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Enhancement of athermal α″ martensitic transformation in Ti–10V–2Fe–3Al alloy due to high-speed hot deformation
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Scripta Materialia 67 (2012) 21–24 www.elsevier.com/locate/scriptamat
Enhancement of athermal a00 martensitic transformation in Ti–10V–2Fe–3Al alloy due to high-speed hot deformation Toshiyuki Akanuma,a Hiroaki Matsumoto,a,⇑ Shigeo Sato,a Akihiko Chiba,a Ikuhiro Inagaki,b Yoshihisa Shiraib and Takashi Maedab a
Institute for Materials Research, Tohoku University, Katahira, Aoba-ku, Sendai 980-8577, Japan b Sumitomo Metal Industries, Ltd., 1-8, Fuso-cho, Amagasaki Hyogo 660-0891, Japan Received 12 January 2012; revised 7 March 2012; accepted 8 March 2012 Available online 15 March 2012
This work examines the origin of the athermal a00 martensitic transformation in Ti–10V–2Fe–3Al alloys arising from high-speed hot deformation on the basis of chemical thermodynamics and the change in stored energy introduced by deformation. The value of the martensitic transformation starting temperature (Ms) is strongly affected by various microstructural factors. This work reveals that a high accumulation of dislocation density, greater than 1015 m2, arising from high-speed deformation, resulted in an enhancement of athermal a00 martensitic transformations. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Titanium alloy; a00 Martensitic transformation; Dislocation density; Stored energy
The metastable beta titanium alloy, Ti–10V– 2Fe–3Al (hereafter designated as Ti-10-2-3 alloy), was developed as a forging alloy for applications in aerospace components owing to a good combination of high strength and fracture toughness. The microstructural evolution during the hot working conditions of Ti-102-3 alloys has been extensively studied [1–4]. The martensitic transformation of b (body-centered cubic, bcc)/a00 (orthorhombic) in Ti alloys is well known to occur while maintaining lattice correspondences of [1 0 0]a00 //[1 0 0]b, [0 1 0]a00 //[1 0 1]b, and [0 0 1]a00 //[1 1 0]b [5,6]. Transformation strains from the b/a00 transformation seem to be accommodated primarily by an internal twinning on the {1 1 1} a00 planes. The retained metastable b phase in Ti-10-2-3 alloys is known to exhibit a stress-induced martensitic (SIM) transformation to orthorhombic a00 after cold deformation [5,7,8]. The quenching process above b transus is well recognized to be accompanied by the formation of a martensite (a0 or a00 ) or an x phase as a non-equilibrium phase. Recently, we have pointed out that an athermal a00 martensitic transformation occurred at a strain rate greater than 0.1 s1 during the isothermal hot forging of Ti-10-2-3 alloys [9]. Similarly, Furuhara [10] and
⇑ Corresponding
author. Tel.: +81 22 215 2118; fax: +81 22 215 2116; e-mail: [email protected]
Lei et al. [11] also observed an a00 martensitic transformation that was dependent on the strain rate in a hot compression test of Ti-10-2-3 alloys. Recently, processing utilizing the martensite phase has been expected to be useful as a new type of microstructural control technique in industrial Ti alloys [12,13]. Thus, it is worthwhile to promote the development of this new type of microstructural technique by clarifying the mechanism of the a00 martensitic transformation arising from highspeed deformation during the isothermal hot forging of Ti-10-2-3 alloys. Specifically, this work examines the origin of the athermal a00 martensitic transformation in Ti-10-2-3 alloys due to high-speed hot deformation in relation to stored dislocations during hot forging and the related thermodynamic considerations. Ti-10-2-3 alloys (consisting of Al 3.16, V 9.6, Fe 1.98, O 0.100, C 0.004, N 0.005, H 0.0046 and Ti balance (in wt.%)) were provided by Sumitomo Metal Industries, Ltd. Cylindrical specimens with a diameter of 8 mm and a height of 12 mm were prepared by a machining process for compression tests. Compression tests were carried out in a vacuum at temperatures of 1173 and 1273 K and at a strain of 0.8 using computer-aided ThermecMaster-Z equipment. The strain rates ranged from 0.001 to 10 s1. Samples were heated at a rate of 10 K s–1 by induction up to the testing temperature. After holding for 5 min, the samples were hot compressed. A mixture of N2 and He was used for
1359-6462/$ - see front matter Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2012.03.011
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T. Akanuma et al. / Scripta Materialia 67 (2012) 21–24
quenching the samples to room temperature (cooling rate: 50 K s–1) as soon as the samples were compressed. Microstructures were identified by electron backscatter diffraction (EBSD) analysis and from X-ray diffraction (XRD) patterns. Dislocation density was evaluated by single line analysis using the real part of the Fourier coefficients of the bcc-200 reflection, which is based on the Garrod method [14]. Figure 1 shows EBSD–orientation imaging microscopy (OIM) images of the isothermally forged microstructure under the conditions (a) 1173 K–0.001 s1, (b) 1173 K–10 s1, (c) 1273 K–0.001 s1 and (d) 1273 K–10 s1. It can be clearly seen that an acicular morphology is obtained under high strain rates. The EBSD analysis and XRD patterns reveal that the a00 martensite also forms at high strain rates. Forging temperatures of 1173 and 1273 K are higher than the martensitic starting temperature (Ms) in Ti-10-2-3 alloys [5]. Hence, we can conclude that the a00 martensite observed at a higher strain rate (Fig. 1) is formed as an athermally transformed martensite during cooling. This result indicates that the apparent Ms temperature increases owing to isothermal hot forging with high-speed deformation. In addition, the results of XRD profiles reveal that the amount of the athermal a00 martensitic transformation after the isothermal hot forging at 10 s1 is higher in forging temperature of 1273 K than that of 1173 K. On the basis of the thermodynamicsbased theory for martensite formation by Ghosh and Olson [15], the critical driving force for heterogeneous martensitic nucleation is modeled as the sum of the strain energy gel, a defect-size dependent interfacial energy and a composition-dependent interfacial frictional work contribution. According to this model, we can suppose that the term gel has a strong effect on the occurrence of an athermal strain rate-dependent a00 martensitic transformation. Figure 2 shows the dislocation density qretained b in a retained b phase, calculated
Figure 1. EBSD-OIM images of isothermally forged microstructures at conditions of (a) 1173 K–0.001 s1, (b) 1173 K–10 s1, (c) 1273 K– 0.001 s1, and (d) 1273 K–10 s1 and at a strain of 0.8.
Figure 2. Dislocation density qretained b in the retained b phase calculated by the Garrod method using the data from the XRD analysis. Dislocation density qm was utilized for microstructural conversion. Intensity ratio I(200)a00 /I(200)b from the XRD analysis relating to an amount of a00 formation in Ti-10-2-3 alloys isothermally hot forged at 1273 K and at various strain rates.
by the Garrod method [14] using the data from the XRD analysis, the dislocation density qm, which was utilized for microstructural conversion, as represented by Eq. (1) [16], and the intensity ratio I(200)a00 /I(200)b in the XRD analysis, which relates to the amount of a00 formation of Ti-10-2-3 alloys, isothermally hot forged at 1273 K and at various strain rates. 2 ðr ryÞ qm ¼ ð1Þ ðMklbÞ In Eq. (1), r and ry are, respectively, the flow stress and the yield stress, M is the Taylor factor, which is equal to 2.954, k is a constant, equal to 0.15, l is the shear modulus, equal to 42.1 GPa, and b is the Burgers vector, equal to 2.8 1010 m. In Figure 2, q, which shows the occurrence of the athermal a00 , is represented by a solid plot. It can be observed that the athermal a00 martensite forms at a strain rate of 0.1 s1 and the amount of a00 increases with an increasing strain rate. Furthermore, an increase in magnitude by two to three orders is observed in the dislocation density, qretained b, at high strain rates, which are greater than 1 s1, as compared to a low strain rate of 0.001 s1, indicating that high-speed deformation enhances the accumulation of plastic strains. The effect of strains induced by the b/a00 martensitic transformation should be considered for an increase in the dislocation density. However, we can ignore this effect on the increase in qretained b because of a small volume change of 0.7% between b and a00 , according to the lattice parameter [5]. In addition, a large difference between qm and qretained b at high strain rates, which are greater than 0.1 s1, can be seen despite the similar values of qm and qretained b at low strain rates of 0.001 s1 and 0.01 s1. This implies that strain is strongly accumulated in the retained b phase as compared to the amount of strain utilized for microstructural conversion by increasing the strain rate. Thus, it can be expected that the term
T. Akanuma et al. / Scripta Materialia 67 (2012) 21–24
23
for the a00 transformation to occur. However, considering that qretained b is in the retained b phase and that its order of magnitude of 1015 is consistent with the order of magnitude for the a00 martensitic transformation at room temperature, the amount of accumulated strain in the case of a high strain rate is thought to be sufficient to enhance the athermal a00 martensitic transformation. However, the stored energy estimated by an analysis of the diffraction line broadening only considers longrange lattice strain [18]. When taking this factor into consideration, we should also consider the local effect. However, the contribution of the stored energy, Ed, by sub-boundary formation is low, at approximately 0.07 J g–1, and is calculated using the following equation [19]: Figure 3. Difference in the free energy of b and a00 , DGb_a00 , as a function of temperature.
gel is high at greater strain rates, thereby resulting in an apparent increase in Ms for high-speed deformations. In order to classify the effect of strain accumulation on the occurrence of the athermal a00 transformation, the relationship between the free energy and the stored energy was evaluated. Figure 3 shows the difference in free energy of b and a00 , DGb_a00 , which was calculated using the data in Duerig et al. [5]. The estimated values of Ms and dr/dT from a relationship of triggering stress for inducing a00 martensitic transformation and testing temperature of tensile test [5] are 48 K and 1.01 MPa K–1, respectively. Based on this data, the enthalpy change, DH, and the entropy change, DS, can be calculated to be 1.83 J g–1 and 6.5 103 J g–1 K–1, respectively. Therefore, the difference in free energy between b and a00 , DGb_a00 (=DH TDS) at Ms (= 48 K) can be estimated to be 1.52 J g–1. The curve of DGb_a00 , represented by a solid line, is estimated using the Clausius–Clapeyron relationship in Ti-10-2-3 alloys with an average grain size of approximately 200 lm. Unfortunately, in this work, the Ms value after isothermal hot forging at high strain rates could not be detected in either the cooling curve or the curve analyzed using a dilatometer equipped with ThermecMaster-Z. However, this value of Ms, which is affected by isothermal hot forging at high strain rates, should be higher than room temperature, and therefore the difference in the free energy DGb_a00 , in which Ms is assumed to be room temperature, represented by Ms0 , is also shown as a dotted line in Figure 3. Herein, the estimated energy required for an increase in Ms to room temperature is approximately 1.6 J g–1. The stored energy, Estore, due to the inhomogeneous lattice strain during hot deformation can be expressed using Eq. (2) [17], which includes the dislocation density qretained b: 1 ð2Þ Estore ¼ qretained b lb2 2 where l is the shear modulus, equal to 42.1 GPa, and b is the Burgers vector, equal to 2.8 1010 m. The estimated value of Estore at a strain rate of 10 s1 is 0.71 J g–1. In Figure 2, the dislocation density satisfying the condition Estore > 1.6 J g–1 is also drawn. Furthermore, we can see that slightly more energy is required
Ed
3cbb Dsubgrain
ð3Þ
where cbb is the subgrain boundary energy at b/b and Dsubgrain is the average size of the subgrains (=4 lm). The misorientation angle of a sub-boundary in the retained b phase (at 1273 K and 10 s1) is roughly estimated to be 5°. The Dsubgrain and the misorientation angle of a sub-boundary are the average values analyzed by the EBSD using the hot-forged sample at condition of 1273K and 101 s1. The value of cbb at a 5° subboundary is calculated to be 0.42 J m–2 according to the formula proposed by Wolf [20]. Therefore, we can conclude that the stored energy, accompanied by the formation of sub-boundaries, is too low to affect the occurrence of an athermal a00 martensitic transformation. EBSD–kernel average misorientation analysis of the sample hot forged at 1273 K10 s1 reveals that geometrically necessary (GN) dislocation accumulates on close to the {1 1 0} plane in retained b phase. Therefore, the accumulation of strain locally close to the {1 1 0} planes should strongly affect the occurrence of an athermal a00 martensitic transformation. By our work, we cannot verify whether a local stress field around the GN dislocations affects the nucleation of an a00 martensite, even though it is thought to be an additional factor. Regarding SIM transformations, Bhattacharjee et al. [21] pointed out that the grain size of the retained b phase had a profound effect on room temperature SIM transformations in Ti-10-2-3 alloys. In fact, SIM transformations occurred in microstructures with an average grain size of 130 lm, while no SIM transformation occurred at room temperature in microstructures with coarse grains. In their report [21], Bhattacharjee et al. modified the free energy change during SIM transformation by taking into account the effect of the grain size in the b phase. As a consequence, Bhattacharjee et al. reported that the effect of B(D, f)D Eel dominates over the free energy change during SIM transformation, thereby resulting in a grain size dependence of the SIM transformation in Ti-10-2-3 alloys. Herein, B(D, f)D Eel is the total elastic energy stored in the unit volume of the alloy, where D is the grain size of prior metastable b and f is the volume fraction of a00 . As mentioned above, the obtained grain sizes in the prior b phase during isothermal hot forging conducted in this work are similar to the grain sizes in the
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T. Akanuma et al. / Scripta Materialia 67 (2012) 21–24
Ti-10-2-3 alloys reported by Duerig et al. [5]. Therefore, the estimation of DGb_a00 on the basis of the result by Duerig et al., shown in Figure 3, is thought to be valid. During hot deformation, Ti-10-2-3 alloys undergo continuous dynamic recrystallization or dynamic recovery [2,9,10], implying that the formation of subgrains followed by evolution into high angle boundary grains is dominant during deformation. Considering the factor B(D, f)DEel, a dynamical change in the grain size during deformation of Ti-10-2-3 alloys would also affect the change in Ms value. However, the formation of subgrains remains dominant at a strain of 0.8, and therefore the effect of B(D, f)DEel on the change in Ms value would be small in our case. The results of Bhattacharjee et al. [21] also indicated that, as a consequence, many factors affect the value of Ms in Ti-10-2-3 alloys. If this is correct, there is a critical question concerning the accurate value of Ms in Ti-10-23 alloys. Recently, Neelakantan et al. [22] have calculated the value of Ms for b-Ti alloys using a thermodynamics-based model in which the Ghosh–Olson approach was applied. They suggested an approximation of Ms in terms of the elemental concentration in wt.% as given by the following equation: M s ðKÞ ¼ 1156 150Fewt:% 96Crwt:% 49Mowt:% 37Vwt:% 17Nbwt:% 7Zrwt:% þ 15Alwt:%
ð4Þ
The Ms value of Ti-10-2-3 alloys can be estimated to be approximately 530 K from Eq. (4). This Ms value, based on the thermodynamical model, can be considered an intrinsic Ms value. However, there is no consideration of an athermal x transformation in this model. The competition between martensitic transformations and x transformations leads to an apparent change in Ms [23,24], thereby making it difficult to identify an accurate Ms value for Ti-10-2-3 alloys. Thus, we can conclude that Ms in Ti-10-2-3 alloys is a complex function of various microstructural factors, such as grain size, dislocation density, dislocation substructure and the extent of competition with x transformations, as well as the difference in chemical thermodynamics. In summary, an athermal a00 martensite was found to appear after hot compression at 1173 and 1273 K and at strain rates greater than 0.1 s1. This work reveals that a high accumulation of dislocation density, which is greater than of 1015 m2 and arises from high-speed deformations, enhanced athermal a00 martensitic transformations. This was explained by the contribution of the dislocation stored energy, 0.5 qretained b lb2, to the chemical potential, which led to the a00 transformation. This result suggests a new type of process design for producing a homogeneous a00 martensitic microstructure by the isothermal hot forging of Ti-10-2-3 alloys.
This work was partially supported by a Grantin-Aid for the Encouragement of Young Scientists (B) (Grant #2276055), Ministry of Culture, Science and Education. [1] I. Weiss, S.L. Semiatin, Mater. Sci. Eng. A243 (1998) 46– 65. [2] V.V. Balasubrahmanyam, Y.V.R.K. Prasad, Mater. Sci. Technol. 17 (2001) 1222–1228. [3] D.G. Robertson, H.B. McShane, Mater. Sci. Technol. 14 (1998) 339–345. [4] M. Jackson, N.G. Jones, D. Dye, R.J. Dashwood, Mater. Sci. Eng. A501 (2009) 248–254. [5] T.W. Duerig, J. Albrecht, D. Richter, P. Fisher, Acta Metall. 30 (1982) 2161–2172. [6] H. Sasano, T. Suzuki, O. Nakano, H. Kimura, Titanium’80 Science and Technology, (AIME, 1980), 1980 pp. 717. [7] T. Grosdidier, Y. Combres, E. Gautier, M.J. Philippe, Metall. Mater. Trans. 31A (2000) 1095–1106. [8] T. Furuhara, S. Annaka, Y. Tomio, T. Maki, Mater. Sci. Eng. A438–440 (2006) 825–829. [9] T. Akanuma, H. Matsumoto, A. Chiba, I. Inagaki, Y. Shirai, T. Maeda, Proceedings of the 12th World Conference on Titanium, Beijing, China, in press. [10] T. Furuhara, Y. Toji, T. Maki, in: G. Lutjering, J. Albrecht (Eds.), Ti-2003 Science and Technology, Weinheim, Wiley-VCH, 2004, pp. 1219–1226. [11] L. Lei, X. Huang, M. Wang, L. Wang, J. Qin, H. Li, S. Lu, Mater. Sci. Eng. A 530 (2011) 591–601. [12] H. Matsumoto, K. Kodaira, K. Sato, T.J. Konno, A. Chiba, Mater. Trans. 50 (2009) 2744–2750. [13] H. Matsumoto, S.H. Lee, Y. Ono, Y. Li, A. Chiba, Adv. Eng. Mater. 13 (2011) 470–474. [14] R.I. Garrod, J.H. Auld, Acta Mater. 3 (1955) 190. [15] G. Ghosh, G.B. Olson, Acta Metall. 42 (1994) 3361–3370. [16] T. Seshacharyulu, B. Dutta, Scripta Mater. 46 (2002) 673– 678. [17] S.S. Hazra, A.A. Gazder, E.V. Pereloma, Mater. Sci. Eng. A524 (2009) 158–167. [18] T. Ungar, Scripta Mater. 51 (2004) 777–781. [19] F. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenomena, Elsevier, Oxford, 1995, p. 17. [20] D. Wolf, Scripta Mater. 23 (1989) 1713–1718. [21] A. Bhattacharjee, S. Bhargava, V.K. Varma, S.V. Kamat, A.K. Gogia, Scripta Mater. 53 (2005) 195–200. [22] S. Neelakantan, P.E.J.R.D. del-Castillo, S. van der Zwaag, Scripta Mater. 60 (2009) 611–614. [23] T. Maeda, H.M. Flower, in: P. Lacombe, R. Tricot, G. Beranger (Eds.), Proceedings of the 6th World Conference on Titanium, 6–9 June 1988, Les Editions de Physique, Paris, 1988, pp. 1589–1594. [24] H. Ohyama, T. Nishimura, in: P.A. Blenkinsop, W.J. Evans, H.M. Flower (Eds.), Proceedings of the 8th World Conference on Titanium, Birmingham, UK, 1995, pp. 2273–2280.
Scripta Materialia 67 (2012) 21–24 www.elsevier.com/locate/scriptamat
Enhancement of athermal a00 martensitic transformation in Ti–10V–2Fe–3Al alloy due to high-speed hot deformation Toshiyuki Akanuma,a Hiroaki Matsumoto,a,⇑ Shigeo Sato,a Akihiko Chiba,a Ikuhiro Inagaki,b Yoshihisa Shiraib and Takashi Maedab a
Institute for Materials Research, Tohoku University, Katahira, Aoba-ku, Sendai 980-8577, Japan b Sumitomo Metal Industries, Ltd., 1-8, Fuso-cho, Amagasaki Hyogo 660-0891, Japan Received 12 January 2012; revised 7 March 2012; accepted 8 March 2012 Available online 15 March 2012
This work examines the origin of the athermal a00 martensitic transformation in Ti–10V–2Fe–3Al alloys arising from high-speed hot deformation on the basis of chemical thermodynamics and the change in stored energy introduced by deformation. The value of the martensitic transformation starting temperature (Ms) is strongly affected by various microstructural factors. This work reveals that a high accumulation of dislocation density, greater than 1015 m2, arising from high-speed deformation, resulted in an enhancement of athermal a00 martensitic transformations. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Titanium alloy; a00 Martensitic transformation; Dislocation density; Stored energy
The metastable beta titanium alloy, Ti–10V– 2Fe–3Al (hereafter designated as Ti-10-2-3 alloy), was developed as a forging alloy for applications in aerospace components owing to a good combination of high strength and fracture toughness. The microstructural evolution during the hot working conditions of Ti-102-3 alloys has been extensively studied [1–4]. The martensitic transformation of b (body-centered cubic, bcc)/a00 (orthorhombic) in Ti alloys is well known to occur while maintaining lattice correspondences of [1 0 0]a00 //[1 0 0]b, [0 1 0]a00 //[1 0 1]b, and [0 0 1]a00 //[1 1 0]b [5,6]. Transformation strains from the b/a00 transformation seem to be accommodated primarily by an internal twinning on the {1 1 1} a00 planes. The retained metastable b phase in Ti-10-2-3 alloys is known to exhibit a stress-induced martensitic (SIM) transformation to orthorhombic a00 after cold deformation [5,7,8]. The quenching process above b transus is well recognized to be accompanied by the formation of a martensite (a0 or a00 ) or an x phase as a non-equilibrium phase. Recently, we have pointed out that an athermal a00 martensitic transformation occurred at a strain rate greater than 0.1 s1 during the isothermal hot forging of Ti-10-2-3 alloys [9]. Similarly, Furuhara [10] and
⇑ Corresponding
author. Tel.: +81 22 215 2118; fax: +81 22 215 2116; e-mail: [email protected]
Lei et al. [11] also observed an a00 martensitic transformation that was dependent on the strain rate in a hot compression test of Ti-10-2-3 alloys. Recently, processing utilizing the martensite phase has been expected to be useful as a new type of microstructural control technique in industrial Ti alloys [12,13]. Thus, it is worthwhile to promote the development of this new type of microstructural technique by clarifying the mechanism of the a00 martensitic transformation arising from highspeed deformation during the isothermal hot forging of Ti-10-2-3 alloys. Specifically, this work examines the origin of the athermal a00 martensitic transformation in Ti-10-2-3 alloys due to high-speed hot deformation in relation to stored dislocations during hot forging and the related thermodynamic considerations. Ti-10-2-3 alloys (consisting of Al 3.16, V 9.6, Fe 1.98, O 0.100, C 0.004, N 0.005, H 0.0046 and Ti balance (in wt.%)) were provided by Sumitomo Metal Industries, Ltd. Cylindrical specimens with a diameter of 8 mm and a height of 12 mm were prepared by a machining process for compression tests. Compression tests were carried out in a vacuum at temperatures of 1173 and 1273 K and at a strain of 0.8 using computer-aided ThermecMaster-Z equipment. The strain rates ranged from 0.001 to 10 s1. Samples were heated at a rate of 10 K s–1 by induction up to the testing temperature. After holding for 5 min, the samples were hot compressed. A mixture of N2 and He was used for
1359-6462/$ - see front matter Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2012.03.011
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T. Akanuma et al. / Scripta Materialia 67 (2012) 21–24
quenching the samples to room temperature (cooling rate: 50 K s–1) as soon as the samples were compressed. Microstructures were identified by electron backscatter diffraction (EBSD) analysis and from X-ray diffraction (XRD) patterns. Dislocation density was evaluated by single line analysis using the real part of the Fourier coefficients of the bcc-200 reflection, which is based on the Garrod method [14]. Figure 1 shows EBSD–orientation imaging microscopy (OIM) images of the isothermally forged microstructure under the conditions (a) 1173 K–0.001 s1, (b) 1173 K–10 s1, (c) 1273 K–0.001 s1 and (d) 1273 K–10 s1. It can be clearly seen that an acicular morphology is obtained under high strain rates. The EBSD analysis and XRD patterns reveal that the a00 martensite also forms at high strain rates. Forging temperatures of 1173 and 1273 K are higher than the martensitic starting temperature (Ms) in Ti-10-2-3 alloys [5]. Hence, we can conclude that the a00 martensite observed at a higher strain rate (Fig. 1) is formed as an athermally transformed martensite during cooling. This result indicates that the apparent Ms temperature increases owing to isothermal hot forging with high-speed deformation. In addition, the results of XRD profiles reveal that the amount of the athermal a00 martensitic transformation after the isothermal hot forging at 10 s1 is higher in forging temperature of 1273 K than that of 1173 K. On the basis of the thermodynamicsbased theory for martensite formation by Ghosh and Olson [15], the critical driving force for heterogeneous martensitic nucleation is modeled as the sum of the strain energy gel, a defect-size dependent interfacial energy and a composition-dependent interfacial frictional work contribution. According to this model, we can suppose that the term gel has a strong effect on the occurrence of an athermal strain rate-dependent a00 martensitic transformation. Figure 2 shows the dislocation density qretained b in a retained b phase, calculated
Figure 1. EBSD-OIM images of isothermally forged microstructures at conditions of (a) 1173 K–0.001 s1, (b) 1173 K–10 s1, (c) 1273 K– 0.001 s1, and (d) 1273 K–10 s1 and at a strain of 0.8.
Figure 2. Dislocation density qretained b in the retained b phase calculated by the Garrod method using the data from the XRD analysis. Dislocation density qm was utilized for microstructural conversion. Intensity ratio I(200)a00 /I(200)b from the XRD analysis relating to an amount of a00 formation in Ti-10-2-3 alloys isothermally hot forged at 1273 K and at various strain rates.
by the Garrod method [14] using the data from the XRD analysis, the dislocation density qm, which was utilized for microstructural conversion, as represented by Eq. (1) [16], and the intensity ratio I(200)a00 /I(200)b in the XRD analysis, which relates to the amount of a00 formation of Ti-10-2-3 alloys, isothermally hot forged at 1273 K and at various strain rates. 2 ðr ryÞ qm ¼ ð1Þ ðMklbÞ In Eq. (1), r and ry are, respectively, the flow stress and the yield stress, M is the Taylor factor, which is equal to 2.954, k is a constant, equal to 0.15, l is the shear modulus, equal to 42.1 GPa, and b is the Burgers vector, equal to 2.8 1010 m. In Figure 2, q, which shows the occurrence of the athermal a00 , is represented by a solid plot. It can be observed that the athermal a00 martensite forms at a strain rate of 0.1 s1 and the amount of a00 increases with an increasing strain rate. Furthermore, an increase in magnitude by two to three orders is observed in the dislocation density, qretained b, at high strain rates, which are greater than 1 s1, as compared to a low strain rate of 0.001 s1, indicating that high-speed deformation enhances the accumulation of plastic strains. The effect of strains induced by the b/a00 martensitic transformation should be considered for an increase in the dislocation density. However, we can ignore this effect on the increase in qretained b because of a small volume change of 0.7% between b and a00 , according to the lattice parameter [5]. In addition, a large difference between qm and qretained b at high strain rates, which are greater than 0.1 s1, can be seen despite the similar values of qm and qretained b at low strain rates of 0.001 s1 and 0.01 s1. This implies that strain is strongly accumulated in the retained b phase as compared to the amount of strain utilized for microstructural conversion by increasing the strain rate. Thus, it can be expected that the term
T. Akanuma et al. / Scripta Materialia 67 (2012) 21–24
23
for the a00 transformation to occur. However, considering that qretained b is in the retained b phase and that its order of magnitude of 1015 is consistent with the order of magnitude for the a00 martensitic transformation at room temperature, the amount of accumulated strain in the case of a high strain rate is thought to be sufficient to enhance the athermal a00 martensitic transformation. However, the stored energy estimated by an analysis of the diffraction line broadening only considers longrange lattice strain [18]. When taking this factor into consideration, we should also consider the local effect. However, the contribution of the stored energy, Ed, by sub-boundary formation is low, at approximately 0.07 J g–1, and is calculated using the following equation [19]: Figure 3. Difference in the free energy of b and a00 , DGb_a00 , as a function of temperature.
gel is high at greater strain rates, thereby resulting in an apparent increase in Ms for high-speed deformations. In order to classify the effect of strain accumulation on the occurrence of the athermal a00 transformation, the relationship between the free energy and the stored energy was evaluated. Figure 3 shows the difference in free energy of b and a00 , DGb_a00 , which was calculated using the data in Duerig et al. [5]. The estimated values of Ms and dr/dT from a relationship of triggering stress for inducing a00 martensitic transformation and testing temperature of tensile test [5] are 48 K and 1.01 MPa K–1, respectively. Based on this data, the enthalpy change, DH, and the entropy change, DS, can be calculated to be 1.83 J g–1 and 6.5 103 J g–1 K–1, respectively. Therefore, the difference in free energy between b and a00 , DGb_a00 (=DH TDS) at Ms (= 48 K) can be estimated to be 1.52 J g–1. The curve of DGb_a00 , represented by a solid line, is estimated using the Clausius–Clapeyron relationship in Ti-10-2-3 alloys with an average grain size of approximately 200 lm. Unfortunately, in this work, the Ms value after isothermal hot forging at high strain rates could not be detected in either the cooling curve or the curve analyzed using a dilatometer equipped with ThermecMaster-Z. However, this value of Ms, which is affected by isothermal hot forging at high strain rates, should be higher than room temperature, and therefore the difference in the free energy DGb_a00 , in which Ms is assumed to be room temperature, represented by Ms0 , is also shown as a dotted line in Figure 3. Herein, the estimated energy required for an increase in Ms to room temperature is approximately 1.6 J g–1. The stored energy, Estore, due to the inhomogeneous lattice strain during hot deformation can be expressed using Eq. (2) [17], which includes the dislocation density qretained b: 1 ð2Þ Estore ¼ qretained b lb2 2 where l is the shear modulus, equal to 42.1 GPa, and b is the Burgers vector, equal to 2.8 1010 m. The estimated value of Estore at a strain rate of 10 s1 is 0.71 J g–1. In Figure 2, the dislocation density satisfying the condition Estore > 1.6 J g–1 is also drawn. Furthermore, we can see that slightly more energy is required
Ed
3cbb Dsubgrain
ð3Þ
where cbb is the subgrain boundary energy at b/b and Dsubgrain is the average size of the subgrains (=4 lm). The misorientation angle of a sub-boundary in the retained b phase (at 1273 K and 10 s1) is roughly estimated to be 5°. The Dsubgrain and the misorientation angle of a sub-boundary are the average values analyzed by the EBSD using the hot-forged sample at condition of 1273K and 101 s1. The value of cbb at a 5° subboundary is calculated to be 0.42 J m–2 according to the formula proposed by Wolf [20]. Therefore, we can conclude that the stored energy, accompanied by the formation of sub-boundaries, is too low to affect the occurrence of an athermal a00 martensitic transformation. EBSD–kernel average misorientation analysis of the sample hot forged at 1273 K10 s1 reveals that geometrically necessary (GN) dislocation accumulates on close to the {1 1 0} plane in retained b phase. Therefore, the accumulation of strain locally close to the {1 1 0} planes should strongly affect the occurrence of an athermal a00 martensitic transformation. By our work, we cannot verify whether a local stress field around the GN dislocations affects the nucleation of an a00 martensite, even though it is thought to be an additional factor. Regarding SIM transformations, Bhattacharjee et al. [21] pointed out that the grain size of the retained b phase had a profound effect on room temperature SIM transformations in Ti-10-2-3 alloys. In fact, SIM transformations occurred in microstructures with an average grain size of 130 lm, while no SIM transformation occurred at room temperature in microstructures with coarse grains. In their report [21], Bhattacharjee et al. modified the free energy change during SIM transformation by taking into account the effect of the grain size in the b phase. As a consequence, Bhattacharjee et al. reported that the effect of B(D, f)D Eel dominates over the free energy change during SIM transformation, thereby resulting in a grain size dependence of the SIM transformation in Ti-10-2-3 alloys. Herein, B(D, f)D Eel is the total elastic energy stored in the unit volume of the alloy, where D is the grain size of prior metastable b and f is the volume fraction of a00 . As mentioned above, the obtained grain sizes in the prior b phase during isothermal hot forging conducted in this work are similar to the grain sizes in the
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T. Akanuma et al. / Scripta Materialia 67 (2012) 21–24
Ti-10-2-3 alloys reported by Duerig et al. [5]. Therefore, the estimation of DGb_a00 on the basis of the result by Duerig et al., shown in Figure 3, is thought to be valid. During hot deformation, Ti-10-2-3 alloys undergo continuous dynamic recrystallization or dynamic recovery [2,9,10], implying that the formation of subgrains followed by evolution into high angle boundary grains is dominant during deformation. Considering the factor B(D, f)DEel, a dynamical change in the grain size during deformation of Ti-10-2-3 alloys would also affect the change in Ms value. However, the formation of subgrains remains dominant at a strain of 0.8, and therefore the effect of B(D, f)DEel on the change in Ms value would be small in our case. The results of Bhattacharjee et al. [21] also indicated that, as a consequence, many factors affect the value of Ms in Ti-10-2-3 alloys. If this is correct, there is a critical question concerning the accurate value of Ms in Ti-10-23 alloys. Recently, Neelakantan et al. [22] have calculated the value of Ms for b-Ti alloys using a thermodynamics-based model in which the Ghosh–Olson approach was applied. They suggested an approximation of Ms in terms of the elemental concentration in wt.% as given by the following equation: M s ðKÞ ¼ 1156 150Fewt:% 96Crwt:% 49Mowt:% 37Vwt:% 17Nbwt:% 7Zrwt:% þ 15Alwt:%
ð4Þ
The Ms value of Ti-10-2-3 alloys can be estimated to be approximately 530 K from Eq. (4). This Ms value, based on the thermodynamical model, can be considered an intrinsic Ms value. However, there is no consideration of an athermal x transformation in this model. The competition between martensitic transformations and x transformations leads to an apparent change in Ms [23,24], thereby making it difficult to identify an accurate Ms value for Ti-10-2-3 alloys. Thus, we can conclude that Ms in Ti-10-2-3 alloys is a complex function of various microstructural factors, such as grain size, dislocation density, dislocation substructure and the extent of competition with x transformations, as well as the difference in chemical thermodynamics. In summary, an athermal a00 martensite was found to appear after hot compression at 1173 and 1273 K and at strain rates greater than 0.1 s1. This work reveals that a high accumulation of dislocation density, which is greater than of 1015 m2 and arises from high-speed deformations, enhanced athermal a00 martensitic transformations. This was explained by the contribution of the dislocation stored energy, 0.5 qretained b lb2, to the chemical potential, which led to the a00 transformation. This result suggests a new type of process design for producing a homogeneous a00 martensitic microstructure by the isothermal hot forging of Ti-10-2-3 alloys.
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