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Mechanism and kinetics of static globularization in TA15 titanium alloy with transformed structure
Journal of Alloys and Compounds 533 (2012) 1–8
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Mechanism and kinetics of static globularization in TA15 titanium alloy with transformed structure X.G. Fan a , H. Yang a,∗ , S.L. Yan a , P.F. Gao a , J.H. Zhou b a State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, P.O. Box 542, Northwestern Polytechnical University, Xi’an, 710072, PR China b Special Steel Branch, Baoshan Steel Co. Ltd., Shanghai, 200940, PR China
a r t i c l e
i n f o
Article history: Received 9 November 2011 Received in revised form 27 March 2012 Accepted 30 March 2012 Available online 10 April 2012 Keywords: TA15 titanium alloy Microstructure evolution Static globularization Annealing
a b s t r a c t The static globularization behavior and mechanism of transformed structure during heat-treatment of hot worked TA15 alloy were investigated. It is found that boundary splitting and microstructure coarsening are two competing mechanisms for static globularization. Boundary splitting is significant in the initial stage of annealing while coarsening occurs throughout the annealing process. Static globularization kinetics increases with annealing temperature and prestrain, but is independent on strain rate. The rate of static globularization kinetics decreases with annealing time. The asymptotic equation can be used to model the static globularization kinetics. © 2012 Elsevier B.V. All rights reserved.
1. Introduction TA15 (Ti–6Al–2Zr–1Mo–1V) is a near-␣ titanium alloy of moderate room-temperature and high-temperature strength, good thermal stability and welding performance, which is widely used to manufacture structural components in airplanes. One important step in hot working of conventional two-phase titanium alloys is the breakdown of transformed structure produced by initial beta-phase field hot working and heat treatment [1], so as to obtain equiaxed-␣ microstructure. This process, which is commonly referred to as globularization, can occur dynamically during deformation and statically in post deformation annealing [2]. Both the dynamic and static globularization are very crucial to microstructural development as two-phase titanium alloys often go through multi-pass deformation. The mechanism of globularization has been extensively investigated for two-phase titanium alloys [1–11]. Generally, the globularization process includes three stages: formation of highenergy defects through the thickness of ␣ laths, separation of ␣ laths into isolated ␣ grains, and the further spheroidization of the segregated ␣ grains. Intraphase high-energy defects provide driving force for globularization. Such defects may be low angle and high angle boundaries, twins or shear bands [12]. Previous studies suggest that these defects can be introduced by recovery,
∗ Corresponding author. Tel.: +86 029 8849 5632; fax: +86 029 8849 5632. E-mail addresses: [email protected], [email protected] (H. Yang). 0925-8388/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.03.113
localized shearing, twinning, discontinuous recrystallization and continuous recrystallization during deformation [12–14]. The presence of intraphase boundaries causes unbalance at the intersections of intraphase and interphase boundaries. The surface tension is balanced by the diffusion of interlamellar phase into intraphase boundaries [6]. This process, known as boundary splitting, results in the separation of lamellas. Microstructure coarsening further reduces the aspect ratio of ␣ grains after boundary splitting [10]. Termination migration and Ostwald ripening are the dominating mechanisms of coarsening. Termination migration consists of the transfer of mass from the curved surfaces of the lamellar terminations to the flat surfaces of the lamellas [10]. Ostwald ripening is characterized by the growth of large ␣ particles and the shrinkage of smaller ␣ particles [15]. Both are driven by the reduction in energy associated with ␣– interfaces. For the process of static globularization, boundary splitting dominates the initial period of heat-treatment, while microstructure coarsening is the primary mechanism during prolonged annealing [10]. The globularization kinetics has received considerable attentions due to its importance in microstructure control. For dynamic globularization, it has been found that a critical strain is needed for the initiation of globularization and the globularized fraction increases with strain in a sigmoid way. Thus the Avrami type equation is often employed to depict the variation of globularized fraction with strain [16–18]. The dynamic globularization kinetics is greatly affected by the processing conditions (such as temperature and strain rate), initial microstructure, strain path as well as the chemical composition. It increases with increasing
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Fig. 1. Microstructure of the as-received TA15 alloy.
Fig. 2. Microstructure of the TA15 alloy after  heat treatment.
temperature and decreasing strain rate [16,17]. Dynamic globularization kinetics is sensitive to the initial microstructure. Shell and Semiatin [19] found that the globularization rate of Ti–6Al–4V is rapider for fine acicular microstructure than coarse colony structure, because boundary splitting is easier in microstructures with thin alpha platelets. Korshunov and Poths [20–22] reported a strong effect of strain path on globularization kinetics. Korshunov et al. [20,21] reported that globularization rate is relatively low under nonmonotonic loading paths. Poths et al. [22] ascribed this phenomenon to a reduced rate of intraphase boundary formation. For static globularization, Stefansson et al. [2] found that the globularization kinetics is dependent on the deformation degree prior to heat treatment and the heat treatment temperature but independent of the deformation temperature. Decreasing the annealing temperature significant retards the static globularization process. They also developed models [10,23] to estimate the required times for static globularization via boundary splitting and microstructure coarsening. However, these models cannot depict the variation of globularized fraction with time. Though extensive investigations have been carried out on the microstructure evolution of TA15 alloy during hot working, systematic studies on static globularization are lacking. In this study, the microstructure evolution during heat-treatment of hot worked TA15 alloy with transformed structure is experimentally investigated and mathematically modeled. The results are useful for microstructural control in primary hot working of titanium alloys.
deformation without cooling down. The annealing temperature is the same to the deformation temperature. After annealing for different times, the specimens were cooled by forced-convection. The processing parameters are as follows: temperature 940 ◦ C, 970 ◦ C; strain rate 0.01 s−1 , 0.1 s−1 ; height reduction 30%, 70%; annealing time 0.5–8 h (940 ◦ C), 0.1–3.0 h (970 ◦ C). Stefansson et al. [2] suggested that the growth of primary ␣ during cool down may affect microstructure. Thus, they employed a procedure including rapidreheating, short-time holding and water quenching to restore high temperature microstructure. In the present work, however, the cooling rate was high enough to suppress the diffusional growth of ␣ phases due to the small size of specimens. This additional process was unnecessary. The heat-treated specimens were sectioned along the compression axis, mechanically grinded and polished, and etched with a solution of 13% HNO3 , 7% HF and 80% H2 O. Micrographs were taken on a LECIA DFC320 microscope, and examined using quantitative image analysis (Image-pro plus 5.0). For each specimen, micrographs were shot at two locations lying on the equatorial plane, one near the center and one near the surface. The local strains at the two image locations were determined to be 0.26, 0.49 for 30% reduction; and 1.00, 1.58 for 70% reduction using FE simulation. In each image location, three adjacent fields of view were analyzed. Globularization was taken to be an ␣-phase morphology with aspect ratio less than 3. The measured globularized fraction fg included both the dynamically globularized part fdg and the static part fsg : fg = fdg + fsg
(1)
fdg was measured by examining the microstructure prior to annealing. Then the static globularization kinetics was determined.
3. Results and discussion 3.1. Microstructure evolution during annealing
2. Experimental procedures 2.1. Material The TA15 titanium alloy, with chemical composition (wt.%) of 6.06 Al, 2.08 Mo, 1.32 V, 1.86 Zr, 0.30 Fe, and Ti in balance, was supplied in the form of 80 mm thick by 170 mm wide hot rolled plate which had been annealed at 1123 K for 2 h and air cooled. The measured -transus temperature was 990 ◦ C. The microstructure of as-received material consisted of approximately 60% equiaxed primary ␣ phases within transformed  matrix, as shown in Fig. 1. The as-received bar was heated to 1020 ◦ C, held for 30 min and cooled in furnace so as to obtain transformed structure (Fig. 2). The ␣ layers at prior  grain boundaries were about 4 m thick and the average thickness of ␣ laths inside  grain is about 1.5 m. 2.2. Experimental procedures The  processed bar was then machined to cylinder specimens of 10 mm in diameter and 15 mm in height. A thin layer of glass lubricant was covered on the surface of specimens to minimize friction and prevent oxidation. The specimens were then heated to the deformation temperature at a rate of 12 ◦ C/min, soaked for 20 min to impart thermal equilibration, and compressed to give reduction at a constant nominal strain rate. Static annealing was conducted immediately after
Fig. 3 illustrates the microstructures deformed at 970 ◦ C, 0.1 s−1 to a strain of 1.58 and annealed for different time intervals. The microstructure prior to annealing (Fig. 3(a)) consisted of a large fraction of lamellar ␣ with high aspect ratio and a small amount of globularized ␣ with in  matrix. The ␣– interfaces were smooth, indicating boundary splitting was not apparent. Though a high level of intraphase defects might have already formed during deformation, the short deformation time suppressed the thermal grooving process. As a result, the dynamic globularized fraction was low. After annealing for 0.3 h, clear ␣– interfaces were produced in the former ␣ laths, separating them to strings of isolated ␣ grains with low aspect ratio (Fig. 3(b)). Though some long ␣ lamellas were not broken down, the boundaries became tortuous due to thermal grooving. Stefansson and Semiatin [10] found that thermal grooving can occur in both ␣ and  phases, resulting the irregularity of ␣– boundaries. The penetration of ␣ phase into  grain boundaries could also be observed in the current study. However, thermal
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Fig. 3. Microstructures after deformation at temperature of 970 ◦ C, strain rate of 0.1 s−1 , strain of 1.58 and annealing for (a) 0 h; (b) 0.3 h; (c) 1.0 h and (d) 3.0 h.
Fig. 4. Microstructures after deformation at temperature of 940 ◦ C, strain rate of 0.1 s−1 , strain of 1.58 and annealing for (a) 0 h; (b) 1.0 h; (c) 2.0 h and (d) 8.0 h.
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grooving of ␣ phase was more significant, as the volume fraction of ␣ phase was relatively low at the annealing temperature. This phenomenon was in accordance with the observation by Lütjering et al. [9]. The thickness of ␣ grains increased, suggesting coarsening was notable. Increasing the annealing time to 1.0 h, more ␣ laths were globularized. Coarsening was significant during this period. The number of ␣ grains decreased sharply due to Ostwald ripening. ␣– boundaries become smoother. There still existed a small fraction of grooved ␣ platelets, in which grooves were not deep enough to segment these ␣ laths. During prolonged annealing, the grooved ␣ platelets were not separated by boundary splitting (Fig. 4(d)). Coarsening might solely account for globularization in this period. The microstructural development at 940 ◦ C is similar to that at 970 ◦ C, as shown in Fig. 4, though the globularization process was much slower. 3.2. Mechanism of static globularization Stefansson and Semiatin [10] found that static globularization could be divided into two stages. The first includes microstructural changes during deformation and the initial stages of static heat treatment; the second occurs during prolonged annealing. The initial stage consists of segmentation of lamellas via boundary splitting, while the latter stage is characterized by microstructure coarsening by mechanisms such as termination migration and Ostwald ripening. The initial stage is driven by the release of distortion energy which embodied by the formation of dislocation substructures whereas the driving force in the second stage is the reduction in interfacial energy. Thus the static globularization fraction can be expressed as: fsg = fsg-s + fsg-c
(2)
where the right two terms represent substructure driven globularization and coarsening controlled globularization. The microstructure evolution in this study was similar to that presented by Stefansson and Semiatin [10]. Boundary splitting was remarkable in the initial stage of annealing. This is confirmed by measuring the average size of ␣ grains, as shown in Fig. 5. The average size decreased with annealing time in this stage, indicating the break down of ␣ phases. With increasing annealing time, the intraphase defects were decreased due to thermal restoration and the lamellas were thickened by microstructure coarsening. Thus, boundary splitting is suppressed in prolonged annealing. Microstructure coarsening occurred throughout the annealing. It was remarkable even in the initial stage of annealing, as shown in Figs. 3 and 4. This is because the coarsening rate was larger at small grain size. Besides, the dislocation structures formed
Fig. 5. Variation of average ␣ grain size with annealing time.
during deformation could accelerate the coarsening process. The pipe diffusion of deformation defects can greatly increase diffusivity of solutes and promote coarsening. Semiatin et al. [24] found dynamic coarsening rate is enhanced by about 5 times relative to those for static coarsening. Coarsening also affected the boundary splitting process, as the increase in platelet thickness hindered the thermal grooving. Boundary splitting and microstructure coarsening may be considered as two competing mechanisms for static globularization, like recrystallization and recovery for thermal restoration. Both can reduce the aspect ratio of ␣ phases. Boundary splitting tends to refine microstructure, whereas coarsening hinders boundary splitting. Boundary splitting is significant in the initial stage while coarsening occurs throughout the annealing. As a result, the average grain size of ␣ phase decreased initially and increased during prolonged annealing, as shown in Fig. 5. 3.3. Globularization kinetics Fig. 6 shows the variation of globularization kinetics with annealing time. A sharp increase in globularized fraction was observed in the beginning of heat treatment, then the globularized fraction increased slowly with annealing time. The rate of globularization kinetics (dfg /dt) decreased with time. The shape of kinetics curve was quite different from the work of Stefansson and Semiatin [10], in which the globularized fraction
Fig. 6. Percent ␣ phase globularized as a function of annealing time at (a) 970 ◦ C and (b) 940 ◦ C.
X.G. Fan et al. / Journal of Alloys and Compounds 533 (2012) 1–8
Fig. 7. Plot of globularized fraction vs. logarithmic annealing time.
increased with time in a sigmoid way. In their work, the globularized fraction was plotted as a function of logarithmic annealing time. Fig. 7 shows the variation of globularized fraction with logarithmic time. It agrees reasonably with the result by Stefansson et al. [2]. Globularization kinetics was greatly influenced by deformation/annealing temperature, as shown in Fig. 6. Boundary splitting and microstructure coarsening are both controlled by diffusion of solutes. As a thermally activated process, the diffusivity of solutes is determined by annealing temperature. Thus, both the static and dynamic globularization were accelerated by
5
increasing temperature. Stefansson et al. [2] reported a tenfold decrease in globularization kinetics when the annealing temperature of Ti–6Al–4V alloy was decreased from 955 ◦ C to 900 ◦ C. It is also found that the thickness of ␣ lamellas is reduced with increasing temperature due to ␣– transformation. The thinning of ␣ lamellas resulted in the relative ease of  penetration along intraphase boundaries and promoted globularization. The amount of deformation also affected the globularization process during subsequent annealing. The dynamically globularized fractions prior to annealing were close at the two strains employed in this study, as shown in Fig. 6. However, the globularized fraction increased more rapidly at larger prestrain in the initial period of annealing. During prolonged annealing, the kinetics rates were close at different prestrains. Prestrain greatly influenced the boundary splitting in the initial stage of annealing, i.e. the substructure driven static globularization. The efficiency of boundary splitting is strongly dependent on the misorientation of intraphase boundaries [12]. Though dislocation substructures can be formed at a relatively low strain, the fraction of high angle boundaries increases with strain. It is also found that the transformed structure undergoes severe heterogeneous deformation [25]. Part of the alpha lamellas may remain undeformed at small strain, which prevents the globularization process. Moreover, the large compressive strain during deformation would thin ␣ lamellas and further promote boundary splitting. Fig. 8 shows the microstructures after deformation to different strains and annealed for the same time. At a strain of 0.26, the microstructure consisted of a large fraction of long ␣ platelets. These platelets had straight boundaries, which means thermal grooving was not significant. With increasing strain, more ␣ lamellas were broken down. The remnant had more tortuous boundaries. Therefore, static globularization was accelerated by
Fig. 8. Microstructures after deformation at 970 ◦ C, 0.1 s−1 to strains of (a) 0.26, (b) 0.50, (c) 1.00 and annealing for 1.0 h.
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the initial stage of annealing. This is correct only if the strain rate is relatively low. Lamellar kinking and shear bands are increased at higher strain rates [4,25], which retards globularization. Stefansson and Semiatin [10] found that lowering deformation temperature did not affect static globularization kinetics. Similar to increasing strain rate, decreasing deformation temperature can give rise to higher stored energy. Therefore, the current study confirms that dislocation substructures have an indirect effect on globularization. 3.4. Prediction of globularization kinetics 3.4.1. Required times for boundary splitting and termination migration Zherebtsov et al. [7] proposed that the Mullins model can be used to analyze boundary splitting. In the case of penetration of ␣ lamellas, the time tp to complete thermal grooving can be expressed as [7]: 3
Fig. 9. Comparison of globularized fraction at different strain rates.
boundary splitting. Stefansson and Semiatin [10] reported the substructure driven static globularization increases with prestrain, which is consistent with the present work. Prestrain did not affect the microstructure coarsening during prolonged annealing. Thus, coarsening induced globularization was irrelevant to prestrain. Fig. 9 compares the globularized fraction at different strain rates. The globularized fractions (including both the dynamically and statically globularized fractions) are close at different strain rates. It has been reported that dynamic globularization decreases with strain rate. Thus, the static globularization kinetics is a little larger at higher strain rate [26]. High deformation speed can suppress the dynamic restoration processes during deformation and result in a higher stored energy, which promotes static globularization. This phenomenon is different from that observed in dynamic globularization [16,17]. The decrease of dynamic globularization kinetics with strain rate has been attributed to the decrease of time for diffusion-controlled processes. During static heat treatment, the annealing time is so long that there is sufficient time for the completion of boundary splitting. It can also be found that the static globularization kinetics was less sensitive to strain rate than to annealing temperature and prestrain. The microstructures at a strain rate of 0.01 s−1 were similar to that at 0.1 s−1 , as shown in Fig. 10. Semiatin et al. [1] reported that dynamic globularization is less dependent on strain rate when deformation is controlled by dislocation activities. It can be deduced that substructure driven static globularization is also insensitive to strain rate as the boundary splitting occurs only in
0.2(l)
tp =
A=
(3)
A(mg )3 C ␣ Vm D
(4)
RT
where l is the thickness of ␣ lamellas (m), mg is the average slope at the root of the triple point, C is the equilibrium concentration (in atomic percent) of the rate limiting solute in the  phase, ␣ is the ␣– interface energy (J m−2 ), Vm is the molar volume of the ␣ platelet material (m3 mol−1 ), D is the diffusivity of the rate limiting solute in the  phase (m2 s−1 ), R is the universal gas constant (8.314 J mol−1 K−1 ), and T is the absolute temperature (K). Because neither the ␣ nor the  phase in TA15 alloy is a terminal solid solution, the term C in Eq. (4) should be replaced by the composition factor CF : CF =
C (1 − C ) (C␣ − C )2 (1 + ∂ ln r/∂ ln C )
(5)
where C␣ is the content of the rate-limiting solute in the ␣ phase and r is the activity coefficient of the solute in the  phase. 1 + ∂ ln r/∂ ln C is the thermodynamic factor. Mo is the rate limiting solutes due to its low diffusivity and strong stabilizing effect on the  phase. The diffusivity of Mo in the  phase can be obtained by [27]: 
DMo = 7.0 × 10−8 exp
−18520 T
(6)
The measured equilibrium concentrations of Mo in the ␣ and  phases were about 0.0013, 0.015 at 970 ◦ C, and 0.002, 0.020 at
Fig. 10. Microstructures after deformation at 0.01 s−1 to a strain of 1.58: (a) 970 ◦ C, 1 h;(b) 940 ◦ C, 2 h.
X.G. Fan et al. / Journal of Alloys and Compounds 533 (2012) 1–8
940 ◦ C. The thermodynamic factor of Mo is about 0.75 [27]. Other physical parameters are given as follows [7]: the average slope mg = 0.35, ␣– interface energy ␣ = 0.26 J m−2 , and the molar volume of ␣ phase Vm = 1.044 × 10−5 m3 mol−1 . The average thickness of ␣ lamellas is measured to be 2.1 m at 970 ◦ C and 2.7 m at 940 ◦ C. The predicted times for the completion of boundary splitting are about 21 h and 68 h at 970 ◦ C and 940 ◦ C, which are much longer than those observed. In fact, Zherebtsov et al. [7] reported a similar behavior in warm working of Ti–6Al–4V alloy and suggested that the retained dislocation structures in  phase would cause a tenfold increase in diffusivity by pipe diffusion thus enhancing the kinetics. Applying the Mullins model to the work of Stefansson et al. [2], it is also found that the predicted time is much longer than observations (Model predictions are about 10.6 h and 39.6 h at 955 ◦ C and 900 ◦ C while the experimental results are 1 h and 14 h, respectively.). These results suggest that the static globularization kinetics would be substantially underestimated without considering the influence of pre-deformation on diffusion. Because the promotion in diffusivity is hard to be quantitatively measured, the Mullins model gives a qualitative or semi-quantitative result. Another model to predict the duration of boundary splitting is proposed by Stefansson and Semiatin [10]. In this model, the time required for boundary splitting can be calculated by [10]:
tp =
Y0 0.86mg K
1/c (7)
Y0 is the distance required for the triple point to move through, which is assimilated to half the lamellar thickness. K and c are the coarsening parameters defined as: d␣ = Kt c
(8)
7
Table 1 Predicted times required for static globularization via boundary splitting. Temperature (◦ C)
␣ Lamellas thickness (m)
K (mh−n )
n
Time (h)
940 970
2.65 2.08
3.54 3.74
0.41 0.41
1.69 0.83
where d␣ is the average grain size of ␣ phase. In this case, the predicted results are in broad agreement with microstructure observations, as shown in Table 1. Thus, this model is useful for rough estimation of the required time for boundary splitting. During prolonged annealing, termination migration mainly accounts for the reduction in aspect ratio. Semiatin et al. [23] developed a model to estimate the globularization time via termination migration:
2
3 − [0.3287/3 (1 + 1 − 0.763−4/3 ) ] g = 2(1+) 0.51/3 +0.6652/3 4 + −1/3 −1/3 3(0.5−0.573
)
3(0.143+0.934
(9)
)
where and are geometric factor and time normalization factor defined as: ≡
w + 0.5 l
(10)
≡
l3 RT CF ␣ Vm D
(11)
where w is the width of ␣ lamellas. Model predictions are in broad agreement with experimental observations, as shown in Table 2.
Fig. 11. Predicted globularized fraction by the (a, b) asymptotic equation and (c, d) JMAK equation.
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Table 2 Predicted times required for static globularization via termination migration. T (◦ C)
w (m)
l (m)
H
(h)
(h)
970 940
13.80 17.73
2.56 3.19
5.89 6.05
7.14 19.9
8.35 25.3
3.4.2. Static globularization kinetics The previous models can be used to estimate the required time for static globularization. However, the variation of globularized fraction with annealing time is also of industrial importance. In general, the kinetics of thermally activated microstructure development can be depicted by: X = 1 − exp(−kt n )
X = 1 − (1 + k t)
−1/m
(12)
splitting is significant in the initial stage of annealing while coarsening occurs throughout the annealing process. (2) Static globularization kinetics is found to increase with annealing temperature and prestrain, but to be less dependent on strain rate. (3) The rate of static globularization kinetics decreases with annealing time. The asymptotic equation can be used to model the static globularization kinetics. Acknowledgments The authors would like to gratefully acknowledge the support of National Natural Science Foundation of China for Key Program (no. 50935007) and National Basic Research Program of China (no. 2010CB731701).
(13)
Eq. (12) is the well known Johnson–Mehl–Avarmi–Kolmogorov (JMAK) equation which is suitable for processes involving nucleation. Eq. (13), known as asymptotic equation, is often applied to the non-nucleation types. In the previous discussion, it has been confirmed that boundary splitting is the primary globularization mechanism in the initial stage while microstructure coarsening occurs throughout annealing. The kinetics of static globularization in the initial stage should be similar to that of dynamic globularization. Dynamic globularization kinetics has been found to increase with strain in a sigmoidal way after reaching a critical strain, which behaves like microstructure transformation involving nucleation. Many researchers use the JMAK equation to characterize dynamic globularization kinetics [16,17]. Therefore, Eq. (12) may be applied to the initial stage. Microstructure coarsening does not involve nucleation. Thus, Eq. (13) may be used to predict globularization kinetics after the completion of boundary splitting. Though theoretical analysis suggests different equations for different stages, the static globularization kinetics may be phenomenologically depicted by either of the two equations, as shown in Fig. 11 (Normalized fraction of static globularization is calculated by fsg /(1 − fsd )). Fig. 11 suggests that both the asymptotic equation and JMAK equation have good fitness. However, the asymptotic equation fits the experimental data better. In fact, the required time for boundary splitting is short compared to coarsening. The rate of globularization kinetics is high in the initial stage. Thus, the kinetics rate decreased with time, which follows the asymptotic equation. The JMAK equation also has a good fitness. The fitting parameter n is less than 1, which eliminates the nucleation stage in the curves. Thus, the JMAK equation loses its physical significance. For the asymptotic equation, m is equal to the coarsening exponent (1/c) when Eq. (13) is used to describe the kinetics of coarsening. In this study, the determined values of m varies under different hot working conditions, which weakens the physical significance. Thus, the phenomenological models can only give a relatively acceptable prediction but cannot effectively depict the complex microstructure evolution procedure of static globularization. 4. Conclusions Microstructure evolution during heat-treatment of hot worked TA15 alloy with transformed structure was investigated by isothermal compression testing. From this work, the following conclusions were drawn: (1) Boundary splitting and microstructure coarsening are two competing mechanisms for static globularization. Boundary
References [1] S.L. Semiatin, V. Seetharaman, I. Weiss, Materials Science and Engineering A 263 (1999) 257–271. [2] N. Stefansson, S.L. Semiatin, D. Eylon, Metallurgical and Materials Transactions A 33 (2002) 3527–3534. [3] T. Seshacharyulu, S.C. Medeiros, J.T. Morgan, J.C. Malas, W.G. Frazier, Y.V.R.K. Prasad, Scripta Materialia 41 (3) (1999) 283–288. [4] T. Seshacharyulu, S.C. Medeiros, W.G. Frazier, Y.V.R.K. Prasad, Materials Science and Engineering A 325 (2002) 112–125. [5] T. Seshacharyulu, S.C. Medeiros, J.T. Morgan, J.C. Malas, W.G. Frazier, Y.V.R.K. Prasad, Materials Science and Engineering A 279 (2000) 289–299. [6] I. Weiss, E.H. Froes, D. Eylon, G.E. Welsch, Metallurgical and Materials Transactions A 17 (1986) 1935–1947. [7] S. Zherebtsov, M. Murzinova, G. Salishchev, S.L. Semiatin, Acta Materialia 59 (2011) 4138–4150. [8] S. Mironov, M. Murzinova, S. Zherebtsov, G.A. Salishchev, S.L. Semiatin, Acta Materialia 57 (2009) 2470–2481. [9] G. Lütjering, Materials Science and Engineering A 243 (1998) 32–45. [10] N. Stefansson, S.L. Semiatin, Metallurgical and Materials Transactions A 34 (2003) 691–698. [11] Chen Huiqin, Cao Chunxiao, Rare Metal Materials and Engineering 40 (6) (2011) 946–950. [12] G.A. Salishchev, S.V. Zerebtsov, S.Y. Mironov, S.L. Semiatin, Materials Science Forum 467–470 (2004) 501–506. [13] T. Furuhara, B. Poorganji, H. Abe, T. Maki, JOM (2007) 64–67. [14] B. Poorganji, M. Yamaguchi, Y. Itsumi, et al., Scripta Materialia 61 (4) (2009) 419–422. [15] S.L. Semiatin, B.C. Kirby, G.A. Salishchev, Metallurgical and Materials Transactions A 35 (2004) 2809–2819. [16] H. Song, S. Zhang, M. Cheng, Journal of Alloys and Compounds 480 (2) (2009) 922–927. [17] K. Wang, W. Zeng, Y. Zhao, et al., Materials Science and Engineering A 527 (10–11) (2010) 2559–2566. [18] S.L. Semiatin, P.A. Kobryn, E.D. Roush, D.U. Furrer, T.E. Howson, R.R. Boyer, D.J. Chellman, Metallurgical and Materials Transactions A 32 (2001) 1801–1811. [19] E.B. Shell, S.L. Semiatin, Metallurgical and Materials Transactions A 30 (1999) 3219–3229. [20] A.A. Korshunov, F.U. Enikeev, M.I. Mazurskii, G.A. Salishchev, A.V. Muravlev, P.V. Chistyakov, O.O. Dimitriev, Russian Metallurgy 3 (1994) 103–108. [21] A.A. Korshunov, F.U. Enikeev, M.I. Mazurskii, G.A. Salishchev, A.V. Muravlev, P.V. Chistyakov, O.O. Dimitriev, A.V. Muravler, P.V. Chistyakov, Journal of Materials Science 31 (1996) 4635–4639. [22] R.M. Poths, G. Angella, B.P. Wynne, W.M. Rainforth, S.L. Seniatin, J.H. Beynon, Metallurgical and Materials Transactions A 35 (2004) 2993– 3001. [23] S.L. Semiatin, N. Stefansson, R.D. Doherty, Metallurgical and Materials Transactions A 36 (2005) 1372–1376. [24] S.L. Semiatin, M.W. Corbett, P.N. Fagin, G.A. Salishchev, C.S. Lee, Metallurgical and Materials Transactions A 37 (2006) 1125–1136. [25] T.R. Bieler, S.L. Semiatin, International Journal of Plasticity 18 (2002) 1165–1189. [26] C.B. Wu, H. Yang, X.G. Fan, Z.C. Sun, The Transactions of Nonferrous Metals Society of China 21 (2011) 1963–1969. [27] S.L. Semiatin, T.M. Lehner, J.D. Miller, R.D. Doherty, D.U. Furrer, Metallurgical and Materials Transactions A 38 (2007) 910–921.
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Mechanism and kinetics of static globularization in TA15 titanium alloy with transformed structure X.G. Fan a , H. Yang a,∗ , S.L. Yan a , P.F. Gao a , J.H. Zhou b a State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, P.O. Box 542, Northwestern Polytechnical University, Xi’an, 710072, PR China b Special Steel Branch, Baoshan Steel Co. Ltd., Shanghai, 200940, PR China
a r t i c l e
i n f o
Article history: Received 9 November 2011 Received in revised form 27 March 2012 Accepted 30 March 2012 Available online 10 April 2012 Keywords: TA15 titanium alloy Microstructure evolution Static globularization Annealing
a b s t r a c t The static globularization behavior and mechanism of transformed structure during heat-treatment of hot worked TA15 alloy were investigated. It is found that boundary splitting and microstructure coarsening are two competing mechanisms for static globularization. Boundary splitting is significant in the initial stage of annealing while coarsening occurs throughout the annealing process. Static globularization kinetics increases with annealing temperature and prestrain, but is independent on strain rate. The rate of static globularization kinetics decreases with annealing time. The asymptotic equation can be used to model the static globularization kinetics. © 2012 Elsevier B.V. All rights reserved.
1. Introduction TA15 (Ti–6Al–2Zr–1Mo–1V) is a near-␣ titanium alloy of moderate room-temperature and high-temperature strength, good thermal stability and welding performance, which is widely used to manufacture structural components in airplanes. One important step in hot working of conventional two-phase titanium alloys is the breakdown of transformed structure produced by initial beta-phase field hot working and heat treatment [1], so as to obtain equiaxed-␣ microstructure. This process, which is commonly referred to as globularization, can occur dynamically during deformation and statically in post deformation annealing [2]. Both the dynamic and static globularization are very crucial to microstructural development as two-phase titanium alloys often go through multi-pass deformation. The mechanism of globularization has been extensively investigated for two-phase titanium alloys [1–11]. Generally, the globularization process includes three stages: formation of highenergy defects through the thickness of ␣ laths, separation of ␣ laths into isolated ␣ grains, and the further spheroidization of the segregated ␣ grains. Intraphase high-energy defects provide driving force for globularization. Such defects may be low angle and high angle boundaries, twins or shear bands [12]. Previous studies suggest that these defects can be introduced by recovery,
∗ Corresponding author. Tel.: +86 029 8849 5632; fax: +86 029 8849 5632. E-mail addresses: [email protected], [email protected] (H. Yang). 0925-8388/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.03.113
localized shearing, twinning, discontinuous recrystallization and continuous recrystallization during deformation [12–14]. The presence of intraphase boundaries causes unbalance at the intersections of intraphase and interphase boundaries. The surface tension is balanced by the diffusion of interlamellar phase into intraphase boundaries [6]. This process, known as boundary splitting, results in the separation of lamellas. Microstructure coarsening further reduces the aspect ratio of ␣ grains after boundary splitting [10]. Termination migration and Ostwald ripening are the dominating mechanisms of coarsening. Termination migration consists of the transfer of mass from the curved surfaces of the lamellar terminations to the flat surfaces of the lamellas [10]. Ostwald ripening is characterized by the growth of large ␣ particles and the shrinkage of smaller ␣ particles [15]. Both are driven by the reduction in energy associated with ␣– interfaces. For the process of static globularization, boundary splitting dominates the initial period of heat-treatment, while microstructure coarsening is the primary mechanism during prolonged annealing [10]. The globularization kinetics has received considerable attentions due to its importance in microstructure control. For dynamic globularization, it has been found that a critical strain is needed for the initiation of globularization and the globularized fraction increases with strain in a sigmoid way. Thus the Avrami type equation is often employed to depict the variation of globularized fraction with strain [16–18]. The dynamic globularization kinetics is greatly affected by the processing conditions (such as temperature and strain rate), initial microstructure, strain path as well as the chemical composition. It increases with increasing
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Fig. 1. Microstructure of the as-received TA15 alloy.
Fig. 2. Microstructure of the TA15 alloy after  heat treatment.
temperature and decreasing strain rate [16,17]. Dynamic globularization kinetics is sensitive to the initial microstructure. Shell and Semiatin [19] found that the globularization rate of Ti–6Al–4V is rapider for fine acicular microstructure than coarse colony structure, because boundary splitting is easier in microstructures with thin alpha platelets. Korshunov and Poths [20–22] reported a strong effect of strain path on globularization kinetics. Korshunov et al. [20,21] reported that globularization rate is relatively low under nonmonotonic loading paths. Poths et al. [22] ascribed this phenomenon to a reduced rate of intraphase boundary formation. For static globularization, Stefansson et al. [2] found that the globularization kinetics is dependent on the deformation degree prior to heat treatment and the heat treatment temperature but independent of the deformation temperature. Decreasing the annealing temperature significant retards the static globularization process. They also developed models [10,23] to estimate the required times for static globularization via boundary splitting and microstructure coarsening. However, these models cannot depict the variation of globularized fraction with time. Though extensive investigations have been carried out on the microstructure evolution of TA15 alloy during hot working, systematic studies on static globularization are lacking. In this study, the microstructure evolution during heat-treatment of hot worked TA15 alloy with transformed structure is experimentally investigated and mathematically modeled. The results are useful for microstructural control in primary hot working of titanium alloys.
deformation without cooling down. The annealing temperature is the same to the deformation temperature. After annealing for different times, the specimens were cooled by forced-convection. The processing parameters are as follows: temperature 940 ◦ C, 970 ◦ C; strain rate 0.01 s−1 , 0.1 s−1 ; height reduction 30%, 70%; annealing time 0.5–8 h (940 ◦ C), 0.1–3.0 h (970 ◦ C). Stefansson et al. [2] suggested that the growth of primary ␣ during cool down may affect microstructure. Thus, they employed a procedure including rapidreheating, short-time holding and water quenching to restore high temperature microstructure. In the present work, however, the cooling rate was high enough to suppress the diffusional growth of ␣ phases due to the small size of specimens. This additional process was unnecessary. The heat-treated specimens were sectioned along the compression axis, mechanically grinded and polished, and etched with a solution of 13% HNO3 , 7% HF and 80% H2 O. Micrographs were taken on a LECIA DFC320 microscope, and examined using quantitative image analysis (Image-pro plus 5.0). For each specimen, micrographs were shot at two locations lying on the equatorial plane, one near the center and one near the surface. The local strains at the two image locations were determined to be 0.26, 0.49 for 30% reduction; and 1.00, 1.58 for 70% reduction using FE simulation. In each image location, three adjacent fields of view were analyzed. Globularization was taken to be an ␣-phase morphology with aspect ratio less than 3. The measured globularized fraction fg included both the dynamically globularized part fdg and the static part fsg : fg = fdg + fsg
(1)
fdg was measured by examining the microstructure prior to annealing. Then the static globularization kinetics was determined.
3. Results and discussion 3.1. Microstructure evolution during annealing
2. Experimental procedures 2.1. Material The TA15 titanium alloy, with chemical composition (wt.%) of 6.06 Al, 2.08 Mo, 1.32 V, 1.86 Zr, 0.30 Fe, and Ti in balance, was supplied in the form of 80 mm thick by 170 mm wide hot rolled plate which had been annealed at 1123 K for 2 h and air cooled. The measured -transus temperature was 990 ◦ C. The microstructure of as-received material consisted of approximately 60% equiaxed primary ␣ phases within transformed  matrix, as shown in Fig. 1. The as-received bar was heated to 1020 ◦ C, held for 30 min and cooled in furnace so as to obtain transformed structure (Fig. 2). The ␣ layers at prior  grain boundaries were about 4 m thick and the average thickness of ␣ laths inside  grain is about 1.5 m. 2.2. Experimental procedures The  processed bar was then machined to cylinder specimens of 10 mm in diameter and 15 mm in height. A thin layer of glass lubricant was covered on the surface of specimens to minimize friction and prevent oxidation. The specimens were then heated to the deformation temperature at a rate of 12 ◦ C/min, soaked for 20 min to impart thermal equilibration, and compressed to give reduction at a constant nominal strain rate. Static annealing was conducted immediately after
Fig. 3 illustrates the microstructures deformed at 970 ◦ C, 0.1 s−1 to a strain of 1.58 and annealed for different time intervals. The microstructure prior to annealing (Fig. 3(a)) consisted of a large fraction of lamellar ␣ with high aspect ratio and a small amount of globularized ␣ with in  matrix. The ␣– interfaces were smooth, indicating boundary splitting was not apparent. Though a high level of intraphase defects might have already formed during deformation, the short deformation time suppressed the thermal grooving process. As a result, the dynamic globularized fraction was low. After annealing for 0.3 h, clear ␣– interfaces were produced in the former ␣ laths, separating them to strings of isolated ␣ grains with low aspect ratio (Fig. 3(b)). Though some long ␣ lamellas were not broken down, the boundaries became tortuous due to thermal grooving. Stefansson and Semiatin [10] found that thermal grooving can occur in both ␣ and  phases, resulting the irregularity of ␣– boundaries. The penetration of ␣ phase into  grain boundaries could also be observed in the current study. However, thermal
X.G. Fan et al. / Journal of Alloys and Compounds 533 (2012) 1–8
Fig. 3. Microstructures after deformation at temperature of 970 ◦ C, strain rate of 0.1 s−1 , strain of 1.58 and annealing for (a) 0 h; (b) 0.3 h; (c) 1.0 h and (d) 3.0 h.
Fig. 4. Microstructures after deformation at temperature of 940 ◦ C, strain rate of 0.1 s−1 , strain of 1.58 and annealing for (a) 0 h; (b) 1.0 h; (c) 2.0 h and (d) 8.0 h.
3
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grooving of ␣ phase was more significant, as the volume fraction of ␣ phase was relatively low at the annealing temperature. This phenomenon was in accordance with the observation by Lütjering et al. [9]. The thickness of ␣ grains increased, suggesting coarsening was notable. Increasing the annealing time to 1.0 h, more ␣ laths were globularized. Coarsening was significant during this period. The number of ␣ grains decreased sharply due to Ostwald ripening. ␣– boundaries become smoother. There still existed a small fraction of grooved ␣ platelets, in which grooves were not deep enough to segment these ␣ laths. During prolonged annealing, the grooved ␣ platelets were not separated by boundary splitting (Fig. 4(d)). Coarsening might solely account for globularization in this period. The microstructural development at 940 ◦ C is similar to that at 970 ◦ C, as shown in Fig. 4, though the globularization process was much slower. 3.2. Mechanism of static globularization Stefansson and Semiatin [10] found that static globularization could be divided into two stages. The first includes microstructural changes during deformation and the initial stages of static heat treatment; the second occurs during prolonged annealing. The initial stage consists of segmentation of lamellas via boundary splitting, while the latter stage is characterized by microstructure coarsening by mechanisms such as termination migration and Ostwald ripening. The initial stage is driven by the release of distortion energy which embodied by the formation of dislocation substructures whereas the driving force in the second stage is the reduction in interfacial energy. Thus the static globularization fraction can be expressed as: fsg = fsg-s + fsg-c
(2)
where the right two terms represent substructure driven globularization and coarsening controlled globularization. The microstructure evolution in this study was similar to that presented by Stefansson and Semiatin [10]. Boundary splitting was remarkable in the initial stage of annealing. This is confirmed by measuring the average size of ␣ grains, as shown in Fig. 5. The average size decreased with annealing time in this stage, indicating the break down of ␣ phases. With increasing annealing time, the intraphase defects were decreased due to thermal restoration and the lamellas were thickened by microstructure coarsening. Thus, boundary splitting is suppressed in prolonged annealing. Microstructure coarsening occurred throughout the annealing. It was remarkable even in the initial stage of annealing, as shown in Figs. 3 and 4. This is because the coarsening rate was larger at small grain size. Besides, the dislocation structures formed
Fig. 5. Variation of average ␣ grain size with annealing time.
during deformation could accelerate the coarsening process. The pipe diffusion of deformation defects can greatly increase diffusivity of solutes and promote coarsening. Semiatin et al. [24] found dynamic coarsening rate is enhanced by about 5 times relative to those for static coarsening. Coarsening also affected the boundary splitting process, as the increase in platelet thickness hindered the thermal grooving. Boundary splitting and microstructure coarsening may be considered as two competing mechanisms for static globularization, like recrystallization and recovery for thermal restoration. Both can reduce the aspect ratio of ␣ phases. Boundary splitting tends to refine microstructure, whereas coarsening hinders boundary splitting. Boundary splitting is significant in the initial stage while coarsening occurs throughout the annealing. As a result, the average grain size of ␣ phase decreased initially and increased during prolonged annealing, as shown in Fig. 5. 3.3. Globularization kinetics Fig. 6 shows the variation of globularization kinetics with annealing time. A sharp increase in globularized fraction was observed in the beginning of heat treatment, then the globularized fraction increased slowly with annealing time. The rate of globularization kinetics (dfg /dt) decreased with time. The shape of kinetics curve was quite different from the work of Stefansson and Semiatin [10], in which the globularized fraction
Fig. 6. Percent ␣ phase globularized as a function of annealing time at (a) 970 ◦ C and (b) 940 ◦ C.
X.G. Fan et al. / Journal of Alloys and Compounds 533 (2012) 1–8
Fig. 7. Plot of globularized fraction vs. logarithmic annealing time.
increased with time in a sigmoid way. In their work, the globularized fraction was plotted as a function of logarithmic annealing time. Fig. 7 shows the variation of globularized fraction with logarithmic time. It agrees reasonably with the result by Stefansson et al. [2]. Globularization kinetics was greatly influenced by deformation/annealing temperature, as shown in Fig. 6. Boundary splitting and microstructure coarsening are both controlled by diffusion of solutes. As a thermally activated process, the diffusivity of solutes is determined by annealing temperature. Thus, both the static and dynamic globularization were accelerated by
5
increasing temperature. Stefansson et al. [2] reported a tenfold decrease in globularization kinetics when the annealing temperature of Ti–6Al–4V alloy was decreased from 955 ◦ C to 900 ◦ C. It is also found that the thickness of ␣ lamellas is reduced with increasing temperature due to ␣– transformation. The thinning of ␣ lamellas resulted in the relative ease of  penetration along intraphase boundaries and promoted globularization. The amount of deformation also affected the globularization process during subsequent annealing. The dynamically globularized fractions prior to annealing were close at the two strains employed in this study, as shown in Fig. 6. However, the globularized fraction increased more rapidly at larger prestrain in the initial period of annealing. During prolonged annealing, the kinetics rates were close at different prestrains. Prestrain greatly influenced the boundary splitting in the initial stage of annealing, i.e. the substructure driven static globularization. The efficiency of boundary splitting is strongly dependent on the misorientation of intraphase boundaries [12]. Though dislocation substructures can be formed at a relatively low strain, the fraction of high angle boundaries increases with strain. It is also found that the transformed structure undergoes severe heterogeneous deformation [25]. Part of the alpha lamellas may remain undeformed at small strain, which prevents the globularization process. Moreover, the large compressive strain during deformation would thin ␣ lamellas and further promote boundary splitting. Fig. 8 shows the microstructures after deformation to different strains and annealed for the same time. At a strain of 0.26, the microstructure consisted of a large fraction of long ␣ platelets. These platelets had straight boundaries, which means thermal grooving was not significant. With increasing strain, more ␣ lamellas were broken down. The remnant had more tortuous boundaries. Therefore, static globularization was accelerated by
Fig. 8. Microstructures after deformation at 970 ◦ C, 0.1 s−1 to strains of (a) 0.26, (b) 0.50, (c) 1.00 and annealing for 1.0 h.
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the initial stage of annealing. This is correct only if the strain rate is relatively low. Lamellar kinking and shear bands are increased at higher strain rates [4,25], which retards globularization. Stefansson and Semiatin [10] found that lowering deformation temperature did not affect static globularization kinetics. Similar to increasing strain rate, decreasing deformation temperature can give rise to higher stored energy. Therefore, the current study confirms that dislocation substructures have an indirect effect on globularization. 3.4. Prediction of globularization kinetics 3.4.1. Required times for boundary splitting and termination migration Zherebtsov et al. [7] proposed that the Mullins model can be used to analyze boundary splitting. In the case of penetration of ␣ lamellas, the time tp to complete thermal grooving can be expressed as [7]: 3
Fig. 9. Comparison of globularized fraction at different strain rates.
boundary splitting. Stefansson and Semiatin [10] reported the substructure driven static globularization increases with prestrain, which is consistent with the present work. Prestrain did not affect the microstructure coarsening during prolonged annealing. Thus, coarsening induced globularization was irrelevant to prestrain. Fig. 9 compares the globularized fraction at different strain rates. The globularized fractions (including both the dynamically and statically globularized fractions) are close at different strain rates. It has been reported that dynamic globularization decreases with strain rate. Thus, the static globularization kinetics is a little larger at higher strain rate [26]. High deformation speed can suppress the dynamic restoration processes during deformation and result in a higher stored energy, which promotes static globularization. This phenomenon is different from that observed in dynamic globularization [16,17]. The decrease of dynamic globularization kinetics with strain rate has been attributed to the decrease of time for diffusion-controlled processes. During static heat treatment, the annealing time is so long that there is sufficient time for the completion of boundary splitting. It can also be found that the static globularization kinetics was less sensitive to strain rate than to annealing temperature and prestrain. The microstructures at a strain rate of 0.01 s−1 were similar to that at 0.1 s−1 , as shown in Fig. 10. Semiatin et al. [1] reported that dynamic globularization is less dependent on strain rate when deformation is controlled by dislocation activities. It can be deduced that substructure driven static globularization is also insensitive to strain rate as the boundary splitting occurs only in
0.2(l)
tp =
A=
(3)
A(mg )3 C ␣ Vm D
(4)
RT
where l is the thickness of ␣ lamellas (m), mg is the average slope at the root of the triple point, C is the equilibrium concentration (in atomic percent) of the rate limiting solute in the  phase, ␣ is the ␣– interface energy (J m−2 ), Vm is the molar volume of the ␣ platelet material (m3 mol−1 ), D is the diffusivity of the rate limiting solute in the  phase (m2 s−1 ), R is the universal gas constant (8.314 J mol−1 K−1 ), and T is the absolute temperature (K). Because neither the ␣ nor the  phase in TA15 alloy is a terminal solid solution, the term C in Eq. (4) should be replaced by the composition factor CF : CF =
C (1 − C ) (C␣ − C )2 (1 + ∂ ln r/∂ ln C )
(5)
where C␣ is the content of the rate-limiting solute in the ␣ phase and r is the activity coefficient of the solute in the  phase. 1 + ∂ ln r/∂ ln C is the thermodynamic factor. Mo is the rate limiting solutes due to its low diffusivity and strong stabilizing effect on the  phase. The diffusivity of Mo in the  phase can be obtained by [27]: 
DMo = 7.0 × 10−8 exp
−18520 T
(6)
The measured equilibrium concentrations of Mo in the ␣ and  phases were about 0.0013, 0.015 at 970 ◦ C, and 0.002, 0.020 at
Fig. 10. Microstructures after deformation at 0.01 s−1 to a strain of 1.58: (a) 970 ◦ C, 1 h;(b) 940 ◦ C, 2 h.
X.G. Fan et al. / Journal of Alloys and Compounds 533 (2012) 1–8
940 ◦ C. The thermodynamic factor of Mo is about 0.75 [27]. Other physical parameters are given as follows [7]: the average slope mg = 0.35, ␣– interface energy ␣ = 0.26 J m−2 , and the molar volume of ␣ phase Vm = 1.044 × 10−5 m3 mol−1 . The average thickness of ␣ lamellas is measured to be 2.1 m at 970 ◦ C and 2.7 m at 940 ◦ C. The predicted times for the completion of boundary splitting are about 21 h and 68 h at 970 ◦ C and 940 ◦ C, which are much longer than those observed. In fact, Zherebtsov et al. [7] reported a similar behavior in warm working of Ti–6Al–4V alloy and suggested that the retained dislocation structures in  phase would cause a tenfold increase in diffusivity by pipe diffusion thus enhancing the kinetics. Applying the Mullins model to the work of Stefansson et al. [2], it is also found that the predicted time is much longer than observations (Model predictions are about 10.6 h and 39.6 h at 955 ◦ C and 900 ◦ C while the experimental results are 1 h and 14 h, respectively.). These results suggest that the static globularization kinetics would be substantially underestimated without considering the influence of pre-deformation on diffusion. Because the promotion in diffusivity is hard to be quantitatively measured, the Mullins model gives a qualitative or semi-quantitative result. Another model to predict the duration of boundary splitting is proposed by Stefansson and Semiatin [10]. In this model, the time required for boundary splitting can be calculated by [10]:
tp =
Y0 0.86mg K
1/c (7)
Y0 is the distance required for the triple point to move through, which is assimilated to half the lamellar thickness. K and c are the coarsening parameters defined as: d␣ = Kt c
(8)
7
Table 1 Predicted times required for static globularization via boundary splitting. Temperature (◦ C)
␣ Lamellas thickness (m)
K (mh−n )
n
Time (h)
940 970
2.65 2.08
3.54 3.74
0.41 0.41
1.69 0.83
where d␣ is the average grain size of ␣ phase. In this case, the predicted results are in broad agreement with microstructure observations, as shown in Table 1. Thus, this model is useful for rough estimation of the required time for boundary splitting. During prolonged annealing, termination migration mainly accounts for the reduction in aspect ratio. Semiatin et al. [23] developed a model to estimate the globularization time via termination migration:
2
3 − [0.3287/3 (1 + 1 − 0.763−4/3 ) ] g = 2(1+) 0.51/3 +0.6652/3 4 + −1/3 −1/3 3(0.5−0.573
)
3(0.143+0.934
(9)
)
where and are geometric factor and time normalization factor defined as: ≡
w + 0.5 l
(10)
≡
l3 RT CF ␣ Vm D
(11)
where w is the width of ␣ lamellas. Model predictions are in broad agreement with experimental observations, as shown in Table 2.
Fig. 11. Predicted globularized fraction by the (a, b) asymptotic equation and (c, d) JMAK equation.
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Table 2 Predicted times required for static globularization via termination migration. T (◦ C)
w (m)
l (m)
H
(h)
(h)
970 940
13.80 17.73
2.56 3.19
5.89 6.05
7.14 19.9
8.35 25.3
3.4.2. Static globularization kinetics The previous models can be used to estimate the required time for static globularization. However, the variation of globularized fraction with annealing time is also of industrial importance. In general, the kinetics of thermally activated microstructure development can be depicted by: X = 1 − exp(−kt n )
X = 1 − (1 + k t)
−1/m
(12)
splitting is significant in the initial stage of annealing while coarsening occurs throughout the annealing process. (2) Static globularization kinetics is found to increase with annealing temperature and prestrain, but to be less dependent on strain rate. (3) The rate of static globularization kinetics decreases with annealing time. The asymptotic equation can be used to model the static globularization kinetics. Acknowledgments The authors would like to gratefully acknowledge the support of National Natural Science Foundation of China for Key Program (no. 50935007) and National Basic Research Program of China (no. 2010CB731701).
(13)
Eq. (12) is the well known Johnson–Mehl–Avarmi–Kolmogorov (JMAK) equation which is suitable for processes involving nucleation. Eq. (13), known as asymptotic equation, is often applied to the non-nucleation types. In the previous discussion, it has been confirmed that boundary splitting is the primary globularization mechanism in the initial stage while microstructure coarsening occurs throughout annealing. The kinetics of static globularization in the initial stage should be similar to that of dynamic globularization. Dynamic globularization kinetics has been found to increase with strain in a sigmoidal way after reaching a critical strain, which behaves like microstructure transformation involving nucleation. Many researchers use the JMAK equation to characterize dynamic globularization kinetics [16,17]. Therefore, Eq. (12) may be applied to the initial stage. Microstructure coarsening does not involve nucleation. Thus, Eq. (13) may be used to predict globularization kinetics after the completion of boundary splitting. Though theoretical analysis suggests different equations for different stages, the static globularization kinetics may be phenomenologically depicted by either of the two equations, as shown in Fig. 11 (Normalized fraction of static globularization is calculated by fsg /(1 − fsd )). Fig. 11 suggests that both the asymptotic equation and JMAK equation have good fitness. However, the asymptotic equation fits the experimental data better. In fact, the required time for boundary splitting is short compared to coarsening. The rate of globularization kinetics is high in the initial stage. Thus, the kinetics rate decreased with time, which follows the asymptotic equation. The JMAK equation also has a good fitness. The fitting parameter n is less than 1, which eliminates the nucleation stage in the curves. Thus, the JMAK equation loses its physical significance. For the asymptotic equation, m is equal to the coarsening exponent (1/c) when Eq. (13) is used to describe the kinetics of coarsening. In this study, the determined values of m varies under different hot working conditions, which weakens the physical significance. Thus, the phenomenological models can only give a relatively acceptable prediction but cannot effectively depict the complex microstructure evolution procedure of static globularization. 4. Conclusions Microstructure evolution during heat-treatment of hot worked TA15 alloy with transformed structure was investigated by isothermal compression testing. From this work, the following conclusions were drawn: (1) Boundary splitting and microstructure coarsening are two competing mechanisms for static globularization. Boundary
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