- Email: [email protected]
Deformation behavior in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy
Materials Science & Engineering A 589 (2014) 15–22
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Deformation behavior in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy S.F. Liu a, M.Q. Li a,n, J. Luo a, Z. Yang b a b
School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China The First Aircraft Institute, Aviation Industry Corporation of China, Xi’an 710089, China
art ic l e i nf o
a b s t r a c t
Article history: Received 23 April 2013 Received in revised form 18 September 2013 Accepted 19 September 2013 Available online 25 September 2013
Isothermal compression of the Ti–5Al–5Mo–5V–1Cr–1Fe alloy was carried out on a Gleeble-1500 hotsimulator at the deformation temperatures ranging from 993 K to 1203 K, strain rates ranging from 0.01 s 1 to 5.0 s 1 and height reductions ranging from 40% to 70%. The results show that the deformation temperature affects significantly the extent of dynamic softening in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy. The apparent activation energy for deformation in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy is 291.73 7 50 kJ mol 1 in αþ β two-phase region and 179.93 7 20 kJ mol 1 in β single-phase region. The dynamic recovery is the dominant deformation mechanism in β single-phase region of Ti–5Al–5Mo–5V–1Cr–1Fe alloy. Finally, the processing map of isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy is exhibited at the strains of 0.3, 0.5 and 0.7, in which two domains with high efficiency of power dissipation and an instable domain are presented, and the main instability mechanism is flow localization. & 2013 Elsevier B.V. All rights reserved.
Keywords: Ti–5Al–5Mo–5V–1Cr–1Fe alloy Isothermal compression Apparent activation energy for deformation Processing map
1. Introduction Titanium alloys are widely used in aviation, aerospace industries as a result of their excellent properties including good resistance against corrosion, low density and high strength [1–4]. It is well-known that microstructure of titanium alloys is very quite sensitive to processing parameters such as deformation temperature, strain rate and strain in forging process. Therefore, it is very important to study the deformation behavior in high temperature deformation process of titanium alloys in order to obtain the desired shape and the microstructure of work-piece. Warchomicka et al. [1] investigated the deformation behavior of Ti-5-5-5-3-1 alloy through isothermal compression. It was shown that dynamic recovery of β single-phase and rotation of α grains occurred predominantly in α þβ two-phase region and dynamic recovery was observed above β transus temperature. Momeni and Abbasi [5] performed the high temperature compression of Ti-6-4 alloy and found that the apparent activation energy for deformation in α þβ two-phase region was higher than that in β single-phase region. Fan et al. [6] established the processing map of near β Ti-7-3-3-3 alloy by using isothermal compression, in which was observed that dynamic recovery and dynamic recrystallization were related to stable regions while flow localization
n
Corresponding author. Tel.: þ 86 29 88460328; fax: þ86 29 88492642. E-mail address: [email protected] (M.Q. Li).
0921-5093/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2013.09.066
led to instable region. Li et al. [7] investigated the deformation behavior of Ti-5-4-4-2-2 alloy through isothermal compression at the deformation temperatures ranging from 1053 K to 1193 K, strain rates ranging from 0.001 s 1 to 10.0 s 1 and height reductions ranging from 50% to 60%. Balasubrahmanyam and Prasad [8] analyzed the deformation behavior of Ti-10-4.5-1.5 alloy through apparent activation energy for deformation. The results showed that dynamic recrystallization corresponded to peak efficiency domain of power dissipation while flow instabilities led to instable regions. Jones et al. [9] calculated the activation energy for deformation of Ti-5-5-5-3 alloy and presented that deformation was dominated by dynamic recovery in the β matrix. Jia et al. [10] studied the high temperature deformation of Ti60 alloy through the stress–strain curves, in which it was reported that flow softening in αþβ two-phase region was caused by break-up and globularization of lamellar α phase as well as deformation heat in deformation, while dynamic recovery and dynamic recrystallization contributed to flow softening in β single-phase region. The Ti–5Al–5Mo–5V–1Cr–1Fe alloy is a near-β titanium alloy, and used to manufacture the forgings with large dimension, such as landing gear system. A few papers reported the high temperature deformation behavior of Ti–5Al–5Mo–5V–1Cr–1Fe alloy [11–13]. Zherebtsov et al. [11] investigated the microstructure evolution in the warm forming of Ti–5Al–5Mo–5V–1Cr–1Fe alloy by SEM and TEM. Li et al. [12] discussed the relationship between the evolution of lamellar α phase and the flow softening effect in the high temperature deformation of Ti–5Al–5Mo–5V–1Cr–1Fe
16
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
alloy. The result showed that the transition of lamellar α evolution from buckling to fragmentation contributed to flow softening greatly, leading to sharp reduction of flow softening extent. Furthermore, the influence of the thickness in lamellar α phase on the microstructure in high temperature deformation of Ti–5Al– 5Mo–5V–1Cr–1Fe alloy was also investigated by Li et al. [13]. Nevertheless, the objective of the above literatures is mainly to investigate the microstructure evolution in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with lamellar microstructures. The high temperature deformation behavior of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with equiaxed α phase has not been studied systematically. In this paper, the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with equiaxed α phase was conducted at a series of deformation temperature, strain rate and strain. The effect of the processing parameters on the flow stress of Ti–5Al–5Mo–5V–1Cr–1Fe alloy is investigated, and the apparent activation energy for deformation is calculated at different deformation conditions. Finally, the processing maps of isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy at the strains of 0.3, 0.5 and 0.7 are constructed.
2. Experimentals The as-received Ti–5Al–5Mo–5V–1Cr–1Fe alloy used in the present study was 400.0 mm in diameter. The chemical composition (wt%) is shown in Table 1. The microstructure of Ti–5Al–5Mo– 5V–1Cr–1Fe alloy consists of β matrix and primary α phase with a grain size about 3.0 μm as shown in Fig. 1. The β transus temperature was 1153 K by using the metallographic observation method. The cylindrical specimens with 8.0 mm in diameter and 12.0 mm in height were machined from the as-received Ti–5Al– 5Mo–5V–1Cr–1Fe alloy. The isothermal compression were performed on a Gleeble-1500 hot-simulator at the deformation temperatures of 993 K, 1023 K, 1053 K, 1083 K, 1103 K, 1123 K, 1143 K, 1163 K, 1183 K and 1203 K, strain rates of 0.01 s 1, 0.1 s 1, 1.0 s 1 and 5.0 s 1, and height reductions of 40%, 50%, 60% and 70%. The Ti–5Al–5Mo–5V–1Cr–1Fe alloy specimens were heated to compression temperature at a heating rate of 20 K s 1 and held for 5 min before compression so as to ensure the uniform temperature, where the phase equilibrium before deformation was not reached probably. The isothermally compressed specimens of Ti–5Al–5Mo–5V–1Cr–1Fe alloy were cooled to room temperature in air and with a cooling rate of about 30 K/s up to 873 K. Then, the isothermally compressed specimens were sectioned parallel to the compression axis and finally prepared for the microstructure observation by using typical procedures. An OLYMPUS PMG3 optical microscope and Tecnai F30 G2 TEM were used to observe the microstructure.
0.01 5.0 s 1. As seen from Fig. 2, all of the flow stress–strain curves exhibit a similar feature. The flow stress decreases with the increasing of strain after a sharp increase. It is a result of a combination of work-hardening effect and dynamic softening effect, because at the beginning of compression, the workhardening effect resulting from the increasing of dislocation density is a dominant factor leading to a rapid increase in flow stress, and then the dynamic softening effect becomes the dominant mechanism and the flow stress tends to decrease gradually. In addition, it can be observed from Fig. 2 that the flow stress decreases with the increasing of deformation temperature at certain strain rate. The reason is in the following: firstly, the flow stress is determined by the morphology and volume fraction of α phase. As seen from Fig. 3(a), at a deformation temperature of 993 K, the fine α phase disperses uniformly in the β matrix, and the volume fraction of primary α phase is measured to be 15.4%, which corresponds to high flow stress. As seen in Fig. 3(b and c), the volume fraction of α phase decreases to 13.5% and 5.4% with the increasing of deformation temperature resulting in the decreasing of flow stress. All of the α phase transformed into β matrix at the deformation temperatures above the β transus temperature as exhibited in Fig. 3(d). Therefore, it can be concluded that the flow stress increases with the increasing of volume fraction of α phase at certain strain rate. Secondly, the atomic binding force decreases and the free energy of atoms enhances with the increasing of deformation temperature, which in turn promotes the dislocation slip and the diffusion ability of grain boundaries and finally results in a decrease in flow stress. Meanwhile, it also can be observed from Fig. 2 that the flow stress increases with the increasing strain rate at a certain deformation temperature. This is because the dislocation density increases with the increasing of strain rate and the tangled dislocation structure prevents the movement of dislocation, resulting in the increasing of flow stress. The deformation temperature affects the extent of dynamic softening obviously. As shown in Fig. 2(a and b), an evident dynamic softening effect can be observed at the deformation temperatures below 1103 K. Whereas at high deformation temperatures, the flow stress exhibits a steady-state condition with the increasing of strain after the peak value. In order to realize further the different extents of flow softening, the variation of flow stress softening (Δs ¼ sp ss ) of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with deformation temperatures at different strain rates is quantitatively shown in Fig. 4, in which the flow stress at a strain of 0.8 is
3. Results and discussion 3.1. Flow stress–strain curves Fig. 2 shows the typical flow stress–strain curves of isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy at the deformation temperatures ranging from 993 K to 1183 K and strain rates of
Fig. 1. The micrograph of as-received Ti–5Al–5Mo–5V–1Cr–1Fe alloy.
Table 1 The chemical composition of Ti–5Al–5Mo–5V–1Cr–1Fe alloy (wt%). Al
V
Mo
Cr
Fe
Zr
Si
C
N
O
H
Ti
5.28
5.05
4.88
1.09
1.03
o 0.01
o 0.01
0.032
0.008
0.1
0.001
Bal.
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
250
17
550 -1
500
Strain rate : 0.01 s
Strain rate : 1.0 s
450
200
-1
993 K
150
Flow stress /MPa
Flow stress /MPa
400
993 K
1053 K
100
1103 K
350
1053 K
300 250
1103 K
200 150
50
100
1143K 0 0.0
0.1
0.2
0.3
1183 K
0.4
0.5
0.6
1143 K
0.7
0 0.0
0.8
0.1
0.2
0.3
strain
0.4
0.5
0.7
0.8
250 Deformation temperature: 1183 K
Deformation temperature: 993 K
500
200
-1
400
Flow stress /MPa
5.0 s
-1
1.0 s
-1
300
0.1 s
200
0.01 s
-1
-1
5.0 s
-1
1.0 s
150
-1
100
0.1 s
0.01 s
-1
50
100
0 0.0
0.6
strain
600
Flow stress /MPa
1183 K
50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
strain
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
strain
Fig. 2. The typical stress–strain curves in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy: (a) 0.01 s 1; (b) 1.0 s 1; (c) 993 K and (d) 1183 K.
regarded as the steady-state stress (ss). As evident from Fig. 4, flow softening occurs at all the deformation conditions. It has been reported that the mechanisms of dynamic softening are mainly related to temperature rise, dynamic recovery, dynamic recrystallization or flow instabilities [14–17]. For the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy, most of the plastic power converts to heat and results in temperature rise because of the low thermal conductivity in the deformation process. So the temperature rise in deformation is a main factor of flow softening for the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy. Other softening mechanisms leading to flow softening of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy can be validated through TEM micrographs in Fig. 5. As seen from Fig. 5(a), a number of recrystallized α grains can be observed, this suggests that dynamic recrystallization also contributes to flow softening. Besides of that, an array of parallel dislocation is found inside the β grains in Fig. 5(b), which indicates that dislocation climb occurs. It is well-known that dislocation climb is a typical microstructure characteristic of dynamic recovery. Therefore, it can be concluded that temperature rise, dynamic recrystallization and dynamic recovery contribute to flow softening of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy. Furthermore, it also can be seen from Fig. 4 that the extent of flow softening in αþβ two-phase region is much higher than that in β single-phase region. The reason leading to different extent of flow softening would be attributed to different dynamic softening mechanisms caused by microstructural change. In αþ β two-phase region, α phase in the β matrix prevents the movement of dislocations, resulting in the increasing of stored energy, which is an impetus for the occurrence of various softening mechanisms including dynamic recrystallization, dynamic recovery and so on.
While in β single-phase region, the higher diffusion coefficient in bcc structure of β phase and the existence of more active slip system in comparison to hcp structure of α phase, result in the more feasible occurrence of dynamic recovery and the suppression of dynamic recrystallization.
3.2. Apparent activation energy for deformation In terms of the high temperature deformation theory, the apparent activation energy for deformation represents the magnitude of the energy barrier which the atomic transition needs to overcome. Therefore, the apparent activation energy for deformation has been regarded as an important phenomenological parameter to reflect the workability of metals and alloys. The apparent activation energy (Q) for deformation can be deduced from a kinetic equation [18]: Q ε_ ¼ Asn exp ð1Þ RT where ε_ is the strain rate (s 1), A is the materials' constant, s is the flow stress (MPa), n is the stress exponent, Q is the apparent activation energy for deformation (kJ mol 1), R is the gas constant (kJ mol 1 K 1), and T is the absolute deformation temperature (K). Taking natural logarithm of Eq. (1) and then partial differentiating, the apparent activation energy (Q) for deformation can be obtained in the following: ∂ ln s Δ ln s Q ¼ nR nR ð2Þ ∂ð1=TÞ ε_ ;ε Δð1=TÞε_ ;ε
18
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
Fig. 3. Microstructure of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy at different deformation temperatures and a strain rate of 0.01 s 1 and height reduction of 60%: (a) 993 K, (b) 1053 K, (c) 1103 K and (d) 1183 K.
270
T
240
-1
0.01s -1 0.1 s -1 1.0 s -1 5.0 s
Flow stress /MPa
210 180 150 120 90 60 30 0
1000
1050
1100
1150
1200
Deformation temperature /K Fig. 4. Flow softening effect of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with increasing of deformation temperature at different strain rates.
And the stress exponent n is given in the following: ∂ ln ε_ Δ ln ε_ n¼ ∂ ln sT;ε Δ ln sT;ε
ð3Þ
Fig. 6(a) shows the variation of the flow stress with the deformation temperature at different strain rates. Fig. 6(b) represents the variation of flow stress with strain rate at different deformation temperatures. It can be seen from Fig. 6(a) that the slope between the flow stress and the deformation temperature in αþ β two-phase region is higher than that in β single-phase region. For the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy, the reason would be caused by α-β phase transformation.
Considering the distinction of the slope value between the flow stress and deformation temperature in αþβ two-phase region and β single-phase region, the apparent activation energy for deformation in αþβ two-phase region and β single-phase region is calculated respectively. According to the experimental flow stress–strain curves of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy, the variation of the apparent activation energy for deformation with strain is illustrated in Fig. 7. It can be seen from Fig. 7 that the apparent activation energy for deformation of isothermally compressed Ti– 5Al–5Mo–5V–1Cr–1Fe alloy in αþβ two-phase region decreases from 386.81790 kJ mol 1 to 227.42758 kJ mol 1 with the increasing of strain continuously. It is because that work hardening effect dominates at the beginning of compression, resulting in the difficulty for deformation, which further leads to the increasing of flow stress and high apparent activation energy for deformation. As the compression proceeds, the effect of various softening mechanisms contributes to the more feasibility of deformation, leading to the distinct decreasing of the apparent activation energy for deformation. When the deformation reaches to a certain extent, the effect of work hardening and softening mechanism attains a balanced condition, so the apparent activation energy for deformation does not decrease too much with the increasing of strain. Meanwhile, the average apparent activation energy for deformation reaches 291.73750 kJ mol 1, which is similar to that of Ti-5-5-5-31 alloy obtained by Warchomicka et al. [1] and that of Ti-10-2-3 alloy obtained by Robertson et al. [19]. In β single-phase region, the apparent activation energy for deformation ranges from 214.17 735 kJ mol 1 to 150.05 7 27 kJ mol 1 and the average value attains 179.937 20 kJ mol 1, which is similar to that of self-diffusion of β-Ti (153 kJ mol 1) and that of Ti-5-5-5-3 alloy obtained by Jones et al. (183 kJ mol 1) [9].
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
19
[011]
[011]
Fig. 5. The TEM micrograph illustrating (a) dynamic recrystallization at 1053 K, 1.0 s 1 and (b) dislocation inside the β grains at 1183 K, 0.1 s 1.
6.0 6.0
5.8 5.6
5.7
5.2 5.0 4.8 4.6 4.4
-1
0.01s -1 0.1 s -1 1.0 s -1 5.0 s
4.2 4.0 3.8 3.6
ln(Flow stress /MPa)
ln(Flow stress /MPa)
5.4 993 K 1023K 1053K 1083K 1103K 1123K 1143K 1163K 1183K 1203K
5.4 5.1 4.8 4.5 4.2 3.9 3.6
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0 10.2
-5
-4
-3
-2 -1 0 1 -1 ln(Strain rate /s )
3
1/T 10 /(1/K)
2
3
4
Fig. 6. Variation of the flow stress with (a) deformation temperature and (b) strain rate at a strain of 0.6.
Activation energy for deformation /(kJ mol-1)
500 450
phase region phase region
400
solute content of the Ti–5Al–5Mo–5V–1Cr–1Fe alloy, a slightly higher activation energy for deformation would be reasonable, compared to pure titanium. 3.3. Processing map
350 300 250 200 150 100 0.1
0.2
0.3
0.4
0.5
0.6
0.7
Strain Fig. 7. Variation of the apparent activation energy for deformation of isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with strain.
This suggests that dynamic recovery is the dominant deformation mechanism in β single-phase region. The typical corresponding microstructure in β single-phase region can be validated by Fig. 5 (b), which reveals the occurrence of dislocation climb. And it has been suggested that dislocation climb can be regarded as vacancy diffusion, so the activation energy for deformation should be similar to that of self-diffusion [9]. Considering the increased
The dynamic material model (DMM) takes work-piece as a dissipation of power in high temperature deformation. The instantaneous power P absorbed by the work-piece in plastic flow consists of two complementary parts: dissipator content G and cocontent J, in which the former represents power dissipated by plastic deformation and the latter relates to the metallurgical mechanism. Then the power P absorbed by the work-piece in plastic flow processes can be written as follows: Z s Z P ¼ s_ε ¼ ε_ ds þ sd_ε ¼ J þ G ð4Þ 0
0_ε
And the power partitioning between J and G is given in the following: ∂J ∂ ln s Δ log s ¼ ¼m ð5Þ ∂GT;ε ∂ ln ε_ T;ε Δ log ε_ T;ε where m is the exponent of strain rate sensitivity. Then, the dissipator co-content J can be written in the following: J¼
m s_ε 1 þm
ð6Þ
20
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
caused by α-β phase transformation. A similar phenomenon has been seen in a wide range of materials [22,23]. Fig. 8(b) shows the processing map in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy at a strain of 0.5. It can be seen that there exist two domains with high power dissipation efficiency and an instable domain. Generally speaking, the microstructure evolution in the stable domains is likely to be dynamic recrystallization, dynamic recovery, superplasticity or spheroidizing. Nevertheless, the occurrence of flow instability is usually related to flow localization, adiabatic shear bands or cracking. In order to obtain optimal processing parameters and realize the underlying deformation mechanism in the stable and instable domains, the domains are characterized with microstructures under specific deformation parameters. The first domain with high dissipation efficiency occurs at the deformation temperatures ranging from 993 K to 1029 K and strain rates ranging from 0.01 s 1 to 0.046 s 1. A similar domain at lower deformation temperature and strain rate has also been observed in previous research for Ti–5Al–5Mo–5V–1Cr–1Fe alloy [24]. In the present investigation, the peak efficiency of power dissipation in this domain is about 0.63 at a deformation temperature of 993 K and strain rate of 0.01 s 1, which corresponds to an optimal condition of Ti–5Al–5Mo–5V–1Cr–1Fe alloy. It has been reported that the power dissipation efficiency as high as 6070% implies the occurrence of superplastic deformation because of the correlative value m is about 0.40.5 [22]. Besides, Wang et al. [25] have suggested that an equiaxed, finely grained and stabilized structure is also necessary to the occurrence of superplastic deformation. Considering the prerequisition mentioned above, the corresponding microstructure is exhibited in Fig. 9, from which it can be seen that the equiaxed primary α phase is well-distributed in β matrix, and shows little
The dimensionless parameter power dissipation efficiency η can be defined as the following [20]: η¼
J 2m ¼ J max 1 þ m
ð7Þ
The variation of η with strain rate and deformation temperature constitutes the power dissipation map, which characterizes the microstructure evolution in high temperature deformation. Considering the instability in deformation, a continuum criterion predicting the occurrence of plastic flow instabilities is in the following [21]: ξð_εÞ ¼
∂ log ½m=ð1 þ mÞ þm o 0 ∂ log ε_
ð8Þ
where ξð_εÞ is the instable parameter that varies with the deformation temperature and strain rate. The different values of ξð_εÞ constitutes the instable map. Then, a superimposition of the instable map on the power dissipation map gives a processing map. Fig. 8(a–c) exhibits the processing maps of isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy established at the deformation temperatures ranging from 993 K to 1203 K and strain rates ranging from 0.01 s 1 to 5.0 s 1 at the strains of 0.3, 0.5 and 0.7. The contour numbers represent the power dissipation efficiency and the shaded domain represents the instable region. As seen from Fig. 8(a– c), the strain has a slight influence on the processing map. And both the power dissipation efficiency and instable efficiency at different strains show a similar variation tendency. Moreover, it can be observed from Fig. 8(a–c) that a noticeable change in the power dissipation efficiency map occurs at about β transus temperature ( 1153 K), which could be related to the microstructure evolution
0.20
0.5
0.20 0.23 0.29
0.25 0.30
0.0 -1
-1
log(Strain rate /s )
0.0 log(Strain rate /s )
0.15
0.5
0.20
0.25
T
-0.5
0.38
0.35
-1.0
0.35 0.38 0.40
-1.5
0.50
0.34 0.25
-0.5
T
0.40
-1.0
0.34 -1.5 0.45
0.30
0.45
0.38 1050
1100
1150
1200
-2.0
0.23
1000
1050
Deformation temperature /K
1100
0.25 1150
1200
Deformation temperature /K
0.15 0.20 0.25 0.28 0.30 0.35
0.5
0.0 -1
log(Strain rate /s )
0.29
0.40
0.50
-2.0 1000
0.15
0.10
T -0.5
0.40 -1.0
0.35 -1.5
0.40 -2.0
0.45 1000
0.25
0.30 0.28
0.15
0.20 1050
1100
1150
1200
Deformation temperature /K Fig. 8. Processing map in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy at the strains of (a) 0.3, (b) 0.5 and (c) 0.7.
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
Fig. 9. Micrograph of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy at a deformation temperature of 993 K, height reduction of 40% and strain rate of 0.01 s 1.
21
Fig. 11. Micrograph of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy at a deformation temperature of 1183 K, height reduction of 40% and strain rate of 1.0 s 1.
60
Temperature rise /K
50
993 K,5.0 s
-1
40
30
20
10 993 K,0.01 s 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-1
Furthermore, an obvious instable domain can be observed in the processing map at a strain of 0.5. When at the deformation temperature below 1008 K, the instable domain occurs almost at the strain rate above 0.046 s 1. With the increasing of deformation temperature, the instable domain shrinks the range of strain rate and only occurs at the strain rates larger of equal than 1.0 s 1. Fig. 11 shows the typical micrograph in the instable domain of Ti–5Al–5Mo– 5V–1Cr–1Fe alloy at a deformation temperature of 1183 K and strain rate of 1.0 s 1. It can be observed from Fig. 11 that the microstructure exhibits obvious flow localization, which is caused by short deformation time in high temperature deformation. Thus, the high temperature deformation of Ti–5Al–5Mo–5V–1Cr–1Fe alloy should not be performed in the above mentioned instable domain.
0.8
Strain Fig. 10. The temperature rise of the isothermally compressed Ti–5Al–5Mo–5V– 1Cr–1Fe alloy at a deformation temperature of 993 K.
difference from the original microstructure in grain size. So it can be deduced that superplastic deformation may contribute to the high power dissipation efficiency. Furthermore, at a deformation temperature of 993 K, with the increasing of strain rate, the power dissipation efficiency decreases continuously until the occurrence of the minimum value at a strain rate of 5.0 s 1. Similar phenomenon has also been reported by Poletti et al. for Ti-5-5-5-3-1 alloy [26]. The lower power dissipation efficiency obtained at a strain rate of 5.0 s 1 suggests that most of the plastic power converts to heat and is dissipated in the form of temperature rise in billet. Fig. 10 shows the temperature rise at a deformation temperature of 993 K and the strain rates of 0.01 s 1 and 5.0 s 1. It can be seen from Fig. 10 that temperature rise at a strain rate of 5.0 s 1 is higher than that at a strain rate of 0.01 s 1. Therefore, the plastic power converting to temperature rise at a strain rate of 5.0 s 1 is higher than that at a strain rate of 0.01 s 1, resulting in the lower power dissipation efficiency at high strain rate. The processing map also exhibits a domain with high power dissipation efficiency in β single-phase region at the deformation temperatures ranging from 1161 K to 1203 K and the strain rates ranging from 0.059 s 1 to 0.21 s 1. The peak efficiency of power dissipation is 0.43 at a deformation temperature of 1183 K and strain rate of 0.1 s 1, which corresponds to optimal processing parameter in the β forging of Ti–5Al–5Mo–5V–1Cr–1Fe alloy. It has been reported that the high stacking fault energy in β single-phase region results in the difficulty for dynamic recrystallization, which is consistent with what shown in Fig. 5(b) that dynamic recovery mainly works at such a deformation condition.
4. Conclusions The isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy is conducted at the deformation temperatures ranging from 993 K to 1203 K, strain rates ranging from 0.01 s 1 to 5.0 s 1 and height reductions ranging from 40% to 70%. The following conclusions can be summarized through the analysis on the flow stress, apparent activation energy for deformation and processing maps: (1). The deformation temperature affects significantly the extent of dynamic softening in the isothermal compression of Ti– 5Al–5Mo–5V–1Cr–1Fe alloy. Meanwhile, temperature rise, dynamic recrystallization and dynamic recovery also contribute to flow softening effect. (2). The apparent activation energy for deformation in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy is higher than that of self-diffusion of β-Ti in αþβ two-phase region and similar to that of self-diffusion of β-Ti in β singlephase region. In addition, dynamic recovery is the dominant mechanism in β single-phase region of Ti–5Al–5Mo–5V–1Cr– 1Fe alloy. (3). The strain affects the processing map in the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy slightly. And in the processing map at a strain of 0.5, the peak efficiency of power dissipation is 0.63 at a deformation temperature of 993 K and strain rate of 0.01 s 1, the two domains with high efficiency of power dissipation cover the range of 993 1029 K at the strain rates ranging from 0.01 s 1 to 0.046 s 1, and the range of 1161 1203 K at the strain rates ranging from 0.059 s 1 to 0.21 s 1. An instable domain is also observed at all of the deformation temperatures and strain rates larger of equal than 1.0 s 1, in which the main instability mechanism is flow localization.
22
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
References [1] F. Warchomicka, C. Poletti, M. Stockinger, Mater. Sci. Eng. A 528 (2011) 8277–8285. [2] F. Warchomicka, M. Stockinger, H.P. Degischer, J. Mater. Process. Technol. 177 (2006) 473–477. [3] X. Wang, M. Jahazi, S. Yue, Mater. Sci. Eng. A 434 (2006) 188–193. [4] R.C. Picu, A. Majorell, Mater. Sci. Eng. A 326 (2002) 306–316. [5] A. Momeni, S.M. Abbasi, Mater. Des. 31 (2010) 3599–3604. [6] J.K. Fan, H.C. Kou, M.J. Lai, et al., Mater. Des. 49 (2013) 945–952. [7] H. Li, M.Q. Li, T. Han, et al., Mater. Sci. Eng. A 546 (2012) 40–45. [8] V.V. Balasubrahmanyam, Y.V.R.K. Prasad, Mater. Sci. Eng. A 336 (2002) 150–158. [9] N.G. Jones, R.J. Dashwood, D. Dye, et al., Mater. Sci. Eng. A 490 (2008) 369–377. [10] W.J. Jia, W.D. Zeng, Y.G. Zhou, et al., Mater. Sci. Eng. A 528 (2011) 4068–4074. [11] S.V. Zherebtsov, M.A. Murzinova, M.V. Klimova, et al., Mater. Sci. Eng. A 563 (2013) 168–176. [12] C. Li, X.Y. Zhang, K.C. Zhou, et al., Mater. Sci. Eng. A 558 (2012) 8277–8285. [13] C. Li, X.Y. Zhang, Z.Y. Li, et al., Mater. Sci. Eng. A 573 (2013) 75–83.
[14] S.L. Semiatin, V. Seetharaman, I. Weiss, Mater. Sci. Eng. A 263 (1999) 257–271. [15] L.X. Li, Y. Lou, L.B. Yang, Mater. Des. 23 (2002) 451–457. [16] N.-K. Park, J.-T. Yeom, Y.-S. Na, J. Mater. Process. Technol. 130–131 (2002) 540–545. [17] L. Li, J. Zhou, J. Duszczyk, J. Mater. Process. Technol. 172 (2006) 372–380. [18] M.Q. Li, H.S. Pan, Y.Y. Lin, et al., J. Mater. Process. Technol. 183 (2007) 71–76. [19] D.G. Robertson, H.B. McShane, Mater. Sci. Technol. 14 (1998) 339–345. [20] Y.V.R.K. Prasad, H.L. Gegel, S.M. Doraivelu, et al., Metall. Trans. A 15 (1984) 1883–1892. [21] Y.V.R.K. Prasad, S. Sasidhara, Hot Working Guide: A Compendium of Processing Maps, ASM International, Materials Park, OH (1997) 25–157. [22] T. Seshacharyulu, S.C. Medeiros, W.G. Frazier, et al., Mater. Sci. Eng. A 284 (2000) 184–194. [23] X.Y. Zhang, M.Q. Li, H. Li, et al., Mater. Des. 31 (2010) 2851–2857. [24] X. Zhao, H. Zhao, R. Zhang, et al., Adv. Mater. Res. 490–495 (2012) 3423–3426. [25] K.X. Wang, W.D. Zeng, Y.Q. Zhao, et al., J. Mater. Sci. 45 (2010) 5883–5891. [26] C. Poletti, F. Warchomicka, M. Dikovits, et al., Mater. Sci. Forum 710 (2012) 93–100.
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Deformation behavior in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy S.F. Liu a, M.Q. Li a,n, J. Luo a, Z. Yang b a b
School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China The First Aircraft Institute, Aviation Industry Corporation of China, Xi’an 710089, China
art ic l e i nf o
a b s t r a c t
Article history: Received 23 April 2013 Received in revised form 18 September 2013 Accepted 19 September 2013 Available online 25 September 2013
Isothermal compression of the Ti–5Al–5Mo–5V–1Cr–1Fe alloy was carried out on a Gleeble-1500 hotsimulator at the deformation temperatures ranging from 993 K to 1203 K, strain rates ranging from 0.01 s 1 to 5.0 s 1 and height reductions ranging from 40% to 70%. The results show that the deformation temperature affects significantly the extent of dynamic softening in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy. The apparent activation energy for deformation in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy is 291.73 7 50 kJ mol 1 in αþ β two-phase region and 179.93 7 20 kJ mol 1 in β single-phase region. The dynamic recovery is the dominant deformation mechanism in β single-phase region of Ti–5Al–5Mo–5V–1Cr–1Fe alloy. Finally, the processing map of isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy is exhibited at the strains of 0.3, 0.5 and 0.7, in which two domains with high efficiency of power dissipation and an instable domain are presented, and the main instability mechanism is flow localization. & 2013 Elsevier B.V. All rights reserved.
Keywords: Ti–5Al–5Mo–5V–1Cr–1Fe alloy Isothermal compression Apparent activation energy for deformation Processing map
1. Introduction Titanium alloys are widely used in aviation, aerospace industries as a result of their excellent properties including good resistance against corrosion, low density and high strength [1–4]. It is well-known that microstructure of titanium alloys is very quite sensitive to processing parameters such as deformation temperature, strain rate and strain in forging process. Therefore, it is very important to study the deformation behavior in high temperature deformation process of titanium alloys in order to obtain the desired shape and the microstructure of work-piece. Warchomicka et al. [1] investigated the deformation behavior of Ti-5-5-5-3-1 alloy through isothermal compression. It was shown that dynamic recovery of β single-phase and rotation of α grains occurred predominantly in α þβ two-phase region and dynamic recovery was observed above β transus temperature. Momeni and Abbasi [5] performed the high temperature compression of Ti-6-4 alloy and found that the apparent activation energy for deformation in α þβ two-phase region was higher than that in β single-phase region. Fan et al. [6] established the processing map of near β Ti-7-3-3-3 alloy by using isothermal compression, in which was observed that dynamic recovery and dynamic recrystallization were related to stable regions while flow localization
n
Corresponding author. Tel.: þ 86 29 88460328; fax: þ86 29 88492642. E-mail address: [email protected] (M.Q. Li).
0921-5093/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2013.09.066
led to instable region. Li et al. [7] investigated the deformation behavior of Ti-5-4-4-2-2 alloy through isothermal compression at the deformation temperatures ranging from 1053 K to 1193 K, strain rates ranging from 0.001 s 1 to 10.0 s 1 and height reductions ranging from 50% to 60%. Balasubrahmanyam and Prasad [8] analyzed the deformation behavior of Ti-10-4.5-1.5 alloy through apparent activation energy for deformation. The results showed that dynamic recrystallization corresponded to peak efficiency domain of power dissipation while flow instabilities led to instable regions. Jones et al. [9] calculated the activation energy for deformation of Ti-5-5-5-3 alloy and presented that deformation was dominated by dynamic recovery in the β matrix. Jia et al. [10] studied the high temperature deformation of Ti60 alloy through the stress–strain curves, in which it was reported that flow softening in αþβ two-phase region was caused by break-up and globularization of lamellar α phase as well as deformation heat in deformation, while dynamic recovery and dynamic recrystallization contributed to flow softening in β single-phase region. The Ti–5Al–5Mo–5V–1Cr–1Fe alloy is a near-β titanium alloy, and used to manufacture the forgings with large dimension, such as landing gear system. A few papers reported the high temperature deformation behavior of Ti–5Al–5Mo–5V–1Cr–1Fe alloy [11–13]. Zherebtsov et al. [11] investigated the microstructure evolution in the warm forming of Ti–5Al–5Mo–5V–1Cr–1Fe alloy by SEM and TEM. Li et al. [12] discussed the relationship between the evolution of lamellar α phase and the flow softening effect in the high temperature deformation of Ti–5Al–5Mo–5V–1Cr–1Fe
16
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
alloy. The result showed that the transition of lamellar α evolution from buckling to fragmentation contributed to flow softening greatly, leading to sharp reduction of flow softening extent. Furthermore, the influence of the thickness in lamellar α phase on the microstructure in high temperature deformation of Ti–5Al– 5Mo–5V–1Cr–1Fe alloy was also investigated by Li et al. [13]. Nevertheless, the objective of the above literatures is mainly to investigate the microstructure evolution in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with lamellar microstructures. The high temperature deformation behavior of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with equiaxed α phase has not been studied systematically. In this paper, the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with equiaxed α phase was conducted at a series of deformation temperature, strain rate and strain. The effect of the processing parameters on the flow stress of Ti–5Al–5Mo–5V–1Cr–1Fe alloy is investigated, and the apparent activation energy for deformation is calculated at different deformation conditions. Finally, the processing maps of isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy at the strains of 0.3, 0.5 and 0.7 are constructed.
2. Experimentals The as-received Ti–5Al–5Mo–5V–1Cr–1Fe alloy used in the present study was 400.0 mm in diameter. The chemical composition (wt%) is shown in Table 1. The microstructure of Ti–5Al–5Mo– 5V–1Cr–1Fe alloy consists of β matrix and primary α phase with a grain size about 3.0 μm as shown in Fig. 1. The β transus temperature was 1153 K by using the metallographic observation method. The cylindrical specimens with 8.0 mm in diameter and 12.0 mm in height were machined from the as-received Ti–5Al– 5Mo–5V–1Cr–1Fe alloy. The isothermal compression were performed on a Gleeble-1500 hot-simulator at the deformation temperatures of 993 K, 1023 K, 1053 K, 1083 K, 1103 K, 1123 K, 1143 K, 1163 K, 1183 K and 1203 K, strain rates of 0.01 s 1, 0.1 s 1, 1.0 s 1 and 5.0 s 1, and height reductions of 40%, 50%, 60% and 70%. The Ti–5Al–5Mo–5V–1Cr–1Fe alloy specimens were heated to compression temperature at a heating rate of 20 K s 1 and held for 5 min before compression so as to ensure the uniform temperature, where the phase equilibrium before deformation was not reached probably. The isothermally compressed specimens of Ti–5Al–5Mo–5V–1Cr–1Fe alloy were cooled to room temperature in air and with a cooling rate of about 30 K/s up to 873 K. Then, the isothermally compressed specimens were sectioned parallel to the compression axis and finally prepared for the microstructure observation by using typical procedures. An OLYMPUS PMG3 optical microscope and Tecnai F30 G2 TEM were used to observe the microstructure.
0.01 5.0 s 1. As seen from Fig. 2, all of the flow stress–strain curves exhibit a similar feature. The flow stress decreases with the increasing of strain after a sharp increase. It is a result of a combination of work-hardening effect and dynamic softening effect, because at the beginning of compression, the workhardening effect resulting from the increasing of dislocation density is a dominant factor leading to a rapid increase in flow stress, and then the dynamic softening effect becomes the dominant mechanism and the flow stress tends to decrease gradually. In addition, it can be observed from Fig. 2 that the flow stress decreases with the increasing of deformation temperature at certain strain rate. The reason is in the following: firstly, the flow stress is determined by the morphology and volume fraction of α phase. As seen from Fig. 3(a), at a deformation temperature of 993 K, the fine α phase disperses uniformly in the β matrix, and the volume fraction of primary α phase is measured to be 15.4%, which corresponds to high flow stress. As seen in Fig. 3(b and c), the volume fraction of α phase decreases to 13.5% and 5.4% with the increasing of deformation temperature resulting in the decreasing of flow stress. All of the α phase transformed into β matrix at the deformation temperatures above the β transus temperature as exhibited in Fig. 3(d). Therefore, it can be concluded that the flow stress increases with the increasing of volume fraction of α phase at certain strain rate. Secondly, the atomic binding force decreases and the free energy of atoms enhances with the increasing of deformation temperature, which in turn promotes the dislocation slip and the diffusion ability of grain boundaries and finally results in a decrease in flow stress. Meanwhile, it also can be observed from Fig. 2 that the flow stress increases with the increasing strain rate at a certain deformation temperature. This is because the dislocation density increases with the increasing of strain rate and the tangled dislocation structure prevents the movement of dislocation, resulting in the increasing of flow stress. The deformation temperature affects the extent of dynamic softening obviously. As shown in Fig. 2(a and b), an evident dynamic softening effect can be observed at the deformation temperatures below 1103 K. Whereas at high deformation temperatures, the flow stress exhibits a steady-state condition with the increasing of strain after the peak value. In order to realize further the different extents of flow softening, the variation of flow stress softening (Δs ¼ sp ss ) of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with deformation temperatures at different strain rates is quantitatively shown in Fig. 4, in which the flow stress at a strain of 0.8 is
3. Results and discussion 3.1. Flow stress–strain curves Fig. 2 shows the typical flow stress–strain curves of isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy at the deformation temperatures ranging from 993 K to 1183 K and strain rates of
Fig. 1. The micrograph of as-received Ti–5Al–5Mo–5V–1Cr–1Fe alloy.
Table 1 The chemical composition of Ti–5Al–5Mo–5V–1Cr–1Fe alloy (wt%). Al
V
Mo
Cr
Fe
Zr
Si
C
N
O
H
Ti
5.28
5.05
4.88
1.09
1.03
o 0.01
o 0.01
0.032
0.008
0.1
0.001
Bal.
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
250
17
550 -1
500
Strain rate : 0.01 s
Strain rate : 1.0 s
450
200
-1
993 K
150
Flow stress /MPa
Flow stress /MPa
400
993 K
1053 K
100
1103 K
350
1053 K
300 250
1103 K
200 150
50
100
1143K 0 0.0
0.1
0.2
0.3
1183 K
0.4
0.5
0.6
1143 K
0.7
0 0.0
0.8
0.1
0.2
0.3
strain
0.4
0.5
0.7
0.8
250 Deformation temperature: 1183 K
Deformation temperature: 993 K
500
200
-1
400
Flow stress /MPa
5.0 s
-1
1.0 s
-1
300
0.1 s
200
0.01 s
-1
-1
5.0 s
-1
1.0 s
150
-1
100
0.1 s
0.01 s
-1
50
100
0 0.0
0.6
strain
600
Flow stress /MPa
1183 K
50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
strain
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
strain
Fig. 2. The typical stress–strain curves in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy: (a) 0.01 s 1; (b) 1.0 s 1; (c) 993 K and (d) 1183 K.
regarded as the steady-state stress (ss). As evident from Fig. 4, flow softening occurs at all the deformation conditions. It has been reported that the mechanisms of dynamic softening are mainly related to temperature rise, dynamic recovery, dynamic recrystallization or flow instabilities [14–17]. For the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy, most of the plastic power converts to heat and results in temperature rise because of the low thermal conductivity in the deformation process. So the temperature rise in deformation is a main factor of flow softening for the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy. Other softening mechanisms leading to flow softening of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy can be validated through TEM micrographs in Fig. 5. As seen from Fig. 5(a), a number of recrystallized α grains can be observed, this suggests that dynamic recrystallization also contributes to flow softening. Besides of that, an array of parallel dislocation is found inside the β grains in Fig. 5(b), which indicates that dislocation climb occurs. It is well-known that dislocation climb is a typical microstructure characteristic of dynamic recovery. Therefore, it can be concluded that temperature rise, dynamic recrystallization and dynamic recovery contribute to flow softening of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy. Furthermore, it also can be seen from Fig. 4 that the extent of flow softening in αþβ two-phase region is much higher than that in β single-phase region. The reason leading to different extent of flow softening would be attributed to different dynamic softening mechanisms caused by microstructural change. In αþ β two-phase region, α phase in the β matrix prevents the movement of dislocations, resulting in the increasing of stored energy, which is an impetus for the occurrence of various softening mechanisms including dynamic recrystallization, dynamic recovery and so on.
While in β single-phase region, the higher diffusion coefficient in bcc structure of β phase and the existence of more active slip system in comparison to hcp structure of α phase, result in the more feasible occurrence of dynamic recovery and the suppression of dynamic recrystallization.
3.2. Apparent activation energy for deformation In terms of the high temperature deformation theory, the apparent activation energy for deformation represents the magnitude of the energy barrier which the atomic transition needs to overcome. Therefore, the apparent activation energy for deformation has been regarded as an important phenomenological parameter to reflect the workability of metals and alloys. The apparent activation energy (Q) for deformation can be deduced from a kinetic equation [18]: Q ε_ ¼ Asn exp ð1Þ RT where ε_ is the strain rate (s 1), A is the materials' constant, s is the flow stress (MPa), n is the stress exponent, Q is the apparent activation energy for deformation (kJ mol 1), R is the gas constant (kJ mol 1 K 1), and T is the absolute deformation temperature (K). Taking natural logarithm of Eq. (1) and then partial differentiating, the apparent activation energy (Q) for deformation can be obtained in the following: ∂ ln s Δ ln s Q ¼ nR nR ð2Þ ∂ð1=TÞ ε_ ;ε Δð1=TÞε_ ;ε
18
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
Fig. 3. Microstructure of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy at different deformation temperatures and a strain rate of 0.01 s 1 and height reduction of 60%: (a) 993 K, (b) 1053 K, (c) 1103 K and (d) 1183 K.
270
T
240
-1
0.01s -1 0.1 s -1 1.0 s -1 5.0 s
Flow stress /MPa
210 180 150 120 90 60 30 0
1000
1050
1100
1150
1200
Deformation temperature /K Fig. 4. Flow softening effect of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with increasing of deformation temperature at different strain rates.
And the stress exponent n is given in the following: ∂ ln ε_ Δ ln ε_ n¼ ∂ ln sT;ε Δ ln sT;ε
ð3Þ
Fig. 6(a) shows the variation of the flow stress with the deformation temperature at different strain rates. Fig. 6(b) represents the variation of flow stress with strain rate at different deformation temperatures. It can be seen from Fig. 6(a) that the slope between the flow stress and the deformation temperature in αþ β two-phase region is higher than that in β single-phase region. For the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy, the reason would be caused by α-β phase transformation.
Considering the distinction of the slope value between the flow stress and deformation temperature in αþβ two-phase region and β single-phase region, the apparent activation energy for deformation in αþβ two-phase region and β single-phase region is calculated respectively. According to the experimental flow stress–strain curves of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy, the variation of the apparent activation energy for deformation with strain is illustrated in Fig. 7. It can be seen from Fig. 7 that the apparent activation energy for deformation of isothermally compressed Ti– 5Al–5Mo–5V–1Cr–1Fe alloy in αþβ two-phase region decreases from 386.81790 kJ mol 1 to 227.42758 kJ mol 1 with the increasing of strain continuously. It is because that work hardening effect dominates at the beginning of compression, resulting in the difficulty for deformation, which further leads to the increasing of flow stress and high apparent activation energy for deformation. As the compression proceeds, the effect of various softening mechanisms contributes to the more feasibility of deformation, leading to the distinct decreasing of the apparent activation energy for deformation. When the deformation reaches to a certain extent, the effect of work hardening and softening mechanism attains a balanced condition, so the apparent activation energy for deformation does not decrease too much with the increasing of strain. Meanwhile, the average apparent activation energy for deformation reaches 291.73750 kJ mol 1, which is similar to that of Ti-5-5-5-31 alloy obtained by Warchomicka et al. [1] and that of Ti-10-2-3 alloy obtained by Robertson et al. [19]. In β single-phase region, the apparent activation energy for deformation ranges from 214.17 735 kJ mol 1 to 150.05 7 27 kJ mol 1 and the average value attains 179.937 20 kJ mol 1, which is similar to that of self-diffusion of β-Ti (153 kJ mol 1) and that of Ti-5-5-5-3 alloy obtained by Jones et al. (183 kJ mol 1) [9].
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
19
[011]
[011]
Fig. 5. The TEM micrograph illustrating (a) dynamic recrystallization at 1053 K, 1.0 s 1 and (b) dislocation inside the β grains at 1183 K, 0.1 s 1.
6.0 6.0
5.8 5.6
5.7
5.2 5.0 4.8 4.6 4.4
-1
0.01s -1 0.1 s -1 1.0 s -1 5.0 s
4.2 4.0 3.8 3.6
ln(Flow stress /MPa)
ln(Flow stress /MPa)
5.4 993 K 1023K 1053K 1083K 1103K 1123K 1143K 1163K 1183K 1203K
5.4 5.1 4.8 4.5 4.2 3.9 3.6
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0 10.2
-5
-4
-3
-2 -1 0 1 -1 ln(Strain rate /s )
3
1/T 10 /(1/K)
2
3
4
Fig. 6. Variation of the flow stress with (a) deformation temperature and (b) strain rate at a strain of 0.6.
Activation energy for deformation /(kJ mol-1)
500 450
phase region phase region
400
solute content of the Ti–5Al–5Mo–5V–1Cr–1Fe alloy, a slightly higher activation energy for deformation would be reasonable, compared to pure titanium. 3.3. Processing map
350 300 250 200 150 100 0.1
0.2
0.3
0.4
0.5
0.6
0.7
Strain Fig. 7. Variation of the apparent activation energy for deformation of isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with strain.
This suggests that dynamic recovery is the dominant deformation mechanism in β single-phase region. The typical corresponding microstructure in β single-phase region can be validated by Fig. 5 (b), which reveals the occurrence of dislocation climb. And it has been suggested that dislocation climb can be regarded as vacancy diffusion, so the activation energy for deformation should be similar to that of self-diffusion [9]. Considering the increased
The dynamic material model (DMM) takes work-piece as a dissipation of power in high temperature deformation. The instantaneous power P absorbed by the work-piece in plastic flow consists of two complementary parts: dissipator content G and cocontent J, in which the former represents power dissipated by plastic deformation and the latter relates to the metallurgical mechanism. Then the power P absorbed by the work-piece in plastic flow processes can be written as follows: Z s Z P ¼ s_ε ¼ ε_ ds þ sd_ε ¼ J þ G ð4Þ 0
0_ε
And the power partitioning between J and G is given in the following: ∂J ∂ ln s Δ log s ¼ ¼m ð5Þ ∂GT;ε ∂ ln ε_ T;ε Δ log ε_ T;ε where m is the exponent of strain rate sensitivity. Then, the dissipator co-content J can be written in the following: J¼
m s_ε 1 þm
ð6Þ
20
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
caused by α-β phase transformation. A similar phenomenon has been seen in a wide range of materials [22,23]. Fig. 8(b) shows the processing map in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy at a strain of 0.5. It can be seen that there exist two domains with high power dissipation efficiency and an instable domain. Generally speaking, the microstructure evolution in the stable domains is likely to be dynamic recrystallization, dynamic recovery, superplasticity or spheroidizing. Nevertheless, the occurrence of flow instability is usually related to flow localization, adiabatic shear bands or cracking. In order to obtain optimal processing parameters and realize the underlying deformation mechanism in the stable and instable domains, the domains are characterized with microstructures under specific deformation parameters. The first domain with high dissipation efficiency occurs at the deformation temperatures ranging from 993 K to 1029 K and strain rates ranging from 0.01 s 1 to 0.046 s 1. A similar domain at lower deformation temperature and strain rate has also been observed in previous research for Ti–5Al–5Mo–5V–1Cr–1Fe alloy [24]. In the present investigation, the peak efficiency of power dissipation in this domain is about 0.63 at a deformation temperature of 993 K and strain rate of 0.01 s 1, which corresponds to an optimal condition of Ti–5Al–5Mo–5V–1Cr–1Fe alloy. It has been reported that the power dissipation efficiency as high as 6070% implies the occurrence of superplastic deformation because of the correlative value m is about 0.40.5 [22]. Besides, Wang et al. [25] have suggested that an equiaxed, finely grained and stabilized structure is also necessary to the occurrence of superplastic deformation. Considering the prerequisition mentioned above, the corresponding microstructure is exhibited in Fig. 9, from which it can be seen that the equiaxed primary α phase is well-distributed in β matrix, and shows little
The dimensionless parameter power dissipation efficiency η can be defined as the following [20]: η¼
J 2m ¼ J max 1 þ m
ð7Þ
The variation of η with strain rate and deformation temperature constitutes the power dissipation map, which characterizes the microstructure evolution in high temperature deformation. Considering the instability in deformation, a continuum criterion predicting the occurrence of plastic flow instabilities is in the following [21]: ξð_εÞ ¼
∂ log ½m=ð1 þ mÞ þm o 0 ∂ log ε_
ð8Þ
where ξð_εÞ is the instable parameter that varies with the deformation temperature and strain rate. The different values of ξð_εÞ constitutes the instable map. Then, a superimposition of the instable map on the power dissipation map gives a processing map. Fig. 8(a–c) exhibits the processing maps of isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy established at the deformation temperatures ranging from 993 K to 1203 K and strain rates ranging from 0.01 s 1 to 5.0 s 1 at the strains of 0.3, 0.5 and 0.7. The contour numbers represent the power dissipation efficiency and the shaded domain represents the instable region. As seen from Fig. 8(a– c), the strain has a slight influence on the processing map. And both the power dissipation efficiency and instable efficiency at different strains show a similar variation tendency. Moreover, it can be observed from Fig. 8(a–c) that a noticeable change in the power dissipation efficiency map occurs at about β transus temperature ( 1153 K), which could be related to the microstructure evolution
0.20
0.5
0.20 0.23 0.29
0.25 0.30
0.0 -1
-1
log(Strain rate /s )
0.0 log(Strain rate /s )
0.15
0.5
0.20
0.25
T
-0.5
0.38
0.35
-1.0
0.35 0.38 0.40
-1.5
0.50
0.34 0.25
-0.5
T
0.40
-1.0
0.34 -1.5 0.45
0.30
0.45
0.38 1050
1100
1150
1200
-2.0
0.23
1000
1050
Deformation temperature /K
1100
0.25 1150
1200
Deformation temperature /K
0.15 0.20 0.25 0.28 0.30 0.35
0.5
0.0 -1
log(Strain rate /s )
0.29
0.40
0.50
-2.0 1000
0.15
0.10
T -0.5
0.40 -1.0
0.35 -1.5
0.40 -2.0
0.45 1000
0.25
0.30 0.28
0.15
0.20 1050
1100
1150
1200
Deformation temperature /K Fig. 8. Processing map in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy at the strains of (a) 0.3, (b) 0.5 and (c) 0.7.
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
Fig. 9. Micrograph of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy at a deformation temperature of 993 K, height reduction of 40% and strain rate of 0.01 s 1.
21
Fig. 11. Micrograph of the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy at a deformation temperature of 1183 K, height reduction of 40% and strain rate of 1.0 s 1.
60
Temperature rise /K
50
993 K,5.0 s
-1
40
30
20
10 993 K,0.01 s 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-1
Furthermore, an obvious instable domain can be observed in the processing map at a strain of 0.5. When at the deformation temperature below 1008 K, the instable domain occurs almost at the strain rate above 0.046 s 1. With the increasing of deformation temperature, the instable domain shrinks the range of strain rate and only occurs at the strain rates larger of equal than 1.0 s 1. Fig. 11 shows the typical micrograph in the instable domain of Ti–5Al–5Mo– 5V–1Cr–1Fe alloy at a deformation temperature of 1183 K and strain rate of 1.0 s 1. It can be observed from Fig. 11 that the microstructure exhibits obvious flow localization, which is caused by short deformation time in high temperature deformation. Thus, the high temperature deformation of Ti–5Al–5Mo–5V–1Cr–1Fe alloy should not be performed in the above mentioned instable domain.
0.8
Strain Fig. 10. The temperature rise of the isothermally compressed Ti–5Al–5Mo–5V– 1Cr–1Fe alloy at a deformation temperature of 993 K.
difference from the original microstructure in grain size. So it can be deduced that superplastic deformation may contribute to the high power dissipation efficiency. Furthermore, at a deformation temperature of 993 K, with the increasing of strain rate, the power dissipation efficiency decreases continuously until the occurrence of the minimum value at a strain rate of 5.0 s 1. Similar phenomenon has also been reported by Poletti et al. for Ti-5-5-5-3-1 alloy [26]. The lower power dissipation efficiency obtained at a strain rate of 5.0 s 1 suggests that most of the plastic power converts to heat and is dissipated in the form of temperature rise in billet. Fig. 10 shows the temperature rise at a deformation temperature of 993 K and the strain rates of 0.01 s 1 and 5.0 s 1. It can be seen from Fig. 10 that temperature rise at a strain rate of 5.0 s 1 is higher than that at a strain rate of 0.01 s 1. Therefore, the plastic power converting to temperature rise at a strain rate of 5.0 s 1 is higher than that at a strain rate of 0.01 s 1, resulting in the lower power dissipation efficiency at high strain rate. The processing map also exhibits a domain with high power dissipation efficiency in β single-phase region at the deformation temperatures ranging from 1161 K to 1203 K and the strain rates ranging from 0.059 s 1 to 0.21 s 1. The peak efficiency of power dissipation is 0.43 at a deformation temperature of 1183 K and strain rate of 0.1 s 1, which corresponds to optimal processing parameter in the β forging of Ti–5Al–5Mo–5V–1Cr–1Fe alloy. It has been reported that the high stacking fault energy in β single-phase region results in the difficulty for dynamic recrystallization, which is consistent with what shown in Fig. 5(b) that dynamic recovery mainly works at such a deformation condition.
4. Conclusions The isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy is conducted at the deformation temperatures ranging from 993 K to 1203 K, strain rates ranging from 0.01 s 1 to 5.0 s 1 and height reductions ranging from 40% to 70%. The following conclusions can be summarized through the analysis on the flow stress, apparent activation energy for deformation and processing maps: (1). The deformation temperature affects significantly the extent of dynamic softening in the isothermal compression of Ti– 5Al–5Mo–5V–1Cr–1Fe alloy. Meanwhile, temperature rise, dynamic recrystallization and dynamic recovery also contribute to flow softening effect. (2). The apparent activation energy for deformation in the isothermal compression of Ti–5Al–5Mo–5V–1Cr–1Fe alloy is higher than that of self-diffusion of β-Ti in αþβ two-phase region and similar to that of self-diffusion of β-Ti in β singlephase region. In addition, dynamic recovery is the dominant mechanism in β single-phase region of Ti–5Al–5Mo–5V–1Cr– 1Fe alloy. (3). The strain affects the processing map in the isothermally compressed Ti–5Al–5Mo–5V–1Cr–1Fe alloy slightly. And in the processing map at a strain of 0.5, the peak efficiency of power dissipation is 0.63 at a deformation temperature of 993 K and strain rate of 0.01 s 1, the two domains with high efficiency of power dissipation cover the range of 993 1029 K at the strain rates ranging from 0.01 s 1 to 0.046 s 1, and the range of 1161 1203 K at the strain rates ranging from 0.059 s 1 to 0.21 s 1. An instable domain is also observed at all of the deformation temperatures and strain rates larger of equal than 1.0 s 1, in which the main instability mechanism is flow localization.
22
S.F. Liu et al. / Materials Science & Engineering A 589 (2014) 15–22
References [1] F. Warchomicka, C. Poletti, M. Stockinger, Mater. Sci. Eng. A 528 (2011) 8277–8285. [2] F. Warchomicka, M. Stockinger, H.P. Degischer, J. Mater. Process. Technol. 177 (2006) 473–477. [3] X. Wang, M. Jahazi, S. Yue, Mater. Sci. Eng. A 434 (2006) 188–193. [4] R.C. Picu, A. Majorell, Mater. Sci. Eng. A 326 (2002) 306–316. [5] A. Momeni, S.M. Abbasi, Mater. Des. 31 (2010) 3599–3604. [6] J.K. Fan, H.C. Kou, M.J. Lai, et al., Mater. Des. 49 (2013) 945–952. [7] H. Li, M.Q. Li, T. Han, et al., Mater. Sci. Eng. A 546 (2012) 40–45. [8] V.V. Balasubrahmanyam, Y.V.R.K. Prasad, Mater. Sci. Eng. A 336 (2002) 150–158. [9] N.G. Jones, R.J. Dashwood, D. Dye, et al., Mater. Sci. Eng. A 490 (2008) 369–377. [10] W.J. Jia, W.D. Zeng, Y.G. Zhou, et al., Mater. Sci. Eng. A 528 (2011) 4068–4074. [11] S.V. Zherebtsov, M.A. Murzinova, M.V. Klimova, et al., Mater. Sci. Eng. A 563 (2013) 168–176. [12] C. Li, X.Y. Zhang, K.C. Zhou, et al., Mater. Sci. Eng. A 558 (2012) 8277–8285. [13] C. Li, X.Y. Zhang, Z.Y. Li, et al., Mater. Sci. Eng. A 573 (2013) 75–83.
[14] S.L. Semiatin, V. Seetharaman, I. Weiss, Mater. Sci. Eng. A 263 (1999) 257–271. [15] L.X. Li, Y. Lou, L.B. Yang, Mater. Des. 23 (2002) 451–457. [16] N.-K. Park, J.-T. Yeom, Y.-S. Na, J. Mater. Process. Technol. 130–131 (2002) 540–545. [17] L. Li, J. Zhou, J. Duszczyk, J. Mater. Process. Technol. 172 (2006) 372–380. [18] M.Q. Li, H.S. Pan, Y.Y. Lin, et al., J. Mater. Process. Technol. 183 (2007) 71–76. [19] D.G. Robertson, H.B. McShane, Mater. Sci. Technol. 14 (1998) 339–345. [20] Y.V.R.K. Prasad, H.L. Gegel, S.M. Doraivelu, et al., Metall. Trans. A 15 (1984) 1883–1892. [21] Y.V.R.K. Prasad, S. Sasidhara, Hot Working Guide: A Compendium of Processing Maps, ASM International, Materials Park, OH (1997) 25–157. [22] T. Seshacharyulu, S.C. Medeiros, W.G. Frazier, et al., Mater. Sci. Eng. A 284 (2000) 184–194. [23] X.Y. Zhang, M.Q. Li, H. Li, et al., Mater. Des. 31 (2010) 2851–2857. [24] X. Zhao, H. Zhao, R. Zhang, et al., Adv. Mater. Res. 490–495 (2012) 3423–3426. [25] K.X. Wang, W.D. Zeng, Y.Q. Zhao, et al., J. Mater. Sci. 45 (2010) 5883–5891. [26] C. Poletti, F. Warchomicka, M. Dikovits, et al., Mater. Sci. Forum 710 (2012) 93–100.