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(TiB+TiC)
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Hot-deformation behaviour and hot-processing map of melt-hydrogenated Tie6Ale4V/(TiBþTiC) Xuejian Lin a,1, Fuyu Dong a,*,1, Yue Zhang a,**, Xiaoguang Yuan a, Hongjun Huang a, Bowen Zheng a, Liang Wang b, Xuan Wang b, Liangshun Luo b, Yanqing Su b, Yanjin Xu c, Baoshuai Han c a
School of Materials Science and Engineering, Shenyang University of Technology, Shenyang 110870, China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China c Beijing Aeronautical Manufacture Technology Research Institute, Beijing 100024, China b
article info
abstract
Article history:
The hydrogen was straight-forward added to the Tie6Ale4V/(TiC þ TiB) composites (TiC]
Received 9 November 2018
TiB¼5 vol.%) by melt hydrogenation. The results of hot compression show that the peak
Received in revised form
resistance of titanium matrix composites (TMCs) decreased by 17.2% when hydrogen
27 January 2019
content was 0.035 wt% compared with the TMCs without hydrogen. Therefore, the TMCs
Accepted 30 January 2019
with a hydrogen content of 0.035 wt% was performed to a thermal compression experi-
Available online 26 February 2019
ment. Thermal-deformation characteristics and hot processing map of TMCs with a hydrogen content of 0.035 wt% were analyzed in the light of the flow stress curve,
Keywords:
constitutive relations, and the dynamic-material model. The computed apparent activation
Melt hydrogenation
energy was 284.54 kJ/mol, and the corresponding strain-rate sensitivity, power dissipation,
Tie6Ale4V/(TiCþTiB) composites
and instability parameter were calculated. The hot-processing map exhibited maximum
Hot compressions simulation
efficiencies of power dissipation at 780e840 C/0.005e0.06 s1 and there was only one
Constitutive equation
instable region. The microstructures corresponding to the stable and instable region were
Processing map
verified, confirming the optimum processing parameters of hot-working that can be used as a reference for hot deformation of hydrogenated composites. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Titanium alloys possess a series of advantages including high strength, high heat-resistance, and good corrosion resistance. However, there are some disadvantages such as easy oxidation at high temperature and poor creep resistance [1,2]. As a new type of material with high-temperature resistance, creep resistance, and low density, TMCs are used in many fields as
high-temperature structural materials [3]. In situ synthesizing TMCs with a simple and common process that is low cost and produces strong interfacial adhesion between the matrix and reinforced phase [4]. TiB and TiC particulates possess similar density and thermal-expansion coefficients to titanium matrix, and have stable and strong bonding interfaces with the titanium matrix, which are considered the most ideal reinforcements for TMCs. However, TMCs have low room-
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (F. Dong), [email protected] (Y. Zhang). 1 Contributed equally to this work. https://doi.org/10.1016/j.ijhydene.2019.01.279 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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temperature plasticity and low deformation limit; therefore, most TMCs must be formed in the hot state. But some shortcomings in thermal processing, such as high deformation temperature and flow stress, limit the application of composite materials [5e7]. As a unique alloying element hydrogen could optimize the hot-working performance of TMCs and has attracted extensive attention in recent years [8e10]. At present, the studies on hydrogen treatment of TMCs mainly focus on microstructures and mechanical properties [11e15]. Machida et al. [16]. Combined hydrogen treatment with superplastic deformation to obtain fine grain structure in TC4 composites. Also, Senkov [17] discovered that hydrogen can enhance the interplay between dislocations and hinders in Tie6Ale2Zr-1.5-V-1Mo, increasing dislocation mobile ability and facilitating hightemperature deformation. Chen et al. [18] found that when the hydrogen content was 0.6%, the plasticity of TiAl alloy was improved and the compressive flow stress was only one-third of the flow stress of the sample without hydrogen. Furthermore, Lu et al. [19] hydrogenated Tie6Ale4V composites, and found that hydrogen can reduce activation energy and flow stress of the TMCs. Most of the hydrogenated methods used in the presented research are solid hydrogenation in a hightemperature furnace, requiring special equipment and a large amount of time consumption, limiting its wider applicability. The melt hydrogenation method was proposed by Su et al. [20], and this method can be quickly and evenly introduced into the TMCs during melting in hydrogen and argon mixed atmosphere [21]. Wang et al. [22e24] investigated the melt hydrogenation processing of TMCs and found that hydrogen caused high-temperature softening (850 C) due to hydrogen induced dynamic recrystallization (DRX) and increases of b phase, and promoted the movement of dislocation and DRX grain boundaries. While the researches about the thermal-deformation behaviour and processing map of hydrogenated TMCs are still insufficient, and the selection of the hot-working process parameters of these hydrogenated TMCs is certainly important, providing guidance for selecting the hot-working process parameters. The processing map can identify the instability domain and reflect the thermaldeformation regularity in distinct experiment conditions to improve the hot working efficiency and reduce cost [25]. In this paper, the hydrogen addition to the Tie6Ale4V/ (TiB þ TiC) composites was achieved by melt hydrogenation, and hot compressions of TMCs before and after melt hydrogenation were performed applying the Gleeble3500 thermal simulator. Then, the hot-deformation behaviours of hydrogenated TMCs under different experimental parameters were studied. Based on experimental data, the rheological stress model and the hot-processing map were acquired. The model and the map provide a theoretical basis for formulating the optimum parameters and improving property and quality of hot-working products.
synthesized by arc melting in hydrogen/argon mixed atmosphere with (1) and (2) in-situ autogenous reactions, which the hydrogen volume fraction was 0%, 5%, and 10% in the process of melt hydrogenation. When the hydrogen volume fractions in the gas mixture were 5% and 10%, the actual hydrogen contents of the TMCs were 0.021 wt% and 0.035 wt %, respectively, which were measured by the LECO ROH600 oxygen-hydrogen analyzer. TiþC¼TiC
(1)
5TiþB4C¼4TiBþTiC
(2)
The ingots were cut into cylinders with radius of 2 mm and heights of 6 mm using the wire-cutting machine. Hotcompression simulations were performed applying the Gleeble3500 thermal simulator, and hot-compression parameters as given in Table 1. Graphite was used as a lube to decrease friction between sample and chuck. To retain microstructure state during hot compression, water quenching is required immediately after the experiment, so the sample compressed at high temperature was cut along the compression direction. After sanding, polishing, and chemically etching (5%HFþ10% HNO3þ85%H2O), the scanning electron microscope (SEM) was applied to observe microstructure of the samples.
Results and discussion Flow stress curves of TMCs with different hydrogen contents Fig. 1 is the flow stress curve of TMCs with different hydrogen contents at 0.01 s1 and 850 C. As shown in Fig. 1, when the strain is small, the deformation resistance raises with strain increases and attains its maximum, which is chiefly owning to work hardening because of dislocation plug-up. After the deformation resistance reaches the peak, it gradually declines with increases strain due to DRX. The deformation resistance is susceptible to the variety of hydrogen content, and the deformation resistance of all hydrogenated samples is less than the resistance of samples without hydrogen, and it has been reported by Wang [26] and co-workers. Moreover, the deformation resistance decreases with increased hydrogen content, which is consistent with the results of many researchers [27e30]. When the hydrogen is 0.035 wt%, the peak resistance of the TMCs decreases 17.2% from 239.8 MPa, which represents the peak stress of the unhydrogenated composites, to 198.47 MPa. Thus, the flow stress at high temperature can be reduced by melt hydrogenation.
Table 1 e Process parameters in the compression of TMCs. Process parameters
Material and methods The experimental raw materials were as-cast Tie6Ale4V alloy and C and B4C powders (micron-grade), and the Tie 6Ale4V/(TiB þ TiC) composites (TiB]TiC¼5 vol.%) was
Deformation-ratio Strain rate Deformation temperature Temperature-rising rate Holding time
Numerical value 60% 0.001s1, 0.01s1, 0.1s1, 1s1 750 C, 800 C, 850 C, 900 C 10 C/s 3min
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hardening. After deformation resistance reaches peak value, it shows a stable decline with increased strain, and the softening mechanism caused by DRX is dominant. Meanwhile, a lower strain rate shows a more obvious behaviour of DRX and a weaker behaviour of work hardening because the deformation time at a low strain rate is longer and the deformed sample has sufficient time for DRX. Furthermore, the deformation resistance curve shows that the slope of true-stress reduction is larger corresponds to the smaller strain rate at beginning of true-stress reduction.
Establishment of the constitutive equation
Fig. 1 e True Stress-strain curves of as-received and hydrogenated TMCs deformed at 850 C and 0.01 s¡1.
Therefore, this paper mainly analyzes the flow-stress curve of TMCs with 0.035 wt% hydrogen, establishes its constitutive equation and hot-processing map.
Flow stress analysis of TMCs with 0.035 wt% hydrogen The flow stress curves of hydrogenated TMCs with 0.035 wt% hydrogen under 750e900 C and 0.001e1 s1 are plotted in Fig. 2. It indicates that the deformation resistance raises with increased strain rate and decreased temperature. While the strain is small, the deformation resistance raises rapidly with increased strain and reaches its maximum due to work
According to the thermal compression data of TMCs with 0.035 wt% hydrogen in Fig. 2, the Arrhenius hyperbolic sine function model [31] is used in this paper, and a mathematical model is built to represent the thermal compression parameter relationship as follows: Q ε_ ¼ A sinhðasÞn exp RT
(3)
Where ε_ is strain rate, A is structural factors, a is parameter of stress level, s is flow stress, n is stress exponent, Q is activation energy related to materials, T is thermodynamic temperature, R is ideal gas constant. When the T is invariable, and A, Q, R, and T are fixed value, the values of n1 and b are obtained by taking logarithm and derivation of Eq. (3): :
n1 ¼
vlnε vln s
(4)
:
b¼
vlnε vs
(5)
Fig. 2 e True Stress-strain curves of hydrogenated TMCs under different conditions (a) 0.001 s¡1, (b) 0.01 s¡1, (c) 0.1 s¡1, (d) 1 s¡1.
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Fig. 3 e Relationship between flow stress and strain rates (a) s-ln_ε and (b) lns-ln_ε
The value of s is taken as the peak resistance under different conditions, and the diagram of s-ln_ε and lns-ln ε_ are drawn respectively for linear fitting, its function image is Fig. 3. According to Eqs. (4) and (5), the mean values of reciprocal slopes of the straight lines at various temperatures are n1 and b, respectively, and a is determined to be 0.0031151 MPa1 according to a ¼ b/n1. Supposing the activation energy (Q) is unconnected of temperature (T) under certain temperature ranges, and logarithm of Eq. (3) is taken to obtain the following Eq.: :
lnε ¼ ln A Q=RT þ n ln½sinhðasÞ
(6)
To compute activation energy (Q), the partial differential of Eq. (6) could be acquired as below: : vln½sinhðasÞ vlnε Q¼R : vT1 vln½sinhðasÞ T ε
(7)
Fig. 4 is the diagram of ln [sinh (as)]-ln_ε and ln [sinh (as)]T1, which are drawn for linear fitting. According to Eq. (7), the mean values of reciprocal slopes of straight lines at various temperatures in Fig. 4 are second-term and third-term values. The value of Q is computed to be 284.54 kJ/mol. The parameter of Zener-Hollomon [32,33] is applied, and relationship between strain rate and temperature could be expressed by Z: , s ¼ s Z; ε
(8)
,
Z ¼ ε expðQ=RTÞ
(9)
where Z is compensation factor of temperature to strain rate. Shi et al. [34] shows that expression between Z and s is determined by the following Eq.: Z ¼ A½sinðasÞn
(10)
According to Eqs. (9) and (10), the following Eq. (11) could be obtained: ,
Z ¼ ε expðQ=RTÞ ¼ A½sinðasÞn
(11)
By taking logarithmic of Eq. (11) to obtain Eq. (12): ln Z ¼ n ln½sinhðasÞ þ ln A
(12)
By putting the T, ε_ , and Q into Eq. (11), the corresponding value of Z is obtained, and the diagrams of lnZ and ln[sinh(as)] are drawn to linear fitting in Fig. 5. The lnZ and ln[sinh(as)] relation curve is linearly dependent, and the rheological behavior of composites under high-temperature compression could be represented by Z using the Arrhenius hyperbolic sine function. The values of n¼4.3829 and lnA¼27.03589 are determined by linear fitting. According to the definition of Arrhenius function and Eq. (12), s could be presented using Z as follows: ( 1 " 2 #12 ) 1 Z n Z n þ þ1 s ¼ ln a A A
Fig. 4 e Relationships of ln [sinh (as)]-ln_ε (a) and ln [sinh (as)]-T¡1(b).
(13)
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Based on theoretics of irreversible thermodynamics [39], the criterion of rheological instability during large deformation is presented: :
xðε Þ ¼
vln½m=ðm þ 1Þ þ m<0 : vlnε
(19)
Where x(_ε) is stability criterion. When instability criterion is met, the material undergoes an unstable rheological process so the unstable deformation behaviour can be predicted, which probably appears adiabatic shear band, cavity nucleation, and kinking, and the process has been applied to several materials [40].
Establishment of the processing map The calculation of power dissipation h
Fig. 5 e Relationship between s and Z.
The obtained values of Q ¼ 284.54 kJ/mol, R ¼ 8.314J/mol$K, a ¼ 0.0031151, and n ¼ 4.3829 are introduced into Eq. (3), and the following Arrhenius rheological stress constitutive equation of TMCs with 0.035 wt% hydrogen was obtained:
ε ¼ 5:5149 1011 ½sinh ð0:0031151Þs4:3829 expð 284:54=RTÞ
(14)
Theoretical basis of processing map Dynamic material model (DMM) was presented by Prasad [35] and was later revised by Rao and Murty [36,37]. DMM relates constitutive behaviour to microstructure change, flow stability, and hot workability [38]. The energy input from outside(P) could be divided into two parts: dissipative quantity (G) and dissipative covariate quantity (J): :
Zε
:
P ¼ sε ¼ G þ J ¼
:
Zs
sdε þ 0
:
ε ds
According to the data of hot compression of TMCs with 0.035 wt% hydrogen (ε ¼ 0.5), the cubic spline function is used to fit the log s log ε_ relationship curve, as shown in Fig. 6. As shown in Fig. 6, log s log ε_ is nonlinear, and logs can be expressed by log_ε, :
2
3
logs ¼ a þ b logε þ cðlogε_ Þ þ dðlogε_ Þ
Basing on Eqs. (16) and (20), the corresponding m can be obtained by introducing the log_ε at different strain rates, then duplicate the step by selecting various temperatures. According to Eq. (18), the power dissipation h is obtained and contour map of h is drawn under the two dimensions of T : logε. Then, the power dissipation map in hot compression of hydrogenated TMCs is obtained, as shown in Fig. 7. Fig. 7 reflects the variable of significantly affect power dissipation h. h is generally decreasing with the increases ε_ , this is identical to the conclusions of many titanium alloy researchers [41,42]. The minimum h is 0.065, which appears in the area with high strain rate. Also, a lower value of h corresponds to a smaller energy dissipated by microstructure evolution.
(15)
0
Where G is energy corresponding to plastic deformation and J is energy corresponding to microstructure evolution. The proportion of G and J is given by strain rate sensitivity m: :
vJ ε vs vðlogsÞ ¼ : ¼ ¼m : vG svε vðlogε Þ
(16)
It is the ideal linear dissipative process when m ¼ 1, J arrives its maximum of Jmax, leading to the following equation: :
Jmax ¼
sε P ¼ 2 2
(17)
In the DMM, the power dissipation h is the utilization rate of energy consumed by microstructure evolution under different thermal-deformation conditions. Therefore, when the value of h is larger, the corresponding processing parameters are the best, leading to the following expression: h¼
J Jmax
¼
2m mþ1
(18)
(20)
Fig. 6 e Graph of log s log ε_ in the isothermal compression of hydrogenated TMCs.
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Fig. 9 e Processing map in isothermal compression of hydrogenated TMCs.
Fig. 7 e Power dissipation efficiency map in isothermal compression of hydrogenated TMCs.
Establishment and analysis of the processing map
The calculation of instability criterion The expression of instability criterion can be derived from Eqs. (16) and (19) as follows: :
xðε Þ ¼
:
vlog½m=ðm þ 1Þ 2c þ 6d logε þm þm¼ : m þ ðm þ 1Þln 10 vlogε
(21)
The instability parameter can be obtained by bringing log_ε and m into Eq. (21). Then, the equivalent contour curve of the instability criterion will be obtained under the two di: mensions of T logε and the instability map of hydrogenated TMCs is obtained, as shown in Fig. 8. : It could be seen in Fig. 8, the variable of T logε significantly impact the instability parameters, and it declines with increased deformation temperature and decreased strain rate. Also, instability parameters that are less than 0 are 0.016, 0.067, and 0.12, which indicates that the material will undergo unstable rheological process. And the rheological instability appears in the area where the strain rate is higher and the material is in unstable region.
Fig. 8 e Instability map in isothermal compression of hydrogenated TMCs.
Superimposing power dissipation map and instability map of the TMCs (0.035 wt%hydrogen), the corresponding processing map can be obtained as Fig. 9. Isoline is the value of h, the gray part represents the instability domain. The processing map can reflect impact of the thermal processing conditions on energy dissipation and instability criterion. Therefore, the unstable region is avoided, and the best thermal processing parameters are obtained. The unstable state of flow stress will be avoided to optimize the microstructure of hot-working materials and promote the performance of workpieces [43]. As shown in Fig. 9, the hydrogenated TMCs exhibits only one instability domain ðε ¼ 0:5Þ, which is the temperature of 750e825 C and strain rate of 0.7e1 s1, that is, lowtemperature and high strain rate domain. The corresponding h value is the lowest, and its value is between 0.065 and 0.16. Thus, the strain rate should not be too high when the hydrogenated TMCs is deformed at middle-low temperature; otherwise, the rheological instability occurs easily. The domains exhibiting the peak value of h ðε ¼ 0:5Þ was the temperature of 780e850 C and strain rate of 0.005e0.6 se1, that is, middle to high-temperature and low strain rate domain. The corresponding h is between 0.065 and 0.16 and corresponds to optimal deformation conditions for high-temperature compression of hydrogenated TMCs. The power dissipation generally decreases with increased strain rate; however, the decrease is not obvious with increased temperature. Also, the influence of thermal deformation energy distribution of composites on the strain rate is significantly greater compared to temperature, when the temperature is between 750 C and 900 C and strain rate is between 0.001 s1 and 1 s1. Microstructures of samples deformed under different domains in the processing map are observed to verify prediction ability about processing map to the unstable and stable domains. Fig. 10a shows the initial microstructure of the hydrogenated TMCs and that the reinforcements distributed along b grain boundary, which is consistent with the microstructures of Wang [19]. And Fig. 10b shows microstructure under deformation conditions of 750 C/1 s1 (low temperature and high strain rate region), which matches to instability
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Fig. 10 e Microstructures of hydrogenated TMCs deformed at different conditions (a)Initial, (b) and (f) 750 C/1 s¡1, (c) 850 C/1 s¡1, (d) 750 C/0.001 s¡1, (e) 850 C/0.001 s¡1.
domain. The figure shows that new grains are formed after deformation, corresponding to DRX. At the same time, the figures show that the grain is elongated by compression, but under this condition, the grain size of microstructure is uneven and some coarse grains appear. As shown in Fig. 10f, cracks appear in multiple SEMs images, indicating that the structure is unsuitable for acquiring homogeneous mechanical properties which ought to be prevented. Fig. 10c and d shows the microstructures under deformation conditions of 850 C/1 s1 (middle-high temperature and high strain rate domain) and 750 C/0.001 s1 (low temperature and low strain rate domain), which match to stability domain. The figures show the microstructure is more homogeneous and there is no crack appears compared with the instability domain. Fig. 10e shows microstructure under deformation conditions under 850 C/0.001s1 (middle-high temperature and low strain rate domain), corresponding to optimal deformation conditions. The figure shows that fine grains are produced after deformation under this condition, and DRX is relatively sufficient. The microstructure is a relatively uniform reticular structure. This kind of microstructure has excellent mechanical properties including plasticity, impact toughness, and fatigue strength, so this deformation condition can be used as the optimal condition during thermal working. The microstructure corresponding to optimal thermal-working parameters is better than the unstable region. Moreover, the microstructure after thermal deformation without cracks, voids, and adiabatic shear bands, showing that the hotworking stable domain determined in this paper is reasonable. The establishment of the hot-processing map has a certain guiding function on the selection of hot-working parameters.
Conclusions (1) When the hydrogen was 0.035 wt%, peak resistance of TMCs decreased 17.2% from 239.8 MPa, which compares
to peak resistance of unhydrogenated TMCs, to 198.47 MPa. (2) The thermal deformation behaviour of Tie6Ale4V/ (TiB þ TiC) composites with 0.035 wt% hydrogen at 750e900 C and 0.001~1s1 was studied, and the deformation resistance declines with increased deformation temperature and decreased strain rate. The constitutive equation of TMCs(0.035 wt%H) is deduced as follows:
ε ¼ 5:5149 1011 ½sinh ð0:0031151Þs4:3829 expð 284:54=RTÞ (3) The establishment and analysis of the processing map in hot compression of TMCs(0.035 wt%H) were constructed at a strain of 0.5. The optimum thermal processing parameters are a deformation temperature range between 780 and 840 C, strain rate range between 0.005 and 0.06 s1. The instability domain occurs in temperature range between 750 and 825 C and the strain rate range between 0.7 and 1 s1. (4) The microstructures corresponding to optimum parameters are relatively uniform and fine reticular structure with no instability such as cracks and voids, and DRX is relatively sufficient. And the microstructures corresponding to instability domain are inhomogeneous and cracks occur; therefore, thermal processing should be avoided in this working environment.
Acknowledgments This work was supported the Natural Science Foundation Key Plan of Liaoning (20180510056), National Natural Science Foundation of China (51401129, 51871075, 51875365), National Key Research and Development Program of China (2016YFB0301201), and Major Science and Technology Special Plan of Yunnan (2018ZE013).
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[20] Su Y, Wang L, Luo L, et al. Investigation of melt hydrogenation on the microstructure and deformation behavior of Ti-6Al-4V alloy. Int J Hydrog Energy 2011;36:1027e36. [21] Wang L, Luo LS, Wu SP, Su YQ, Wang SJ, Wang GT, et al. The influence of melt hydrogenation on Ti600 alloy. Int J Hydrog Energy 2014;39:6089e94. [22] Wang X, Wang L, Luo LS, et al. High temperature deformation behavior of melt hydrogenated (TiB þ TiC)/Ti6Al-4V composites. Mater Des 2017;121:335e44. [23] Wang X, Wang L, Luo LS, et al. Hydrogen induced softening and hardening for hot workability of (TiB þ TiC)/Ti-6Al-4V composites. Int J Hydrog Energy 2017;42:3380e8. [24] Wang X, Wang L, Luo LS, et al. Positive effect of hydrogen on interface of in situ, synthesized Ti-6Al-4V matrix composites. Mater Sci Eng 2018;711:12e21. [25] Peng W, Zeng W, Wang Q, et al. Characterization of hightemperature deformation behavior of as-cast Ti60 titanium alloy using processing map. Mater Sci Eng 2013;571:116e22. [26] Wang X, Wang L, Luo LS, et al. Hot deformation behavior and dynamic recrystallization of melt hydrogenated Ti-6Al-4V alloy. J Alloy Comp 2018;728:709e18. [27] Lu J, Qin J, Lu W, et al. Hot deformation behavior and microstructure evaluation of hydrogenated Ti-6Al-4V matrix composite. Int J Hydrog Energy 2009;34:9266e73. [28] Yang K, Guo ZX, Edmonds DV. Processing of titanium matrix composites with hydrogen as a temporary alloying element. Scripta Metall Mater 1992;27:1695e700. [29] Yang K, Guo ZX, Edmonds DV. Study of the effect of hydrogen on titanium alloy foils to be used as potential composite matrices. Scripta Metall Mater 1992;27:1021e6. [30] Liu XW, Su YQ, Luo LS, Liu JP, Guo JJ, Fu HZ. Effect of hydrogen on hot deformation behaviors of TiAl alloys. Int J Hydrog Energy 2010;35. 13322-133283. [31] Liu P, Liu D, Luo Z, et al. Flow behavior and dynamic recrystallization model for GH761 superalloy during hot deformation. Rare Metal Mater Eng 2009;38:275e80. [32] Zener C, Hollomon JH. Effect of strain rate upon plastic flow of steel. J Appl Phys 2004;15:22e32. [33] Mirzadeh H, Cabrera JM, Najafizadeh A. Constitutive relationships for hot deformation of austenite. Acta Mater 2011;59:6441e8. [34] Shi H, Mclaren AJ, Sellars CM, et al. Constitutive equations for high temperature flow stress of aluminium alloys. Metal Sci J 1997;13:210e6. [35] Sagar PK, Banerjee D, Muraleedharan K, et al. Hightemperature deformation processing of Ti-24Al-20Nb. Metall Mater Trans 1996;27:2593e604. [36] Raj R. Development of a processing map for use in warmforming and hot-forming processes. Metall Trans 1981;12:1089e97. [37] Zhang J, Di H, Mao K, et al. Hot deformation behavior of Ti15-3 titanium alloy: a study using processing maps, activation energy map, and ZenereHollomon parameter map. J Mater Sci 2012;47:4000e11. [38] Prasad YV, Rao KP. Processing maps for hot deformation of rolled AZ31 magnesium alloy plate: anisotropy of hot workability. Mater Sci Eng 2008;487:316e27. [39] Liu J, Xiong Y, He W, et al. Hot deformation and processing maps of TC4-DT titanium alloy. Rare Metal Mater Eng 2013;42:1674e8. [40] Chen T, Nie X, Yi D, et al. High temperature deformation behavior and processing map of TC18 titanium alloy. Hot Work Technol 2012;41:24e8. [41] Murty SVSN, Rao BN. On the flow localization concepts in the processing maps of titanium alloy Ti-24Al-20Nb. J Mater Process Technol 2000;104:103e9.
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Hot-deformation behaviour and hot-processing map of melt-hydrogenated Tie6Ale4V/(TiBþTiC) Xuejian Lin a,1, Fuyu Dong a,*,1, Yue Zhang a,**, Xiaoguang Yuan a, Hongjun Huang a, Bowen Zheng a, Liang Wang b, Xuan Wang b, Liangshun Luo b, Yanqing Su b, Yanjin Xu c, Baoshuai Han c a
School of Materials Science and Engineering, Shenyang University of Technology, Shenyang 110870, China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China c Beijing Aeronautical Manufacture Technology Research Institute, Beijing 100024, China b
article info
abstract
Article history:
The hydrogen was straight-forward added to the Tie6Ale4V/(TiC þ TiB) composites (TiC]
Received 9 November 2018
TiB¼5 vol.%) by melt hydrogenation. The results of hot compression show that the peak
Received in revised form
resistance of titanium matrix composites (TMCs) decreased by 17.2% when hydrogen
27 January 2019
content was 0.035 wt% compared with the TMCs without hydrogen. Therefore, the TMCs
Accepted 30 January 2019
with a hydrogen content of 0.035 wt% was performed to a thermal compression experi-
Available online 26 February 2019
ment. Thermal-deformation characteristics and hot processing map of TMCs with a hydrogen content of 0.035 wt% were analyzed in the light of the flow stress curve,
Keywords:
constitutive relations, and the dynamic-material model. The computed apparent activation
Melt hydrogenation
energy was 284.54 kJ/mol, and the corresponding strain-rate sensitivity, power dissipation,
Tie6Ale4V/(TiCþTiB) composites
and instability parameter were calculated. The hot-processing map exhibited maximum
Hot compressions simulation
efficiencies of power dissipation at 780e840 C/0.005e0.06 s1 and there was only one
Constitutive equation
instable region. The microstructures corresponding to the stable and instable region were
Processing map
verified, confirming the optimum processing parameters of hot-working that can be used as a reference for hot deformation of hydrogenated composites. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Titanium alloys possess a series of advantages including high strength, high heat-resistance, and good corrosion resistance. However, there are some disadvantages such as easy oxidation at high temperature and poor creep resistance [1,2]. As a new type of material with high-temperature resistance, creep resistance, and low density, TMCs are used in many fields as
high-temperature structural materials [3]. In situ synthesizing TMCs with a simple and common process that is low cost and produces strong interfacial adhesion between the matrix and reinforced phase [4]. TiB and TiC particulates possess similar density and thermal-expansion coefficients to titanium matrix, and have stable and strong bonding interfaces with the titanium matrix, which are considered the most ideal reinforcements for TMCs. However, TMCs have low room-
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (F. Dong), [email protected] (Y. Zhang). 1 Contributed equally to this work. https://doi.org/10.1016/j.ijhydene.2019.01.279 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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temperature plasticity and low deformation limit; therefore, most TMCs must be formed in the hot state. But some shortcomings in thermal processing, such as high deformation temperature and flow stress, limit the application of composite materials [5e7]. As a unique alloying element hydrogen could optimize the hot-working performance of TMCs and has attracted extensive attention in recent years [8e10]. At present, the studies on hydrogen treatment of TMCs mainly focus on microstructures and mechanical properties [11e15]. Machida et al. [16]. Combined hydrogen treatment with superplastic deformation to obtain fine grain structure in TC4 composites. Also, Senkov [17] discovered that hydrogen can enhance the interplay between dislocations and hinders in Tie6Ale2Zr-1.5-V-1Mo, increasing dislocation mobile ability and facilitating hightemperature deformation. Chen et al. [18] found that when the hydrogen content was 0.6%, the plasticity of TiAl alloy was improved and the compressive flow stress was only one-third of the flow stress of the sample without hydrogen. Furthermore, Lu et al. [19] hydrogenated Tie6Ale4V composites, and found that hydrogen can reduce activation energy and flow stress of the TMCs. Most of the hydrogenated methods used in the presented research are solid hydrogenation in a hightemperature furnace, requiring special equipment and a large amount of time consumption, limiting its wider applicability. The melt hydrogenation method was proposed by Su et al. [20], and this method can be quickly and evenly introduced into the TMCs during melting in hydrogen and argon mixed atmosphere [21]. Wang et al. [22e24] investigated the melt hydrogenation processing of TMCs and found that hydrogen caused high-temperature softening (850 C) due to hydrogen induced dynamic recrystallization (DRX) and increases of b phase, and promoted the movement of dislocation and DRX grain boundaries. While the researches about the thermal-deformation behaviour and processing map of hydrogenated TMCs are still insufficient, and the selection of the hot-working process parameters of these hydrogenated TMCs is certainly important, providing guidance for selecting the hot-working process parameters. The processing map can identify the instability domain and reflect the thermaldeformation regularity in distinct experiment conditions to improve the hot working efficiency and reduce cost [25]. In this paper, the hydrogen addition to the Tie6Ale4V/ (TiB þ TiC) composites was achieved by melt hydrogenation, and hot compressions of TMCs before and after melt hydrogenation were performed applying the Gleeble3500 thermal simulator. Then, the hot-deformation behaviours of hydrogenated TMCs under different experimental parameters were studied. Based on experimental data, the rheological stress model and the hot-processing map were acquired. The model and the map provide a theoretical basis for formulating the optimum parameters and improving property and quality of hot-working products.
synthesized by arc melting in hydrogen/argon mixed atmosphere with (1) and (2) in-situ autogenous reactions, which the hydrogen volume fraction was 0%, 5%, and 10% in the process of melt hydrogenation. When the hydrogen volume fractions in the gas mixture were 5% and 10%, the actual hydrogen contents of the TMCs were 0.021 wt% and 0.035 wt %, respectively, which were measured by the LECO ROH600 oxygen-hydrogen analyzer. TiþC¼TiC
(1)
5TiþB4C¼4TiBþTiC
(2)
The ingots were cut into cylinders with radius of 2 mm and heights of 6 mm using the wire-cutting machine. Hotcompression simulations were performed applying the Gleeble3500 thermal simulator, and hot-compression parameters as given in Table 1. Graphite was used as a lube to decrease friction between sample and chuck. To retain microstructure state during hot compression, water quenching is required immediately after the experiment, so the sample compressed at high temperature was cut along the compression direction. After sanding, polishing, and chemically etching (5%HFþ10% HNO3þ85%H2O), the scanning electron microscope (SEM) was applied to observe microstructure of the samples.
Results and discussion Flow stress curves of TMCs with different hydrogen contents Fig. 1 is the flow stress curve of TMCs with different hydrogen contents at 0.01 s1 and 850 C. As shown in Fig. 1, when the strain is small, the deformation resistance raises with strain increases and attains its maximum, which is chiefly owning to work hardening because of dislocation plug-up. After the deformation resistance reaches the peak, it gradually declines with increases strain due to DRX. The deformation resistance is susceptible to the variety of hydrogen content, and the deformation resistance of all hydrogenated samples is less than the resistance of samples without hydrogen, and it has been reported by Wang [26] and co-workers. Moreover, the deformation resistance decreases with increased hydrogen content, which is consistent with the results of many researchers [27e30]. When the hydrogen is 0.035 wt%, the peak resistance of the TMCs decreases 17.2% from 239.8 MPa, which represents the peak stress of the unhydrogenated composites, to 198.47 MPa. Thus, the flow stress at high temperature can be reduced by melt hydrogenation.
Table 1 e Process parameters in the compression of TMCs. Process parameters
Material and methods The experimental raw materials were as-cast Tie6Ale4V alloy and C and B4C powders (micron-grade), and the Tie 6Ale4V/(TiB þ TiC) composites (TiB]TiC¼5 vol.%) was
Deformation-ratio Strain rate Deformation temperature Temperature-rising rate Holding time
Numerical value 60% 0.001s1, 0.01s1, 0.1s1, 1s1 750 C, 800 C, 850 C, 900 C 10 C/s 3min
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hardening. After deformation resistance reaches peak value, it shows a stable decline with increased strain, and the softening mechanism caused by DRX is dominant. Meanwhile, a lower strain rate shows a more obvious behaviour of DRX and a weaker behaviour of work hardening because the deformation time at a low strain rate is longer and the deformed sample has sufficient time for DRX. Furthermore, the deformation resistance curve shows that the slope of true-stress reduction is larger corresponds to the smaller strain rate at beginning of true-stress reduction.
Establishment of the constitutive equation
Fig. 1 e True Stress-strain curves of as-received and hydrogenated TMCs deformed at 850 C and 0.01 s¡1.
Therefore, this paper mainly analyzes the flow-stress curve of TMCs with 0.035 wt% hydrogen, establishes its constitutive equation and hot-processing map.
Flow stress analysis of TMCs with 0.035 wt% hydrogen The flow stress curves of hydrogenated TMCs with 0.035 wt% hydrogen under 750e900 C and 0.001e1 s1 are plotted in Fig. 2. It indicates that the deformation resistance raises with increased strain rate and decreased temperature. While the strain is small, the deformation resistance raises rapidly with increased strain and reaches its maximum due to work
According to the thermal compression data of TMCs with 0.035 wt% hydrogen in Fig. 2, the Arrhenius hyperbolic sine function model [31] is used in this paper, and a mathematical model is built to represent the thermal compression parameter relationship as follows: Q ε_ ¼ A sinhðasÞn exp RT
(3)
Where ε_ is strain rate, A is structural factors, a is parameter of stress level, s is flow stress, n is stress exponent, Q is activation energy related to materials, T is thermodynamic temperature, R is ideal gas constant. When the T is invariable, and A, Q, R, and T are fixed value, the values of n1 and b are obtained by taking logarithm and derivation of Eq. (3): :
n1 ¼
vlnε vln s
(4)
:
b¼
vlnε vs
(5)
Fig. 2 e True Stress-strain curves of hydrogenated TMCs under different conditions (a) 0.001 s¡1, (b) 0.01 s¡1, (c) 0.1 s¡1, (d) 1 s¡1.
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Fig. 3 e Relationship between flow stress and strain rates (a) s-ln_ε and (b) lns-ln_ε
The value of s is taken as the peak resistance under different conditions, and the diagram of s-ln_ε and lns-ln ε_ are drawn respectively for linear fitting, its function image is Fig. 3. According to Eqs. (4) and (5), the mean values of reciprocal slopes of the straight lines at various temperatures are n1 and b, respectively, and a is determined to be 0.0031151 MPa1 according to a ¼ b/n1. Supposing the activation energy (Q) is unconnected of temperature (T) under certain temperature ranges, and logarithm of Eq. (3) is taken to obtain the following Eq.: :
lnε ¼ ln A Q=RT þ n ln½sinhðasÞ
(6)
To compute activation energy (Q), the partial differential of Eq. (6) could be acquired as below: : vln½sinhðasÞ vlnε Q¼R : vT1 vln½sinhðasÞ T ε
(7)
Fig. 4 is the diagram of ln [sinh (as)]-ln_ε and ln [sinh (as)]T1, which are drawn for linear fitting. According to Eq. (7), the mean values of reciprocal slopes of straight lines at various temperatures in Fig. 4 are second-term and third-term values. The value of Q is computed to be 284.54 kJ/mol. The parameter of Zener-Hollomon [32,33] is applied, and relationship between strain rate and temperature could be expressed by Z: , s ¼ s Z; ε
(8)
,
Z ¼ ε expðQ=RTÞ
(9)
where Z is compensation factor of temperature to strain rate. Shi et al. [34] shows that expression between Z and s is determined by the following Eq.: Z ¼ A½sinðasÞn
(10)
According to Eqs. (9) and (10), the following Eq. (11) could be obtained: ,
Z ¼ ε expðQ=RTÞ ¼ A½sinðasÞn
(11)
By taking logarithmic of Eq. (11) to obtain Eq. (12): ln Z ¼ n ln½sinhðasÞ þ ln A
(12)
By putting the T, ε_ , and Q into Eq. (11), the corresponding value of Z is obtained, and the diagrams of lnZ and ln[sinh(as)] are drawn to linear fitting in Fig. 5. The lnZ and ln[sinh(as)] relation curve is linearly dependent, and the rheological behavior of composites under high-temperature compression could be represented by Z using the Arrhenius hyperbolic sine function. The values of n¼4.3829 and lnA¼27.03589 are determined by linear fitting. According to the definition of Arrhenius function and Eq. (12), s could be presented using Z as follows: ( 1 " 2 #12 ) 1 Z n Z n þ þ1 s ¼ ln a A A
Fig. 4 e Relationships of ln [sinh (as)]-ln_ε (a) and ln [sinh (as)]-T¡1(b).
(13)
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Based on theoretics of irreversible thermodynamics [39], the criterion of rheological instability during large deformation is presented: :
xðε Þ ¼
vln½m=ðm þ 1Þ þ m<0 : vlnε
(19)
Where x(_ε) is stability criterion. When instability criterion is met, the material undergoes an unstable rheological process so the unstable deformation behaviour can be predicted, which probably appears adiabatic shear band, cavity nucleation, and kinking, and the process has been applied to several materials [40].
Establishment of the processing map The calculation of power dissipation h
Fig. 5 e Relationship between s and Z.
The obtained values of Q ¼ 284.54 kJ/mol, R ¼ 8.314J/mol$K, a ¼ 0.0031151, and n ¼ 4.3829 are introduced into Eq. (3), and the following Arrhenius rheological stress constitutive equation of TMCs with 0.035 wt% hydrogen was obtained:
ε ¼ 5:5149 1011 ½sinh ð0:0031151Þs4:3829 expð 284:54=RTÞ
(14)
Theoretical basis of processing map Dynamic material model (DMM) was presented by Prasad [35] and was later revised by Rao and Murty [36,37]. DMM relates constitutive behaviour to microstructure change, flow stability, and hot workability [38]. The energy input from outside(P) could be divided into two parts: dissipative quantity (G) and dissipative covariate quantity (J): :
Zε
:
P ¼ sε ¼ G þ J ¼
:
Zs
sdε þ 0
:
ε ds
According to the data of hot compression of TMCs with 0.035 wt% hydrogen (ε ¼ 0.5), the cubic spline function is used to fit the log s log ε_ relationship curve, as shown in Fig. 6. As shown in Fig. 6, log s log ε_ is nonlinear, and logs can be expressed by log_ε, :
2
3
logs ¼ a þ b logε þ cðlogε_ Þ þ dðlogε_ Þ
Basing on Eqs. (16) and (20), the corresponding m can be obtained by introducing the log_ε at different strain rates, then duplicate the step by selecting various temperatures. According to Eq. (18), the power dissipation h is obtained and contour map of h is drawn under the two dimensions of T : logε. Then, the power dissipation map in hot compression of hydrogenated TMCs is obtained, as shown in Fig. 7. Fig. 7 reflects the variable of significantly affect power dissipation h. h is generally decreasing with the increases ε_ , this is identical to the conclusions of many titanium alloy researchers [41,42]. The minimum h is 0.065, which appears in the area with high strain rate. Also, a lower value of h corresponds to a smaller energy dissipated by microstructure evolution.
(15)
0
Where G is energy corresponding to plastic deformation and J is energy corresponding to microstructure evolution. The proportion of G and J is given by strain rate sensitivity m: :
vJ ε vs vðlogsÞ ¼ : ¼ ¼m : vG svε vðlogε Þ
(16)
It is the ideal linear dissipative process when m ¼ 1, J arrives its maximum of Jmax, leading to the following equation: :
Jmax ¼
sε P ¼ 2 2
(17)
In the DMM, the power dissipation h is the utilization rate of energy consumed by microstructure evolution under different thermal-deformation conditions. Therefore, when the value of h is larger, the corresponding processing parameters are the best, leading to the following expression: h¼
J Jmax
¼
2m mþ1
(18)
(20)
Fig. 6 e Graph of log s log ε_ in the isothermal compression of hydrogenated TMCs.
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Fig. 9 e Processing map in isothermal compression of hydrogenated TMCs.
Fig. 7 e Power dissipation efficiency map in isothermal compression of hydrogenated TMCs.
Establishment and analysis of the processing map
The calculation of instability criterion The expression of instability criterion can be derived from Eqs. (16) and (19) as follows: :
xðε Þ ¼
:
vlog½m=ðm þ 1Þ 2c þ 6d logε þm þm¼ : m þ ðm þ 1Þln 10 vlogε
(21)
The instability parameter can be obtained by bringing log_ε and m into Eq. (21). Then, the equivalent contour curve of the instability criterion will be obtained under the two di: mensions of T logε and the instability map of hydrogenated TMCs is obtained, as shown in Fig. 8. : It could be seen in Fig. 8, the variable of T logε significantly impact the instability parameters, and it declines with increased deformation temperature and decreased strain rate. Also, instability parameters that are less than 0 are 0.016, 0.067, and 0.12, which indicates that the material will undergo unstable rheological process. And the rheological instability appears in the area where the strain rate is higher and the material is in unstable region.
Fig. 8 e Instability map in isothermal compression of hydrogenated TMCs.
Superimposing power dissipation map and instability map of the TMCs (0.035 wt%hydrogen), the corresponding processing map can be obtained as Fig. 9. Isoline is the value of h, the gray part represents the instability domain. The processing map can reflect impact of the thermal processing conditions on energy dissipation and instability criterion. Therefore, the unstable region is avoided, and the best thermal processing parameters are obtained. The unstable state of flow stress will be avoided to optimize the microstructure of hot-working materials and promote the performance of workpieces [43]. As shown in Fig. 9, the hydrogenated TMCs exhibits only one instability domain ðε ¼ 0:5Þ, which is the temperature of 750e825 C and strain rate of 0.7e1 s1, that is, lowtemperature and high strain rate domain. The corresponding h value is the lowest, and its value is between 0.065 and 0.16. Thus, the strain rate should not be too high when the hydrogenated TMCs is deformed at middle-low temperature; otherwise, the rheological instability occurs easily. The domains exhibiting the peak value of h ðε ¼ 0:5Þ was the temperature of 780e850 C and strain rate of 0.005e0.6 se1, that is, middle to high-temperature and low strain rate domain. The corresponding h is between 0.065 and 0.16 and corresponds to optimal deformation conditions for high-temperature compression of hydrogenated TMCs. The power dissipation generally decreases with increased strain rate; however, the decrease is not obvious with increased temperature. Also, the influence of thermal deformation energy distribution of composites on the strain rate is significantly greater compared to temperature, when the temperature is between 750 C and 900 C and strain rate is between 0.001 s1 and 1 s1. Microstructures of samples deformed under different domains in the processing map are observed to verify prediction ability about processing map to the unstable and stable domains. Fig. 10a shows the initial microstructure of the hydrogenated TMCs and that the reinforcements distributed along b grain boundary, which is consistent with the microstructures of Wang [19]. And Fig. 10b shows microstructure under deformation conditions of 750 C/1 s1 (low temperature and high strain rate region), which matches to instability
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Fig. 10 e Microstructures of hydrogenated TMCs deformed at different conditions (a)Initial, (b) and (f) 750 C/1 s¡1, (c) 850 C/1 s¡1, (d) 750 C/0.001 s¡1, (e) 850 C/0.001 s¡1.
domain. The figure shows that new grains are formed after deformation, corresponding to DRX. At the same time, the figures show that the grain is elongated by compression, but under this condition, the grain size of microstructure is uneven and some coarse grains appear. As shown in Fig. 10f, cracks appear in multiple SEMs images, indicating that the structure is unsuitable for acquiring homogeneous mechanical properties which ought to be prevented. Fig. 10c and d shows the microstructures under deformation conditions of 850 C/1 s1 (middle-high temperature and high strain rate domain) and 750 C/0.001 s1 (low temperature and low strain rate domain), which match to stability domain. The figures show the microstructure is more homogeneous and there is no crack appears compared with the instability domain. Fig. 10e shows microstructure under deformation conditions under 850 C/0.001s1 (middle-high temperature and low strain rate domain), corresponding to optimal deformation conditions. The figure shows that fine grains are produced after deformation under this condition, and DRX is relatively sufficient. The microstructure is a relatively uniform reticular structure. This kind of microstructure has excellent mechanical properties including plasticity, impact toughness, and fatigue strength, so this deformation condition can be used as the optimal condition during thermal working. The microstructure corresponding to optimal thermal-working parameters is better than the unstable region. Moreover, the microstructure after thermal deformation without cracks, voids, and adiabatic shear bands, showing that the hotworking stable domain determined in this paper is reasonable. The establishment of the hot-processing map has a certain guiding function on the selection of hot-working parameters.
Conclusions (1) When the hydrogen was 0.035 wt%, peak resistance of TMCs decreased 17.2% from 239.8 MPa, which compares
to peak resistance of unhydrogenated TMCs, to 198.47 MPa. (2) The thermal deformation behaviour of Tie6Ale4V/ (TiB þ TiC) composites with 0.035 wt% hydrogen at 750e900 C and 0.001~1s1 was studied, and the deformation resistance declines with increased deformation temperature and decreased strain rate. The constitutive equation of TMCs(0.035 wt%H) is deduced as follows:
ε ¼ 5:5149 1011 ½sinh ð0:0031151Þs4:3829 expð 284:54=RTÞ (3) The establishment and analysis of the processing map in hot compression of TMCs(0.035 wt%H) were constructed at a strain of 0.5. The optimum thermal processing parameters are a deformation temperature range between 780 and 840 C, strain rate range between 0.005 and 0.06 s1. The instability domain occurs in temperature range between 750 and 825 C and the strain rate range between 0.7 and 1 s1. (4) The microstructures corresponding to optimum parameters are relatively uniform and fine reticular structure with no instability such as cracks and voids, and DRX is relatively sufficient. And the microstructures corresponding to instability domain are inhomogeneous and cracks occur; therefore, thermal processing should be avoided in this working environment.
Acknowledgments This work was supported the Natural Science Foundation Key Plan of Liaoning (20180510056), National Natural Science Foundation of China (51401129, 51871075, 51875365), National Key Research and Development Program of China (2016YFB0301201), and Major Science and Technology Special Plan of Yunnan (2018ZE013).
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