 (Laves)

AT873

¢ + Ti3Au + Zr33Ti40Au27 (Laves) + ¡

was also carried out for the AT1073; Figs. 3(b) and (c) show a SEM image and a corresponding EDX mapping image of Au, respectively. Au-rich precipitates with an averaged diameter of 1.5 µm were observed, and their chemical compositions were determined as shown in Table 3; Au concentration is 18 mol% and 4.7 mol% in the precipitate and the matrix, respectively. The results of EDX indicate that this Au-rich precipitate was Ti3Au, and this was consistent with the phase constitution determined by XRD (Fig. 1(b)). A BF image of the AT973 is shown in Fig. 4. The ¢ matrix with an averaged grain size of 1 µm and the contrast of high density dislocations introduced by the cold-rolling was observed; the specimen was not recrystallized. The precipitation of Zr33Ti40Au27 Laves phase was also detected. The inset of Fig. 4 corresponds to the SADP of Zr33Ti40Au27  Laves that was taken Laves phase with a zone axis of ½4 23 from the encircled region of the BF image. The averaged particle size of Zr33Ti40Au27 Laves phase was about 500 nm. Ti3Au was observed by XRD (Fig. 1) in AT973, even though they were not observed by TEM. Ti3Au particles were considered to be preferentially polished or lost during the jet polishing.

406

Y. Shinohara, M. Tahara, T. Inamura, S. Miyazaki and H. Hosoda

Fig. 2 TEM images of the AT1173. (a) Bright field image, (b) dark field image and corresponding selected area diffraction pattern. Zone axis was parallel to ½110¢ .

Figure 5(a) shows a BF image and a SADP of AT873. Fine grains with an averaged size of 200 nm and Debye ring-like pattern were observed. In addition, the contrast of dislocations was also observed and the specimen was not recrystallized. The diffraction intensity was integrated and superimposed on a one-dimensional diffraction profile as a function of the distance from 000 (transmitted beam) and shown in Fig. 5(b). The existence of ¡, ¢, Ti3Au and Zr33Ti40Au27 Laves phases was confirmed and is in good agreement with the result of the XRD analysis. Averaged grain sizes of the ¢ phase for all the specimens are plotted as a function of annealing temperature in Fig. 6. The averaged grain sizes of the AT1073 and AT1173 were determined by EBSD measurements. The averaged grain size sharply increased above 973 K due to the onset of the recrystallization. 3.2

Effect of annealing temperature on superelastic behavior of Ti-4Au-5Cr-8Zr alloy Cyclic loading-unloading tensile tests were carried out to reveal the effect of annealing temperature on the superelasticity of Ti-4Au-5Cr-8Zr alloy. Figure 7 shows stress­ strain curves of the (a) AT1173, (b) AT1073, (c) AT973 and (d) AT873. Superelasticity appeared in the AT1173 and AT1073, though it was not observed in the AT973 and AT873. The precipitations of Zr33Ti40Au27 Laves phase and ¡ phase were not effective on the improvement of the

Fig. 3 (a) TEM bright field image of the AT1073. Inset shows corresponding diffraction pattern of Ti3Au. Zone axis was parallel to ½001Ti3 Au . (b) SEM image of the AT1073 and (c) EDX mapping of Au. Table 3 Results of EDX analysis for the AT1073. Ti (mol%)

Au (mol%)

Cr (mol%)

Zr (mol%)

Precipitate

76.0

18.0

2.0

4.0

Matrix

82.6

4.7

4.8

7.9

superelasticity in Ti-4Au-5Cr-8Zr alloy at RT. It is likely that these precipitations brought about a change in the chemical composition of ¢ matrix and degradation of ductility, even though the detailed mechanism of the disappearance of the superelasticity was not clear. On the other hand, the specimen with the precipitation of Ti3Au exhibited superelasticity as shown in Fig. 7(b). The stress for inducing martensite (·SIM)

Effect of Annealing Temperature on Microstructure and Superelastic Properties of Ti-Au-Cr-Zr Alloy

407

Fig. 6 Annealing temperature dependence of the grain size of ¢ phase. Fig. 4 TEM bright field image of the AT973. Inset shows the diffraction  Laves . pattern of Zr33Ti40Au27 Laves phase. Zone axis was parallel to ½4 23

Fig. 5 (a) TEM bright field image and diffraction pattern of the AT873, (b) one-dimensional intensity profile along the radial direction of the diffraction pattern of (a).

Fig. 7 Stress-strain curves obtained by the cyclic loading-unloading tensile tests for the (a) AT1173, (b) AT1073, (c) AT973 and (d) AT873 K.

of the AT1173 and AT1073 was 400 MPa and 450 MPa, respectively. It has been reported in literatures that d·SIM/dT of ¢-Ti SMAs is about 3³4 MPa/K independent of alloy compositions.5,7,36) In this study, it is presumed that d·SIM/dT of ¢-matrix was not significantly changed by the precipitation of Ti3Au. Therefore, the increase in ·SIM by decreasing the annealing temperature is due to the decrease in the martensitic transformation temperature (Ms). The decrease in Ms is explained by the precipitation of Ti3Au. The precipitation of Ti3Au causes the enrichment of Cr in ¢ matrix. It has been reported that the increase in Cr content stabilizes the ¢ phase and decreases Ms.31)

To clarify the effect of the Ti3Au precipitates on the reverse transformation strain of Ti-4Au-5Cr-8Zr alloy, two types of strain are defined by cyclic loading-unloading tensile tests as shown in Fig. 8(a): (1) the applied strain, ¾a, and (2) the recovery strain by the reverse martensitic transformation, ¾SE. These strains were evaluated for each stress-strain curve in Figs. 7(a) and (b) and the relationship between ¾a and ¾SE is shown in Fig. 8(b). In AT1173, ¾SE increased with increasing ¾a and took maximum value of 1.2%, then decreased with further increase in ¾a. On the other hand, ¾SE increased with increasing ¾a and reached 1.7% in AT1073; the shape recovery property was improved in AT1073.

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Fig. 8 (a) The definition of the ¾a and ¾SE, (b) ¾SE as a function of the applied strain of each deformation cycle.

Fig. 9 (a) The definition of the ¾p, (b) ¾p as a function of the applied strain of each deformation cycle and the definition of the ·s.

Effect of Ti3Au precipitates on critical stress for slip was evaluated by the loading-unloading tensile tests. Various tensile stresses were applied until ¾a reached 2³9%, and then the stress was removed. After unloading, the specimens were heated up to about 500 K; the dashed arrow indicates the shape recovery by heating. The residual strain after heating, ¾p, was defined as shown in Fig. 9(a). The ¾p was plotted as a function of applied stress, ·a, in Fig. 9(b). In both alloys, ¾p increased with further increase in ·a. In this study, the critical stress for slip, ·s, is defined by linear approximation of the plot as shown in Fig. 9(b). The ·s of AT1173 and AT1073 was 400 MPa and 570 MPa, respectively. The precipitation of Ti3Au is effective on the increase in ·s. The increase of ·s by Ti3Au is the origin of the increase in the maximum value of ¾SE in AT1073 under a higher stress level compared with AT1173. The precipitation of Ti3Au caused grain refinement as shown in Fig. 6. The Hall-Petch effect was, therefore, evaluated to separate the contribution of the grain refinement and the precipitation hardening by Ti3Au to the increase in ·s. The relationship between the stress for slip deformation ·HP and grain size d is given by the Hall-Petch relationship;37,38)

where d1073 and d1173 are the grain size of the AT1073 and AT1173, respectively. It has been reported in literatures that ky is 0.37 MN/m3/2 in Ti-15.2Mo (mol%) alloy39) and 0.4 MN/m3/2 in Ti-22Nb-6Zr (mol%) alloy.28) Therefore, ky of Ti-4Au-5Cr-8Zr alloy was regarded to be 0.4 MN/m3/2 in this study. "·HP is 15 MPa by using d1073 = 79 µm and d1173 = 150 µm (Fig. 6) and is smaller by one order than the increase in ·s by the precipitation of Ti3Au. The increase in ·s in the AT1073 compared to the AT1173 was, therefore, mainly due to the precipitation hardening by Ti3Au. The precipitation of Ti3Au is effective on increase in ·s and the improvement of the superelasticity of Ti-4Au-5Cr-8Zr alloy.

· HP ¼ · 0 þ ky d 1=2 ;

ð1Þ

where ·0 is the friction stress and ky is the Hall-Petch slope. From eq. (1), the relationship between the amount of strengthening, "·HP, and the difference in the grain size is given as; · HP ¼ ky ðd1073 1=2  d1173 1=2 Þ;

ð2Þ

4.

Conclusions

Effect of annealing temperature on microstructure and superelasticity of Ti-4Au-5Cr-8Zr alloy was investigated and following conclusions were obtained. (1) Three phases were formed by annealing between 873 K and 1073 K: Ti3Au was formed by annealing between 873 K and 1073 K, Zr33Ti40Au27 (Laves phase) was formed by annealing at 873 K and 973 K and ¡ phase was formed by annealing at 873 K. Recrystallization took place above 1073 K in the alloy cold-rolled with a reduction in thickness of 98%. (2) Superelasticity was clearly observed in the specimens annealed at 1073 K and 1173 K. The maximum superelastic recovery strain is increased by the precipitation of Ti3Au.

Effect of Annealing Temperature on Microstructure and Superelastic Properties of Ti-Au-Cr-Zr Alloy

(3) Critical stress for slip, ·s, was increased by 170 MPa due to the precipitation of Ti3Au. This strengthening was not due to the grain refinement but the precipitation hardening by Ti3Au. The precipitation of Ti3Au is, therefore, effective on increase in ·s and the improvement of the superelasticity of Ti-4Au-5Cr-8Zr alloy. Acknowledgments This work was supported by Grant-in-Aid for JSPS Fellows (12J09335), Funding Program for Next Generation World-Leading Researchers (LR015), the Advanced Low Carbon Technology Research and Development Program (JY240121) of Japan Science and Technology Agency and Grant-in-Aid of Scientific Research (Kiban S: 26220907, Wakate A: 24686077, Wakate B: 26870194) from the Japan Society for the Promotion of Science. REFERENCES 1) K. Otsuka and C. M. Wayman: Shape Memory Materials, (Cambridge University Press, 1999). 2) H. Ohnishi: Jinko Zoki 12 (1983) 862­871. 3) T. W. Duerig, J. Albrecht, D. Richter and P. Fischer: Acta Metall. 30 (1982) 2161­2172. 4) S. Miyazaki, H. Y. Kim and H. Hosoda: Mater. Sci. Eng. A 438­440 (2006) 18­24. 5) H. Y. Kim, Y. Ikehara, J. I. Kim, H. Hosoda and S. Miyazaki: Acta Mater. 54 (2006) 2419­2429. 6) Y. Fukui, T. Inamura, H. Hosoda, K. Wakashima and S. Miyazaki: Mater. Trans. 45 (2004) 1077­1082. 7) J. I. Kim, H. Y. Kim, T. Inamura, H. Hosoda and S. Miyazaki: Mater. Sci. Eng. A 403 (2005) 334­339. 8) N. Sakaguchi, M. Niinomi, T. Akahori, J. Takeda and H. Toda: Mater. Sci. Eng. C 25 (2005) 363­369. 9) Y. Al-Zain, H. Y. Kim, H. Hosoda, T. H. Nam and S. Miyazaki: Acta Mater. 58 (2010) 4212­4223. 10) H. Sasano and T. Suzuki: Titanium Sci. Technol. 3 (1984) 1667­1674. 11) T. Maeshima, S. Ushimaru, K. Yamauchi and M. Nishida: Mater. Trans. 47 (2006) 513­517. 12) K. Endoh, M. Tahara, T. Inamura, H. Y. Kim, S. Miyazaki and H. Hosoda: Adv. Mater. Res. 922 (2014) 137­142.

409

13) P. J. S. Buenconsejo, H. Y. Kim, H. Hosoda and S. Miyazaki: Acta Mater. 57 (2009) 1068­1077. 14) H. Y. Kim, T. Fukushima, P. J. S. Buenconsejo, T.-h. Nam and S. Miyazaki: Mater. Sci. Eng. A 528 (2011) 7238­7246. 15) L. López Pavón, H. Y. Kim, H. Hosoda and S. Miyazaki: Scr. Mater. 95 (2015) 46­49. 16) T. Saburi, S. Nenno, Y. Nishimoto and M. Zeniya: Tetsu-to-Hagane 72 (1986) 571­578. 17) S. D. Prokoshkin, A. V. Korotitskiy, V. Brailovski, K. E. Inaekyan and S. M. Dubinskiy: Phys. Met. Metall. 112 (2011) 170­187. 18) S. Miyazaki, K. Otsuka and Y. Suzuki: Scr. Metall. 15 (1981) 287­292. 19) Y. Shinohara, T. Ishigaki, T. Inamura, H. Kanetaka, S. Miyazaki and H. Hosoda: Mater. Sci. Forum 654­656 (2010) 2122­2125. 20) D. Granchi, G. Ciapetti, S. Stea, L. Savarino, F. Filippini, A. Sudanese, G. Zinghi and L. Montanaro: Biomaterials 20 (1999) 1079­1086. 21) J. C. Wataha: J. Prosthetic Dent. 83 (2000) 223­234. 22) Y. Shinohara, M. Tahara, T. Inamura, S. Miyazaki and H. Hosoda: Mater. Trans., to be submitted. 23) M. Gunji, K. Kitano, N. Niwa and K. Ito: Tetsu-to-Hagane 72 (1986) 610­616. 24) G. T. Terlinde, T. W. Duerig and J. C. Williams: Metall. Trans. A 14 (1983) 2101­2115. 25) M. Tahara, H. Y. Kim, T. Inamura, H. Hosoda and S. Miyazaki: Mater. Trans. 50 (2009) 2726­2730. 26) T. Furuhara, S. Annaka, Y. Tomio and T. Maki: Mater. Sci. Eng. A 438­ 440 (2006) 825­829. 27) M. Niinomi, T. Kobayashi, H. Honda and Y. Oyabu: Tetsu-to-Hagane 78 (1992) 1862­1869. 28) J. I. Kim, H. Y. Kim, T. Inamura, H. Hosoda and S. Miyazaki: Mater. Trans. 47 (2006) 505­512. 29) J. L. Murray: Bull. Alloy Phase Diagrams 4 (1983) 278­283. 30) J. L. Murray: Bull. Alloy Phase Diagrams 2 (1981) 174­181. 31) Y. Shinohara, M. Tahara, T. Inamura, S. Miyazaki and H. Hosoda: Mater. Today Proc., in press. 32) R. M. Waterstrat: J. Alloy. Compd. 179 (1992) L33. 33) E. W. Collings: The Physical Metallurgy of Titanium Alloys, (American Society for Metals, 1984). 34) B. Hickman: J. Mater. Sci. 4 (1969) 554­563. 35) H. Ikawa, S. Shin, M. Miyagi and M. Morikawa: J. Jpn. Inst. Met. 35 (1971) 628­632. 36) H. Y. Kim, S. Hashimoto, J. I. Kim, T. Inamura, H. Hosoda and S. Miyazaki: Mater. Sci. Eng. A 417 (2006) 120­128. 37) E. O. Hall: Proc. Phys. Soc. Lond. B 64 (1951) 747­753. 38) N. J. Petch: J. Iron Steel Inst. 174 (1953) 25­28. 39) K.-H. Chia, K. Jung and H. Conrad: Mater. Sci. Eng. A 409 (2005) 32­ 38.