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The research on the constitutive modeling and hot working characteristics of as-cast V–5Cr–5Ti alloy during hot deformation
Journal of Alloys and Compounds 663 (2016) 552e559
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The research on the constitutive modeling and hot working characteristics of as-cast Ve5Cre5Ti alloy during hot deformation F.S. Qu*, Z.Y. Reng, R.R. Ma, Z.H. Wang, D.M. Chen Institute of Materials, China Academy of Engineering Physics, 9 Huafeng Street, Jiangyou, Mianyang 621908, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 August 2015 Received in revised form 8 November 2015 Accepted 4 December 2015 Available online 11 December 2015
Isothermal compression tests of as-cast Ve5Cre5Ti vanadium alloy are conducted in the deformation temperature ranging from 1150 to 1400 C with an interval of 50 C, strain rate ranging from 0.001 to 1 s1 and height reductions of 55% on a computer controlled thermal simulation machine. The hot deformation behavior of as-cast is characterized based on the analysis of the stressestrain behaviors, the constitutive equations and process map for obtaining optimum processing parameters and achieving desired microstructure during hot working. A constitutive equation by which the flow stress was expressed as a function of strain rate and deformation temperature was established and the apparent activation energy of deformation was calculated to be 428.480 kJ/mol. The processing maps are constructed at the true strain of 0.5 and 0.7 based on dynamic materials model (DMM) to delineate the safe and unsafe regions in the axes of temperature and strain rate. The area of unsafe region increases with the increasing of strain. These instability domains exhibited localized flow and cracking along grain boundaries which should be taken care of during hot processing. The recommended domain is in the condition of the temperature range of 1250e1400 C and strain rate range of 0.001e0.02 s1. And in this state the main soften mechanism is dynamic recovery. It is worth noting that when as-cast Ve5Cre5Ti alloys deformed in the recommended deformation zone, the continuous dynamic recrystallization occurred, which display the feature of serrate grain boundaries and the equiaxed grains in the grain boundaries. Microstructure observation of deformed specimens validated the applicability of the processing map at obtaining the optimum processing parameters of as-cast Ve5Cre5Ti alloy. © 2015 Elsevier B.V. All rights reserved.
Keywords: Ve5Cre5Ti alloy Hot deformation Processing map Constitutive equation Microstructure
1. Introduction Vanadium-based alloys are considered as one of the candidate structural materials for fusion reactors because of their attractive properties such as low radiation-induced activation, high thermal conductivity, low thermal expansion, excellent high temperature performance and superior resistance against radiation-induced swelling [1e4]. The focus of researches for VeCreTi alloy concentrates on V-(4e5)Cr-(4e5)Ti alloys. Ve5Cre5Ti alloy is commonly produced by vacuum consumable arc melting (VAR), which is characterized by coarse grains. The grains in the ingots may reach millimeter level. At the same time, that the alloy solidified in a water-cooled copper crucible with a great solidification rate results in the large residual stress in the alloy ingot. Therefore, as-cast Ve5Cre5Ti alloys with poor mechanical properties require the
* Corresponding author. E-mail address: [email protected] (F.S. Qu). http://dx.doi.org/10.1016/j.jallcom.2015.12.014 0925-8388/© 2015 Elsevier B.V. All rights reserved.
reasonable hot pressure work, cold rolling and heat treatment processing to improve the microstructure and performance, which makes it meet engineering requirements of the fusion reactor. The deformation capacity of as-cast Ve5Cre5Ti alloy is relatively limited even at high temperature. In the actual thermal deformation processing, the instability phenomena can be easily generated such as crack. Therefore, it is very important for as-cast Ve5Cre5Ti alloy how to optimize hot pressure working parameters. The researches on the hot deformation behavior of as-cast Ve5Cre5Ti alloy in the actual process will result in higher costs, longer approach period and greater technical challenge. Unfortunately, the research efforts on VeCreTi alloys have mainly been focused on the irradiation properties [5,6], the thermal creep properties [7e9], the welding performance [10e12], effects impurity such as oxygen on properties of vanadium-based alloys [13e15], etc. Few researches have been focused on hot deformation behavior for as-cast Ve5Cre5Ti alloy. X.Z. Yu et al. [16] studied the thermal deformation performance of as-cast Ve5Cre5Ti alloy by uniaxial hot
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compression method at temperature range of 1150e1250 C and strain rate of 10 s1. The reasonable hot working parameters of the alloy are discussed from the surface cracks of the specimens. But the hot deformation performance of as-cast Ve5Cre5Ti alloy has not been studied systematically such as the constitutive equation, processing maps, etc. With the rapid development of computer technology, finite element method (FEM) has played on an important role in reducing the amount of experiments and improving work efficiency. And the establishment of the accurate hot deformation constitutive model is the key to improve the precision of the numerical simulation result. Therefore, the establishment of hot deformation constitutive equation for as-cast Ve5Cre5Ti alloys can provide the accurate basis for the optimization researches by subsequent numerical simulation. In addition, the processing map based on the dynamic material model (dynamic materials model, DMM) which was developed by Prasad et al. [17] is widely used to predict the thermal processing defects, the improvement of the workability of materials, the control of heat processing microstructure of materials and the research of performance and deformation mechanism, etc. In the present, the processing map has been applied to titanium alloy [18e21], magnesium alloy [22], stainless steel [23], nickel alloy [24], iron-base super alloy [25], etc. The effectiveness of processing map has been verified by the results of microstructure observation. Thus in the present work, the hot deformation constitutive equation and the processing maps of ascast Ve5Cre5Ti alloy are established to optimize hot processing parameters of as-cast Ve5Cre5Ti alloy by the stressestrain curves of hot deformation experiment. Through observing the microstructure before and after hot deformation of as-cast Ve5Cre5Ti alloy, the availability of the process maps is proved. This is very important to develop hot pressure processing parameters of as-cast Ve5Cre5Ti alloy and effectively control and improve performance and quality of the components.
2. Materials and experimental methods Ve5Cre5Ti alloy rod used in the hot compression experiment is obtained after twice vacuum consumable arc melting. The chemical composition of Ve5Cre5Ti alloy is Cr (4.78e4.82%), Ti (4.79e5.21%), O (450 wppm), N (50e60 wppm), C (60 wppm), and balance V. The alloy samples are taken from the equiaxed grain zone of cast ingot, which are shown in Fig. 1. The alloy is machined as F10 mm 12 mm cylindrical test specimen. The specimens are resistance heated to the deformation temperature at a heating rate of 7 C/s and held at that temperature for 120s by thermo-coupledfeedback-controlled AC current. The compression tests corresponding to a height reduction 55% are carried out six temperatures
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of 1150 C, 1200 C, 1250 C, 1300 C, 1350 C and 1400 C and four strain rates of 0.001 s1, 0.01 s1, 0.1 s1 and 1 s1. After each compression, the deformed specimens are rapidly quenched with water to retain the recrystallized microstructures. The cutting surfaces are parallel to the axial direction of the compression. The cut surfaces are prepared by using standard polishing and etching techniques for optical microstructure examination. During the compression process, the variations of stress and strain are monitored continuously by a personal computer equipped with an automatic data acquisition system. The true stress and true strain are derived from the measurement of nominal stressestrain relationship according to the following formula: sT ¼ sN ð1 þ εN Þ, εT ¼ lnð1 þ εN Þ, where sT is true stress, sN is nominal stress, εT is true strain and εN is nominal strain [26].
3. Results and discussion 3.1. The stressestrain curves The flow stress curves of as-cast Ve5Cre5Ti alloy obtained at various deformation temperatures (1150, 1200, 1250, 1300, 1350, 1400) and different strain rates (0.001, 0.01, 0.1, 1 s1) are shown in Fig. 2. The shapes of the curves indicate some features that help in identifying the mechanisms of hot deformation. It is shown that the flow stress increases with increasing strain rate and decreasing temperature. Some other typical characteristics of stressestrain curves in the temperature and strain rate ranges are observed. The results reveal that all the true stressestrain curves show the characteristics of the strain hardening at a small true strain, which leads to a pronounced peak stress. Subsequently, there are some curves in which a slow softening occurs (such as 1150 C, 0.001 s1) with the increasing strain, followed by a steady state flow at the large strain. There are other curves (such as 1400 C, 0.001 s1 and 1350 C, 0.1 s1) in which the steady state flowing occurs. Such steadyestate curves indicate that the mechanism of work hardening is balanced by the rate of softening which may be induced by the mechanisms like DRX, DRV, or SP occurring at very high rates [27]. In the initial stage, the work hardening is caused by the increment of dislocation density and the formation of poorly developed subgrain boundaries [28]. With the increasing strain, the effect of work hardening can be partially neutralized by occurrence of dynamic softening mechanisms, which leads to the decrease of the flow stress. At last, a steadyestate flow stress can be reached when the work hardening and dynamic softening mechanism, such as dynamic recovery (DRV) and dynamic recrystallization (DRX), can occur simultaneously during hot deformation. In addition, it was interesting to note that these curves exhibit
Fig. 1. Microstructure of Ve5Cre5Ti alloy before hot compression deformation: (a) microstructure for as-cast ingot; (b) microstructure in equiaxed area.
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Fig. 2. Curves of true stressestrain for Ve5Cre5Ti alloy under different conditions: (a) 0.001 s1; (b) 0.01 s1; (c) 0.1 s1; (d) 1 s1.
significant serrations in flow stress as a function of strain, which is more obvious with increasing strain rates, as shown in Fig. 2. The occurrence of dynamic strain aging (DSA) is considered as an important factor producing this serration at most of the temperature and strain rates [29], which is in accordance with the research result addressed by Cui et al. [30]. Moreover, the occurrence of DSA during hot working process has an influence on the flow behavior and even the final microstructure of the product [31]. But the actual mechanism which dominates in the different processes of microstructural evolution still needs further analysis of the flow stress data as a function of temperature and strain rate and microstructural examination, and these will be discussed in detail subsequently.
3.2. The constitutive equations In order to understand the hot plastic deformation behavior of Ve5Cre5Ti alloy, the flow curves obtained by the hot compression tests are analyzed to determine the constitutive equation. Based on the phenomenological approach developed for creep deformation [32], the constitutive equation can be expressed as
Z ¼ A½sinhðasÞn
(1)
where s is the flow stress (MPa); a, A and n are the material parameters, Z is the Zener-Hollomon parameter defined as
Q Z ¼ ε_ exp RT
(2)
where ε_ is the strain rate (s1), Q is the apparent activation energy of deformation (kJ/mol), R is the gas constant (8.314 J/(molK)), T is the absolute deformation temperature (K). From Eqns (1) and (2), the stress exponent, n is defined by
n¼
! v ln ε_ v ln½sinhðasÞ
(3)
T
And the activation energy Q can be defined as
Q¼
Rnv ln sinðasÞ vð1=TÞ ε_
(4)
The constant a is determined by the slop coefficients of ln ε_ versus s (peak stress) and ln ε_ versus ln s (peak stress), as is shown in Fig. 3. The a value is 0.00837766 MPa1. The fitting curves of ln½sinhðasÞ versus ln ε_ and ln½sinhðasÞ versus 1=T are shown in Fig. 4. From Fig. 4, the activation energy of V-5Cr-5Ti alloy is determined to be 428.47972 kJ/mol. According to Eqns. (1) and (5) can be obtained
ln Z ¼ n ln½sinhðasÞ þ ln A
(5)
Fig. 5 shows the plots of ln Z versus ln sinðasÞ. From Fig. 5, the n is 4.42602 by calculation and lnA is 27.6614. The constitutive equation for Ve5Cre5Ti alloy may be written as:
ε_ ¼ 1:0357 1012 ½sinhð0:0083776sÞ4:42602 expð 428:4797=RTÞ
(6)
The flow stress can be described with expression containing Z parameter as:
s ¼ 119:3659 ln
8 <Z 0:22593 : A
" #1 9 2= Z 0:45187 þ þ1 ; A
(7)
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Fig. 3. Relationships between peak stress and strain rate: (a) s ln_ε; (b) ln s ln_ε.
Fig. 4. Relationship of ln½sinhðasÞ ln_ε and ln½sinhðasÞ T 1 .
deforming. The total power dissipated per unit volume P, is given by
Z ε_ P ¼ s_ε ¼ G þ J ¼
Zs
Fig. 5. Relationship between ln Z and ln ½sinhðasÞ.
3.3. The processing map for as-cast Ve5Cre5Ti alloy In DMM model proposed by Prasad and Gegel, the flow behavior of the material undergoing thermoplastic deformation can be described as dissipative, nonlinear, dynamic, irreversible, and away from equilibrium [33e37]. DMM theory considers thermoplastic forming process as a system and workpiece undergoing deformation as a dissipater of power (not a storage element). According to this model, the system consists of a source of power, a store of power (tool) and a dissipater (workpiece), which dissipates energy while
ε_ ds
sd_ε þ 0
(8)
0
where s is instantaneous flow stress, ε_ is applied strain rate. At ant moment, the total power dissipation P consists of two complimentary functions, G content represents the major power input dissipated in the form of a temperature rise, and J co-content represent the power through metallurgical process such as dynamic recovery, dynamic recrystallization, cavity formation, super plastic flow and phase transformations. As a constant temperature, the instantaneous response (s) of workpiece material to the applied strain rate (_ε) for creating a large plastic strain is given by the dynamic constitutive equation s ¼ K ε_ , where K is a stress coefficient, ε_ strain rate, m strain rate sensitivity. The power partitioning between G and J is controlled by constitutive flow behavior of material and decided by strain rate sensitivity (m) as given below
m¼
dJ ð_εdsÞ dlgs ¼ ¼ dG ðsd_εÞ dlg_ε
(9)
J co-content is given by
Zs ε_ ds ¼
J¼ 0
ms_ε mþ1
(10)
where ε_ is the strain rate and m is the strain rate sensitivity. For an ideal linear dissipater, m ¼ 1 and Jmax ¼ s_ε=2.
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The power dissipation capacity of metals during deformation can be properly measured by the efficiency of dissipation (h) defined by Eqn. (11). The variation of h with temperature and strain rate constitutes power dissipation map. The various domains in the power dissipation map may be correlated with specific microstructure mechanisms.
h¼
J 2m ¼ Jmax m þ 1
(11)
A continuum instability criterion based on the extremum principle of irreversible thermodynamics as applied to large plastic flow is used in this study to identify the regimes of flow instabilities. The principle of maximum rate of entropy production in the metallurgical system results in an instability criterion (as Eqn. (12)) given by Prasad in 1987 [21]. The variation of instability parameter xð_εÞ with temperature and strain rate constitutes an instability map.
xð_εÞ ¼ vlgðm=ðm þ 1ÞÞ=vlg_ε þ m 0
(12)
The superimposed map is called a processing map, on the basis of which metal working process may be designed and controlled to optimize hot workability and to produce desired microstructures. This methodology has applied for various materials. According to Eqns. (11) and (12), the processing maps of Ve5Cre5Ti alloy in the deformation range of 1150e1400 C and strain rate of 0.001e1 s1 at the true strain of 0.5 and 0.7 is developed in Fig. 6 (a) and (b) which consist of a superimposition of the power dissipation map and instability map indicating the safe domain and unsafe domain during the plastic processing. In those figures, the iso-efficiency contours represent the efficiency value of power dissipation, and the shaded regions represent the unstable regions (the values of xð_εÞ are negative). From Fig. 6, it is found that instability regions increases with the increasing of strain, indicating that the strain has a significantly effect on the processing maps. In the safe areas in Fig. 6, there are common regions which are marked by the red dotted line with high values of h, which owns to greater dimension occurring at the temperature and strain rate (1250e1400 C, 0.001e0.02 s1). The range of h values is about 0.32e0.44. In Fig. 6, there are other safe regions but the areas is too small or the values of h is lower. So, the processing parameters in the actual forging are selected in the range of the temperature and strain rate (1250e1400 C, 0.001e0.02 s1) while those in the range of unsafe regions such as the temperature of 1150 C and strain rate of 0.1 s1, the temperature of 1400 C and strain rate of 1 s1 et al. The region of the processing map could be interpreted based on the characteristic efficiency variation associated with the microstructure mechanisms. To investigate the microscopic deformation
mechanisms and verify the reliability of process parameters predicted by processing maps, the evidence of deformation in these domains are identified and validated through microstructure observations in the following sections. 3.4. Discussion for processing maps by microstructure 3.4.1. Stability domains It can be seen from Fig. 6 that efficiency of power dissipation decreases with the increasing strain rates as a whole. Similarly, the efficiency of power dissipation of Ti-alloy decreased with the increasing of strain rate as expected by Prasad et al. [17]. And it can be also seen from Fig. 6 that the efficiency of increases with the increasing temperature as a whole. In Fig. 6 (a) and (b), the recommended deformation zone of the processing maps with different strain is indicated by red dotted line, respectively. And integrating from Fig. 6 (a) and (b), that the hot deformation occurs at the temperature range from 1250 to 1400 C and the strain rate range from 0.001 to 0.02 s1 is recommended. At this time, the deformation own to greater efficiency, which the efficiency of power dissipation is at the range of 0.30e0.44. In addition, there are some narrower stability domains such as the deformation range from 1225 to 1250 C and strain rate range from 0.001 to 0.0016 s1. However, the deformation parameters range of this deformation zone is narrower, which is not conducive to the actual operation. Therefore, from a practical point of view, the optimum condition for hot processing of as-cast Ve5Cre5Ti vanadium alloy is in the condition of the temperature range of 1250e1400 C and strain rate range of 0.001e0.02 s1. In this condition, the efficiency of power dissipation is higher and the area of stability domains is greater. Generally speaking, microstructure evolution of stable region may be dynamic recrystallization, superplasticity, spheroidizing and dynamic recovery. It is widely recognized that high peak power dissipation efficiency is often associated with dynamic recrystallization [27] or superplasticity. To investigates the microscopic deformation mechanisms and verify the reliability of processes parameters predicted by the processing maps, the microstructures of the specimen deformed under the specific parameters at the stable deformation zones are characterized and analyzed. The microstructures of the specimens deformed at the stable domains are shown in Fig. 7. From Fig. 7, the dynamic recrystallization grains occur in the deformed specimen. It is seen that, in the certain strain rate, the recrystallization grains increase with increasing deformation temperature, such as Fig. 7 (a), (b) and (e). It further indicates that the deformation temperature range of 1250e1400 C are correspondent to an optimal deformation condition of as-cast Ve5Cre5Ti alloy. This is in a good agreement with
Fig. 6. The processing maps developed at the different strains: (a) 0.5; (b) 0.7.
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Fig. 7. Microstructure of the specimens deformed in the stability domains for Ve5Cre5Ti alloy: (a) T ¼ 1250 C, ε_ ¼ 0:001s1 ; (b) T ¼ 1300 C, ε_ ¼ 0:001s1 ; (c) T ¼ 1300 C, ε_ ¼ 0:01s1 ; (d) T ¼ 1350 C, ε_ ¼ 0:01s1 ; (e) T ¼ 1400 C, ε_ ¼ 0:001s1 ; (f) T ¼ 1400 C, ε_ ¼ 0:01s1 .
the results from processing maps. Fig. 7 (b), (c) and Fig. 7(e), (f) shows the microstructures of the specimens deformed at 1300 C and 1400 C at different strain rates corresponding to 0.001 and 0.01 s1. It can be seen from Fig. 7 (b), (c) and Fig. 7 (e), (f) that the recrystallization grains sizes decrease with increasing strain rates. This is because that there is no sufficient time for dynamic recrystallization at high strain rate corresponding to that at low strain rate. This phenomenon which, the grain size increasing with the temperature increasing and the strain rate decreasing can be explained by Ref. [38].
tE ¼ hdn R
(13)
where h is a constant, tE is the flow stress, dR is the grain size. Because the increase of the strain rate will cause tE to increase, the increase of strain rate can lead to the generation of fine dynamic recrystallization grains. And the increase of the temperature will cause tE to decrease, so the increase of temperature can lead to the generation of great dynamic recrystallization grains. Moreover, the high temperature is conducive to the grain boundary movement, which leads to the greater recrystallization grain. From Fig. 7, it can be seen that the grains are elongated due to deformation, and grain
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boundaries are irregular, which presents typical dynamic recovery feature. Sivakesavam and Prasad [39] pointed out that the dynamic recrystallization may be considered to consist of two competing processes: formation of interfaces (nucleation), and migration of interfaces (growth), the nucleation consists of the formation of grain boundary due to the dislocation generation simultaneous recovery and rearrangement. However, it is difficult to see from Fig. 7 that there are no obvious processes for nucleation and growth occurring during hot deformation of as-cast Ve5Cre5Ti alloy. Thus the microstructure revealed by Fig. 7 is a continuous recrystallization with serrated grain boundaries, which is attributed to substructure occurred at lower strain rates (0.1 s1), as mentioned in Ref. [40]. Thus, it can be concluded from Fig. 7 that the main soften mechanism of as-cast Ve5Cre5Ti alloy during hot deformation is dynamic recovery, the microstructure after plastic deformation is constituted of flat elongated grains and continuous recrystallization grains of indention on the grain boundary. These microstructures also confirm that steadyestate flow and flow soften features of stressestrain curves display the phenomena of dynamic recovery and continuous recrystallization, respectively. In addition, the deformation of as-cast Ve5Cre5Ti alloy can be more stable at higher temperatures and lower strain rates by means of the analysis of the process maps and microstructure, which shows that the deformation ability of the cast Ve5Cre5Ti alloy is limited. In the actual process, the cogging of as-cast Ve5Cre5Ti alloys can adopt the water pressure machine, the hydraulic machine and vacuum isothermal billet. 3.4.2. Instability domains It is well known that instability mechanism is probably associated with cracking, localized plastic flow and adiabatic shear bands [41]. From Fig. 6, it can be obviously that the instability domains expand with the increase of strain. The microstructure manifestation of instability domains regarding the present alloy is shown in Fig. 8 which corresponds to specimen deformed at 1150 C/1 s1 and 1250 C/1 s1. Fig. 8(a) exhibits the cracks along the grain boundaries. In the hot deformation process of metal materials, the critical dislocation density of the dynamic recrystallization can be influenced by the strain rate. Roberts and Ahlblom [42] proposed a formula of critical dislocation density rc of DRX is:
rc ¼
20gi ε_ 3blMt2
1=3 (14)
where gi is grain boundary energy, J/m2; b is Burgers vector of
mold, m; l is subgrain size, m; M is grain boundary migration rate, m/s; and t is dislocation lines energy, N; ε_ is the strain rate. By Eqn. (13), the increase of strain rate will make the critical dislocation density of dynamic recrystallization grow up. This will make dynamic recrystallization difficult and lead to the higher dislocation density at the grain boundary. This will result in the stress concentration at grain boundaries and then cause cracking. Fig. 8 (b) exhibits the bands of flow localizations. From Fig. 2, there are serrated fluctuations on the stressestrain curves of Ve5Cre5Ti alloy and the phenomenon is caused by dynamic strain aging (DSA). The greater the strain rates are, the more obvious the effects of dynamic strain rate are. DSA is a micro-process occurring in plastic deformation of the alloy, which is caused by the interaction of the solute atoms and the motion of dislocation [43]. DSA is easy to cause the material strain rate sensitivity and strain localization [44]. In addition, when the strain rate of the Ve5Cre5Ti alloy increases, adiabatic deformation heat generated during hot working can not be conducted due to insufficient deformation time. Therefore, flow instability is induced by the bands of flow localization, which is undesired in obtaining consistent mechanism and thus should be avoided during processing. Through the above analysis, the thermal process of as-cast Ve5Cre5Ti alloy should be avoided in the above-mentioned unstable regions which contain the deformation at temperature of 1150e1225 C and strain rate of 0.00126e1 s1 and at the temperature range of 1150e1225 C and the strain rate of 0.00126e1 s1 and at the temperature range of 1225e1400 C and the strain rate of 0.1e1 s1.
4. Conclusions The hot deformation behavior and the corresponding microstructure of as-cast Ve5Cre5Ti vanadium alloy were investigated in the temperature range of 1150e1400 C and strain rate of 0.001e1 s1. The following conclusions have been drawn from this investigation: (1) The peak stress can be described by hyperbolic sine-type equation and the hot activation energy of the alloy is about 428.480 kJ/mol. (2) According to the processing map, the optimum processing parameters for good workability are obtained in the temperature range of 1250e1400 C and strain rate range of 0.001e0.02 s1. Microstructure observations reveal that dynamic recrystallization occurred in the optimum conditions.
Fig. 8. Microstructure of the specimens deformed in the instability domains for Ve5Cre5Ti alloy: (a) T ¼ 1150 C, ε_ ¼ 1s1 ; (b) T ¼ 1250 C, ε_ ¼ 1s1 .
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The main soften mechanism is dynamic recovery in the optimum conditions. (3) The flow instability is predicted to occur at two regions. The first region is located in the temperature range of 1150e1225 C and strain rate range of 0.0012e0.1 s1, and the second region is located in the temperature range of 1150e1400 C and the strain rate range of 0.1e1 s1. The instability domains expand with the increase of strain. These instability domains exhibited localized flow and cracking along grain boundaries. The unstable regions must be avoided in the hot working processing of the alloy. References [1] H. Matsui, K. Fukumoto, D.L. Smith, H.M. Chung, W. VanWitzenburg, S.N. Votinov, J. Nucl. Mater. 92 (1996) 233e237. [2] H.M. Chung, B.A. Loomis, D.L. Smith, J. Nucl. Mater. 239 (1996) 139. [3] Xingzhe Yu, Yueqing Song, Shun Cui, Ming Li, Dev. Appl. Mater. 6 (2006) 36e40. [4] E.E. Bloom, R.W. Conn, J.W. Davis, et al., J. Nucl. Mater. 17 (1984) 122e123. [5] D.S. Gelles, J. Nucl. Mater. 283e287 (2000) 344e348. [6] E.V. van Osch, M.I. de Vries, J. Nucl. Mater. 271&272 (1999) 162e166. [7] D.S. Gelles, M.B. Toloczko, R.J. Kurtz, J. Nucl. Mater. 367e370 (2007) 869e3875. [8] R.J. Kurtz, M.L. Hamilton, J. Nucl. Mater. 283e287 (2000) 628e632. [9] K. Natesan, W.K. Soppet, A. Purohit, Uniaxial creep behavior of V-4Cr-4Ti alloy, J. Nucl. Mater. 307e311 (2002) 585e590. [10] C.B. Reed, K. Natesan, Z. Xu, D.L. Smith, The effect of laser welding process parameters on the mechanical and microstructural properties of V-4Cr-4Ti structural materials, J. Nucl. Mater. 283e287 (2000) 1206e1209. [11] Zhiyue Xu, Ken Natesan, Claude B. Reed, Dale L. Smith, Procedure development of laser welding of V-4Cr-4Ti alloy, Int. J. Refract. Metal. Hard Mater. 18 (2000) 231e236. [12] M.L. Grossbeck, J.F. King, T. Nagasaka, S.A. David, Gas tungsten arc welding of vanadium alloys with impurity control, J. Nucl. Mater. 307e311 (2002) 1590e1594. [13] Richard J. Kurtz, Effect of oxygen on the crack growth behavior of V-4Cr-4Ti at 600 C, J. Nucl. Mater. 283e287 (2000) 822e826. [14] B.A. Pint, J.R. DiStefano, Oxygen embrittlement of vanadium alloys with and without surface oxide formation, J. Nucl. Mater. 307e311 (2002) 560e565. [15] A.N. Tyumentsev, A.D. Korotaev, Yu P. Pinzhin, S.V. Ovchinnikov, I.A. Ditenberg, A.K. Shikov, M.M. Potapenko, V.M. Chernov, Effect of internal oxidation on the microstructure and mechanical properties of vanadium alloys, J. Nucl. Mater. 367e370 (2007) 853e857. [16] Xingzhe Yu, Yutqing Song, Sun Cui, Ming Li, Zengde Li, Chin. J. Rare Met. 32 (6) (2008) 705e708. [17] Y.V.R.K. Prasad, H.L. Gegel, S.M. Doraivelu, J.C. Malas, J.T. Morgan, K.A. Lark, D.R. Barker, Metall. Trans. A15 (1984) 1883e1892.
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[18] Weidong Zeng, Yiyang Zhou, Ying Shu, Yongqing Zhao, Jin Yang, Xuemin Zhang, A study of hot deformation in Ti-40 burn resistant titanium alloy using processing maps, Rare Metal. Mater. Eng. 36 (2007) 1e5. [19] Yuanfei Han, WeiDong Zeng, Yunlian Qi, Yongqing Zhao, Optimization of forging process parameters of Ti600 alloy by using processing map, Mater. Sci. Eng. A 529 (2011) 393e400. [20] Xiaona Peng, Hongzhen Guo, Zhifeng Shi, Chun Qin Zhanglong Zhao, Zekun Yao, Study on hot deformation behavior of TC4-DT alloy with equiaxed aþb starting structure based on processing map, Mater. Sci. Eng. A 605 (2014) 80e88. [21] Y.V.R.K. Prasad, T. Seshacharyulu, Processing maps for hot working of titanium alloys, Mater. Sci. Eng. A 243 (1998) 82e88. [22] Juqiang Li, Juan Liu, Zhenshan Cui, Characterization of hot deformation behavior of extruded ZK60 magnesium alloy using 3D processing maps, Mater. Des. 56 (2014) 889e897. [23] Enxiang Pu, Wenjie Zheng, Jinzhong Xiang, Zhigang Song, Ji Li, Hot deformation characteristic and processing map of superaustenitic, Mater. Sci. Eng. A 598 (2014) 174e184. [24] Hongbin Zhang, Kaifeng Zhang, Zhen Lu, Changhong Zhao, Xiaoli Yang, Hot deformation behavior and processing map of a g'-hardened nickel-based superalloy, Mater. Sci. Eng. A 604 (2014) 1e8. [25] J.U. Quan, L.I. Dianguo, L.I.U. Guoquan, Acta Metall. Sin. 42 (2006) 218e224. [26] G.Z. Quan, L. Zhao, T. Chen, Y. Wang, Y.P. Mao, W.Q. Lv, J. Zhou, Mater. Sci. Eng. A 538 (2012) 364e373. [27] T. Seshacharyulu, S.C. Medeiros, W.G. Frazier, Y.V.R.K. Prasad, Mater. Sci. Eng. A 284 (2000) 184e194. [28] D. Cai, L. Xiong, W. Liu, G. Sun, M. Yao, Mater Charact. 58 (2007) 941e946. [29] H. Jiang, Q. Zhang, X. Chen, Z. Chen, Z. Jiang, X. Wu, J. Fan, Acta Mater. 55 (2007) 2219e2228. [30] C. Cui, Y. Cu, Y. Yuan, H. Harada, Scr. Mater. 64 (2011) 502e505. [31] S. Serajzadeh, Mater. Lett. 57 (2003) 4515e4519. [32] C.M. Sellars, W.J. Mctegart, On the mechanism of hot deformation, Acta Metall. 14 (9) (1966) 1136. [33] Y.V.R.K. Prasad, K.P. Rao, Mater. Sci. Eng. A 487 (2008) 316e327. [34] Y.V.R.K. Prasad, K.P. Rao, Mater. Sci. Eng. A 391 (2005) 141e150. [35] S. Anbuselvan, S. Ramanathan, Mater. Des. 31 (2010) 2319e2323. [36] G. Ganesan, K. Raghukandan, R. Karthikeyanm, J. Mater. Process. Technol. 166 (2005) 423e429. [37] G. Jagan Reddy, N. Srinivansan, Amol A. Gokhale, B.P. Kashyap, J. Mater. Process. Technol. 209 (2009) 5964e5972. [38] Weimin Mao, Xinbing Zhao, Recrystallization and Grain Growth of Metals[M], Metallurgical Industry Press, Beijing, 1994, pp. 197e216. [39] O. Sivakesavam, Y.V.R.K. Prasad, Mater. Sci. Eng. A 362 (2003) 118e124. [40] W.D. Zeng, B. Xu, D.H. He, et al., Rare Metal. Mater. Eng. 36 (2007) 592e596 (in Chinese). [41] M. Srinivansan, C. Loganathan, R. Narayanasamy, V. Senthilkumar, Q.B. Nguyen, M. Gupta, Mater. Des. 47 (2013) 449e455. [42] W. Roberts, B. Ahlblom, Acta Metall. 26 (5) (1978) 801e813. [43] A.H. Cottrell, Dislocation and Plastic Flow in Crystals, Oxford University Press, London, 1973, pp. 41e649. [44] R.A. Mulford, U.F. Kocks, Acta Metall. 27 (1979) 1125.
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
The research on the constitutive modeling and hot working characteristics of as-cast Ve5Cre5Ti alloy during hot deformation F.S. Qu*, Z.Y. Reng, R.R. Ma, Z.H. Wang, D.M. Chen Institute of Materials, China Academy of Engineering Physics, 9 Huafeng Street, Jiangyou, Mianyang 621908, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 August 2015 Received in revised form 8 November 2015 Accepted 4 December 2015 Available online 11 December 2015
Isothermal compression tests of as-cast Ve5Cre5Ti vanadium alloy are conducted in the deformation temperature ranging from 1150 to 1400 C with an interval of 50 C, strain rate ranging from 0.001 to 1 s1 and height reductions of 55% on a computer controlled thermal simulation machine. The hot deformation behavior of as-cast is characterized based on the analysis of the stressestrain behaviors, the constitutive equations and process map for obtaining optimum processing parameters and achieving desired microstructure during hot working. A constitutive equation by which the flow stress was expressed as a function of strain rate and deformation temperature was established and the apparent activation energy of deformation was calculated to be 428.480 kJ/mol. The processing maps are constructed at the true strain of 0.5 and 0.7 based on dynamic materials model (DMM) to delineate the safe and unsafe regions in the axes of temperature and strain rate. The area of unsafe region increases with the increasing of strain. These instability domains exhibited localized flow and cracking along grain boundaries which should be taken care of during hot processing. The recommended domain is in the condition of the temperature range of 1250e1400 C and strain rate range of 0.001e0.02 s1. And in this state the main soften mechanism is dynamic recovery. It is worth noting that when as-cast Ve5Cre5Ti alloys deformed in the recommended deformation zone, the continuous dynamic recrystallization occurred, which display the feature of serrate grain boundaries and the equiaxed grains in the grain boundaries. Microstructure observation of deformed specimens validated the applicability of the processing map at obtaining the optimum processing parameters of as-cast Ve5Cre5Ti alloy. © 2015 Elsevier B.V. All rights reserved.
Keywords: Ve5Cre5Ti alloy Hot deformation Processing map Constitutive equation Microstructure
1. Introduction Vanadium-based alloys are considered as one of the candidate structural materials for fusion reactors because of their attractive properties such as low radiation-induced activation, high thermal conductivity, low thermal expansion, excellent high temperature performance and superior resistance against radiation-induced swelling [1e4]. The focus of researches for VeCreTi alloy concentrates on V-(4e5)Cr-(4e5)Ti alloys. Ve5Cre5Ti alloy is commonly produced by vacuum consumable arc melting (VAR), which is characterized by coarse grains. The grains in the ingots may reach millimeter level. At the same time, that the alloy solidified in a water-cooled copper crucible with a great solidification rate results in the large residual stress in the alloy ingot. Therefore, as-cast Ve5Cre5Ti alloys with poor mechanical properties require the
* Corresponding author. E-mail address: [email protected] (F.S. Qu). http://dx.doi.org/10.1016/j.jallcom.2015.12.014 0925-8388/© 2015 Elsevier B.V. All rights reserved.
reasonable hot pressure work, cold rolling and heat treatment processing to improve the microstructure and performance, which makes it meet engineering requirements of the fusion reactor. The deformation capacity of as-cast Ve5Cre5Ti alloy is relatively limited even at high temperature. In the actual thermal deformation processing, the instability phenomena can be easily generated such as crack. Therefore, it is very important for as-cast Ve5Cre5Ti alloy how to optimize hot pressure working parameters. The researches on the hot deformation behavior of as-cast Ve5Cre5Ti alloy in the actual process will result in higher costs, longer approach period and greater technical challenge. Unfortunately, the research efforts on VeCreTi alloys have mainly been focused on the irradiation properties [5,6], the thermal creep properties [7e9], the welding performance [10e12], effects impurity such as oxygen on properties of vanadium-based alloys [13e15], etc. Few researches have been focused on hot deformation behavior for as-cast Ve5Cre5Ti alloy. X.Z. Yu et al. [16] studied the thermal deformation performance of as-cast Ve5Cre5Ti alloy by uniaxial hot
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compression method at temperature range of 1150e1250 C and strain rate of 10 s1. The reasonable hot working parameters of the alloy are discussed from the surface cracks of the specimens. But the hot deformation performance of as-cast Ve5Cre5Ti alloy has not been studied systematically such as the constitutive equation, processing maps, etc. With the rapid development of computer technology, finite element method (FEM) has played on an important role in reducing the amount of experiments and improving work efficiency. And the establishment of the accurate hot deformation constitutive model is the key to improve the precision of the numerical simulation result. Therefore, the establishment of hot deformation constitutive equation for as-cast Ve5Cre5Ti alloys can provide the accurate basis for the optimization researches by subsequent numerical simulation. In addition, the processing map based on the dynamic material model (dynamic materials model, DMM) which was developed by Prasad et al. [17] is widely used to predict the thermal processing defects, the improvement of the workability of materials, the control of heat processing microstructure of materials and the research of performance and deformation mechanism, etc. In the present, the processing map has been applied to titanium alloy [18e21], magnesium alloy [22], stainless steel [23], nickel alloy [24], iron-base super alloy [25], etc. The effectiveness of processing map has been verified by the results of microstructure observation. Thus in the present work, the hot deformation constitutive equation and the processing maps of ascast Ve5Cre5Ti alloy are established to optimize hot processing parameters of as-cast Ve5Cre5Ti alloy by the stressestrain curves of hot deformation experiment. Through observing the microstructure before and after hot deformation of as-cast Ve5Cre5Ti alloy, the availability of the process maps is proved. This is very important to develop hot pressure processing parameters of as-cast Ve5Cre5Ti alloy and effectively control and improve performance and quality of the components.
2. Materials and experimental methods Ve5Cre5Ti alloy rod used in the hot compression experiment is obtained after twice vacuum consumable arc melting. The chemical composition of Ve5Cre5Ti alloy is Cr (4.78e4.82%), Ti (4.79e5.21%), O (450 wppm), N (50e60 wppm), C (60 wppm), and balance V. The alloy samples are taken from the equiaxed grain zone of cast ingot, which are shown in Fig. 1. The alloy is machined as F10 mm 12 mm cylindrical test specimen. The specimens are resistance heated to the deformation temperature at a heating rate of 7 C/s and held at that temperature for 120s by thermo-coupledfeedback-controlled AC current. The compression tests corresponding to a height reduction 55% are carried out six temperatures
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of 1150 C, 1200 C, 1250 C, 1300 C, 1350 C and 1400 C and four strain rates of 0.001 s1, 0.01 s1, 0.1 s1 and 1 s1. After each compression, the deformed specimens are rapidly quenched with water to retain the recrystallized microstructures. The cutting surfaces are parallel to the axial direction of the compression. The cut surfaces are prepared by using standard polishing and etching techniques for optical microstructure examination. During the compression process, the variations of stress and strain are monitored continuously by a personal computer equipped with an automatic data acquisition system. The true stress and true strain are derived from the measurement of nominal stressestrain relationship according to the following formula: sT ¼ sN ð1 þ εN Þ, εT ¼ lnð1 þ εN Þ, where sT is true stress, sN is nominal stress, εT is true strain and εN is nominal strain [26].
3. Results and discussion 3.1. The stressestrain curves The flow stress curves of as-cast Ve5Cre5Ti alloy obtained at various deformation temperatures (1150, 1200, 1250, 1300, 1350, 1400) and different strain rates (0.001, 0.01, 0.1, 1 s1) are shown in Fig. 2. The shapes of the curves indicate some features that help in identifying the mechanisms of hot deformation. It is shown that the flow stress increases with increasing strain rate and decreasing temperature. Some other typical characteristics of stressestrain curves in the temperature and strain rate ranges are observed. The results reveal that all the true stressestrain curves show the characteristics of the strain hardening at a small true strain, which leads to a pronounced peak stress. Subsequently, there are some curves in which a slow softening occurs (such as 1150 C, 0.001 s1) with the increasing strain, followed by a steady state flow at the large strain. There are other curves (such as 1400 C, 0.001 s1 and 1350 C, 0.1 s1) in which the steady state flowing occurs. Such steadyestate curves indicate that the mechanism of work hardening is balanced by the rate of softening which may be induced by the mechanisms like DRX, DRV, or SP occurring at very high rates [27]. In the initial stage, the work hardening is caused by the increment of dislocation density and the formation of poorly developed subgrain boundaries [28]. With the increasing strain, the effect of work hardening can be partially neutralized by occurrence of dynamic softening mechanisms, which leads to the decrease of the flow stress. At last, a steadyestate flow stress can be reached when the work hardening and dynamic softening mechanism, such as dynamic recovery (DRV) and dynamic recrystallization (DRX), can occur simultaneously during hot deformation. In addition, it was interesting to note that these curves exhibit
Fig. 1. Microstructure of Ve5Cre5Ti alloy before hot compression deformation: (a) microstructure for as-cast ingot; (b) microstructure in equiaxed area.
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Fig. 2. Curves of true stressestrain for Ve5Cre5Ti alloy under different conditions: (a) 0.001 s1; (b) 0.01 s1; (c) 0.1 s1; (d) 1 s1.
significant serrations in flow stress as a function of strain, which is more obvious with increasing strain rates, as shown in Fig. 2. The occurrence of dynamic strain aging (DSA) is considered as an important factor producing this serration at most of the temperature and strain rates [29], which is in accordance with the research result addressed by Cui et al. [30]. Moreover, the occurrence of DSA during hot working process has an influence on the flow behavior and even the final microstructure of the product [31]. But the actual mechanism which dominates in the different processes of microstructural evolution still needs further analysis of the flow stress data as a function of temperature and strain rate and microstructural examination, and these will be discussed in detail subsequently.
3.2. The constitutive equations In order to understand the hot plastic deformation behavior of Ve5Cre5Ti alloy, the flow curves obtained by the hot compression tests are analyzed to determine the constitutive equation. Based on the phenomenological approach developed for creep deformation [32], the constitutive equation can be expressed as
Z ¼ A½sinhðasÞn
(1)
where s is the flow stress (MPa); a, A and n are the material parameters, Z is the Zener-Hollomon parameter defined as
Q Z ¼ ε_ exp RT
(2)
where ε_ is the strain rate (s1), Q is the apparent activation energy of deformation (kJ/mol), R is the gas constant (8.314 J/(molK)), T is the absolute deformation temperature (K). From Eqns (1) and (2), the stress exponent, n is defined by
n¼
! v ln ε_ v ln½sinhðasÞ
(3)
T
And the activation energy Q can be defined as
Q¼
Rnv ln sinðasÞ vð1=TÞ ε_
(4)
The constant a is determined by the slop coefficients of ln ε_ versus s (peak stress) and ln ε_ versus ln s (peak stress), as is shown in Fig. 3. The a value is 0.00837766 MPa1. The fitting curves of ln½sinhðasÞ versus ln ε_ and ln½sinhðasÞ versus 1=T are shown in Fig. 4. From Fig. 4, the activation energy of V-5Cr-5Ti alloy is determined to be 428.47972 kJ/mol. According to Eqns. (1) and (5) can be obtained
ln Z ¼ n ln½sinhðasÞ þ ln A
(5)
Fig. 5 shows the plots of ln Z versus ln sinðasÞ. From Fig. 5, the n is 4.42602 by calculation and lnA is 27.6614. The constitutive equation for Ve5Cre5Ti alloy may be written as:
ε_ ¼ 1:0357 1012 ½sinhð0:0083776sÞ4:42602 expð 428:4797=RTÞ
(6)
The flow stress can be described with expression containing Z parameter as:
s ¼ 119:3659 ln
8 <Z 0:22593 : A
" #1 9 2= Z 0:45187 þ þ1 ; A
(7)
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Fig. 3. Relationships between peak stress and strain rate: (a) s ln_ε; (b) ln s ln_ε.
Fig. 4. Relationship of ln½sinhðasÞ ln_ε and ln½sinhðasÞ T 1 .
deforming. The total power dissipated per unit volume P, is given by
Z ε_ P ¼ s_ε ¼ G þ J ¼
Zs
Fig. 5. Relationship between ln Z and ln ½sinhðasÞ.
3.3. The processing map for as-cast Ve5Cre5Ti alloy In DMM model proposed by Prasad and Gegel, the flow behavior of the material undergoing thermoplastic deformation can be described as dissipative, nonlinear, dynamic, irreversible, and away from equilibrium [33e37]. DMM theory considers thermoplastic forming process as a system and workpiece undergoing deformation as a dissipater of power (not a storage element). According to this model, the system consists of a source of power, a store of power (tool) and a dissipater (workpiece), which dissipates energy while
ε_ ds
sd_ε þ 0
(8)
0
where s is instantaneous flow stress, ε_ is applied strain rate. At ant moment, the total power dissipation P consists of two complimentary functions, G content represents the major power input dissipated in the form of a temperature rise, and J co-content represent the power through metallurgical process such as dynamic recovery, dynamic recrystallization, cavity formation, super plastic flow and phase transformations. As a constant temperature, the instantaneous response (s) of workpiece material to the applied strain rate (_ε) for creating a large plastic strain is given by the dynamic constitutive equation s ¼ K ε_ , where K is a stress coefficient, ε_ strain rate, m strain rate sensitivity. The power partitioning between G and J is controlled by constitutive flow behavior of material and decided by strain rate sensitivity (m) as given below
m¼
dJ ð_εdsÞ dlgs ¼ ¼ dG ðsd_εÞ dlg_ε
(9)
J co-content is given by
Zs ε_ ds ¼
J¼ 0
ms_ε mþ1
(10)
where ε_ is the strain rate and m is the strain rate sensitivity. For an ideal linear dissipater, m ¼ 1 and Jmax ¼ s_ε=2.
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The power dissipation capacity of metals during deformation can be properly measured by the efficiency of dissipation (h) defined by Eqn. (11). The variation of h with temperature and strain rate constitutes power dissipation map. The various domains in the power dissipation map may be correlated with specific microstructure mechanisms.
h¼
J 2m ¼ Jmax m þ 1
(11)
A continuum instability criterion based on the extremum principle of irreversible thermodynamics as applied to large plastic flow is used in this study to identify the regimes of flow instabilities. The principle of maximum rate of entropy production in the metallurgical system results in an instability criterion (as Eqn. (12)) given by Prasad in 1987 [21]. The variation of instability parameter xð_εÞ with temperature and strain rate constitutes an instability map.
xð_εÞ ¼ vlgðm=ðm þ 1ÞÞ=vlg_ε þ m 0
(12)
The superimposed map is called a processing map, on the basis of which metal working process may be designed and controlled to optimize hot workability and to produce desired microstructures. This methodology has applied for various materials. According to Eqns. (11) and (12), the processing maps of Ve5Cre5Ti alloy in the deformation range of 1150e1400 C and strain rate of 0.001e1 s1 at the true strain of 0.5 and 0.7 is developed in Fig. 6 (a) and (b) which consist of a superimposition of the power dissipation map and instability map indicating the safe domain and unsafe domain during the plastic processing. In those figures, the iso-efficiency contours represent the efficiency value of power dissipation, and the shaded regions represent the unstable regions (the values of xð_εÞ are negative). From Fig. 6, it is found that instability regions increases with the increasing of strain, indicating that the strain has a significantly effect on the processing maps. In the safe areas in Fig. 6, there are common regions which are marked by the red dotted line with high values of h, which owns to greater dimension occurring at the temperature and strain rate (1250e1400 C, 0.001e0.02 s1). The range of h values is about 0.32e0.44. In Fig. 6, there are other safe regions but the areas is too small or the values of h is lower. So, the processing parameters in the actual forging are selected in the range of the temperature and strain rate (1250e1400 C, 0.001e0.02 s1) while those in the range of unsafe regions such as the temperature of 1150 C and strain rate of 0.1 s1, the temperature of 1400 C and strain rate of 1 s1 et al. The region of the processing map could be interpreted based on the characteristic efficiency variation associated with the microstructure mechanisms. To investigate the microscopic deformation
mechanisms and verify the reliability of process parameters predicted by processing maps, the evidence of deformation in these domains are identified and validated through microstructure observations in the following sections. 3.4. Discussion for processing maps by microstructure 3.4.1. Stability domains It can be seen from Fig. 6 that efficiency of power dissipation decreases with the increasing strain rates as a whole. Similarly, the efficiency of power dissipation of Ti-alloy decreased with the increasing of strain rate as expected by Prasad et al. [17]. And it can be also seen from Fig. 6 that the efficiency of increases with the increasing temperature as a whole. In Fig. 6 (a) and (b), the recommended deformation zone of the processing maps with different strain is indicated by red dotted line, respectively. And integrating from Fig. 6 (a) and (b), that the hot deformation occurs at the temperature range from 1250 to 1400 C and the strain rate range from 0.001 to 0.02 s1 is recommended. At this time, the deformation own to greater efficiency, which the efficiency of power dissipation is at the range of 0.30e0.44. In addition, there are some narrower stability domains such as the deformation range from 1225 to 1250 C and strain rate range from 0.001 to 0.0016 s1. However, the deformation parameters range of this deformation zone is narrower, which is not conducive to the actual operation. Therefore, from a practical point of view, the optimum condition for hot processing of as-cast Ve5Cre5Ti vanadium alloy is in the condition of the temperature range of 1250e1400 C and strain rate range of 0.001e0.02 s1. In this condition, the efficiency of power dissipation is higher and the area of stability domains is greater. Generally speaking, microstructure evolution of stable region may be dynamic recrystallization, superplasticity, spheroidizing and dynamic recovery. It is widely recognized that high peak power dissipation efficiency is often associated with dynamic recrystallization [27] or superplasticity. To investigates the microscopic deformation mechanisms and verify the reliability of processes parameters predicted by the processing maps, the microstructures of the specimen deformed under the specific parameters at the stable deformation zones are characterized and analyzed. The microstructures of the specimens deformed at the stable domains are shown in Fig. 7. From Fig. 7, the dynamic recrystallization grains occur in the deformed specimen. It is seen that, in the certain strain rate, the recrystallization grains increase with increasing deformation temperature, such as Fig. 7 (a), (b) and (e). It further indicates that the deformation temperature range of 1250e1400 C are correspondent to an optimal deformation condition of as-cast Ve5Cre5Ti alloy. This is in a good agreement with
Fig. 6. The processing maps developed at the different strains: (a) 0.5; (b) 0.7.
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Fig. 7. Microstructure of the specimens deformed in the stability domains for Ve5Cre5Ti alloy: (a) T ¼ 1250 C, ε_ ¼ 0:001s1 ; (b) T ¼ 1300 C, ε_ ¼ 0:001s1 ; (c) T ¼ 1300 C, ε_ ¼ 0:01s1 ; (d) T ¼ 1350 C, ε_ ¼ 0:01s1 ; (e) T ¼ 1400 C, ε_ ¼ 0:001s1 ; (f) T ¼ 1400 C, ε_ ¼ 0:01s1 .
the results from processing maps. Fig. 7 (b), (c) and Fig. 7(e), (f) shows the microstructures of the specimens deformed at 1300 C and 1400 C at different strain rates corresponding to 0.001 and 0.01 s1. It can be seen from Fig. 7 (b), (c) and Fig. 7 (e), (f) that the recrystallization grains sizes decrease with increasing strain rates. This is because that there is no sufficient time for dynamic recrystallization at high strain rate corresponding to that at low strain rate. This phenomenon which, the grain size increasing with the temperature increasing and the strain rate decreasing can be explained by Ref. [38].
tE ¼ hdn R
(13)
where h is a constant, tE is the flow stress, dR is the grain size. Because the increase of the strain rate will cause tE to increase, the increase of strain rate can lead to the generation of fine dynamic recrystallization grains. And the increase of the temperature will cause tE to decrease, so the increase of temperature can lead to the generation of great dynamic recrystallization grains. Moreover, the high temperature is conducive to the grain boundary movement, which leads to the greater recrystallization grain. From Fig. 7, it can be seen that the grains are elongated due to deformation, and grain
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boundaries are irregular, which presents typical dynamic recovery feature. Sivakesavam and Prasad [39] pointed out that the dynamic recrystallization may be considered to consist of two competing processes: formation of interfaces (nucleation), and migration of interfaces (growth), the nucleation consists of the formation of grain boundary due to the dislocation generation simultaneous recovery and rearrangement. However, it is difficult to see from Fig. 7 that there are no obvious processes for nucleation and growth occurring during hot deformation of as-cast Ve5Cre5Ti alloy. Thus the microstructure revealed by Fig. 7 is a continuous recrystallization with serrated grain boundaries, which is attributed to substructure occurred at lower strain rates (0.1 s1), as mentioned in Ref. [40]. Thus, it can be concluded from Fig. 7 that the main soften mechanism of as-cast Ve5Cre5Ti alloy during hot deformation is dynamic recovery, the microstructure after plastic deformation is constituted of flat elongated grains and continuous recrystallization grains of indention on the grain boundary. These microstructures also confirm that steadyestate flow and flow soften features of stressestrain curves display the phenomena of dynamic recovery and continuous recrystallization, respectively. In addition, the deformation of as-cast Ve5Cre5Ti alloy can be more stable at higher temperatures and lower strain rates by means of the analysis of the process maps and microstructure, which shows that the deformation ability of the cast Ve5Cre5Ti alloy is limited. In the actual process, the cogging of as-cast Ve5Cre5Ti alloys can adopt the water pressure machine, the hydraulic machine and vacuum isothermal billet. 3.4.2. Instability domains It is well known that instability mechanism is probably associated with cracking, localized plastic flow and adiabatic shear bands [41]. From Fig. 6, it can be obviously that the instability domains expand with the increase of strain. The microstructure manifestation of instability domains regarding the present alloy is shown in Fig. 8 which corresponds to specimen deformed at 1150 C/1 s1 and 1250 C/1 s1. Fig. 8(a) exhibits the cracks along the grain boundaries. In the hot deformation process of metal materials, the critical dislocation density of the dynamic recrystallization can be influenced by the strain rate. Roberts and Ahlblom [42] proposed a formula of critical dislocation density rc of DRX is:
rc ¼
20gi ε_ 3blMt2
1=3 (14)
where gi is grain boundary energy, J/m2; b is Burgers vector of
mold, m; l is subgrain size, m; M is grain boundary migration rate, m/s; and t is dislocation lines energy, N; ε_ is the strain rate. By Eqn. (13), the increase of strain rate will make the critical dislocation density of dynamic recrystallization grow up. This will make dynamic recrystallization difficult and lead to the higher dislocation density at the grain boundary. This will result in the stress concentration at grain boundaries and then cause cracking. Fig. 8 (b) exhibits the bands of flow localizations. From Fig. 2, there are serrated fluctuations on the stressestrain curves of Ve5Cre5Ti alloy and the phenomenon is caused by dynamic strain aging (DSA). The greater the strain rates are, the more obvious the effects of dynamic strain rate are. DSA is a micro-process occurring in plastic deformation of the alloy, which is caused by the interaction of the solute atoms and the motion of dislocation [43]. DSA is easy to cause the material strain rate sensitivity and strain localization [44]. In addition, when the strain rate of the Ve5Cre5Ti alloy increases, adiabatic deformation heat generated during hot working can not be conducted due to insufficient deformation time. Therefore, flow instability is induced by the bands of flow localization, which is undesired in obtaining consistent mechanism and thus should be avoided during processing. Through the above analysis, the thermal process of as-cast Ve5Cre5Ti alloy should be avoided in the above-mentioned unstable regions which contain the deformation at temperature of 1150e1225 C and strain rate of 0.00126e1 s1 and at the temperature range of 1150e1225 C and the strain rate of 0.00126e1 s1 and at the temperature range of 1225e1400 C and the strain rate of 0.1e1 s1.
4. Conclusions The hot deformation behavior and the corresponding microstructure of as-cast Ve5Cre5Ti vanadium alloy were investigated in the temperature range of 1150e1400 C and strain rate of 0.001e1 s1. The following conclusions have been drawn from this investigation: (1) The peak stress can be described by hyperbolic sine-type equation and the hot activation energy of the alloy is about 428.480 kJ/mol. (2) According to the processing map, the optimum processing parameters for good workability are obtained in the temperature range of 1250e1400 C and strain rate range of 0.001e0.02 s1. Microstructure observations reveal that dynamic recrystallization occurred in the optimum conditions.
Fig. 8. Microstructure of the specimens deformed in the instability domains for Ve5Cre5Ti alloy: (a) T ¼ 1150 C, ε_ ¼ 1s1 ; (b) T ¼ 1250 C, ε_ ¼ 1s1 .
F.S. Qu et al. / Journal of Alloys and Compounds 663 (2016) 552e559
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