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Hot deformation behavior and processing workability of a Ni-based alloy
Accepted Manuscript Hot deformation behavior and processing workability of a Ni-based alloy Zhipeng Wan, Lianxi Hu, Yu Sun, Tao Wang, Zhao Li PII:
S0925-8388(18)32884-6
DOI:
10.1016/j.jallcom.2018.08.010
Reference:
JALCOM 47098
To appear in:
Journal of Alloys and Compounds
Received Date: 16 April 2018 Revised Date:
1 August 2018
Accepted Date: 2 August 2018
Please cite this article as: Z. Wan, L. Hu, Y. Sun, T. Wang, Z. Li, Hot deformation behavior and processing workability of a Ni-based alloy, Journal of Alloys and Compounds (2018), doi: 10.1016/ j.jallcom.2018.08.010. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Graphical Abstract
ACCEPTED MANUSCRIPT Hot deformation behavior and processing workability of a Ni-based alloy Zhipeng Wan1, 2, 3, Lianxi Hu1, 2*, Yu Sun1, 2**, Tao Wang3, Zhao Li3 1 National Key Laboratory for Precision Hot Processing of Metals, Harbin Institute of Technology, Harbin 150001, P.R. China
Harbin 150001, China
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2 School of Materials Science and Engineering, Harbin Institute of Technology,
3 Science and Technology on Advanced High Temperature Structural Materials
China
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ABSTRACT
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Laboratory, AEEC Beijing Institute of Aeronautical Materials, Beijing 100095, P.R.
In the present work, the high-temperature deformation behavior of a U720LI alloy was investigated by means of hot compression tests at temperatures of 1060-1180oC, strain rates of 0.001-10s-1 under true strain of 0.8. The Arrhenius-type model, considering the dissolution of γ' precipitates, was established on the basis of the friction
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and adiabatic heating corrected flow stress data. The hot deformation activation energies for quasi-γ phase and γ+γ' dual-phase microstructures were determined as 417 kJ·mol-1 and 687 kJ·mol-1, respectively. The high activation energy for γ+γ' dual-phase
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microstructures was mainly attributed to the precipitation hardening effect of γ' (Ni3(Al,Ti)) particles which hindered dislocation slip via the pinning effect during hot
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deformation. The processing map was developed based on the dynamic material model. According to the detailed microstructural investigations, the optimum hot deformation domains of U720LI alloy were identified as 1080-1100oC/0.01-0.3s-1 for γ+γ' dual-phase microstructure and 1140-1160oC/0.01-0.1s−1 for quasi-γ phase microstructure, respectively. * Corresponding author. ** Corresponding author. Tel.: +86 451 86418613. Fax: +86 451 86418613. E-mail addresses: [email protected] (L.X. Hu), [email protected] (Y. Sun). 1
ACCEPTED MANUSCRIPT Keywords: U720LI alloy; Hot deformation behavior; Processing map; Workability.
1. Introduction U720LI alloy is a typical cast-wrought nickel-based alloy used for turbine discs and
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blades up to 730oC [1]. Compared with the Udimet720 alloy, U720LI alloy was developed by decreasing the chemistry of interstitials, i.e. C and B in Udimet720 alloy, and then the term ‘‘low interstitial” abbreviated as ‘‘LI”. Chromium content has also been reduced from 18% to 16% to prevent the formation of sigma phase to long-term
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high-temperature exposure [2]. U720LI alloy possesses excellent mechanical properties at high temperature [3, 4] and is quite stable in the long-term (as long as
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1000h) exposed at 760oC [5]. Generally, the mechanical properties of materials rely on the microstructure which, in turn, are controlled by hot deformation parameters such as temperature, strain and strain rate. Thus, the Arrhenius-type equation and processing map play important roles in characterization of flow stress behavior, optimization of process parameters and microstructure control for metals and alloys during hot
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deformation. Tan et al. [6] have studied the hot deformation behavior of fine grained Inconel 718 superalloy. The flow stress values predicted by the developed Arrhenius-type constitutive equation were in reasonable agreement with the
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experimental values, and optimum process parameters were determined based on the established processing maps. Zhang et al. [7] have investigated the hot working
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characteristics of Ni-Cr-Mo-based C276 superalloy based on the flow stress curves and microstructure. Two peaks of efficiency corresponding to the occurrence of DRX were determined to be deformed at 1125oC and 0.1s-1 as well as 1025oC and 0.001s-1. Wu et al. [8] have developed the Arrhenius-type equation and processing map in the temperature range of 1050-1150oC and strain rates of 0.001-1 s-1 for hot isostatic pressed spray formed FGH100 alloy. Pu et al. [9] have studied the flow stress behavior and hot workability of nickel-based alloy UNS10276. The flow instability behavior, induced by microbands, deformation twins and restrained dynamic recrystallization (DRX) behavior, was identified at temperatures lower than 1180oC and strain rates 2
ACCEPTED MANUSCRIPT higher than 5s-1. Moreover, the roles of glide or climbing of dislocations, microtwins, stacking faults and atomic diffusion in various hot deformation conditions have been revealed [10-13]. Over the past few years, lots of efforts have been made on the U720LI alloy. Chang
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et al. [14] have studied the solidification behavior of U720LI superalloy. It demonstrated that the formation of η-phase, which was harmful to the mechanical property, was mainly attributed to the limited solubility of Ti in primary γ phase and γ/γ' Eutectic. However, increasing boron content can significantly retard the γ matrix
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solidification, which would increase the eutectic (γ+γ') precipitation and reduce the formation of η-phase phase and Zr-rich particles [15]. The interactions of slip bands
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with grain boundaries for U720LI alloy have been investigated by SEM and EBSD techniques during tensile tests [16]. The twist angle between projections of slip bands and the boundary plane was identified to govern slip transfer processes. Németh et al. [17] have identified a relationship between tensile ductility and oxidation kinetics for
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U720LI superalloy. The results suggested that the internal intergranular oxidation along the γ-grain boundaries, and in particular, at incoherent interfaces of the primary γ' precipitates and γ matrix may cause the embrittlement of the alloy. Furthermore, the flow stress behavior and microstructural changes during hot deformation of U720LI
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alloy have been proposed in some previous studies. Liu et al. [18] have studied the hot deformation behavior of U720LI alloy with fine, coarse and mixed grains,
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respectively. Dynamic softening mechanism and the effect of γ' precipitates on microstructure evolution were identified. For the coarse grain, the nucleation of DRX grains was influenced by the γ′ interparticle spacing [19]. Qu et al. [20] have established the constitutive equation and the processing map of GH4720Li alloy based on the flow stress during hot compression tests. However, the effect of phase transformation during hot compression tests was not considered and the validity of the optimum process parameters were not testified by the microstructure. In this study, the hot deformation behavior of U720LI nickel-based alloy is investigated according to 3
ACCEPTED MANUSCRIPT hot compression tests. The Arrhenius-type model considering the dissolution of γ' precipitates is established using the corrected stress-strain data and the optimum process parameters for hot deformation are determined with the validation of
2. Experimental materials and procedures
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deformed microstructure in both quasi-γ phase and γ+γ' dual-phase regions.
The main chemical composition (wt %) of U720LI alloy used in this research is as follows: C 0.018, Cr 15.94, Co 14.5, W 1.25, Mo 2.94, Al 2.56, Ti 4.91, Zr 0.03, and
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balance Ni. The microstructure of the initial material from an as-forged bar is shown in Fig. 1 and its average grain size is 21µm. The specimen with a diameter of 10 mm
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and a height of 15 mm was cut by electric-discharge machining and were deformed using a Gleeble 3800 thermal simulation machine. High quality graphite sheet with thickness of 0.05 mm was utilized between anvils and specimen surface to reduce the friction effect during hot deformation. As shown in Fig. 2, the specimens were heated up to deformation temperatures of 1060oC, 1080oC, 1100oC, 1120oC, 1140oC, 1160oC
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and 1180oC at a rate of 10oC/s and held for 5min to minimize temperature gradient. Compression tests were conducted to a true strain of 0.8 at strain rates ( ε& ) of 0.001s-1, 0.01s-1, 0.1s-1, 1s-1 and 10s-1, and then immediately quenched in water to freeze the
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microstructure. All of the compressed specimens were cut parallel to the compression axis by wire-electric discharge machine. After mechanical polishing, the specimens
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were chemical-etched using 5g CuCl2+100ml C2H5OH+100ml HCl, and optical microscope (OM) was employed for microstructure observations.
Fig. 1. Initial microstructure of as-forged U720LI alloy. 4
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Fig. 2. Schematic diagram of hot compression test in this work.
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3. Results and discussion
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3.1. Corrections of friction and adiabatic heating on flow stress curves 3.1.1. Correction of the friction effect
During uniaxial hot compression tests, the presence of friction can lead to the formation of dead zones and inhomogeneous deformation, and flow stress deviates from their true values. Compared with the sliding friction, the effect of sticking one at
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higher temperature would increase the flow stress significantly. Therefore, in order to evaluate the effect of friction and determine the accurate flow stress during hot deformation, researchers employed the simplified relations to eliminate the effect of
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friction on flow stress curves at high deformation temperatures. The corrected flow stress considering the friction effect can be written as [21, 22]:
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σf =
(
)
σ
1 + 2 3 3 f ( r0 h0 ) exp ( 3ε 2 )
(1)
where σf is the corrected flow stress, σ is the measured flow stress, ε is the measured strain and f is the friction factor. r0 and h0 are the initial radius and height of samples, respectively. It can be noted from the Eq. 1 that the friction factor (f) plays an important role in determining the value of corrected flow stress. The friction factor f is always taken as a constant [22, 23], while the experimental evidence demonstrates that the friction factor f is related to the deformation temperature and strain rate [21]. Based on the theory proposed by Ebrahimi and Najafizadeh, the friction factor can be 5
ACCEPTED MANUSCRIPT determined by [21, 24]: f =
(r h)b
(2)
( 4 3 ) − ( 2b 3 3 )
where b is the barrel parameter, h and r are height and average radius of cylinder after
b=4
∆r h r ∆h
r = r0
h0 h
(3)
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as:
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deformation. The barrel parameter (b) and average radius(r) in Eq. 2 can be expressed
(4)
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where ∆h and ∆r are reduction of height and difference between maximum and top radius of cylinder after deformation. According to Eqs. 2-4, the friction factor can be determined by measuring the height, maximum radius and top radius of cylinder after deformation. However, it is difficult to measure the top radius of cylinder after deformation accurately. Therefore, with approximation of the profile of the barreled
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samples with an arc of a circle, top radius of cylinder after deformation can be calculated by following equation[21]:
h0 2 r0 − 2rM2 h
(5)
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rT = 3
where rM and rT are maximum and top radius of cylinder after deformation, as shown
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in Fig. 3. Therefore, the friction factor (f) can be calculated by measuring the maximum radius (rM) as well as the height of cylinder after deformation (h) according to the Eqs. 2-5. The predicted frictionless flow stress curves derive from the Eq. 1 are shown in Fig. 4a. It can be seen from the figure that the corrected flow stress is lower than measured flow stress. The difference between corrected and uncorrected flow stress curves increases with increasing strain, which is mainly attributed to the increased contact surface between the specimen and die. In additions, compared with the uncorrected flow stress curves, the work hardening behavior is eliminated after correction of the friction effect. 6
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Fig. 3. Schematic diagram of parameters in Eqs. 1-5.
Fig. 4. Corrected flow stress curves due to the friction and adiabatic heating effects of
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U720LI alloy under various temperatures and strain rates: (a) 1100 oC and (b) 10s-1. 3.1.2. Correction of the adiabatic heating effect The decrease of flow stress after reaching a peak stress is a familiar appearance for
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various alloys attributing to the flow softening effect. The softening effect can be arisen from microstructural change and increase of temperature in alloys during hot
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deformation, both or either alone. Microstructural changes mainly indicate the occurrence of continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX) behavior in nickel-based alloy. The increase of temperature in alloys during hot deformation is related to the stain rate. At high strain rate, the hot compression tests are considered as the adiabatic condition, and temperature of the samples increases significantly. While temperature variation caused by deformation is negligible at low strain rate (isothermal condition). Therefore, to remove the effect of temperature rise caused by adiabatic heating, an expression for temperature correction should be performed on the flow stress curves. The flow stress 7
ACCEPTED MANUSCRIPT ( σ ) corresponding to the actual temperature T can be expressed as follows [22, 23, 25, 26]:
σ =σ f +
0.95 ρC p
( ∫ σ dε ) B ddσT ε
f
(6)
f
0
ε& ,ε
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where ρ and Cp are the density and specific heat of deformed material, respectively. T is the absolute temperature (K) during hot deformation. The adiabatic correction factor (B) in Eq. 6 can be calculated using the following equation:
−1
(7)
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ε B = 1 + ( ( xw K w ) + (1 HTC ) + ( xD K D ) ) xw ρ C pε&
where xw is half height of the deformed sample, Kw is the thermal conductivity of
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deformed material, HTC is the interface heat-transfer coefficient, xD is the distance from the die surface to the die interior where temperature is constant and KD is the thermal conductivity of die. The parameters in Eqs. 6 and 7 are shown in Table 1. In this study, the effect of adiabatic heating is ignored because of the negligible
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temperature rise effect for the strain rates lower than 1s-1, and the similarity conditions are performed on 904L austenitic stainless steel and powder metallurgy Ti-47Al-2Cr-2Nb-0.2W alloy [24, 27]. The corrected flow stress curves due to the adiabatic heating and friction effects are shown in Fig. 4b. These curves exhibit a peak
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in the flow stress at a strain and reach a steady state, which indicates that the corrected flow stress curve displays the characteristic of dynamic recrystallization (DRX).
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Table 1 Parameters in Eq. 3 and 4[25, 28, 29].
Parameter ρ Cp Kw KD HTC xD
Value 8140 (kg·m-3) 750 (J·kg-1·K-1) 29 (W·mK-1) 21 (W·mK-1) 25000 (W·m-2·K-1) 0.015 (m)
3.2. Arrhenius-type constitutive equation Generally, the relationship among the flow stress, deformation temperature and 8
ACCEPTED MANUSCRIPT strain rate for a give strain can be described by the Arrhenius-type equation. The Zener-Holloman parameter (Z) which represents the effects of strain rate and temperature on flow stress can be expressed as [30]:
A sinh ασ n ( ) Q n Z = ε& exp( ) = f (σ ) = A1σ 1 RT A exp βσ ( ) 2
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(8)
where Q is the activation energy (kJ·mol-1), R is the universal gas constant (8.314
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kJ·mol-1·K-1). As shown in Eq. 8 that correlationship between Z and the flow stress can be determined by exponential, power and hyperbolic type equations. A, A1, A2, n1,
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α and β are material constants and n is stress exponent. The peak stress level is employed to depict the hot deformation behavior. Taking the natural logarithm of Eq. 8:
ln ( A ) + n ln sinh (ασ ) Q 1 ln ( ε& ) + = ln ( A1 ) + n1 ln (σ ) R T ln ( A2 ) + βσ
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(9)
Material constants β, n1 and n can be determined by taking partial differential on
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both sides of Eq. 9 for a given deformation temperature, as expressed in the following equations [31, 32].
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∂ ln ε& ∂ ln ε& ∂ ln ε& β = ; n1 = ; n= σ σ ∂ ∂ ln ασ ∂ ln sinh T T ( p ) p p
(10) T
The values of β and n1 can be determined from the Eq. 10 by employing the
corrected flow stress. Hence, the material constant α can be obtained (α=β/n1), and the stress exponent n is deduced by linear regression. Taking partial differential on both sides of Eq. 9 and rearranging yields:
∂ ln ε& Q = R ∂ ln sinh (ασ p ) T 9
∂ ln sinh (ασ p ) ∂ 1 T ( ) ε&
(11)
ACCEPTED MANUSCRIPT In Eq. 11, the activation energy can be determined by the slope of ln [sinh(ασ)] versus 1/T. Based on the quantitative metallography, the majority amount of the γ' precipitates are dissolved at a temperature of 1140oC and a hold time of 5min, and the mass percent of the γ' precipitates is no more than 5% according to the phase
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diagram[18]. The precipitation hardening effect induced by γ' precipitates reduces significantly. Thus the samples deformed at the temperature of 1140oC can be approximately considered as in the single γ phase region. Then the deformation temperature over 1140oC is termed as quasi-γ phase region. The plots used to derive
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average values of n1, β, α, n, Q and InA are shown in Fig. 5. Based on the experimental data (shown in Fig. 5), the average values of n1, β, α, n, Q and InA for
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U720LI alloy during hot compression tests are shown in Table 2. The microstructure of γ+γ' dual-phase and quasi-γ phase is modelled using two linear ranges from which the activation energy is determined separately for the two phase regions, as shown in Fig. 5c. It can be seen from Table 2 that the value of stress exponent is 3.571, which is similar to other nickel-based alloys [33-35]. The activation energies Q for quasi-γ
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phase and γ+γ' dual-phase microstructures of U720LI alloy are 417 kJ·mol-1 and 687 kJ·mol-1, respectively. They are higher than the self-diffusion energy of pure nickel alloy (270 kJ·mol-1) [36]. This suggests that the pinning effect of γ' precipitates and
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hardening effect induced by alloying element are able to enhance the deformation activation process significantly. However, the activation energies for U720LI alloy are
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lower than that of Udimet720 alloy in the range of 470-743 kJ·mol-1 [37], which is mainly attributed to the high content of interstitials (carbon, C and boron, N) and alloying element (chromium, Cr) compared with the U720LI alloy [38]. Consequently, by substituting the parameters listed in Table 2, the constitutive equations at peak stress level can be expressed as:
ε& = 9.535 × 1024 sinh ( 0.00687σ p ) for γ+γ' dual-phase microstructure, and:
10
3.571
exp(−
687000 ) RT
(12)
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p
)
3.571
exp(−
417000 ) RT
(13)
for quasi-γ phase microstructure. Comparison between peak stresses experimentally determined and calculated by the established Arrhenius-type constitutive equation is shown in Fig. 6. It can be seen from the figure that the calculated peak stresses agree
model prediction can be identified at a strain rate of 10s-1.
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well with the experimental results at strain rates of 0.001-1s-1, while a low accuracy of
U720LI alloy. n1
β
4.544
0.0312
γ+γ' dual-phase
n
Q (kJ·mol-1)
lnA
0.00687
687
57.517
417
34.026
3.571
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Quasi-γ phase
α
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Phase region
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Table 2 Kinetic parameters for γ+γ' dual-phase and quasi-γ phase microstructures of
Fig. 5. Plots of ln ε& -ln σ p (a) and ln ε& -ln[sinh(α σ p )] (b) at different temperatures, (c) Plot of ln[sinh(α σ p )]-1000/T for quasi-γ phase and γ+γ' dual-phase microstructures and (d) relationship between lnZ and ln[sinh(α σ p )] of U720LI alloy. 11
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Fig. 6. Comparison between peak stresses experimentally determined and calculated by
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the established Arrhenius-type constitutive equation. 3.3. Establishment of processing map
To predict the optimum processing conditions of U720LI alloy during hot deformation, the processing map is presented in this section. A processing map is developed based on dynamic materials model (DMM) which is proposed by
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Prasad[39]. In the DMM, the total power energy P can be divided into two main parts, one is the power dissipation (G) indicating the dissipation energy value arising from plastic deformation, and the other one is metallurgical processes (J) which is related to
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the energy concerning the microstructural changes, like dynamic recovery and dynamic recrystallization. The correlationship among P, G and J can be expressed
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mathematically as [40, 41]:
σ
ε
0
0
P = G + J = ∫ ε& dσ + ∫ σ d ε&
(13)
The partitioning of power between J and G is given by the following equation:
& d ln σ ∆ log σ dJ ε& dσ εσ = = ≈ =m dG σ d ε& σ ε&d ln ε& ∆ log ε&
(14)
where m is the strain rate sensitivity. For a certain temperature, J can be simplified to: J max =
12
mσ ε& m +1
(15)
ACCEPTED MANUSCRIPT Eq. 15 indicates that the value of J at any given temperature and strain rate can be determined according to the flow stress ( σ ), strain rate ( ε& ) and strain rate sensitivity (m). A maximum value of J can be obtained when m equals to 1, and the process is considered as an ideal linear dissipator, thus:
σ ε&
(16)
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J max =
2
The efficiency of power dissipation (η), which indicates the power dissipation
dimensionless parameter [31]: 2m m +1
(17)
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η = J J max =
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capacity of the sample, for a non-linear dissipator can be defined in terms of a
Domains with high η in power dissipation map can be identified as the optimum processing conditions, which should be further supported by the microstructure of deformed samples. The flow instability characterized by adiabatic shear bands, slip localization and crack formation based on the grain boundary cavitation should also be
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considered when the optimum processing conditions are determined [42]. Therefore, the flow instability map based on a continuum instability criterion is established. Further, the extremum principles of irreversible thermodynamics as applied to continuum mechanics of large plastic deformation are employed to identify the
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occurrence of flow instability. The instability criteria ξ ( ε& ) is expressed by [43]:
ξ ( ε& ) =
∂ ln m ( m + 1) +m≤0 ∂ ln ε&
(18)
It can be deduced from the Eq. 18 that the instability domains are characterized by
the negative value of ξ ( ε& ) . In this study, the corrected flow stress curves are used to determine m, η and ξ, and then the processing map is established according to the superimposition of power dissipation map and instability map at a strain of 0.8, as shown in Fig. 7. The processing map is a three dimensional plot with isocontour lines which is dependent on deformation temperature and strain rate at a given strain. It can 13
ACCEPTED MANUSCRIPT be seen from the Fig. 7 that the gray colored regions represent the unstable zones and the white colored domain denotes stable zones. The processing map in this study is divided into three main domains, and the workability of the sample in each domain is discussed with the help of the deformed microstructure. The domain C with the η of
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10-25% and negative ξ ( ε& ) exists in the temperature range of 1060-1100oC and strain rates of 1-10s-1 for a true strain of 0.8. In general, the flow instability of the samples during hot deformation could be probably associated with adiabatic shear
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bands, localized plastic flow or cracking[44]. It could be seen from the Fig. 7 that the main instability domain, identified from the microstructure in Domain C, is
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characterized by the adiabatic shear bands. It has been widely acknowledged that the adiabatic heating during hot deformation is occurred at higher strain rates due to insufficient deformation times [43]. Domain B indicates the unstable zone with high η (the maximum η is about 25%) deformed in the temperature range of 1140-1180oC and strain rates of 1-10s-1 for a true strain of 0.8. The microstructure in Domain B
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corresponds to the instability mechanisms characterized by cracking along the compressed grain boundary, as shown in Fig. 7. At high strain rates and temperature, grain boundary length per unit area decreases with the increase of deformation
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temperature and the stress concentration at grain boundaries could not be released instantly due to insufficient time [43], and then the intergranular cracking initiates. In
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addition, the microstructure shown in domain B of Fig. 7 exhibits the typical incomplete DRX behavior with necklace structure, which suggests that initiation of DRX nuclei distributes along the large size of deformed grain boundaries. The deformation condition with high power dissipation efficiency in the stable
region are termed as domain A, as seen from Fig. 7. Domain A is mainly composed of two stable regions with high η found to be nearly 31-43%, which corresponds to microstructure representing a homogeneous and completed dynamic recrystallization structures without deformation defect. Moreover, it could be seen from the processing map shown in Fig. 7, the high efficiency of power dissipation (about 49%) deformed 14
ACCEPTED MANUSCRIPT at 1180oC/0.01s-1 is presented in the stable zone, while the average grain size of the deformed sample exhibits extraordinary grain growth behavior depended on its high temperature and low strain rate, as shown in Fig. 8. Therefore, based on Eqs. 17 and 18 as well as validation of micrographs, optimum processing conditions for the alloy in
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this study are 1080-1100oC/0.01-0.3s-1 and 1140-1160oC/0.01-0.1s−1.
Fig. 7. Processing map of U720LI alloy at ε=0.8 with microstructure validation in
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different deformation regions.
The microstructure evolution of samples deformed at a strain of 0.8 and various
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deformation conditions is shown in Fig. 8. It can be seen from the figure that the growth of dynamic recrystallized grain is promoted by the increase of deformation temperature and decrease of strain rate. Generally, the correlationship between Z and DRX grain size can be expressed by an exponential function[45]. However, the presence of precipitates corresponding to the chemical composition of the alloy and the adiabatic shear bands because of the inhomogeneous deformation would affect the deformed microstructure of the materials significantly. Thus, the correlationship between Z and DRX grain size (dDRX) is not always possible to be established or 15
ACCEPTED MANUSCRIPT presents poor correlation coefficient for some specific alloys [36, 46, 47]. The distribution of DRX grain size under various deformation conditions as well as the variation of Z with respect to DRX grain size are shown in Fig. 9. It can be seen from Fig. 9a that the average DRX grain size is not sensible to the deformation temperature
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at high strain rate due to the occurrence of complete DRX behavior and the restrained grain growth behavior. Hence, as shown in Fig. 9b, it is impossible to establish a
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relation between Z and DRX grain size in the present investigation.
Fig. 8. Microstructure of U720LI alloy at the strain of 0.8 with different hot compression conditions.
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Fig. 9. (a) Distribution of DRX grain size under various deformation conditions and (b) relationship between Z and DRX grain size of U720LI alloy.
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4. Conclusions
Hot deformation behavior and workability of U720LI alloy were investigated by using the hot compression tests on Gleeble 3800 thermal-mechanical simulator, and following conclusions can be drawn:
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(1) The experimental flow stress for all deformation conditions was modified by the correction of friction effect, and the influence of adiabatic heating effect on the flow stress was also discussed for strain rates of 10s-1 and 1s-1. The dynamic recrystallization was identified as the dominant softening mechanism for U720LI
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alloy based on the corrected flow stress curves due to the friction and adiabatic heating effects.
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(2) The Arrhenius-type model considering the dissolution of γ' precipitates was
established using corrected flow stress. The dependence of flow stress on strain rate and temperature during hot deformation can be expressed as: 3.571
exp(−
687000 ) RT
3.571
exp(−
417000 ) RT
ε& = 9.535 × 1024 sinh ( 0.00687σ )
for γ+γ' dual-phase microstructure,
ε& = 5.988 × 1014 sinh ( 0.00687σ ) for quasi-γ phase microstructure.
(3) Activation energies Q for quasi-γ phase and γ+γ' dual-phase microstructuress of 17
ACCEPTED MANUSCRIPT U720LI alloy were 417 kJ·mol-1 and 687 kJ·mol-1, respectively. The activation energy of U720LI alloy was higher than the self-diffusion energy of pure nickel alloy and lower than Udimet720 alloy in the range of 470-743 kJ·mol-1. (4) Based on the analysis of power dissipation efficiency and microstructure
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evolution, the optimum hot deformation processing conditions for γ+γ' dual-phase and quasi-γ phase microstructures were determined be 1080-1100oC/0.01-0.3s-1 and
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1140-1160oC/0.01-0.1s−1, respectively.
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ACCEPTED MANUSCRIPT Acknowledgment This research did not receive any specific grant from funding agencies in the public,
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commercial, or not-for-profit sectors.
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ACCEPTED MANUSCRIPT Data availability The raw/processed data required to reproduce these findings can be shared, and data
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will be available on request.
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References [1] K. Gopinath, A.K. Gogia, S.V. Kamat, et al., Dynamic strain ageing in Ni-base superalloy 720Li, Acta Mater. 57 (2009) 1243-1253. [2] M.P. Jackson, R.C. Reed, Heat treatment of Udimet 720Li: the effect of
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microstructure on properties, Mater. Sci. Eng. A 259 (1999) 85-97. [3] M. Marchionni, G.A. Osinkolu, G. Onofrio, High temperature low cycle fatigue behaviour of Udimet 720 Li superalloy, Int. J. Fatigue 24 (2002) 1261-1267.
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alloy 720 billet, Superalloys 2008 (2008) 311-316. [14] L.T. Chang, H. Jin, W.R. Sun, Solidification behavior of Ni-base superalloy Udimet 720Li, J. Alloys Compd. 653 (2015) 266-270.
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[27] X.P. Liang, Y. Liu, H.Z. Li, et al., Constitutive relationship for high temperature deformation of powder metallurgy Ti–47Al–2Cr–2Nb–0.2W alloy, Mater. Des. 37
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Part Ⅰ , China Zhijian Publishing House, Standards Press of China, 2012, pp. 870-872. [30] Y.T. Wu, Y.C. Liu, C. Li, et al., Deformation behavior and processing maps of Ni3Al-based superalloy during isothermal hot compression, J. Alloys Compd. 712 (2017) 687-695.
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[31] S.A. Sajjadi, A. Chaichi, H.R. Ezatpour, et al., Hot Deformation Processing Map and Microstructural Evaluation of the Ni-Based Superalloy IN-738LC, J. Mater, Eng.
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Perform. 25 (2016) 1269-1275. [32] H.R. Ezatpour, A. Chaichi, S.A. Sajjadi, The effect of Al2O3-nanoparticles as the reinforcement additive on the hot deformation behavior of 7075 aluminum alloy, Mater. Des. 88 (2015) 1049-1056. [33] X.M. Chen, Y.C. Lin, D.X. Wen, et al., Dynamic recrystallization behavior of a typical nickel-based superalloy during hot deformation, Mater. Des. 57 (2014) 568-577. [34] H.B. Zhang, K.F. Zhang, Z. Lu, et al., Hot deformation behavior and processing map of a γ′-hardened nickel-based superalloy, Mater. Sci. Eng. A 604 (2014) 1-8. 23
ACCEPTED MANUSCRIPT [35] Y.H. Liu, Y.Q. Ning, Z.K. Yao, et al., Plastic deformation and dynamic recrystallization of a powder metallurgical nickel-based superalloy, J. Alloys Compd. 675 (2016) 73-80. [36] N.R. Jaladurgam, A.K. Kanjarla, Hot deformation characteristics and
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microstructure evolution of Hastelloy C-276, Mater. Sci. Eng. A 712 (2018) 240-254. [37] T. Sakai, M. Ohashi, Dislocation substructures developed during dynamic recrystallisation in polycrystalline nickel, Mater. Sci. Tech. 6 (1990) 1251-1257.
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observation, J. Alloys Compd. 652 (2015) 30-38. [42] Y.M. Kim, Y.B. Song, S.H. Lee, et al., Characterization of the hot deformation
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behavior and microstructural evolution of Ti–6Al–4V sintered preforms using materials modeling techniques, J. Alloys Compd. 676 (2016) 15-25. [43] S.W. Zeng, A.M. Zhao, H.T. Jiang, et al., Flow behavior and processing maps of Ti-44.5Al-3.8Nb-1.0Mo-0.3Si-0.1B alloy, J. Alloys Compd. 698 (2017) 786-793. [44] X.N. Peng, H.Z. Guo, Z.F. Shi, et al., Study on the hot deformation behavior of TC4-DT alloy with equiaxed α+β starting structure based on processing map, Mater. Sci. Eng. A 605 (2014) 80-88. [45] V.A. Kumar, R.K. Gupta, S.V.S.N. Murty, et al., Hot workability and 24
ACCEPTED MANUSCRIPT microstructure control in Co20Cr15W10Ni cobalt-based superalloy, J. Alloys Compd. 676 (2016) 527-541. [46] G. Meng, B.L. Li, H.M. Li, et al., Hot deformation behavior of an Al–5.7wt.%Mg alloy with erbium, Mater. Sci. Eng. A 516 (2009) 131-137.
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superalloy 718, Mater. Sci. Eng. A 528 (2011) 3218-3227.
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[47] Y. Wang, W.Z. Shao, L. Zhen, et al., Hot deformation behavior of delta-processed
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Figure captions Fig. 1. Initial microstructure of as-forged U720LI alloy. Fig. 2. Schematic diagram of hot compression test in this work. Fig. 3. Schematic diagram of parameters in Eqs. 1-5.
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Fig. 4. Corrected flow stress curves due to the friction and adiabatic heating effects of U720LI alloy under various temperatures and strain rates: (a) 1100 oC and (b) 10s-1.
Fig. 5. Plots of ln ε& -ln σ p (a) and ln ε& -ln[sinh(α σ p )] (b) at different temperatures, (c)
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Plot of ln[sinh(α σ p )]-1000/T for quasi-γ phase and γ+γ' dual-phase microstructures and (d) relationship between lnZ and ln[sinh(α σ p )] of U720LI alloy.
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Fig. 6. Comparison between peak stresses experimentally determined and calculated by the established Arrhenius-type constitutive equation.
Fig. 7. Processing map of U720LI alloy at ε=0.8 with microstructure validation in different deformation regions.
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Fig. 8. Microstructure of U720LI alloy at the strain of 0.8 with different hot compression conditions.
Fig. 9. (a) Distribution of DRX grain size under various deformation conditions and
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(b) relationship between Z and DRX grain size of U720LI alloy.
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Table captions Table 1 Parameters in Eq. 3 and 4[25, 28, 29]. Table 2 Kinetic parameters for γ+γ' dual-phase and quasi-γ phase microstructures of
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U720LI alloy.
27
ACCEPTED MANUSCRIPT Highlights Hot deformation behavior was investigated in a wide range of processing conditions. Arrhenius-type model was established considering the dissolution of γ’
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precipitates. Hot workability was discussed according to processing map and microstructure.
Optimal processing conditions were determined in quasi-γ and γ+γ’ phase
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regions.
S0925-8388(18)32884-6
DOI:
10.1016/j.jallcom.2018.08.010
Reference:
JALCOM 47098
To appear in:
Journal of Alloys and Compounds
Received Date: 16 April 2018 Revised Date:
1 August 2018
Accepted Date: 2 August 2018
Please cite this article as: Z. Wan, L. Hu, Y. Sun, T. Wang, Z. Li, Hot deformation behavior and processing workability of a Ni-based alloy, Journal of Alloys and Compounds (2018), doi: 10.1016/ j.jallcom.2018.08.010. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Graphical Abstract
ACCEPTED MANUSCRIPT Hot deformation behavior and processing workability of a Ni-based alloy Zhipeng Wan1, 2, 3, Lianxi Hu1, 2*, Yu Sun1, 2**, Tao Wang3, Zhao Li3 1 National Key Laboratory for Precision Hot Processing of Metals, Harbin Institute of Technology, Harbin 150001, P.R. China
Harbin 150001, China
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2 School of Materials Science and Engineering, Harbin Institute of Technology,
3 Science and Technology on Advanced High Temperature Structural Materials
China
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ABSTRACT
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Laboratory, AEEC Beijing Institute of Aeronautical Materials, Beijing 100095, P.R.
In the present work, the high-temperature deformation behavior of a U720LI alloy was investigated by means of hot compression tests at temperatures of 1060-1180oC, strain rates of 0.001-10s-1 under true strain of 0.8. The Arrhenius-type model, considering the dissolution of γ' precipitates, was established on the basis of the friction
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and adiabatic heating corrected flow stress data. The hot deformation activation energies for quasi-γ phase and γ+γ' dual-phase microstructures were determined as 417 kJ·mol-1 and 687 kJ·mol-1, respectively. The high activation energy for γ+γ' dual-phase
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microstructures was mainly attributed to the precipitation hardening effect of γ' (Ni3(Al,Ti)) particles which hindered dislocation slip via the pinning effect during hot
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deformation. The processing map was developed based on the dynamic material model. According to the detailed microstructural investigations, the optimum hot deformation domains of U720LI alloy were identified as 1080-1100oC/0.01-0.3s-1 for γ+γ' dual-phase microstructure and 1140-1160oC/0.01-0.1s−1 for quasi-γ phase microstructure, respectively. * Corresponding author. ** Corresponding author. Tel.: +86 451 86418613. Fax: +86 451 86418613. E-mail addresses: [email protected] (L.X. Hu), [email protected] (Y. Sun). 1
ACCEPTED MANUSCRIPT Keywords: U720LI alloy; Hot deformation behavior; Processing map; Workability.
1. Introduction U720LI alloy is a typical cast-wrought nickel-based alloy used for turbine discs and
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blades up to 730oC [1]. Compared with the Udimet720 alloy, U720LI alloy was developed by decreasing the chemistry of interstitials, i.e. C and B in Udimet720 alloy, and then the term ‘‘low interstitial” abbreviated as ‘‘LI”. Chromium content has also been reduced from 18% to 16% to prevent the formation of sigma phase to long-term
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high-temperature exposure [2]. U720LI alloy possesses excellent mechanical properties at high temperature [3, 4] and is quite stable in the long-term (as long as
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1000h) exposed at 760oC [5]. Generally, the mechanical properties of materials rely on the microstructure which, in turn, are controlled by hot deformation parameters such as temperature, strain and strain rate. Thus, the Arrhenius-type equation and processing map play important roles in characterization of flow stress behavior, optimization of process parameters and microstructure control for metals and alloys during hot
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deformation. Tan et al. [6] have studied the hot deformation behavior of fine grained Inconel 718 superalloy. The flow stress values predicted by the developed Arrhenius-type constitutive equation were in reasonable agreement with the
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experimental values, and optimum process parameters were determined based on the established processing maps. Zhang et al. [7] have investigated the hot working
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characteristics of Ni-Cr-Mo-based C276 superalloy based on the flow stress curves and microstructure. Two peaks of efficiency corresponding to the occurrence of DRX were determined to be deformed at 1125oC and 0.1s-1 as well as 1025oC and 0.001s-1. Wu et al. [8] have developed the Arrhenius-type equation and processing map in the temperature range of 1050-1150oC and strain rates of 0.001-1 s-1 for hot isostatic pressed spray formed FGH100 alloy. Pu et al. [9] have studied the flow stress behavior and hot workability of nickel-based alloy UNS10276. The flow instability behavior, induced by microbands, deformation twins and restrained dynamic recrystallization (DRX) behavior, was identified at temperatures lower than 1180oC and strain rates 2
ACCEPTED MANUSCRIPT higher than 5s-1. Moreover, the roles of glide or climbing of dislocations, microtwins, stacking faults and atomic diffusion in various hot deformation conditions have been revealed [10-13]. Over the past few years, lots of efforts have been made on the U720LI alloy. Chang
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et al. [14] have studied the solidification behavior of U720LI superalloy. It demonstrated that the formation of η-phase, which was harmful to the mechanical property, was mainly attributed to the limited solubility of Ti in primary γ phase and γ/γ' Eutectic. However, increasing boron content can significantly retard the γ matrix
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solidification, which would increase the eutectic (γ+γ') precipitation and reduce the formation of η-phase phase and Zr-rich particles [15]. The interactions of slip bands
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with grain boundaries for U720LI alloy have been investigated by SEM and EBSD techniques during tensile tests [16]. The twist angle between projections of slip bands and the boundary plane was identified to govern slip transfer processes. Németh et al. [17] have identified a relationship between tensile ductility and oxidation kinetics for
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U720LI superalloy. The results suggested that the internal intergranular oxidation along the γ-grain boundaries, and in particular, at incoherent interfaces of the primary γ' precipitates and γ matrix may cause the embrittlement of the alloy. Furthermore, the flow stress behavior and microstructural changes during hot deformation of U720LI
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alloy have been proposed in some previous studies. Liu et al. [18] have studied the hot deformation behavior of U720LI alloy with fine, coarse and mixed grains,
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respectively. Dynamic softening mechanism and the effect of γ' precipitates on microstructure evolution were identified. For the coarse grain, the nucleation of DRX grains was influenced by the γ′ interparticle spacing [19]. Qu et al. [20] have established the constitutive equation and the processing map of GH4720Li alloy based on the flow stress during hot compression tests. However, the effect of phase transformation during hot compression tests was not considered and the validity of the optimum process parameters were not testified by the microstructure. In this study, the hot deformation behavior of U720LI nickel-based alloy is investigated according to 3
ACCEPTED MANUSCRIPT hot compression tests. The Arrhenius-type model considering the dissolution of γ' precipitates is established using the corrected stress-strain data and the optimum process parameters for hot deformation are determined with the validation of
2. Experimental materials and procedures
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deformed microstructure in both quasi-γ phase and γ+γ' dual-phase regions.
The main chemical composition (wt %) of U720LI alloy used in this research is as follows: C 0.018, Cr 15.94, Co 14.5, W 1.25, Mo 2.94, Al 2.56, Ti 4.91, Zr 0.03, and
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balance Ni. The microstructure of the initial material from an as-forged bar is shown in Fig. 1 and its average grain size is 21µm. The specimen with a diameter of 10 mm
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and a height of 15 mm was cut by electric-discharge machining and were deformed using a Gleeble 3800 thermal simulation machine. High quality graphite sheet with thickness of 0.05 mm was utilized between anvils and specimen surface to reduce the friction effect during hot deformation. As shown in Fig. 2, the specimens were heated up to deformation temperatures of 1060oC, 1080oC, 1100oC, 1120oC, 1140oC, 1160oC
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and 1180oC at a rate of 10oC/s and held for 5min to minimize temperature gradient. Compression tests were conducted to a true strain of 0.8 at strain rates ( ε& ) of 0.001s-1, 0.01s-1, 0.1s-1, 1s-1 and 10s-1, and then immediately quenched in water to freeze the
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microstructure. All of the compressed specimens were cut parallel to the compression axis by wire-electric discharge machine. After mechanical polishing, the specimens
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were chemical-etched using 5g CuCl2+100ml C2H5OH+100ml HCl, and optical microscope (OM) was employed for microstructure observations.
Fig. 1. Initial microstructure of as-forged U720LI alloy. 4
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Fig. 2. Schematic diagram of hot compression test in this work.
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3. Results and discussion
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3.1. Corrections of friction and adiabatic heating on flow stress curves 3.1.1. Correction of the friction effect
During uniaxial hot compression tests, the presence of friction can lead to the formation of dead zones and inhomogeneous deformation, and flow stress deviates from their true values. Compared with the sliding friction, the effect of sticking one at
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higher temperature would increase the flow stress significantly. Therefore, in order to evaluate the effect of friction and determine the accurate flow stress during hot deformation, researchers employed the simplified relations to eliminate the effect of
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friction on flow stress curves at high deformation temperatures. The corrected flow stress considering the friction effect can be written as [21, 22]:
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σf =
(
)
σ
1 + 2 3 3 f ( r0 h0 ) exp ( 3ε 2 )
(1)
where σf is the corrected flow stress, σ is the measured flow stress, ε is the measured strain and f is the friction factor. r0 and h0 are the initial radius and height of samples, respectively. It can be noted from the Eq. 1 that the friction factor (f) plays an important role in determining the value of corrected flow stress. The friction factor f is always taken as a constant [22, 23], while the experimental evidence demonstrates that the friction factor f is related to the deformation temperature and strain rate [21]. Based on the theory proposed by Ebrahimi and Najafizadeh, the friction factor can be 5
ACCEPTED MANUSCRIPT determined by [21, 24]: f =
(r h)b
(2)
( 4 3 ) − ( 2b 3 3 )
where b is the barrel parameter, h and r are height and average radius of cylinder after
b=4
∆r h r ∆h
r = r0
h0 h
(3)
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as:
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deformation. The barrel parameter (b) and average radius(r) in Eq. 2 can be expressed
(4)
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where ∆h and ∆r are reduction of height and difference between maximum and top radius of cylinder after deformation. According to Eqs. 2-4, the friction factor can be determined by measuring the height, maximum radius and top radius of cylinder after deformation. However, it is difficult to measure the top radius of cylinder after deformation accurately. Therefore, with approximation of the profile of the barreled
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samples with an arc of a circle, top radius of cylinder after deformation can be calculated by following equation[21]:
h0 2 r0 − 2rM2 h
(5)
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rT = 3
where rM and rT are maximum and top radius of cylinder after deformation, as shown
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in Fig. 3. Therefore, the friction factor (f) can be calculated by measuring the maximum radius (rM) as well as the height of cylinder after deformation (h) according to the Eqs. 2-5. The predicted frictionless flow stress curves derive from the Eq. 1 are shown in Fig. 4a. It can be seen from the figure that the corrected flow stress is lower than measured flow stress. The difference between corrected and uncorrected flow stress curves increases with increasing strain, which is mainly attributed to the increased contact surface between the specimen and die. In additions, compared with the uncorrected flow stress curves, the work hardening behavior is eliminated after correction of the friction effect. 6
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Fig. 3. Schematic diagram of parameters in Eqs. 1-5.
Fig. 4. Corrected flow stress curves due to the friction and adiabatic heating effects of
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U720LI alloy under various temperatures and strain rates: (a) 1100 oC and (b) 10s-1. 3.1.2. Correction of the adiabatic heating effect The decrease of flow stress after reaching a peak stress is a familiar appearance for
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various alloys attributing to the flow softening effect. The softening effect can be arisen from microstructural change and increase of temperature in alloys during hot
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deformation, both or either alone. Microstructural changes mainly indicate the occurrence of continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX) behavior in nickel-based alloy. The increase of temperature in alloys during hot deformation is related to the stain rate. At high strain rate, the hot compression tests are considered as the adiabatic condition, and temperature of the samples increases significantly. While temperature variation caused by deformation is negligible at low strain rate (isothermal condition). Therefore, to remove the effect of temperature rise caused by adiabatic heating, an expression for temperature correction should be performed on the flow stress curves. The flow stress 7
ACCEPTED MANUSCRIPT ( σ ) corresponding to the actual temperature T can be expressed as follows [22, 23, 25, 26]:
σ =σ f +
0.95 ρC p
( ∫ σ dε ) B ddσT ε
f
(6)
f
0
ε& ,ε
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where ρ and Cp are the density and specific heat of deformed material, respectively. T is the absolute temperature (K) during hot deformation. The adiabatic correction factor (B) in Eq. 6 can be calculated using the following equation:
−1
(7)
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ε B = 1 + ( ( xw K w ) + (1 HTC ) + ( xD K D ) ) xw ρ C pε&
where xw is half height of the deformed sample, Kw is the thermal conductivity of
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deformed material, HTC is the interface heat-transfer coefficient, xD is the distance from the die surface to the die interior where temperature is constant and KD is the thermal conductivity of die. The parameters in Eqs. 6 and 7 are shown in Table 1. In this study, the effect of adiabatic heating is ignored because of the negligible
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temperature rise effect for the strain rates lower than 1s-1, and the similarity conditions are performed on 904L austenitic stainless steel and powder metallurgy Ti-47Al-2Cr-2Nb-0.2W alloy [24, 27]. The corrected flow stress curves due to the adiabatic heating and friction effects are shown in Fig. 4b. These curves exhibit a peak
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in the flow stress at a strain and reach a steady state, which indicates that the corrected flow stress curve displays the characteristic of dynamic recrystallization (DRX).
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Table 1 Parameters in Eq. 3 and 4[25, 28, 29].
Parameter ρ Cp Kw KD HTC xD
Value 8140 (kg·m-3) 750 (J·kg-1·K-1) 29 (W·mK-1) 21 (W·mK-1) 25000 (W·m-2·K-1) 0.015 (m)
3.2. Arrhenius-type constitutive equation Generally, the relationship among the flow stress, deformation temperature and 8
ACCEPTED MANUSCRIPT strain rate for a give strain can be described by the Arrhenius-type equation. The Zener-Holloman parameter (Z) which represents the effects of strain rate and temperature on flow stress can be expressed as [30]:
A sinh ασ n ( ) Q n Z = ε& exp( ) = f (σ ) = A1σ 1 RT A exp βσ ( ) 2
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(8)
where Q is the activation energy (kJ·mol-1), R is the universal gas constant (8.314
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kJ·mol-1·K-1). As shown in Eq. 8 that correlationship between Z and the flow stress can be determined by exponential, power and hyperbolic type equations. A, A1, A2, n1,
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α and β are material constants and n is stress exponent. The peak stress level is employed to depict the hot deformation behavior. Taking the natural logarithm of Eq. 8:
ln ( A ) + n ln sinh (ασ ) Q 1 ln ( ε& ) + = ln ( A1 ) + n1 ln (σ ) R T ln ( A2 ) + βσ
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(9)
Material constants β, n1 and n can be determined by taking partial differential on
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both sides of Eq. 9 for a given deformation temperature, as expressed in the following equations [31, 32].
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∂ ln ε& ∂ ln ε& ∂ ln ε& β = ; n1 = ; n= σ σ ∂ ∂ ln ασ ∂ ln sinh T T ( p ) p p
(10) T
The values of β and n1 can be determined from the Eq. 10 by employing the
corrected flow stress. Hence, the material constant α can be obtained (α=β/n1), and the stress exponent n is deduced by linear regression. Taking partial differential on both sides of Eq. 9 and rearranging yields:
∂ ln ε& Q = R ∂ ln sinh (ασ p ) T 9
∂ ln sinh (ασ p ) ∂ 1 T ( ) ε&
(11)
ACCEPTED MANUSCRIPT In Eq. 11, the activation energy can be determined by the slope of ln [sinh(ασ)] versus 1/T. Based on the quantitative metallography, the majority amount of the γ' precipitates are dissolved at a temperature of 1140oC and a hold time of 5min, and the mass percent of the γ' precipitates is no more than 5% according to the phase
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diagram[18]. The precipitation hardening effect induced by γ' precipitates reduces significantly. Thus the samples deformed at the temperature of 1140oC can be approximately considered as in the single γ phase region. Then the deformation temperature over 1140oC is termed as quasi-γ phase region. The plots used to derive
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average values of n1, β, α, n, Q and InA are shown in Fig. 5. Based on the experimental data (shown in Fig. 5), the average values of n1, β, α, n, Q and InA for
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U720LI alloy during hot compression tests are shown in Table 2. The microstructure of γ+γ' dual-phase and quasi-γ phase is modelled using two linear ranges from which the activation energy is determined separately for the two phase regions, as shown in Fig. 5c. It can be seen from Table 2 that the value of stress exponent is 3.571, which is similar to other nickel-based alloys [33-35]. The activation energies Q for quasi-γ
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phase and γ+γ' dual-phase microstructures of U720LI alloy are 417 kJ·mol-1 and 687 kJ·mol-1, respectively. They are higher than the self-diffusion energy of pure nickel alloy (270 kJ·mol-1) [36]. This suggests that the pinning effect of γ' precipitates and
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hardening effect induced by alloying element are able to enhance the deformation activation process significantly. However, the activation energies for U720LI alloy are
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lower than that of Udimet720 alloy in the range of 470-743 kJ·mol-1 [37], which is mainly attributed to the high content of interstitials (carbon, C and boron, N) and alloying element (chromium, Cr) compared with the U720LI alloy [38]. Consequently, by substituting the parameters listed in Table 2, the constitutive equations at peak stress level can be expressed as:
ε& = 9.535 × 1024 sinh ( 0.00687σ p ) for γ+γ' dual-phase microstructure, and:
10
3.571
exp(−
687000 ) RT
(12)
ACCEPTED MANUSCRIPT ε& = 5.988 × 1014 sinh ( 0.00687σ
p
)
3.571
exp(−
417000 ) RT
(13)
for quasi-γ phase microstructure. Comparison between peak stresses experimentally determined and calculated by the established Arrhenius-type constitutive equation is shown in Fig. 6. It can be seen from the figure that the calculated peak stresses agree
model prediction can be identified at a strain rate of 10s-1.
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well with the experimental results at strain rates of 0.001-1s-1, while a low accuracy of
U720LI alloy. n1
β
4.544
0.0312
γ+γ' dual-phase
n
Q (kJ·mol-1)
lnA
0.00687
687
57.517
417
34.026
3.571
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Quasi-γ phase
α
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Phase region
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Table 2 Kinetic parameters for γ+γ' dual-phase and quasi-γ phase microstructures of
Fig. 5. Plots of ln ε& -ln σ p (a) and ln ε& -ln[sinh(α σ p )] (b) at different temperatures, (c) Plot of ln[sinh(α σ p )]-1000/T for quasi-γ phase and γ+γ' dual-phase microstructures and (d) relationship between lnZ and ln[sinh(α σ p )] of U720LI alloy. 11
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Fig. 6. Comparison between peak stresses experimentally determined and calculated by
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the established Arrhenius-type constitutive equation. 3.3. Establishment of processing map
To predict the optimum processing conditions of U720LI alloy during hot deformation, the processing map is presented in this section. A processing map is developed based on dynamic materials model (DMM) which is proposed by
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Prasad[39]. In the DMM, the total power energy P can be divided into two main parts, one is the power dissipation (G) indicating the dissipation energy value arising from plastic deformation, and the other one is metallurgical processes (J) which is related to
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the energy concerning the microstructural changes, like dynamic recovery and dynamic recrystallization. The correlationship among P, G and J can be expressed
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mathematically as [40, 41]:
σ
ε
0
0
P = G + J = ∫ ε& dσ + ∫ σ d ε&
(13)
The partitioning of power between J and G is given by the following equation:
& d ln σ ∆ log σ dJ ε& dσ εσ = = ≈ =m dG σ d ε& σ ε&d ln ε& ∆ log ε&
(14)
where m is the strain rate sensitivity. For a certain temperature, J can be simplified to: J max =
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mσ ε& m +1
(15)
ACCEPTED MANUSCRIPT Eq. 15 indicates that the value of J at any given temperature and strain rate can be determined according to the flow stress ( σ ), strain rate ( ε& ) and strain rate sensitivity (m). A maximum value of J can be obtained when m equals to 1, and the process is considered as an ideal linear dissipator, thus:
σ ε&
(16)
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J max =
2
The efficiency of power dissipation (η), which indicates the power dissipation
dimensionless parameter [31]: 2m m +1
(17)
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η = J J max =
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capacity of the sample, for a non-linear dissipator can be defined in terms of a
Domains with high η in power dissipation map can be identified as the optimum processing conditions, which should be further supported by the microstructure of deformed samples. The flow instability characterized by adiabatic shear bands, slip localization and crack formation based on the grain boundary cavitation should also be
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considered when the optimum processing conditions are determined [42]. Therefore, the flow instability map based on a continuum instability criterion is established. Further, the extremum principles of irreversible thermodynamics as applied to continuum mechanics of large plastic deformation are employed to identify the
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occurrence of flow instability. The instability criteria ξ ( ε& ) is expressed by [43]:
ξ ( ε& ) =
∂ ln m ( m + 1) +m≤0 ∂ ln ε&
(18)
It can be deduced from the Eq. 18 that the instability domains are characterized by
the negative value of ξ ( ε& ) . In this study, the corrected flow stress curves are used to determine m, η and ξ, and then the processing map is established according to the superimposition of power dissipation map and instability map at a strain of 0.8, as shown in Fig. 7. The processing map is a three dimensional plot with isocontour lines which is dependent on deformation temperature and strain rate at a given strain. It can 13
ACCEPTED MANUSCRIPT be seen from the Fig. 7 that the gray colored regions represent the unstable zones and the white colored domain denotes stable zones. The processing map in this study is divided into three main domains, and the workability of the sample in each domain is discussed with the help of the deformed microstructure. The domain C with the η of
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10-25% and negative ξ ( ε& ) exists in the temperature range of 1060-1100oC and strain rates of 1-10s-1 for a true strain of 0.8. In general, the flow instability of the samples during hot deformation could be probably associated with adiabatic shear
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bands, localized plastic flow or cracking[44]. It could be seen from the Fig. 7 that the main instability domain, identified from the microstructure in Domain C, is
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characterized by the adiabatic shear bands. It has been widely acknowledged that the adiabatic heating during hot deformation is occurred at higher strain rates due to insufficient deformation times [43]. Domain B indicates the unstable zone with high η (the maximum η is about 25%) deformed in the temperature range of 1140-1180oC and strain rates of 1-10s-1 for a true strain of 0.8. The microstructure in Domain B
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corresponds to the instability mechanisms characterized by cracking along the compressed grain boundary, as shown in Fig. 7. At high strain rates and temperature, grain boundary length per unit area decreases with the increase of deformation
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temperature and the stress concentration at grain boundaries could not be released instantly due to insufficient time [43], and then the intergranular cracking initiates. In
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addition, the microstructure shown in domain B of Fig. 7 exhibits the typical incomplete DRX behavior with necklace structure, which suggests that initiation of DRX nuclei distributes along the large size of deformed grain boundaries. The deformation condition with high power dissipation efficiency in the stable
region are termed as domain A, as seen from Fig. 7. Domain A is mainly composed of two stable regions with high η found to be nearly 31-43%, which corresponds to microstructure representing a homogeneous and completed dynamic recrystallization structures without deformation defect. Moreover, it could be seen from the processing map shown in Fig. 7, the high efficiency of power dissipation (about 49%) deformed 14
ACCEPTED MANUSCRIPT at 1180oC/0.01s-1 is presented in the stable zone, while the average grain size of the deformed sample exhibits extraordinary grain growth behavior depended on its high temperature and low strain rate, as shown in Fig. 8. Therefore, based on Eqs. 17 and 18 as well as validation of micrographs, optimum processing conditions for the alloy in
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this study are 1080-1100oC/0.01-0.3s-1 and 1140-1160oC/0.01-0.1s−1.
Fig. 7. Processing map of U720LI alloy at ε=0.8 with microstructure validation in
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different deformation regions.
The microstructure evolution of samples deformed at a strain of 0.8 and various
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deformation conditions is shown in Fig. 8. It can be seen from the figure that the growth of dynamic recrystallized grain is promoted by the increase of deformation temperature and decrease of strain rate. Generally, the correlationship between Z and DRX grain size can be expressed by an exponential function[45]. However, the presence of precipitates corresponding to the chemical composition of the alloy and the adiabatic shear bands because of the inhomogeneous deformation would affect the deformed microstructure of the materials significantly. Thus, the correlationship between Z and DRX grain size (dDRX) is not always possible to be established or 15
ACCEPTED MANUSCRIPT presents poor correlation coefficient for some specific alloys [36, 46, 47]. The distribution of DRX grain size under various deformation conditions as well as the variation of Z with respect to DRX grain size are shown in Fig. 9. It can be seen from Fig. 9a that the average DRX grain size is not sensible to the deformation temperature
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at high strain rate due to the occurrence of complete DRX behavior and the restrained grain growth behavior. Hence, as shown in Fig. 9b, it is impossible to establish a
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relation between Z and DRX grain size in the present investigation.
Fig. 8. Microstructure of U720LI alloy at the strain of 0.8 with different hot compression conditions.
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Fig. 9. (a) Distribution of DRX grain size under various deformation conditions and (b) relationship between Z and DRX grain size of U720LI alloy.
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4. Conclusions
Hot deformation behavior and workability of U720LI alloy were investigated by using the hot compression tests on Gleeble 3800 thermal-mechanical simulator, and following conclusions can be drawn:
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(1) The experimental flow stress for all deformation conditions was modified by the correction of friction effect, and the influence of adiabatic heating effect on the flow stress was also discussed for strain rates of 10s-1 and 1s-1. The dynamic recrystallization was identified as the dominant softening mechanism for U720LI
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alloy based on the corrected flow stress curves due to the friction and adiabatic heating effects.
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(2) The Arrhenius-type model considering the dissolution of γ' precipitates was
established using corrected flow stress. The dependence of flow stress on strain rate and temperature during hot deformation can be expressed as: 3.571
exp(−
687000 ) RT
3.571
exp(−
417000 ) RT
ε& = 9.535 × 1024 sinh ( 0.00687σ )
for γ+γ' dual-phase microstructure,
ε& = 5.988 × 1014 sinh ( 0.00687σ ) for quasi-γ phase microstructure.
(3) Activation energies Q for quasi-γ phase and γ+γ' dual-phase microstructuress of 17
ACCEPTED MANUSCRIPT U720LI alloy were 417 kJ·mol-1 and 687 kJ·mol-1, respectively. The activation energy of U720LI alloy was higher than the self-diffusion energy of pure nickel alloy and lower than Udimet720 alloy in the range of 470-743 kJ·mol-1. (4) Based on the analysis of power dissipation efficiency and microstructure
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evolution, the optimum hot deformation processing conditions for γ+γ' dual-phase and quasi-γ phase microstructures were determined be 1080-1100oC/0.01-0.3s-1 and
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1140-1160oC/0.01-0.1s−1, respectively.
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ACCEPTED MANUSCRIPT Acknowledgment This research did not receive any specific grant from funding agencies in the public,
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commercial, or not-for-profit sectors.
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will be available on request.
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behavior and microstructural evolution of Ti–6Al–4V sintered preforms using materials modeling techniques, J. Alloys Compd. 676 (2016) 15-25. [43] S.W. Zeng, A.M. Zhao, H.T. Jiang, et al., Flow behavior and processing maps of Ti-44.5Al-3.8Nb-1.0Mo-0.3Si-0.1B alloy, J. Alloys Compd. 698 (2017) 786-793. [44] X.N. Peng, H.Z. Guo, Z.F. Shi, et al., Study on the hot deformation behavior of TC4-DT alloy with equiaxed α+β starting structure based on processing map, Mater. Sci. Eng. A 605 (2014) 80-88. [45] V.A. Kumar, R.K. Gupta, S.V.S.N. Murty, et al., Hot workability and 24
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superalloy 718, Mater. Sci. Eng. A 528 (2011) 3218-3227.
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[47] Y. Wang, W.Z. Shao, L. Zhen, et al., Hot deformation behavior of delta-processed
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Figure captions Fig. 1. Initial microstructure of as-forged U720LI alloy. Fig. 2. Schematic diagram of hot compression test in this work. Fig. 3. Schematic diagram of parameters in Eqs. 1-5.
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Fig. 4. Corrected flow stress curves due to the friction and adiabatic heating effects of U720LI alloy under various temperatures and strain rates: (a) 1100 oC and (b) 10s-1.
Fig. 5. Plots of ln ε& -ln σ p (a) and ln ε& -ln[sinh(α σ p )] (b) at different temperatures, (c)
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Plot of ln[sinh(α σ p )]-1000/T for quasi-γ phase and γ+γ' dual-phase microstructures and (d) relationship between lnZ and ln[sinh(α σ p )] of U720LI alloy.
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Fig. 6. Comparison between peak stresses experimentally determined and calculated by the established Arrhenius-type constitutive equation.
Fig. 7. Processing map of U720LI alloy at ε=0.8 with microstructure validation in different deformation regions.
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Fig. 8. Microstructure of U720LI alloy at the strain of 0.8 with different hot compression conditions.
Fig. 9. (a) Distribution of DRX grain size under various deformation conditions and
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(b) relationship between Z and DRX grain size of U720LI alloy.
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Table captions Table 1 Parameters in Eq. 3 and 4[25, 28, 29]. Table 2 Kinetic parameters for γ+γ' dual-phase and quasi-γ phase microstructures of
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U720LI alloy.
27
ACCEPTED MANUSCRIPT Highlights Hot deformation behavior was investigated in a wide range of processing conditions. Arrhenius-type model was established considering the dissolution of γ’
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precipitates. Hot workability was discussed according to processing map and microstructure.
Optimal processing conditions were determined in quasi-γ and γ+γ’ phase
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regions.