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Strain rate sensitivity and strain hardening exponent during the isothermal compression of Ti60 alloy
Materials Science and Engineering A 538 (2012) 156–163
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Strain rate sensitivity and strain hardening exponent during the isothermal compression of Ti60 alloy J. Luo ∗ , M.Q. Li School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, PR China
a r t i c l e
i n f o
Article history: Received 1 November 2011 Received in revised form 30 December 2011 Accepted 2 January 2012 Available online 18 January 2012 Keywords: Ti60 alloy Flow stress Strain rate sensitivity Strain hardening exponent
a b s t r a c t In this paper, the flow stress was investigated in detail during the isothermal compression of Ti60 alloy. The strain rate sensitivity and the strain hardening exponent of Ti60 alloy were calculated based on the flow stress–strain curves. The results showed that the softening effect in the ␣ +  two-phase region was more significant than that in the  single-phase region due to the change in the deformation heat of the alloy. An initial yield drop was observed at or above 1273 K and in the strain rate range of 0.1–10.0 s−1 . The  phase became the continuous phase above 1273 K, which led to little temperature dependence of flow stress. The maximum m value of 0.34 occurred at 1253 K and a strain rate of 0.001 s−1 during the isothermal compression of Ti60 alloy. The strain rate sensitivity at a strain of 0.7 and a strain rate of 10.0 s−1 decreased with increasing deformation temperature after a peak value. And the m values decreased with increasing strain rate. This phenomenon could be reasonably explained based on the microstructure evolution during the isothermal compression of Ti60 alloy. The strain hardening exponent increased with increasing deformation temperature at the strain rates of 0.001 s−1 , 1.0 s−1 and 10.0 s−1 . The variation of strain hardening exponent with strain was observed to be dependent on the strain rate and the deformation temperature. © 2012 Elsevier B.V. All rights reserved.
1. Introduction In recent years, a series of commercial near-␣ titanium alloys, such as IMI685 alloy, IMI834 alloy, TIMETAL-1100 alloy, Ti600 alloy and Ti60 alloy were designed for a service temperature of at least 873 K. High temperature deformation behavior of these alloys was continuously paid attention and reported in the open literatures due to the benefits of extended formability. For example, Weinem et al. [1] investigated the microstructure evolution and the mechanical properties of TIMETAL-1100 alloy after different thermomechanical treatments. The results showed that the yield strength of TIMETAL-1100 alloy was lower for the fine-grained lamellar structure than for the coarse-grained structure. Wanjara et al. [2,3] studied the effect of processing parameters on the flow stress and the microstructure evolution during the isothermal compression of IMI834 alloy, and proposed the constitutive equations using an Arrhenius-type hyperbolic–sine relationship. Zhou [4] described the effect of average grain size on the flow behavior of IMI834 alloy by introducing internal variables to characterize the phenomenon of flow softening. The deformation behavior and the processing map of IMI685 alloy were investigated during
∗ Corresponding author. Tel.: +86 29 88460465; fax: +86 29 88492642. E-mail addresses: [email protected], [email protected] (J. Luo). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2012.01.021
the isothermal compression [5–7]. Moreover, many experimental investigations had been carried out in order to evaluate the flow behavior, the microstructure evolution and the constitutive equations of Ti600 alloy at different hydrogen contents [8–12]. Ti60 alloy as a near-␣ type titanium alloy has excellent combination of mechanical and physical properties, i.e., good strength, good fatigue resistance and creep resistance characteristics at a service temperature of 873 K, that enables this alloy to be one of the most important high temperature materials to fabricate engine parts such as blades and discs in the aviation and aerospace industries. Xiong et al. [13,14] investigated the corrosion behavior of Ti60 alloy with an aluminide, TiAlCr and enamel coatings in moist air containing NaCl vapor at 973–1073 K, proposed that the enamel coating could protect Ti60 alloy from corrosion due to high thermochemical stability and matched thermal expansion coefficient with substrates of Ti-base alloys during corrosion. Li et al. [15] characterized the high temperature deformation behavior of Ti60 alloy based on an analysis of the stress–strain behavior, kinetics and processing map. Subsequently, Li et al. [16,17] refined grain of Ti60 alloy using thermohydrogenation treatment and equal-channel angular pressing. Luo et al. [18] modeled the constitutive relationships and microstructural variables of Ti60 alloy during high temperature deformation by using a fuzzy set and artificial neural network (FNN) technique with a back-propagation learning algorithm. Although many studies have been focused on this alloy, the effect of
J. Luo, M.Q. Li / Materials Science and Engineering A 538 (2012) 156–163 Table 1 Chemical composition of the as-received Ti60 alloy (mass fraction in %). Al
Sn
Zr
Mo
6.62
5.14
1.82
0.54
Si 0.36
Nd
Ti
0.85
Bal.
processing parameters on the strain rate sensitivity and the strain hardening exponent of Ti60 alloy was not discussed. Therefore, additional studies are necessary to model the deformation behavior during the isothermal compression of Ti60 alloy. The objective of present study is to reveal the variations of the strain rate sensitivity and the strain hardening exponent with processing parameters during the isothermal compression of Ti60 alloy. To reach this objective, isothermal compression is carried out in order to investigate the flow behavior of Ti60 alloy. The effect of processing parameters on the strain rate sensitivity and the strain hardening exponent is analyzed and detail explanation is given with the help of the microstructure evolution of Ti60 alloy.
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were grooved for retention of glass lubricants. A series of isothermal compressions were carried out using the Thermecmaster-Z simulator at the deformation temperatures ranging from 1173 K to 1333 K, strain rates of 0.001, 0.01, 0.1, 1.0 and 10.0 s−1 , and height reductions of 50%, 60%, and 70%. The specimens were heated for 3 min to obtain a uniform deformation temperature prior to isothermal compression. The flow stress–strain curves were recorded automatically during the isothermal compression. After isothermal compression, the specimens were cooled in air to room temperature. To examine the microstructure, the specimens were axially sectioned and prepared using standard metallographic techniques. The grain size and volume fraction of phase were measured using an OLYMPUS PMG3 microscope with the quantitative metallography SISC IAS V8.0 image analysis software.
3. Results and discussion
2. Experimental
3.1. Flow stress
2.1. Material
A series of flow stress–strain curves during the isothermal compression of Ti60 alloy at different deformation temperatures and strain rates are shown in Fig. 2 and Fig. 3, respectively. It is observed from Fig. 2 that the flow stress increases with increasing strain, reaches a peak at a critical strain, and then decreases to a steady value because the dynamic softening is sufficient to counteract the work-hardening of the material during the isothermal compression. As illustrated in Fig. 2, the overall shapes of flow curves are dependent on the deformation temperature and the strain rate. Firstly, it can be seen that the softening effect in the ␣ +  two-phase region is significantly different from those in the  single-phase region. In the ␣ +  two-phase region, the softening effect is more significant for all tested strain rates, and a steady flow is observed up to a strain of 0.7, as illustrated in Fig. 2(a)–(g). In contrast, the softening effect in the  single-phase region is relatively low. The flow stress in the  single-phase region appears to be the steady flow behavior at a small strain, which implies that the effect of strain on the flow stress is negligible, as shown in Fig. 2(h)–(j). The noticeable softening phenomenon in the ␣ +  two-phase region may be attributed to the adiabatic heating generated during deformation, which raises the actual temperature of the specimens and also the proportion of soft  phase. Similarly, Wanjara et al. [3] also observed that flow softening behavior in the  single-phase region appeared to be significantly different from the deformation behavior in the ␣ +  two-phase region. Secondly, the overall shapes of flow curves at or above 1273 K and at high strain rates ranging from 0.1 s−1 to 10.0 s−1 are significantly different from those at low deformation temperatures and low strain rates. An initial yield drop is observed at or above 1273 K and at high strain rates ranging from 0.1 s−1 to 10.0 s−1 , followed by flow softening whose softening rate is higher at low strains and considerably less at high strains. This yield drop phenomenon is related to the fact that high strain rates promote less time for recovery processes and higher local stress concentrations due to dislocation pile-up [20]. Similarly, an initial yield drop was reported previously for the deformation processes of IMI834 alloy at 1303 K and strain rates ranging from 0.1 s−1 to 1.0 s−1 [2]. The occurrence of yield drop phenomenon in IMI834 alloy was rationalized through existing static and/or dynamic deformation theories. Moreover, it is also seen from Fig. 2 that the flow stress greatly increases with increasing strain rate at a set deformation temperature. In other words, the flow stress is sensitive to the strain rate during the isothermal compression of Ti60 alloy. Main reason is that the rate of dislocation generation increases with increasing strain rate. The tangled dislocation structures hinder the dislocation movement, leading to an increase
In this study, an as-received bar stock of Ti60 alloy with an 18.0 mm diameter was used. The chemical composition and a micrograph of this alloy are shown in Table 1 and Fig. 1, respectively. Fig. 1 shows that the typical alloy microstructure at room temperature is composed of equiaxed primary ␣ phase with a grain size about 6.0 m and a small amount of intergranular . The INCA ENERGY 350 energy dispersive X-ray spectrometer (EDX) analysis reveals that the dark particles marked with white arrows are Nd-rich rare earth phase. The heat treatment prior to isothermal compression was conducted in the following procedures: (1) heating to 1263 K and holding for 2 h, (2) air-cooling to room temperature, (3) heating to 973 K and holding for 2 h, and (4) air-cooling to room temperature. The beta-transus temperature for this alloy was determined to be 1303 K via a technique involving heat treatment followed by optical metallography. Jia et al. [19] found that the  transus temperature of another Ti60 alloy was about 1318 K. The increase in the  transus temperature was attributed to the slight change of alloy elements. 2.2. Experimental procedures The cylindrical compression specimens of Ti60 alloy were 8.0 mm in diameter and 12.0 mm in height. The cylinder ends
Fig. 1. Optical micrograph of the as-received Ti60 alloy.
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Fig. 2. Flow stress–strain curves during the isothermal compression of Ti60 alloy at different deformation temperatures.
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Strain Fig. 2. (Continued ).
in the flow stress during the isothermal compression of Ti60 alloy. From Fig. 3, it is seen that the flow stress sharply decreases with increasing deformation temperature below 1273 K, then it varies indistinctively with deformation temperature above 1273 K. This phenomenon demonstrates that the decreasing degree of flow stress is relatively low at high deformation temperatures primarily because the volume fraction of ␣ phase is less 10% at 1273 K, and the  phase becomes the continuous phase above 1273 K due to the deformation heat of the alloy, which results in the little temperature dependence of the flow stress. The change of flow behavior during the isothermal compression of Ti60 alloy is similar to that reported for previous work on IMI834 alloy. For IMI834 alloy, the flow stress was observed to be relatively insensitive to the deformation temperature above 1323 K [2]. Compared the flow stress in Fig. 3(a) with that in (b), it is seen that the flow stress of Ti60 alloy at a strain rate of 10.0 s−1 and a strain of 0.1 decreases from 217 MPa to 87 MPa at the deformation temperatures ranging from 1233 K to 1333 K, but it decreases from 152 MPa to 55 MPa at a strain rate of 1.0 s−1 and a strain of 0.1 and at the deformation temperatures ranging from 1233 K to 1333 K. This phenomenon demonstrates that the decreasing degree of flow stress decreases with increasing strain rate. As discussed earlier, the adiabatic deformation at a high strain rate leads to a greater dynamic softening effect than that at a low strain rate, but the strain hardening effect at a high strain rate is more significant because the rate of dislocation generation increases with increasing strain rate. In present study, the strain hardening effect may play a dominant role in the strain rate range
of 10.0–0.1 s−1 , which leads to that the decreasing degree of flow stress decreases with increasing strain rate. 3.2. Strain rate sensitivity The strain rate sensitivity is usually used to determine the superplastic behavior and the deformation mechanism of material. In present work, the strain rate sensitivity is determined using the following expression [21]: m=
(1)
where is the flow stress (MPa), ε˙ is the strain rate (s−1 ), ε is the strain, and T is the absolute deformation temperature (K). Based on the flow stress data during the isothermal compression of Ti60 alloy, the strain rate sensitivity is calculated at a constant strain and deformation temperature using Eq. (1). Fig. 4 shows the effect of deformation temperature on the strain rate sensitivity during the isothermal compression of Ti60 alloy at a strain of 0.7. From Fig. 4, it is seen that the maximum m value of 0.34 occurs at 1253 K and a strain rate of 0.001 s−1 during the isothermal compression of Ti60 alloy. Subsequently, the strain rate sensitivity sharply decreases with increasing deformation temperature, and reach a minimum value at a deformation temperature of 1283 K. This phenomenon can be reasonably explained based on previous superplastic deformation theory [22]. According to previous superplastic theory, the strain rate sensitivity of alloy is dependent on alloy composition, grain size, volume fraction of phase,
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Fig. 3. Flow stress–strain curves during the isothermal compression of Ti60 alloy at the strain rates of 10.0 s−1 (a) and 1.0 s−1 (b).
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Fig. 4. The effect of deformation temperature on the strain rate sensitivity and micrographs during the isothermal compression of Ti60 alloy at a strain of 0.7: (a) T = 1253 K, ε˙ = 0.001 s−1 , (b) T = 1283 K, ε˙ = 0.001 s−1 , (c) T = 1253 K, ε˙ = 10.0 s−1 , and (d) T = 1273 K, ε˙ = 10.0 s−1 .
deformation temperature and so on. Moreover, the optimum deformation temperature is one at which the volume fractions of ␣ phase and  phase in the alloy are approximately equal because the mixture of these two phases can contribute to grain boundary sliding and accommodation. Fig. 4(a) demonstrates that the microstructure at a deformation temperature of 1253 K and a strain rate of 0.001 s−1 consists of primary ␣ phase with a grain size of approximately 7.3 m and intergranular  with a volume fraction of 41%. Thus, approximately equal phase proportions are beneficial for grain boundary sliding and accommodation, which results in the maximum m value at a deformation temperature of 1253 K and a strain rate of 0.001 s−1 . Similarly, Cope et al. [23] reported that Ti–6Al–4V alloy exhibited a high elongation when the volume fraction of  phase was approximately 42%. Moreover, the ␣ grains at a
deformation temperature of 1253 K and a strain rate of 0.001 s−1 are equiaxed and uniform, which are beneficial for the grain boundary sliding. However, the ␣ phase begins to transform into the  phase with increasing deformation temperature, and the phase transition is completed at a deformation temperature of 1283 K due to the adiabatic heating, as shown in Fig. 4(b). Thus, the rapid increase of  phase leads to the drop of the m values. From the discussion above, it is concluded that the strain rate sensitivity sharply decreases near  transus temperature during the isothermal compression of Ti60 alloy, which may be attributed to a rapid increase of the volume fraction of  phase. The strain rate sensitivity at a strain of 0.7 and a strain rate of 10.0 s−1 firstly tends to increase with increasing deformation temperature, reach a peak value at a deformation temperature of
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Fig. 5. The effect of strain on the strain rate sensitivity during the isothermal compression of Ti60 alloy at the deformation temperatures of 1253 K (a) and 1333 K (b).
3.3. Strain hardening exponent The strain hardening exponent resulted from a balance between strain hardening mechanism and softening mechanism. In present work, the strain hardening exponent is calculated using the following expression: n=
d log d log ε ε,T ˙
(2)
where is the flow stress(MPa), ε˙ is the strain rate (s−1 ), ε is the strain, and T is the absolute deformation temperature (K). Based on the flow stress data during the isothermal compression of Ti60 alloy, the strain hardening exponent is computed at a constant strain rate and deformation temperature using Eq. (2). Fig. 6 shows the effect of deformation temperature on the strain hardening exponent during the isothermal compression of Ti60 alloy at a strain of 0.4. It is observed from Fig. 6 that the deformation temperature affects significantly the strain hardening exponent during the isothermal compression of Ti60 alloy. The strain hardening exponent during the isothermal compression of Ti60 alloy increases with increasing deformation temperature at the strain rates of 0.001 s−1 , 1.0 s−1 , and 10.0 s−1 . This phenomenon can be reasonably explained based on the analysis of flow behavior during the isothermal compression of Ti60 alloy. According to the
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1273 K and then drops at high deformation temperatures during the isothermal compression of Ti60 alloy. The similar variation of strain rate sensitivity was reported during the isothermal compression of Ti–6Al–4V alloy [24]. The m value at a deformation temperature of 1253 K and a strain rate of 10.0 s−1 is 0.11, which is lower than that at a deformation temperature of 1253 K and strain rate of 0.001 s−1 , i.e., the strain rate sensitivity decreases with increasing strain rate, as shown in Fig. 4. This phenomenon is related to the fact that the strain rate has an effect on the microstructure during the isothermal compression of Ti60 alloy. Compared the micrograph in Fig. 4(c) with that in (a), it is observed that the microstructure at a deformation temperature of 1253 K and a strain rate of 10.0 s−1 is non-uniform and has slight oriented characteristics. Equiaxed primary ␣ phase of both large and small grains is surrounded by the deformed and elongated ␣ phase during the isothermal compression of Ti60 alloy. But the ␣ grains at a deformation temperature of 1253 K and a strain rate of 0.001 s−1 are equiaxed and uniform. Therefore, the nonuniformity of microstructure finally leads to the decrease of strain rate sensitivity at a strain rate of 10.0 s−1 . Fig. 4(d) shows the microstructure at a deformation temperature of 1273 K and a strain rate of 10.0 s−1 . It is seen that the ␣ grains are finer than that at a deformation temperature of 1253 K and a strain rate of 10.0 s−1 , which is likely to lead to the increase of strain rate sensitivity. According to above-mentioned analysis, the deformation temperature and the strain rate have a significant effect on the strain rate sensitivity during the isothermal compression of Ti60 alloy. The effect of strain on the strain rate sensitivity during the isothermal compression of Ti60 alloy is shown in Fig. 5. As seen from Fig. 5, the strain has an influence on the strain rate sensitivity at the strain rates of 0.001 s−1 and 10.0 s−1 , but the variation of strain rate sensitivity is negligible at the strain rates ranging from 0.01 s−1 to 0.1 s−1 . The strain rate sensitivity at the strain rates of 0.001 s−1 and 10.0 s−1 mostly decreases with increasing strain during the isothermal compression of Ti60 alloy. In general, the variation of strain rate sensitivity with strain is controlled by three mechanisms: (i) thermal softening related to the dislocation annihilation, (ii) work hardening due to the dislocation accumulation and the dislocation-dislocation interaction, and (iii) microstructure evolution. In present study, thermal softening mechanism may play a dominant role in the strain range of 0.4–0.7, which promotes the decrease of the strain rate sensitivity at the strain rates of 0.001 s−1 and 10.0 s−1 . According to the observation in Fig. 3, the noticeable softening effect of flow stress in the strain range of 0.4–0.7 supports the present work. Similarly, Krishna et al. [6] also proposed that the strain rate sensitivity of IMI685 alloy decreased with increasing strain.
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Fig. 7. The effect of strain on the strain hardening exponent during the isothermal compression of Ti60 alloy at the deformation temperatures of 1233 K (a) and 1333 K (b).
deformation behavior, it is concluded that the softening effect in the  single-phase region is lower than that in the ␣ +  twophase region, as shown in Fig. 3. It is well known that the strain hardening exponent results from a competition between thermal softening and strain hardening. Therefore, the decrease in softening effect leads to the increase in strain hardening exponent during the isothermal compression of Ti60 alloy. Luo et al. [24] reported that the strain hardening exponent of Ti–6Al–4V alloy increased with increasing deformation temperature during the isothermal compression. The strain hardening exponent at the strain rates of 0.01 s−1 and 0.1 s−1 is oscillatory with increasing deformation temperature during the isothermal compression isothermal compression of Ti60 alloy.
The effect of strain on the strain hardening exponent during the isothermal compression of Ti60 alloy is shown in Fig. 7. As seen from Fig. 7, the strain hardening exponent during the isothermal compression of Ti60 alloy is negative at the strain rates ranging from 0.01 s−1 to 10.0 s−1 , which implies that the softening effect plays a dominant role in the strain rate range of 0.01–10.0 s−1 . Fig. 7 also demonstrates that the strain rate has an effect on the strain hardening exponent during the isothermal compression of Ti60 alloy. This phenomenon may be attributed to the microstructure evolution of Ti60 alloy. Fig. 8 shows the effect of strain rate on the microstructure during the isothermal compression of Ti60 alloy at a deformation temperature of 1233 K and a strain of 0.7. The microstructure varies slightly with strain rate at the strain rates ranging from 10.0 s−1
Fig. 8. The effect of strain rate on the microstructure during the isothermal compression of Ti60 alloy at a deformation temperature of 1233 K and a strain of 0.7: (a) 10.0 s−1 , (b) 1.0 s−1 , (c) 0.01 s−1 , and (d) 0.001 s−1 .
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to 1.0 s−1 , as illustrated in Fig. 8(a) and (b). The equiaxed ␣ phase is surrounded by the deformed and elongated ␣ phase and intergranular . However, at the strain rates ranging from 0.01 s−1 to 0.001 s−1 , the morphology of ␣ phase is an equiaxed structure and well distributed in the Ti60 alloy matrix primarily because the ␣ phase has enough time to grow and spheroidize, as illustrated in Fig. 8(c) and (d). Therefore, the microstructure evolution at different strain rates finally leads to the variation of strain hardening exponent during the isothermal compression of Ti60 alloy. From Fig. 7(a), it is observed that the influence of strain on the strain hardening exponent is significant at the strain rates ranging from 0.001 s−1 to 0.1 s−1 , but it becomes to be unobvious at the strain rates of 1.0 s−1 and 10.0 s−1 . And roughly speaking, the n values decrease with increasing strain at the strain rates ranging from 0.001 s−1 to 0.1 s−1 . This phenomenon is related to the fact that the rate of dislocation storage is proportional to 1/2 , and the rate of dislocation annihilation is proportional to (where is the dislocation density). Thus, the softening effect plays a dominant role in the strain range of 0.2–0.6, and the degree of softening effect increases with strain. Similarly, the effect of strain on the strain hardening exponent is not remarkable in the  single-phase region at the strain rates of 1.0 s−1 and 10.0 s−1 , as illustrated in Fig. 7(b). However, the n values increase with increasing strain at the strain rates ranging from 0.001 s−1 to 0.1 s−1 because the softening effect in the  single-phase region is significantly different from those in the ␣ +  two-phase region. In the  single-phase region, the flow stress appears to be the steady flow behavior at a small strain. Therefore, the softening effect plays no role in the n values. But the microstructure evolution during the isothermal compression of Ti60 alloy results in the variation of strain hardening exponent. According to above-mentioned analysis, it is concluded that the variation of strain hardening exponent with strain is dependent on the strain rate and the deformation temperature during the isothermal compression of Ti60 alloy. 4. Conclusions The strain rate sensitivity and the strain hardening exponent during the isothermal compression of Ti60 alloy are calculated based on the flow stress–strain curves. The following conclusions are obtained from the present investigation. (1) An initial yield drop is observed at or above 1273 K and at high strain rates ranging from 0.1 s−1 to 10.0 s−1 . This yield drop phenomenon is related to the fact that high strain rates promote less time for recovery processes and higher local stress concentrations due to dislocation pile-up. (2) The flow stress sharply decreases with increasing deformation temperature below 1273 K, then it varies indistinctively with deformation temperature above 1273 K. (3) The maximum m value of 0.34 occurs at 1253 K and a strain rate of 0.001 s−1 during the isothermal compression of Ti60 alloy.
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The strain rate sensitivity at a strain of 0.7 and a strain rate of 10.0 s−1 decreases with increasing deformation temperature after a peak value. (4) The strain rate sensitivity during the isothermal compression of Ti60 alloy decreases with increasing strain rate. This phenomenon can be reasonably explained based on the microstructure evolution during the isothermal compression of Ti60 alloy. The strain has an effect on the strain rate sensitivity at the strain rates of 0.001 s−1 and 10.0 s−1 . (5) The strain hardening exponent during the isothermal compression of Ti60 alloy increases with increasing deformation temperature at the strain rates of 0.001 s−1 , 1.0 s−1 and 10.0 s−1 . The variation of strain hardening exponent with strain is dependent on the strain rate and the deformation temperature during the isothermal compression of Ti60 alloy. Acknowledgments The authors would like to thank the financial supports from the National Natural Science Foundation of China under the Grant No. 50975234, China Postdoctoral Science Foundation under the Grant No. 20110491685 and the “111” Project under the Grant No. 08040. References [1] D. Weinem, J. Kumpfert, M. Peters, W.A. Kaysser, Mater. Sci. Eng. A 206 (1) (1996) 55–62. [2] P. Wanjara, M. Jahazi, H. Monajati, S. Yue, J.P. Immarigeon, Mater. Sci. Eng. A 396 (1/2) (2005) 50–60. [3] P. Wanjara, M. Jahazi, H. Monajati, S. Yue, Mater. Sci. Eng. A 416 (1/2) (2006) 300–311. [4] M. Zhou, Mater. Sci. Eng. A 245 (1) (1998) 29–38. [5] Y. Liu, T.N. Baker, Mater. Sci. Eng. A 197 (2) (1995) 125–131. [6] V.G. Krishna, Y.V.R.K. Prasad, N.C. Birla, G.S. Rao, J. Mater. Process. Technol. 71 (3) (1997) 377–383. [7] T. Rajagopalachary, V.V. Kutumbarao, Scr. Mater. 35 (3) (1996) 305–309. [8] Y. Niu, J. Luo, M.Q. Li, Int. J. Hydrogen Energy 36 (1) (2011) 1006–1013. [9] M.Q. Li, J. Luo, Y. Niu, Mater. Sci. Eng. A 527 (24/25) (2010) 6626–6632. [10] X.M. Zhang, Y.Q. Zhao, W.D. Zeng, Int. J. Hydrogen Energy 35 (9) (2010) 4354–4360. [11] J.W. Zhao, H. Ding, H.L. Hou, Z.Q. Li, J. Alloys Compd. 491 (1/2) (2010) 673–678. [12] X.L. Wang, Y.Q. Zhao, M. Hagiwara, H.L. Hou, T. Suzuki, J. Alloys Compd. 490 (1/2) (2010) 531–536. [13] Y.M. Xiong, S.L. Zhu, F.H. Wang, Surf. Coat. Technol. 190 (2/3) (2005) 195– 199. [14] Y.M. Xiong, S.L. Zhu, F.H. Wang, Corros. Sci. 50 (1) (2008) 15–22. [15] M.Q. Li, H.S. Pan, Y.Y. Lin, J. Luo, J. Mater. Process. Technol. 183 (1) (2007) 71–76. [16] M.Q. Li, Y.Y. Lin, Int. J. Hydrogen Energy 32 (5) (2007) 626–629. [17] M.Q. Li, Y.Y. Lin, Int. J. Hydrogen Energy 35 (11) (2010) 5703–5707. [18] J. Luo, M.Q. Li, Y.Q. Hu, M.W. Fu, Mater. Charact. 59 (10) (2008) 1386–1394. [19] W.J. Jia, W.D. Zeng, J.R. Liu, Y.G. Zhou, Q.J. Wang, Mater. Sci. Eng. A 530 (2011) 511–518. [20] I. Philippart, H.J. Rack, Mater. Sci. Eng. A 243 (1/2) (1998) 196–200. [21] W.A. Backfen, I.R. Turner, D.H. Avery, ASM Trans. Quart. 57 (1964) 980–990. [22] J.W.D. Patterson, N. Ridley, J. Mater. Sci. 16 (2) (1981) 457–464. [23] M.T. Cope, D.R. Evetts, N. Ridley, J. Mater. Sci. 21 (11) (1986) 4003–4008. [24] J. Luo, M.Q. Li, W.X. Yu, H. Li, Mater. Des. 31 (2) (2010) 741–748.
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Strain rate sensitivity and strain hardening exponent during the isothermal compression of Ti60 alloy J. Luo ∗ , M.Q. Li School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, PR China
a r t i c l e
i n f o
Article history: Received 1 November 2011 Received in revised form 30 December 2011 Accepted 2 January 2012 Available online 18 January 2012 Keywords: Ti60 alloy Flow stress Strain rate sensitivity Strain hardening exponent
a b s t r a c t In this paper, the flow stress was investigated in detail during the isothermal compression of Ti60 alloy. The strain rate sensitivity and the strain hardening exponent of Ti60 alloy were calculated based on the flow stress–strain curves. The results showed that the softening effect in the ␣ +  two-phase region was more significant than that in the  single-phase region due to the change in the deformation heat of the alloy. An initial yield drop was observed at or above 1273 K and in the strain rate range of 0.1–10.0 s−1 . The  phase became the continuous phase above 1273 K, which led to little temperature dependence of flow stress. The maximum m value of 0.34 occurred at 1253 K and a strain rate of 0.001 s−1 during the isothermal compression of Ti60 alloy. The strain rate sensitivity at a strain of 0.7 and a strain rate of 10.0 s−1 decreased with increasing deformation temperature after a peak value. And the m values decreased with increasing strain rate. This phenomenon could be reasonably explained based on the microstructure evolution during the isothermal compression of Ti60 alloy. The strain hardening exponent increased with increasing deformation temperature at the strain rates of 0.001 s−1 , 1.0 s−1 and 10.0 s−1 . The variation of strain hardening exponent with strain was observed to be dependent on the strain rate and the deformation temperature. © 2012 Elsevier B.V. All rights reserved.
1. Introduction In recent years, a series of commercial near-␣ titanium alloys, such as IMI685 alloy, IMI834 alloy, TIMETAL-1100 alloy, Ti600 alloy and Ti60 alloy were designed for a service temperature of at least 873 K. High temperature deformation behavior of these alloys was continuously paid attention and reported in the open literatures due to the benefits of extended formability. For example, Weinem et al. [1] investigated the microstructure evolution and the mechanical properties of TIMETAL-1100 alloy after different thermomechanical treatments. The results showed that the yield strength of TIMETAL-1100 alloy was lower for the fine-grained lamellar structure than for the coarse-grained structure. Wanjara et al. [2,3] studied the effect of processing parameters on the flow stress and the microstructure evolution during the isothermal compression of IMI834 alloy, and proposed the constitutive equations using an Arrhenius-type hyperbolic–sine relationship. Zhou [4] described the effect of average grain size on the flow behavior of IMI834 alloy by introducing internal variables to characterize the phenomenon of flow softening. The deformation behavior and the processing map of IMI685 alloy were investigated during
∗ Corresponding author. Tel.: +86 29 88460465; fax: +86 29 88492642. E-mail addresses: [email protected], [email protected] (J. Luo). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2012.01.021
the isothermal compression [5–7]. Moreover, many experimental investigations had been carried out in order to evaluate the flow behavior, the microstructure evolution and the constitutive equations of Ti600 alloy at different hydrogen contents [8–12]. Ti60 alloy as a near-␣ type titanium alloy has excellent combination of mechanical and physical properties, i.e., good strength, good fatigue resistance and creep resistance characteristics at a service temperature of 873 K, that enables this alloy to be one of the most important high temperature materials to fabricate engine parts such as blades and discs in the aviation and aerospace industries. Xiong et al. [13,14] investigated the corrosion behavior of Ti60 alloy with an aluminide, TiAlCr and enamel coatings in moist air containing NaCl vapor at 973–1073 K, proposed that the enamel coating could protect Ti60 alloy from corrosion due to high thermochemical stability and matched thermal expansion coefficient with substrates of Ti-base alloys during corrosion. Li et al. [15] characterized the high temperature deformation behavior of Ti60 alloy based on an analysis of the stress–strain behavior, kinetics and processing map. Subsequently, Li et al. [16,17] refined grain of Ti60 alloy using thermohydrogenation treatment and equal-channel angular pressing. Luo et al. [18] modeled the constitutive relationships and microstructural variables of Ti60 alloy during high temperature deformation by using a fuzzy set and artificial neural network (FNN) technique with a back-propagation learning algorithm. Although many studies have been focused on this alloy, the effect of
J. Luo, M.Q. Li / Materials Science and Engineering A 538 (2012) 156–163 Table 1 Chemical composition of the as-received Ti60 alloy (mass fraction in %). Al
Sn
Zr
Mo
6.62
5.14
1.82
0.54
Si 0.36
Nd
Ti
0.85
Bal.
processing parameters on the strain rate sensitivity and the strain hardening exponent of Ti60 alloy was not discussed. Therefore, additional studies are necessary to model the deformation behavior during the isothermal compression of Ti60 alloy. The objective of present study is to reveal the variations of the strain rate sensitivity and the strain hardening exponent with processing parameters during the isothermal compression of Ti60 alloy. To reach this objective, isothermal compression is carried out in order to investigate the flow behavior of Ti60 alloy. The effect of processing parameters on the strain rate sensitivity and the strain hardening exponent is analyzed and detail explanation is given with the help of the microstructure evolution of Ti60 alloy.
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were grooved for retention of glass lubricants. A series of isothermal compressions were carried out using the Thermecmaster-Z simulator at the deformation temperatures ranging from 1173 K to 1333 K, strain rates of 0.001, 0.01, 0.1, 1.0 and 10.0 s−1 , and height reductions of 50%, 60%, and 70%. The specimens were heated for 3 min to obtain a uniform deformation temperature prior to isothermal compression. The flow stress–strain curves were recorded automatically during the isothermal compression. After isothermal compression, the specimens were cooled in air to room temperature. To examine the microstructure, the specimens were axially sectioned and prepared using standard metallographic techniques. The grain size and volume fraction of phase were measured using an OLYMPUS PMG3 microscope with the quantitative metallography SISC IAS V8.0 image analysis software.
3. Results and discussion
2. Experimental
3.1. Flow stress
2.1. Material
A series of flow stress–strain curves during the isothermal compression of Ti60 alloy at different deformation temperatures and strain rates are shown in Fig. 2 and Fig. 3, respectively. It is observed from Fig. 2 that the flow stress increases with increasing strain, reaches a peak at a critical strain, and then decreases to a steady value because the dynamic softening is sufficient to counteract the work-hardening of the material during the isothermal compression. As illustrated in Fig. 2, the overall shapes of flow curves are dependent on the deformation temperature and the strain rate. Firstly, it can be seen that the softening effect in the ␣ +  two-phase region is significantly different from those in the  single-phase region. In the ␣ +  two-phase region, the softening effect is more significant for all tested strain rates, and a steady flow is observed up to a strain of 0.7, as illustrated in Fig. 2(a)–(g). In contrast, the softening effect in the  single-phase region is relatively low. The flow stress in the  single-phase region appears to be the steady flow behavior at a small strain, which implies that the effect of strain on the flow stress is negligible, as shown in Fig. 2(h)–(j). The noticeable softening phenomenon in the ␣ +  two-phase region may be attributed to the adiabatic heating generated during deformation, which raises the actual temperature of the specimens and also the proportion of soft  phase. Similarly, Wanjara et al. [3] also observed that flow softening behavior in the  single-phase region appeared to be significantly different from the deformation behavior in the ␣ +  two-phase region. Secondly, the overall shapes of flow curves at or above 1273 K and at high strain rates ranging from 0.1 s−1 to 10.0 s−1 are significantly different from those at low deformation temperatures and low strain rates. An initial yield drop is observed at or above 1273 K and at high strain rates ranging from 0.1 s−1 to 10.0 s−1 , followed by flow softening whose softening rate is higher at low strains and considerably less at high strains. This yield drop phenomenon is related to the fact that high strain rates promote less time for recovery processes and higher local stress concentrations due to dislocation pile-up [20]. Similarly, an initial yield drop was reported previously for the deformation processes of IMI834 alloy at 1303 K and strain rates ranging from 0.1 s−1 to 1.0 s−1 [2]. The occurrence of yield drop phenomenon in IMI834 alloy was rationalized through existing static and/or dynamic deformation theories. Moreover, it is also seen from Fig. 2 that the flow stress greatly increases with increasing strain rate at a set deformation temperature. In other words, the flow stress is sensitive to the strain rate during the isothermal compression of Ti60 alloy. Main reason is that the rate of dislocation generation increases with increasing strain rate. The tangled dislocation structures hinder the dislocation movement, leading to an increase
In this study, an as-received bar stock of Ti60 alloy with an 18.0 mm diameter was used. The chemical composition and a micrograph of this alloy are shown in Table 1 and Fig. 1, respectively. Fig. 1 shows that the typical alloy microstructure at room temperature is composed of equiaxed primary ␣ phase with a grain size about 6.0 m and a small amount of intergranular . The INCA ENERGY 350 energy dispersive X-ray spectrometer (EDX) analysis reveals that the dark particles marked with white arrows are Nd-rich rare earth phase. The heat treatment prior to isothermal compression was conducted in the following procedures: (1) heating to 1263 K and holding for 2 h, (2) air-cooling to room temperature, (3) heating to 973 K and holding for 2 h, and (4) air-cooling to room temperature. The beta-transus temperature for this alloy was determined to be 1303 K via a technique involving heat treatment followed by optical metallography. Jia et al. [19] found that the  transus temperature of another Ti60 alloy was about 1318 K. The increase in the  transus temperature was attributed to the slight change of alloy elements. 2.2. Experimental procedures The cylindrical compression specimens of Ti60 alloy were 8.0 mm in diameter and 12.0 mm in height. The cylinder ends
Fig. 1. Optical micrograph of the as-received Ti60 alloy.
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Fig. 2. Flow stress–strain curves during the isothermal compression of Ti60 alloy at different deformation temperatures.
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(i)
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Deformation temperature: 1333 K
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Strain Fig. 2. (Continued ).
in the flow stress during the isothermal compression of Ti60 alloy. From Fig. 3, it is seen that the flow stress sharply decreases with increasing deformation temperature below 1273 K, then it varies indistinctively with deformation temperature above 1273 K. This phenomenon demonstrates that the decreasing degree of flow stress is relatively low at high deformation temperatures primarily because the volume fraction of ␣ phase is less 10% at 1273 K, and the  phase becomes the continuous phase above 1273 K due to the deformation heat of the alloy, which results in the little temperature dependence of the flow stress. The change of flow behavior during the isothermal compression of Ti60 alloy is similar to that reported for previous work on IMI834 alloy. For IMI834 alloy, the flow stress was observed to be relatively insensitive to the deformation temperature above 1323 K [2]. Compared the flow stress in Fig. 3(a) with that in (b), it is seen that the flow stress of Ti60 alloy at a strain rate of 10.0 s−1 and a strain of 0.1 decreases from 217 MPa to 87 MPa at the deformation temperatures ranging from 1233 K to 1333 K, but it decreases from 152 MPa to 55 MPa at a strain rate of 1.0 s−1 and a strain of 0.1 and at the deformation temperatures ranging from 1233 K to 1333 K. This phenomenon demonstrates that the decreasing degree of flow stress decreases with increasing strain rate. As discussed earlier, the adiabatic deformation at a high strain rate leads to a greater dynamic softening effect than that at a low strain rate, but the strain hardening effect at a high strain rate is more significant because the rate of dislocation generation increases with increasing strain rate. In present study, the strain hardening effect may play a dominant role in the strain rate range
of 10.0–0.1 s−1 , which leads to that the decreasing degree of flow stress decreases with increasing strain rate. 3.2. Strain rate sensitivity The strain rate sensitivity is usually used to determine the superplastic behavior and the deformation mechanism of material. In present work, the strain rate sensitivity is determined using the following expression [21]: m=
(1)
where is the flow stress (MPa), ε˙ is the strain rate (s−1 ), ε is the strain, and T is the absolute deformation temperature (K). Based on the flow stress data during the isothermal compression of Ti60 alloy, the strain rate sensitivity is calculated at a constant strain and deformation temperature using Eq. (1). Fig. 4 shows the effect of deformation temperature on the strain rate sensitivity during the isothermal compression of Ti60 alloy at a strain of 0.7. From Fig. 4, it is seen that the maximum m value of 0.34 occurs at 1253 K and a strain rate of 0.001 s−1 during the isothermal compression of Ti60 alloy. Subsequently, the strain rate sensitivity sharply decreases with increasing deformation temperature, and reach a minimum value at a deformation temperature of 1283 K. This phenomenon can be reasonably explained based on previous superplastic deformation theory [22]. According to previous superplastic theory, the strain rate sensitivity of alloy is dependent on alloy composition, grain size, volume fraction of phase,
250
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100
1233 K 1243 K 1253 K 1263 K 1273 K 1313 K 1333 K
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Fig. 3. Flow stress–strain curves during the isothermal compression of Ti60 alloy at the strain rates of 10.0 s−1 (a) and 1.0 s−1 (b).
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Fig. 4. The effect of deformation temperature on the strain rate sensitivity and micrographs during the isothermal compression of Ti60 alloy at a strain of 0.7: (a) T = 1253 K, ε˙ = 0.001 s−1 , (b) T = 1283 K, ε˙ = 0.001 s−1 , (c) T = 1253 K, ε˙ = 10.0 s−1 , and (d) T = 1273 K, ε˙ = 10.0 s−1 .
deformation temperature and so on. Moreover, the optimum deformation temperature is one at which the volume fractions of ␣ phase and  phase in the alloy are approximately equal because the mixture of these two phases can contribute to grain boundary sliding and accommodation. Fig. 4(a) demonstrates that the microstructure at a deformation temperature of 1253 K and a strain rate of 0.001 s−1 consists of primary ␣ phase with a grain size of approximately 7.3 m and intergranular  with a volume fraction of 41%. Thus, approximately equal phase proportions are beneficial for grain boundary sliding and accommodation, which results in the maximum m value at a deformation temperature of 1253 K and a strain rate of 0.001 s−1 . Similarly, Cope et al. [23] reported that Ti–6Al–4V alloy exhibited a high elongation when the volume fraction of  phase was approximately 42%. Moreover, the ␣ grains at a
deformation temperature of 1253 K and a strain rate of 0.001 s−1 are equiaxed and uniform, which are beneficial for the grain boundary sliding. However, the ␣ phase begins to transform into the  phase with increasing deformation temperature, and the phase transition is completed at a deformation temperature of 1283 K due to the adiabatic heating, as shown in Fig. 4(b). Thus, the rapid increase of  phase leads to the drop of the m values. From the discussion above, it is concluded that the strain rate sensitivity sharply decreases near  transus temperature during the isothermal compression of Ti60 alloy, which may be attributed to a rapid increase of the volume fraction of  phase. The strain rate sensitivity at a strain of 0.7 and a strain rate of 10.0 s−1 firstly tends to increase with increasing deformation temperature, reach a peak value at a deformation temperature of
J. Luo, M.Q. Li / Materials Science and Engineering A 538 (2012) 156–163 0.6
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Fig. 5. The effect of strain on the strain rate sensitivity during the isothermal compression of Ti60 alloy at the deformation temperatures of 1253 K (a) and 1333 K (b).
3.3. Strain hardening exponent The strain hardening exponent resulted from a balance between strain hardening mechanism and softening mechanism. In present work, the strain hardening exponent is calculated using the following expression: n=
d log d log ε ε,T ˙
(2)
where is the flow stress(MPa), ε˙ is the strain rate (s−1 ), ε is the strain, and T is the absolute deformation temperature (K). Based on the flow stress data during the isothermal compression of Ti60 alloy, the strain hardening exponent is computed at a constant strain rate and deformation temperature using Eq. (2). Fig. 6 shows the effect of deformation temperature on the strain hardening exponent during the isothermal compression of Ti60 alloy at a strain of 0.4. It is observed from Fig. 6 that the deformation temperature affects significantly the strain hardening exponent during the isothermal compression of Ti60 alloy. The strain hardening exponent during the isothermal compression of Ti60 alloy increases with increasing deformation temperature at the strain rates of 0.001 s−1 , 1.0 s−1 , and 10.0 s−1 . This phenomenon can be reasonably explained based on the analysis of flow behavior during the isothermal compression of Ti60 alloy. According to the
0.2
Strain hardening exponent
1273 K and then drops at high deformation temperatures during the isothermal compression of Ti60 alloy. The similar variation of strain rate sensitivity was reported during the isothermal compression of Ti–6Al–4V alloy [24]. The m value at a deformation temperature of 1253 K and a strain rate of 10.0 s−1 is 0.11, which is lower than that at a deformation temperature of 1253 K and strain rate of 0.001 s−1 , i.e., the strain rate sensitivity decreases with increasing strain rate, as shown in Fig. 4. This phenomenon is related to the fact that the strain rate has an effect on the microstructure during the isothermal compression of Ti60 alloy. Compared the micrograph in Fig. 4(c) with that in (a), it is observed that the microstructure at a deformation temperature of 1253 K and a strain rate of 10.0 s−1 is non-uniform and has slight oriented characteristics. Equiaxed primary ␣ phase of both large and small grains is surrounded by the deformed and elongated ␣ phase during the isothermal compression of Ti60 alloy. But the ␣ grains at a deformation temperature of 1253 K and a strain rate of 0.001 s−1 are equiaxed and uniform. Therefore, the nonuniformity of microstructure finally leads to the decrease of strain rate sensitivity at a strain rate of 10.0 s−1 . Fig. 4(d) shows the microstructure at a deformation temperature of 1273 K and a strain rate of 10.0 s−1 . It is seen that the ␣ grains are finer than that at a deformation temperature of 1253 K and a strain rate of 10.0 s−1 , which is likely to lead to the increase of strain rate sensitivity. According to above-mentioned analysis, the deformation temperature and the strain rate have a significant effect on the strain rate sensitivity during the isothermal compression of Ti60 alloy. The effect of strain on the strain rate sensitivity during the isothermal compression of Ti60 alloy is shown in Fig. 5. As seen from Fig. 5, the strain has an influence on the strain rate sensitivity at the strain rates of 0.001 s−1 and 10.0 s−1 , but the variation of strain rate sensitivity is negligible at the strain rates ranging from 0.01 s−1 to 0.1 s−1 . The strain rate sensitivity at the strain rates of 0.001 s−1 and 10.0 s−1 mostly decreases with increasing strain during the isothermal compression of Ti60 alloy. In general, the variation of strain rate sensitivity with strain is controlled by three mechanisms: (i) thermal softening related to the dislocation annihilation, (ii) work hardening due to the dislocation accumulation and the dislocation-dislocation interaction, and (iii) microstructure evolution. In present study, thermal softening mechanism may play a dominant role in the strain range of 0.4–0.7, which promotes the decrease of the strain rate sensitivity at the strain rates of 0.001 s−1 and 10.0 s−1 . According to the observation in Fig. 3, the noticeable softening effect of flow stress in the strain range of 0.4–0.7 supports the present work. Similarly, Krishna et al. [6] also proposed that the strain rate sensitivity of IMI685 alloy decreased with increasing strain.
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Fig. 7. The effect of strain on the strain hardening exponent during the isothermal compression of Ti60 alloy at the deformation temperatures of 1233 K (a) and 1333 K (b).
deformation behavior, it is concluded that the softening effect in the  single-phase region is lower than that in the ␣ +  twophase region, as shown in Fig. 3. It is well known that the strain hardening exponent results from a competition between thermal softening and strain hardening. Therefore, the decrease in softening effect leads to the increase in strain hardening exponent during the isothermal compression of Ti60 alloy. Luo et al. [24] reported that the strain hardening exponent of Ti–6Al–4V alloy increased with increasing deformation temperature during the isothermal compression. The strain hardening exponent at the strain rates of 0.01 s−1 and 0.1 s−1 is oscillatory with increasing deformation temperature during the isothermal compression isothermal compression of Ti60 alloy.
The effect of strain on the strain hardening exponent during the isothermal compression of Ti60 alloy is shown in Fig. 7. As seen from Fig. 7, the strain hardening exponent during the isothermal compression of Ti60 alloy is negative at the strain rates ranging from 0.01 s−1 to 10.0 s−1 , which implies that the softening effect plays a dominant role in the strain rate range of 0.01–10.0 s−1 . Fig. 7 also demonstrates that the strain rate has an effect on the strain hardening exponent during the isothermal compression of Ti60 alloy. This phenomenon may be attributed to the microstructure evolution of Ti60 alloy. Fig. 8 shows the effect of strain rate on the microstructure during the isothermal compression of Ti60 alloy at a deformation temperature of 1233 K and a strain of 0.7. The microstructure varies slightly with strain rate at the strain rates ranging from 10.0 s−1
Fig. 8. The effect of strain rate on the microstructure during the isothermal compression of Ti60 alloy at a deformation temperature of 1233 K and a strain of 0.7: (a) 10.0 s−1 , (b) 1.0 s−1 , (c) 0.01 s−1 , and (d) 0.001 s−1 .
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to 1.0 s−1 , as illustrated in Fig. 8(a) and (b). The equiaxed ␣ phase is surrounded by the deformed and elongated ␣ phase and intergranular . However, at the strain rates ranging from 0.01 s−1 to 0.001 s−1 , the morphology of ␣ phase is an equiaxed structure and well distributed in the Ti60 alloy matrix primarily because the ␣ phase has enough time to grow and spheroidize, as illustrated in Fig. 8(c) and (d). Therefore, the microstructure evolution at different strain rates finally leads to the variation of strain hardening exponent during the isothermal compression of Ti60 alloy. From Fig. 7(a), it is observed that the influence of strain on the strain hardening exponent is significant at the strain rates ranging from 0.001 s−1 to 0.1 s−1 , but it becomes to be unobvious at the strain rates of 1.0 s−1 and 10.0 s−1 . And roughly speaking, the n values decrease with increasing strain at the strain rates ranging from 0.001 s−1 to 0.1 s−1 . This phenomenon is related to the fact that the rate of dislocation storage is proportional to 1/2 , and the rate of dislocation annihilation is proportional to (where is the dislocation density). Thus, the softening effect plays a dominant role in the strain range of 0.2–0.6, and the degree of softening effect increases with strain. Similarly, the effect of strain on the strain hardening exponent is not remarkable in the  single-phase region at the strain rates of 1.0 s−1 and 10.0 s−1 , as illustrated in Fig. 7(b). However, the n values increase with increasing strain at the strain rates ranging from 0.001 s−1 to 0.1 s−1 because the softening effect in the  single-phase region is significantly different from those in the ␣ +  two-phase region. In the  single-phase region, the flow stress appears to be the steady flow behavior at a small strain. Therefore, the softening effect plays no role in the n values. But the microstructure evolution during the isothermal compression of Ti60 alloy results in the variation of strain hardening exponent. According to above-mentioned analysis, it is concluded that the variation of strain hardening exponent with strain is dependent on the strain rate and the deformation temperature during the isothermal compression of Ti60 alloy. 4. Conclusions The strain rate sensitivity and the strain hardening exponent during the isothermal compression of Ti60 alloy are calculated based on the flow stress–strain curves. The following conclusions are obtained from the present investigation. (1) An initial yield drop is observed at or above 1273 K and at high strain rates ranging from 0.1 s−1 to 10.0 s−1 . This yield drop phenomenon is related to the fact that high strain rates promote less time for recovery processes and higher local stress concentrations due to dislocation pile-up. (2) The flow stress sharply decreases with increasing deformation temperature below 1273 K, then it varies indistinctively with deformation temperature above 1273 K. (3) The maximum m value of 0.34 occurs at 1253 K and a strain rate of 0.001 s−1 during the isothermal compression of Ti60 alloy.
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The strain rate sensitivity at a strain of 0.7 and a strain rate of 10.0 s−1 decreases with increasing deformation temperature after a peak value. (4) The strain rate sensitivity during the isothermal compression of Ti60 alloy decreases with increasing strain rate. This phenomenon can be reasonably explained based on the microstructure evolution during the isothermal compression of Ti60 alloy. The strain has an effect on the strain rate sensitivity at the strain rates of 0.001 s−1 and 10.0 s−1 . (5) The strain hardening exponent during the isothermal compression of Ti60 alloy increases with increasing deformation temperature at the strain rates of 0.001 s−1 , 1.0 s−1 and 10.0 s−1 . The variation of strain hardening exponent with strain is dependent on the strain rate and the deformation temperature during the isothermal compression of Ti60 alloy. Acknowledgments The authors would like to thank the financial supports from the National Natural Science Foundation of China under the Grant No. 50975234, China Postdoctoral Science Foundation under the Grant No. 20110491685 and the “111” Project under the Grant No. 08040. References [1] D. Weinem, J. Kumpfert, M. Peters, W.A. Kaysser, Mater. Sci. Eng. A 206 (1) (1996) 55–62. [2] P. Wanjara, M. Jahazi, H. Monajati, S. Yue, J.P. Immarigeon, Mater. Sci. Eng. A 396 (1/2) (2005) 50–60. [3] P. Wanjara, M. Jahazi, H. Monajati, S. Yue, Mater. Sci. Eng. A 416 (1/2) (2006) 300–311. [4] M. Zhou, Mater. Sci. Eng. A 245 (1) (1998) 29–38. [5] Y. Liu, T.N. Baker, Mater. Sci. Eng. A 197 (2) (1995) 125–131. [6] V.G. Krishna, Y.V.R.K. Prasad, N.C. Birla, G.S. Rao, J. Mater. Process. Technol. 71 (3) (1997) 377–383. [7] T. Rajagopalachary, V.V. Kutumbarao, Scr. Mater. 35 (3) (1996) 305–309. [8] Y. Niu, J. Luo, M.Q. Li, Int. J. Hydrogen Energy 36 (1) (2011) 1006–1013. [9] M.Q. Li, J. Luo, Y. Niu, Mater. Sci. Eng. A 527 (24/25) (2010) 6626–6632. [10] X.M. Zhang, Y.Q. Zhao, W.D. Zeng, Int. J. Hydrogen Energy 35 (9) (2010) 4354–4360. [11] J.W. Zhao, H. Ding, H.L. Hou, Z.Q. Li, J. Alloys Compd. 491 (1/2) (2010) 673–678. [12] X.L. Wang, Y.Q. Zhao, M. Hagiwara, H.L. Hou, T. Suzuki, J. Alloys Compd. 490 (1/2) (2010) 531–536. [13] Y.M. Xiong, S.L. Zhu, F.H. Wang, Surf. Coat. Technol. 190 (2/3) (2005) 195– 199. [14] Y.M. Xiong, S.L. Zhu, F.H. Wang, Corros. Sci. 50 (1) (2008) 15–22. [15] M.Q. Li, H.S. Pan, Y.Y. Lin, J. Luo, J. Mater. Process. Technol. 183 (1) (2007) 71–76. [16] M.Q. Li, Y.Y. Lin, Int. J. Hydrogen Energy 32 (5) (2007) 626–629. [17] M.Q. Li, Y.Y. Lin, Int. J. Hydrogen Energy 35 (11) (2010) 5703–5707. [18] J. Luo, M.Q. Li, Y.Q. Hu, M.W. Fu, Mater. Charact. 59 (10) (2008) 1386–1394. [19] W.J. Jia, W.D. Zeng, J.R. Liu, Y.G. Zhou, Q.J. Wang, Mater. Sci. Eng. A 530 (2011) 511–518. [20] I. Philippart, H.J. Rack, Mater. Sci. Eng. A 243 (1/2) (1998) 196–200. [21] W.A. Backfen, I.R. Turner, D.H. Avery, ASM Trans. Quart. 57 (1964) 980–990. [22] J.W.D. Patterson, N. Ridley, J. Mater. Sci. 16 (2) (1981) 457–464. [23] M.T. Cope, D.R. Evetts, N. Ridley, J. Mater. Sci. 21 (11) (1986) 4003–4008. [24] J. Luo, M.Q. Li, W.X. Yu, H. Li, Mater. Des. 31 (2) (2010) 741–748.