Thermo-physical simulation of the compression testing for constitutive modeling of GH4169 superalloy during linear friction welding

Accepted Manuscript Thermo-physical simulation of the compression testing for constitutive modeling of GH4169 superalloy during linear friction welding Xiawei Yang, Wenya Li, Juan Ma, Shitian Hu, Yong He, Long Li, Bo Xiao PII:

S0925-8388(15)31251-2

DOI:

10.1016/j.jallcom.2015.09.267

Reference:

JALCOM 35542

To appear in:

Journal of Alloys and Compounds

Received Date: 9 June 2015 Revised Date:

14 September 2015

Accepted Date: 30 September 2015

Please cite this article as: X. Yang, W. Li, J. Ma, S. Hu, Y. He, L. Li, B. Xiao, Thermo-physical simulation of the compression testing for constitutive modeling of GH4169 superalloy during linear friction welding, Journal of Alloys and Compounds (2015), doi: 10.1016/j.jallcom.2015.09.267. 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.

600

600 -1

1000℃ 1050℃ 1100℃ 1150℃

100 0.6

0.8

True strain 4.6 4.4

n=4.89778-3.9442ε+3.366ε2 R=0.99848

R=0.9996

3.8 3.6

100

0.2

0.4

0.6

-1

1s

-1

0.1s -1 0.01s 0.8

1.0

True strain

34

380

Q=375.736-23.4156ε R=0.82255

0.0055

33

370 360

0.0050

α=0.00438-0.00403ε +0.0171ε2-0.01265ε3

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4.0

200

0 0.0

1.0

α

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

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True strain

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n

4.2

-1

10s

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0.4

300

0.0045

0.0040

32

lnA=32.0895-2.5069ε

340

R=0.8399

31

350

330 30

0.1 0.2

0.3

0.4

0.5 0.6

True strain

0.7

0.8

320

Q(kJ/mol)

200

400

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300

True stress(MPa)

970℃

lnA

True stress(MPa)

400

0.2

Temperature = 1100℃

500

Strain rate = 1s

500

0 0.0

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ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

Thermo-physical simulation of the compression testing for constitutive modeling of GH4169 superalloy during linear friction welding Xiawei Yang, Wenya Li*, Juan Ma, Shitian Hu, Yong He, Long Li, Bo Xiao State Key Laboratory of Solidification Processing, Shaanxi Key Laboratory of Friction Welding

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Technologies, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, PR China

Abstract:

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In order to simulate the flow behavior of GH4169 superalloy during linear friction welding (LFW), the novel isothermal compression tests of GH4169

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superalloy were performed using a Gleeble-3500 device, up to a 60% height reduction of the specimens at deformation temperatures ranging from 970 ℃ to 1150 ℃, and strain rates ranging from 0.01 s-1 to 10 s-1. In this investigation, a constitutive

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Arrhenius-type equation model was used to characterize the deformation behavior of the GH4169 superalloy during compression process. Under the different strains (0.1-0.7), the corresponding material constants and the activation energy for GH4169

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were determined. The flow stresses calculated by constitutive equation were in a very

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good agreement with the experimental data. Further, the microstructures of the deformed specimens were observed and the microhardnesses of the deformed specimens were measured. Keywords:

Flow

behavior;

GH4169

superalloy;

linear

friction

welding;

Arrhenius-type equation model; Microstructure evolution; Microhardnesses

1. Introduction *

Corresponding author at: School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, PR China. E-mail address: [email protected], [email protected] (W.Y. Li) 1

ACCEPTED MANUSCRIPT GH4169 (Ni-Fe-Cr) superalloy is broadly applied in gas turbines, modern aero engines and high-temperature applications due to its excellent fatigue resistance, radiation resistance, corrosion resistance, high temperatures strength and good

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welding performance[1-4]. Linear friction welding (LFW) is an efficient solid-phase joining process and is able to join two components through the relative reciprocating motion of the two components under a force[5]. It has been applied successfully in

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steels[5-7] and titanium alloys[8-11]. In recent years, the investigation on LFW of

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nickel-based single crystal and polycrystalline superalloys was gradually carried out[12], even for the manufacture of compressor or turbine stages[13]. In turbine engine industries, the blade integrated disks were manufactured using LFW. The disk assembly can be replaced by the fir-tree blade. The total weight of the turbine engines

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can be largely reduced using LFW [12,14]. In the LFW process, the mechanical and thermal behaviors of the LFW joints change with the change of the key process parameters (oscillation frequency, amplitude, friction pressures and weld time).

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However, to investigate the influence of these key process parameters on the

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mechanical and thermal behaviors of the LFW joints is merely a superficial issue, while the strain rate and deformation temperature of a GH4169 superalloy during LFW are the two sensitive factors to influence the mechanical and thermal behaviors of the LFW joints. The mechanical and thermal behaviors of a GH4169 superalloy during LFW process have a particularly close relationship with its microstructure and properties. Therefore, in order to express the mechanical and thermal behaviors of GH4169 superalloy during LFW process, a constitutive model for the relationship 2

ACCEPTED MANUSCRIPT between the flow stress and the sensitive factors (the strain rate and the deformation temperature) must be established. Constitutive modeling has been broadly and successfully applied to predict the

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dynamic deformation behavior of various materials. The materials’ constitutive model is a relationship among the flow stress, the strain, the strain rate and the temperature, which is a main foundation for the theoretical investigation of the mechanical and

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thermal behaviors of materials. In the past decades, many researchers have developed

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different constitutive models to investigate the deformation behaviors of different materials. These materials include steels[15-17], titanium alloys[18-20], magnetic alloys[21,22], aluminum alloys[23-25], Ni-base superalloys[26-28] and so on[29]. These studies mainly focused on the followings aspects. The first is that the thermal

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physical simulated method based on the Gleeble thermal simulator was adopted in their study. The second is that the modeling (constitutive equations, artificial neural network or FEM) of the hot deformation behavior was investigated in their paper. The

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third is that the dynamic softening behavior and the microstructure evolution during

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the hot deformation process were researched in their paper. In addition, the researchers have carried out these studies using hot isothermal tests based on the Gleeble - X thermal simulator. Here “X” denotes the type of Gleeble machine. Although there are some similarities between the above investigations and the present studies, there are some differences. One of the key similaritie lies in the deformation type of materials. The LFW process belongs to a solid-phase joining, so it has the characteristic of elastic plastic deformation of solid phase metal. Gleeble - X machine 3

ACCEPTED MANUSCRIPT can be used to carry out the thermo-physical simulation of the LFW processing for GH4169 superalloy. Therefore, the above works can provide a basis for the revalent research on the deformation behavior of the GH4169 superalloy during LFW process.

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One of the main differences between the above works and the present studies is that the numbers of deformed parts are carried out in the compression test. In the research of metal plastic forming fields, a part is generally needed to be deformed in the

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machine system, while the others parts such as molds, located parts, supported parts

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and so forth, are all considered as the rigid bodies. However, two deformable workpieces are conducted during the LFW process. Therefore, in the present study, based on the Gleeble machine, the authors do not plan to select one sample to carry out the thermo-physical simulation of the LFW processing for GH4169 superalloy,

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while determine to select two samples to do it. It is closer to the LFW process that two deformable workpieces are involved in the processing. In this investigation, hot isothermal compression tests have been employed to

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explore the flow behavior of GH4169 superalloy during upsetting joining process in a

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wide range of temperatures (970℃, 1000℃, 1050℃, 1100℃ and 1150℃) and strain rates (0.01 s-1, 0.1 s-1, 1 s-1 and 10 s-1). Based on the experimental true stress-true strain data derived from the compression tests, a constitutive Arrhenius-type material model has been employed to predict the flow behavior of GH4169 superalloy at a wide range of strain rates and elevated temperatures. A comparative study was made on the accuracy of current Arrhenius-type and experimental data for GH4169 superalloy at a wide range of strain rates and elevated temperatures. Further, in order 4

ACCEPTED MANUSCRIPT to reveal the deformation mechanisms, the microstructures of the deformed specimens were observed and the microhardnesses of the deformed specimens were measured.

2. Experimental procedures

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In the present investigation, commercial GH4169 superalloy was selected as the raw material. The chemical composition (wt.%) of this alloy in the present paper have been given as follows: Ni 52.69, Cr 18.43, Nb 5.17, Mo 2.90, Ti 0.98, Al 0.60, Co 0.18, C

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0.04 and Fe bal. Fig. 1 shows the microstructure of the GH4169 superalloy base metal.

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It can be seen from Fig. 1(a) or (b) that the equiaxed grains appeared in the microstructure of this alloy. The average grain size of this alloy is appropriately 25µm.

Fig. 2 shows the schematic of LFW process (Fig. 2(a)) and the novel hot

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compression tests (Fig. 2(b)). Based on the Fig. 2(a), the authors make a description in detail for LFW process. The LFW process has four distinct stages, including the initial stage, the transition stage, the equilibrium stage and the deceleration (or forging) stage.

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At the beginning, the two components contacted each other under a given axial force.

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Frictional heat and deformation strain are generated during LFW, which leads to the plasticization of the interfacial region between the workpieces. Meanwhile, new deformed metal continues to be accumulated in weld interface and the flash forms in the weld edges. A forging force is applied when there have sufficient plastically deformed material. Enough frictional heat generated during the previous stage can soften the interface material. Axial shortening of the workpieces will be increased due to the upset. The plasticized layer formed at the interface with the assistance of the 5

ACCEPTED MANUSCRIPT oscillatory movement extrudes material from the interface into the flash. The novel hot compression test was designed as shown in Fig. 2(b). It can be seen from Fig. 2(b) that upset force was applied during hot compression deformation. The compression tests

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were carried out on a Gleeble-3500 thermal physical simulator. In the LFW process (Fig. 2(a)), the linear motion is applied along x-direction. The forging force is applied along z-direction. In the hot compression process

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presented in this paper (Fig. 2(b)), pressure is applied in right-punch along z-direction,

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while no linear motion is applied in the test system during the process. There are two purposes of doing the hot compression tests for GH4169 superalloy. The first is to establish the constitutive models, which can be used to express the deformation behavior of GH4169 superalloy during LFW. The second is to research the

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microstructure evolution and the microhardness distribution of the joint interface during compression test.

The original material has a cylindrical shape and its dimensions are shown in Fig.

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3(a). Cylindrical samples with a diameter of 8 mm and a height of 6 mm were

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machined from the original material using a wire-electrode cutting machine. Details of the positions and directions of samples are given in Fig. 3(a). Fig. 3(b) shows the actual specimens. Hot compression tests were conducted in a Gleeble-3500 thermal simulator at the strain rate of 0.01 - 10 s−1 and in the temperature range of 970 - 1150℃ until the engineering compressive strain reached 60%. A total of 20 compression tests were performed using the Gleeble-3500 thermal simulator. The lubricants of graphite mixed with machine oil were adopted so that friction at the specimen/die could be 6

ACCEPTED MANUSCRIPT reduced. One group with two actual specimens was simultaneously heated to the selected deformation temperature, and then kept for 120 s for structural homogeneity and finally compressed by the Gleeble-3500 thermal simulator.

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3. Experimental results and discussion 3.1 Flow curves

True stress-strain curves of the GH4169 superalloy can be plotted from the data

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recorded by the thermal simulator. Fig. 4 shows the true stress- true strain curves of

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the GH4169 superalloy for a wide range of deformation temperature and strain rate conditions. Fig. 5 shows the true stress-true strain curves for GH4169 superalloy tested at 970 ℃, 1000 ℃, 1050 ℃, 1100 ℃ and 1150 ℃. As shown in Fig. 4 and Fig. 5, the flow stress values are dependent on the deformation temperature and strain

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rate. As shown in Fig. 4, for the same strain rate, the flow stress increases with increasing deformation temperature. As shown in Fig. 5, for the same deformation temperature, the flow stress increases with increasing strain rate. It can be seen from

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Fig. 4 and Fig. 5 that as the strain increases, the flow stress rapidly increases and

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quickly reaches a peak value, and then decreases. As shown in Fig. 4, for a particular strain rate condition, the extent of the decline of flow stress increases with the decrease of the deformation temperature. As shown in Fig. 5, for a particular deformation temperature condition, the extent of the decline of flow stress increases with the increase of the strain rate. For a fixed deformation temperature condition, at the strain rates from 0.01 to 1 s−1, the strain corresponding to the peak flow stress increases with increasing strain rate. But it is not suitable for strain rate 10 s−1. As 7

ACCEPTED MANUSCRIPT shown in Fig. 5, at the highest strain rate (10 s−1) and the lowest deformation temperature (970 ℃), the GH4169 superalloy shows an evident peak stress, and then shows a sharply decrease of flow stress. For the two higher deformation temperature

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experiments (1100 ℃ and 1150 ℃), no evident peak stress appears in stress-strain curves at the two lower strain rate experiments (0.01 and 0.1 s-1). The competing deformation mechanisms indicated by the flow stress curves are work hardening,

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dynamic recovery and dynamic recrystallization[30]. The obvious work hardening

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appeared at the initial deformation stage because of the domination of the dislocation generation and multiplication[30, 31]. The dynamic recrystallization will occur when the accumulated dislocation density exceeds a critical strain, which decreases the work hardening rate[30]. After reaching the peak stress, the evident dynamic softening

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phenomenon is induced by dynamic recrystallization. Finally, a steady-state flow behavior can be obtained [32].

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3.2 Constitutive equation

The relationship between the flow stress, the strain rate and the deformation

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temperature during hot deformation at a given strain can be expressed by several basic equations as follows [33-35]:

ε& = A1σ n exp(−Q / RT) 1

(1)

ε& = A2 exp(βσ ) exp(−Q / RT )

(2)

ε& = A3 [sinh( ασ )] n exp( − Q / RT )

(3)

Z = ε& exp( Q / RT ) = A3 [sinh( ασ )] n

(4)

where ε& is the strain rate (s-1), σ is the flow stress (Mpa), A1, n1, A2, A3, n, α and β 8

ACCEPTED MANUSCRIPT are material constants. T is absolute temperature (K). Q is deformation activation energy (kJ/mol). R is the gas constant (8.3154 J·mol-1·K-1). Z is Zener-Hollomon parameter(s-1).α (α = β/n1) is an adjustable constant (MPa-1).

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Eqs. (5) and (6) can respectively derived by taking natural logarithm of Eqs. (1) and (2).

ln ε& = ln A1 − Q / RT + n1 ln σ

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ln ε& = ln A2 − Q / RT + βσ

(5)

(6)

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At constant deformation temperature condition, Eqs. (7) and (8) can be respectively derived by taking partial differentiation of Eqs. (5) and (6). (7)

 ∂ ln ε&  β =   ∂σ  T

(8)

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 ∂ ln ε&  n1 =    ∂ ln σ  T

Here, strain was selected as 0.1. The value of stress is the flow stress under the strain of 0.1. n1 can be obtained from the slope of the plot of ln( ε& ) against lnσ, shown

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as Fig. 6(a). β can be obtained from the slope of the plot of ln( ε& ) against σ, shown as

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Fig. 6(b). The authors respectively calculated the average value of the slopes of these five straight lines in Fig. 6(a) and Fig. 6(b). The value of n1 and β are 6.1063 and 0.0253 MPa-1, respectively. α can be calculated by expression of α = β/n1, and it is 0.00414 mm2 / N.

Eq. (3) can also be expressed as ln ε& = ln( A3 ) + n ln[sinh(ασ )] − (Q / RT )

(9)

Supposing the deformation activation energy is independent of temperature, for a 9

ACCEPTED MANUSCRIPT particular strain rate condition, differentiating Eq. (9) and n can be expressed as,   ∂ ln ε& n=   ∂ ln[sinh(ασ )]  T

(10)

as,  ∂ ln[sinh(ασ )]  Q = Rn   ∂ (1 / T )   ε&

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For a particular strain rate condition, differentiating Eq. (9), Q can be expressed

(11)

Now, by substituting Eq. (10) into Eq. (11), the value of Q can be expressed as:

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 ∂ ln ε&   ∂ ln[sinh(ασ )]  Q = R    ∂ (1 / T )  ∂ ln[sinh(ασ )] T   ε&

(12)

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Q can be calculated from the slope of the plot of ln[sinh (ασ)] against ln(strain rate) and the slope of the plot of ln[sinh (ασ)] against 1/T. Fig. 7(a) shows the relationship between ln[sinh (ασ)] and ln(strain rate). Fig. 7(b) shows the relationship between ln[sinh (ασ)] and 1/T. The value of Q can be calculated by Eq. (12), and it is

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373.927kJ/mol. Z value can be calculated by using Eq. (4). By logarithmic transformation of the Eq. (4), the following expression can be

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written as:

lnZ = lnA3+ n ln[sinh(ασ)]

(13)

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The relationship between lnZ and ln [sinh (ασ)] is shown in Fig. 8. A3 and n can

be obtained from Fig. 8. A3 and n are 8.137×1013 and 4.5274, respectively. The correlation coefficient is 0.99319 in Fig. 8, revealing good linear relation between lnZ and ln [sinh (ασ)]. Therefore, a constitutive equation between flow stress, strain rate and temperature during hot deformation at strain of 0.1 can be written as:

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ACCEPTED MANUSCRIPT  − 373927  ε& = 8.137 × 1013[sinh(0.00414σ )]4.5274 ⋅ exp   RT 

(14)

Fig. 9 shows the values of materials constants (α, Q, lnA and n) of constitutive equations of GH4169 superalloy under different strains in the practical range of 0.1 -

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0.7 and the interval of 0.1. The fitting results of α, Q, lnA and n of GH4169 superalloy are provided in Table 1.

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As shown in Fig. 9(a), the minimum value of n appears in the strain of 0.6. When the strain is in the range of 0.1-0.3, n decreases sharply by increasing the strain. The

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decreasing extent of n with increasing strain at the strain range of 0.3 to 0.6 is less than that in the strain range of 0.1 to 0.3. As shown in Fig. 9(a), the value of α increases with the increase of the strain. α increases slowly with increasing the strain at the strain range of 0.1 to 0.2, increases in a large scale at the strain range of 0.2 to

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0.3, and then increases sharply at the strain range of 0.3 to 0.6. Finally, the increasing extent of n with increasing strain at the strain range of 0.6 to 0.7 shows a slight

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decline. As shown in Fig. 9(b), the relationship of ln A-strain or Q-strain can be expressed by curve fitting method. Q or ln A value decreases with the increase of the

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strain. The decreasing extent of ln A with increasing the strain is larger than that Q with increasing the strain. 3.3 Validation

Comparison between the predicted flow stress and the experimental data was conducted, shown as Fig. 10. In order to thoroughly investigate the capability of constitutive equation, the authors selected a very wide deformation parameters range

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ACCEPTED MANUSCRIPT to verify the constitutive equation. The deformation parameters include strain rates (0.01s-1, 0.1 s-1, 1 s-1 and 10 s-1), deformation temperatures (970 ℃, 1000 ℃, 1050 ℃, 1100 ℃ and 1150 ℃) and strains (0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55,

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0.6 and 0.65). As can be seen from Fig. 10, the experimental results agree well with the calculation values obtained from constitutive equation. The authors made the statistics error analysis of flow stress between experimental values and calculated data.

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It is found that the mean relative error between calculated data and experimental

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values maintains at approximately 4.6% and the maximum relative error is 17.2%. The results show that the constitutive equation of GH4169 superalloy established by this paper has high precision.

3.4 Macrostructure and microstructure

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3.4.1 Macrostructure observation

Fig. 11 shows the macrostructure of the section plane of the deformed specimens

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at the temperatures range of 970 ℃-1150 ℃ and the highest strain rate 10 s-1. Fig. 11(a) shows the schematic of the section view. In Fig. 11(b), (c), (d) and (e), the red

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lines denote the joining lines between the two specimens after compression tests. The joining lines in Fig. 11(b) and (c) both show a certain angle to the horizontal line, while the joining lines in Fig. 11(d), (e) and (f) are all basically parallel to the horizontal line. The results show that when the strain rate is the highest value of 10s-1 and the deformation temperature is the two lower value of 970℃ and 1000℃, the joining lines is very sensitive to the deformation temperature. But at the three higher temperature experiments (1050, 1100 and 1150 ℃), the joining line is not sensitive to 12

ACCEPTED MANUSCRIPT the deformation temperature. In order to further investigate the effects of the strain rate on the joining line, the macrostructure of the deformed specimens was observed in the conditions of the high deformation temperature and the different strain rates.

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Fig. 12 shows the macrostructure of the section plane of the deformed specimens at the highest deformation temperature 1150 ℃ and the strain rate range of 0.01 s-1 to 10 s-1. In Fig. 12(a), (b), (c) and (d), the red lines denote the joining lines between

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the two specimens after compression tests. The joining lines in Fig 12(a), (b), (c) and

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(d) are all basically parallel to the horizontal line. The results shows that when the deformation temperature is the highest value 1150 ℃ and the strain rates are in the range of 0.01 s-1 to 10 s-1, the joining line is not sensitive to the deformation temperature.

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As shown in Figs. 11 and 12, the increase in deformation temperature greatly influences the trend of the joining line at low temperatures (≤ 1000℃), while in the experiments carried out above 1000 ℃, the increase in temperature hardly influences

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the trend of the joining line. Although temperature and strain rate are the two key parameters that influence the flow stress of materials during hot compression process,

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there are some other factors that influence the flow stress. These factors include the microstructure uniformity of materials, the roughness and flatness of specimen surface, the condition of the contact surface between the two specimens, the condition of the contact surface between the two specimens with the two punches. As shown in Fig. 2(b), the two specimens during the compression process have the characteristic of symmetry, so under ideal conditions, the joining lines are all parallel to the horizontal line during the compression process. However, in actual situations, the joining lines show a certain angle to the horizontal line at low deformation temperatures (≤ 13

ACCEPTED MANUSCRIPT 1000℃), while in the experiments carried out above 1000 ℃, the joining lines are basically parallel to the horizontal line. With decreasing deformation temperature of GH4169 superalloy during compression process, the softening degree decreases and the deformation resistance increases.

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Although the temperature and the strain rate are the two key parameters to influence the deformation process, with the change of deformation parameters, the influence of other factors that described above on the degree of deformation processes

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will also change. When in the experiments carried out above 1000 ℃, material

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obtains sufficiently softened. So the deformation resistance of GH4169 superalloy greatly decreases during the compression process, the influence of other factors on the deformation process can be overlooked. Therefore, the joining lines are basically parallel to the horizontal line. When in the experiments carried out below 1000 ℃, material does not obtain sufficiently softened. So the deformation resistance of

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GH4169 superalloy is relatively high. The other factors (conditions of specimen surface, of the contact surface between the two specimens, and of the contact surface

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between the two specimens with the two punches) have a greater effect on the deformation process, especially the trend of the joining line. Therefore, the joining

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lines show a certain angle to the horizontal line. 3.3.2 Microstructure observation Based on the theoretical foundation of metal forming, a specimen deformed by

upset forming can be divided into three regions during deformation process. Fig. 13 shows the original cylinder specimen (Fig. 13(a)) and its deformed shape (Fig. 13(b)). In Fig. 13(b), the symbols of I, II and III are defined as the difficult deformation region, the big deformation region and the free deformation region, respectively. In 14

ACCEPTED MANUSCRIPT this paper, a novel hot conpression test was adopted. Two specimens are used to carry out the hot compression test. It is necessary for us to investigate clearly about the deformation regions of the two joined specimens. In the present investigation, six

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regions were selected based on the characteristic of the section plane of the deformed specimen (Fig. 14).

Fig. 15 shows microstructure of the section plane of the deformed specimens in

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different regions at temperature 1000 ℃ and strain rate 10 s-1. As shown in Fig. 15(a)

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and Fig. 1(b), the grain size in small deformation region A has little difference with the parent material. A large number of grains in regions C and D were evidently extruded and refined due to the deformation (Fig. 15(c) and (d)). As shown in Fig. 15(c), several recrystallized grains, marked as the three red regions, can be evidently

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observed in region C. As shown in Fig. 15(a), (e) and (f), compared with the microstructure of parent material (Fig. 1), the grains in regions A, E and F were slightly refined due to the deformation. In addition, the average grain size in regions C

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and D is smaller than that in the other regions. Based on the above descriptions,

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compared with the other regions, regions C and D can be defined as large deformation region of the deformed specimen. It can be seen from Fig. 15(c) and Fig. 15(d), the deformation extent in region C is larger than that in region D. From the region C to the region D, then to region E, the grain size shows increasing trend, which indicates that the large deformation region gradually transit to the small deformation region. From the region C to the region B, then to region A, the grain size also shows increasing trend, which indicates that the large deformation region gradually transit to 15

ACCEPTED MANUSCRIPT the small deformation region. Compared the region A and E, the grains in region A is larger than the region E, which indicates that the deformation degree of region A is smaller than the region E.

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During hot working the processes of strain hardening and subsequent dynamic recovery and dynamic re-crystallization may occur depending upon the temperature and strain. As shown in Fig. 15(c), new grains, marked as the red arrows, emerged in

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the large deformation region C. This is called re-crystallization. Fig. 1(a) shows initial

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microstructure of an undeformed metal piece. A number of equiaxed grains appeared in the initial microstructure. In Fig.15, the microstructure after the specimen has been compressed along its height. The grains get elongated in the direction normal to the direction of applied force. In the difficult deformation region and the free deformation

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region, there are no new grains appeared, indicating that the material in these two regions gets strain hardened, microhardness increase. This is called recovery process. As for the change of microhardness, the authors discuss it in the section 3.4.

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Based on the above descriptions, when the compression test is carried out at the

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temperature 1000 ℃ and the strain rate 10 s-1, and the compression ratio is 60% height reduction of the specimen, the re-crystallization phenomenon can be observed in the large deformation region, the recovery process can be observed in the difficult deformation region and the free deformation region. Therefore, the authors defined the region C as the large deformation region, defined the region E as the free deformation region, and defined the region A as the difficult deformation region. Region B is defined as the transition region between 16

ACCEPTED MANUSCRIPT regions A and C. Region D is defined as the transition region between regions C and E. The grain size in Fig. 15(f) shows that the region F belongs to the difficult deformation region. According to the above analysis for deformed specimen

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microstructure, the authors can initially consider that the two joined specimen can be divided into three regions. The result is accord with the one deformed specimen.

In order to further verify the observation results from Fig .15, the authors give

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the microstructure of compression specimen at another process parameter. Fig. 16

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shows the microstructure of specimen at temperature 1150 ℃ and strain rate 10 s-1. The average grain size in Fig. 16 is larger than that in Fig. 15 due to the temperature increasing. The higher the deformation temperature is, the larger the average grain size is. As shown in Fig. 16, the microstructure of deformed specimen in the section

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plane is non-uniform. As shown in Fig. 16, the re-crystallization phenomenon can be observed in the large deformation region, difficult deformation region and free deformation region, indicating that when the experiments was conducted in the

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highest strain rate (10 s-1) and the highest deformation temperature (1150 ℃), the

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re-crystallization phenomenon can be observed in the whole deformed specimen. 3.4 Microhardness change Fig. 17 shows the microhardness change of the deformed specimens in different

process parameters. The x-distance between two adjacent points is 250 µm, and the y-distance between two adjacent points is 200µm (Fig. 17(a), (b) and (c)). As shown in Fig. 17(d) and (e), the microhardness present with fluctuating character. It can be seen from Fig. 17(d) that the microhardness increases with the decreasing deformation 17

ACCEPTED MANUSCRIPT temperature. It can be seen from Fig. 17(e) that the microhardness increases with the increasing strain rate. The change trend of microhardness is the same with the flow stress. In publications [36, 37], as for the titanium alloy, the change trend of

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microhardness is the same with the flow stress. As shown in Fig. 17(d), when the strain rate is 10 s-1 and temperature is 970 ℃, the microhardness value is ~355 Hv in the center of the deformed specimen, decreases

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to a valley value of ~343 Hv at displacement of ~700 µm from the center and then

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increases to ~368 Hv at displacement of 2000 µm from the center. When the strain rate is 10 s-1 and temperature is 1050 ℃, the microhardness value is ~310 Hv in the center of the deformed specimen, decreases to a valley value of ~295 Hv at displacement of ~700 µm from the center and then increases to ~330 Hv at

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displacement of 2000 µm from the center. As shown in Fig. 17(d) and (e), when the strain rate is 10 s-1 and temperature is 1150 ℃, the microhardness value is ~267 Hv in the center of the deformed specimen, decreases to a valley value of ~255 Hv at

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displacement of ~1000 µm from the center and then increases to ~262 Hv at

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displacement of 2000 µm from the center. As shown in Fig. 17(e), when the strain rate is 0.01 s-1 and temperature is 1150 ℃, the microhardness value is ~237 Hv in the center of the deformed specimen, decreases to a valley value of ~220 Hv at displacement of ~900 µm from the center and then increases to ~243 Hv at displacement of 2000 µm from the center. It can be seen from Fig. 17 that the microhardness has the distinct shape of a W along y-direction. The non-uniform of microstructure leads to the non-uniform of 18

ACCEPTED MANUSCRIPT microhardness. The average grain size of microstructure increases with the increase of the temperature. The smaller the average grain size is, the higher the microhardness is. As shown in Fig. 17(e), when the strain rate is in the range of 0.01 s-1 to 0.1 s-1, the

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microhardness evidently increases with the increase of strain rate. While when the strain rate is in the range of 0.1 s-1 to 10 s-1, the microhardness slowly increases with the increase of strain rate. Here, the microhardness changes with the change of strain

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rates is analysed from the angle of microstructure changing in different strain rates.

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Fig. 18 shows the microstructure of region C at the temperature of 1150 ℃ and the strain rates of 0.01, 0.1, 1 and 10 s-1. It can be seen from Fig. 18, the variation extent of grain size in the strain rate range of 0.01 - 0.1 s-1 is more evident than that in the strain rate range of 0.1 - 10 s-1. Based on the above descriptions, the authors can

microhardness.

4. Conclusions

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conclude that the influence of the strain rate on microstructure is the same with the

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(1) A novel hot compression tests were designed. True stress-true strain curves

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are sensitive to the strain rate and deformation temperature. Under the same strain rate, the flow stress increases with decreasing deformation temperature. Under the same deformation temperature the flow stress increases with increasing strain rate. (2) When the strain is set as 0.1, the value of deformation activation energy (Q)

was obtained, and it is 373.927kJ/mol. A constitutive equation for GH4169 superalloy was established by using a hyperbolic sine equation. It can be expressed by:  − 373927  ε& = 8.137 × 1013[sinh(0.00414σ )]4.5274 ⋅ exp   RT  19

ACCEPTED MANUSCRIPT (3) The constitutive equation parameters (α, Q, ln A and n) of GH4169 superalloy were calculated at different strains (0.1, 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7). The mean relative error between predicted data and experimental data maintains at

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approximately 4.6% and the maximum relative error is less than 17.2%, which indicates that the experimental curves agree well with the calculated curves.

(4) When the experiments were carried out in the highest rate 10 s-1 and the

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lower temperatures (970 and 1000 ℃), the joining lines show a certain angle to the

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horizontal line, indicating that the joining line is very sensitive to the temperature. When the experiments were carried out in the highest rate 10 s-1 and the higher temperatures (1050, 1100 and 1150 ℃), the joining lines basically parallel to the horizontal line, indicating that the joining line is not sensitive to the temperature.

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(5) Microstructure of the compressed specimens in the section plane is non-uniform. The average grain size in the large deformation region is relatively much smaller than that in the other two regions. When the experiment is carried out at

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the lower temperature 1000 ℃ and the highest strain rate 10 s-1, the re-crystallization

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phenomenon is observed in the large deformation region, while the recovery process is observed in the difficult and free deformation regions. When it is carried out at the highest temperature 1150 ℃ and the highest strain rate 10 s-1, the re-crystallization phenomenon is observed in three regions (the large, difficult and free deformation regions. (6) The microhardness value was found to be dependent on temperature and strain rate (increasing with decreasing deformation temperature and/or increasing with 20

ACCEPTED MANUSCRIPT increasing strain rate. At the highest strain rate (10 s-1) and lowest temperature (970 ℃), the microhardness value is ~355 Hv in the center of the deformed specimen, decreases to a valley value of ~343 Hv at displacement of ~700 µm from the center and then increases

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to ~368 Hv at displacement of 2000 µm from the center. At the highest strain rate (10 s-1) and highest temperature (1150 ℃), the microhardness value is ~267 Hv in the center, decreases to a valley value of ~255 Hv at displacement of ~1000 µm from the center and

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then increases to ~262 Hv at displacement of 2000 µm from the center. At the lowest

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strain rate (0.01 s-1) and highest temperature (1150 ℃), the microhardness value is ~237 Hv in the center of the deformed specimen, decreases to a valley value of ~220 Hv at displacement of ~900 µm from the center and then increases to ~243 Hv at displacement of 2000 µm from the center. Obvious work-hardening effect could be demonstrated under

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lower temperatures and higher strain rates.

Acknowledgements

The authors would like to acknowledge the financial support from the National

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Natural Science Foundation of China (No. 51405389). The project was supported by

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the Fundamental Research Funds for the Central Universities (No. 3102015ZY024, No. 3102014JC02010404), by the Open Fund of Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures (No. 2014003) and by the Research Fund of the State Key Laboratory of Solidification Processing (NPU, China) (108-QP-2014).

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Tables

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Table 1 Parameters for the constitutive equation parameters.

25

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Figures Fig. 1. Low magnification microstructure (a) and high magnification microstructure (b). Fig. 2. Schematic of LWF process (a) and novel hot compression test (b).

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Fig. 3. Shape of the original materials, cutting position and direction of the cylindrical samples (a), and image of several groups of the actual specimens (b)

Fig. 4. True stress-true strain curves of GH4169 superalloy during hot deformation at strain rates of (a) 0.01, (b) 0.1, (c) 1 and (d) 10 s-1

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Fig. 5. True stress-true strain curves of the GH4169 superalloy during hot deformation at deformation temperatures of (a) 970, (b) 1050, (c) 1100 and (d) 1150 ℃.

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Fig. 6. Relationship between ln( ε& ) and (a) lnσ and (b) σ.

Fig. 7. Relationships between ln[sinh (ασ)] and (a) ln( ε& ) and (b) 1/T. Fig. 8. Relationship between ln Z and ln[sinh (ασ)]

Fig. 9. Relationship between true strain and constitutive equation parameters:(a) n-strain curve and α-strain curve and (b) lnA-strain curve and Q-strain curve.

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Fig. 10. Comparison of flow stress between experimental data and calculated results at strain rates of (a) 0.01, (b) 0.1, (c) 1 and (d) 10 s-1. Fig. 11. Schematic of the section view (a) and macrostructure of the deformed

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specimens at the highest strain rate 10 s-1 and the temperatures of (b) 970, (c) 1000, (d) 1050, (e) 1100 and (f) 1150 ℃.

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Fig. 12. The macrostructure of the deformed specimens at the highest deformation temperature 1150 ℃ and the strain rates of (a) 0.01, (b) 0.1, (c) 1 and (d) 10 s-1 Fig. 13. Schematic of the original cylinder specimen (a) and its deformed shape (b). Fig. 14. Characteristic regions in the section plane of specimen in two different conditions: (a) Horizontal joining line and (b) Joining line with a certain angle to the horizontal line. Fig. 15. The microstructure of deformed specimens at the temperature 1000 ℃ and the strain rate 10 s-1 in (a) Region A, (b) Region B, (c) Region C, (d) Region D, (e) Region E and (f) Region F. 26

ACCEPTED MANUSCRIPT Fig. 16. The microstructure of compression tested specimens at the temperature 1150 ℃ and the strain rate 10 s-1 in (a) Region A, (b) Region B, (c) Region C, (d) Region D, (e) Region E and (f) Region F. Fig. 17. Microhardness tested position (a), (b) and (c) and microhardness value of

1150 ℃ and (e) T = 1150 ℃ and ε& = 0.01, 0.1,1 and 10 s-1.

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joint at different process parameters: (d) ε& = 10 s-1, T = 970, 1000, 1050, 1100 and

Fig. 18. Microstructure of region C at the temperature 1150 ℃ and the strain rates of

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(a) 0.01, (b) 0.1, (c) 1 and (d) 10 s-1

27

ACCEPTED MANUSCRIPT Table 1 Parameters for the constitutive equation parameters. n C0 = 7.898 C1 = -3.944 C2 = 3.366

Q D0 = 375.739 D1 = -23.416

lnA E0 = 32.090 E1 = -2.507

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α B0 = 0.0044 B1 = -0.004 B2 = 0.017 B3 = -0.0127

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Fig. 1 Low magnification microstructure (a) and high magnification microstructure (b).

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Fig. 2 Schematic of LWF process (a) and novel hot compression test (b).

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Fig. 3 Shape of the original materials, cutting position and direction of the cylindrical samples (a), and image of several groups of the actual specimens (b)

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(b) 600

970℃ 1000℃ 1050℃ 1100℃ 1150℃

400 300

-1

500

200 100 0 0.0

0.2

0.4

0.6

0.8

400 300 200 100 0 0.0

1.0

0.2

0.4

True strain

(d) 600 True stress(MPa)

400 300 200

0 0.0

0.2

1000℃ 1100℃

0.4

0.6

True strain

1.0

400 300 200 100

1150℃

0.8

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Strain rate = 10s

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100

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970℃ 1000℃ 1050℃ 1100℃ 1150℃

Strain rate = 0.1s

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500

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Strain rate = 0.01s

True stress(MPa)

(a) 600

1.0

0 0.0

970℃ 1050℃

0.2

0.4

1000℃ 1100℃

0.6

1150℃

0.8

1.0

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Fig. 4 True stress-true strain curves of GH4169 superalloy during hot deformation at strain rates of (a) 0.01, (b) 0.1, (c) 1 and (d) 10 s-1

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Temperature = 970℃

(b) 600

10s

400

-1

1s 300

-1

0.1s

200

-1

0.01s

100 0 0.0

0.2

0.4

0.6

Temperature = 1050℃

500

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0.8

True stress(MPa)

True stress(MPa)

500

400

200

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0.1s -1 0.01s

100 0 0.0

1.0

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10s -1 1s

300

0.2

(d) 600

300

10s

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1s

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0.1s -1 0.01s 0.4

0.6

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0.8

True stress(MPa)

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0.2

0.8

1.0

400 300

Temperature = 1150℃

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(c) 600 500

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1.0

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0.4

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True strain Fig. 5. True stress-true strain curves of the GH4169 superalloy during hot deformation at deformation temperatures of (a) 970, (b) 1050, (c) 1100 and (d) 1150 ℃.

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6.0

500

5.6

400

5.2

970℃ 1000℃ 1100℃

4.8 4.4 -5

-4

-3

-2

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0

1050℃ 1150℃ 1

2

970℃ 1000℃ 1100℃

300 200 100

3

ln(ε)

1050℃ 1150℃

-5

-4

-3

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σ(MPa)

(b) 600

lnσ(MPa)

(a) 6.4

-2

-1

ln(ε)

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Fig. 6. Relationship between ln( ε& ) and (a) lnσ and (b) σ.

1

2

3

ACCEPTED MANUSCRIPT (a) 2.0

970℃ 1000℃ 1100℃

1.5

(b)

2.0 -1

1050℃ 1150℃

1.5

0.0 -0.5

0.5 0.0

-1.0

-5

-4

-3

-2

-1

ln(ε)

0

1

2

3

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-1.0 -1.5

-1

0.1s -1 10s

1.0

0.5

ln[sinh(ασ)]

ln[sinh(ασ)]

1.0

0.01s -1 1s

0.00070 0.00072 0.00074 0.00076 0.00078 0.00080 0.00082 -1

1/T(K )

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Fig. 7 Relationships between ln[sinh (ασ)] and (a) ln( ε& ) and (b) 1/T.

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lnZ=32.032+4.498ln[sinh(ασ)]

36

lnZ

34

R=0.99319

32

28 26 -1.5 -1.0 -0.5

0.0

0.5

ln[sinh(ασ)]

1.0

1.5

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Fig. 8. Relationship between ln Z and ln[sinh (ασ)]

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0.0055

4.0

360

α=0.0044-0.004ε 2

+0.017ε -0.0127ε

3

0.0045

3.8 3.6

370

0.0050

α

32

lnA=32.090-2.507ε R=0.8399

31

350 340 330

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.0040

True strain

30

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

320

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Fig. 9. Relationship between true strain and constitutive equation parameters: (a) n-strain curve and α-strain curve and (b) lnA-strain curve and Q-strain curve.

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n

4.2

R=0.8226

33

R=0.9996

380

Q(kJ/mol)

R=0.9985

Q=375.736-23.416ε

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(b) 34

n=4.898-3.944ε+3.366ε2

lnA

(a) 4.6

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experimental 970℃ 1000℃ 1050℃ 1100℃ 1150℃

300

experimental 970℃ 1000℃ 1050℃ 1100℃ 1150℃

400 350 300

200

σ(MPa)

150 100

250 200 150

50

100 -1

Strain rate=0.01s 0

50

0.2

0.3

0.4

0.5

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Strain rate=0.1s 0.2

0.3

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0.5

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calculated 970℃ 1000℃ 1050℃ 1100℃ 1150℃

(d) 750 650 600 550

300

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calculated 970 ℃ 1000 ℃ 1050 ℃ 1100 ℃ 1150 ℃

experimental 970 ℃ 1000 ℃ 1050 ℃ 1100 ℃ 1150 ℃

700

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experimental 970℃ 1000℃ 1050℃ 1100℃ 1150℃

(c)

0.4

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True strain

True strain

σ(MPa)

calculated 970℃ 1000℃ 1050℃ 1100℃ 1150℃

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σ(MPa)

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(b) 450

calculated 970℃ 1000℃ 1050℃ 1100℃ 1150℃

400 350

200

300 250

-1

100

Strain rate=1s 0.2

0.3

0.4

0.5

True strain

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0.7

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Strain rate=10s

0.2

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Fig. 10. Comparison of flow stress between experimental data and calculated results at strain rates of (a) 0.01, (b) 0.1, (c) 1 and (d) 10 s-1.

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Fig. 11 Schematic of the section view (a) and macrostructure of the deformed specimens at the highest strain rate 10 s-1 and the temperatures of (b) 970, (c) 1000, (d) 1050, (e) 1100 and (f) 1150 ℃.

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Fig. 12 The macrostructure of the deformed specimens at the highest deformation temperature 1150 ℃ and the strain rates of (a) 0.01, (b) 0.1, (c) 1 and (d) 10 s-1

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Fig. 13 Schematic of the original cylinder specimen (a) and its deformed shape (b).

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Fig. 14. Characteristic regions in the section plane of specimen in two different conditions: (a) Horizontal joining line and (b) Joining line with a certain angle to the horizontal line.

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Fig. 15 The microstructure of deformed specimens at the temperature 1000 ℃ and the strain rate 10 s-1 in (a) Region A, (b) Region B, (c) Region C, (d) Region D, (e) Region E and (f) Region F.

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Fig. 16 The microstructure of compression tested specimens at the temperature 1150 ℃ and the strain rate 10 s-1 in (a) Region A, (b) Region B, (c) Region C, (d) Region D, (e) Region E and (f) Region F.

-1

330 300 270 240 210

(e) 280

1050℃ 1150℃

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360

970℃ 1000℃ 1100℃

EP

Hardness(Hv)

390

Strain rate=10s

-2000-1500-1000 -500

0

500 1000 1500 2000

AC C

Position (μm)

270

Temperature = 1150℃

-1

0.01s -1 1s

-1

0.1s -1 10s

260

Hardness(Hv)

(d) 420

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250 240 230 220 210 -2000-1500-1000-500 0

500 1000 1500 2000

Position(μm)

Fig. 17 Microhardness tested position (a), (b) and (c) and microhardness value of joint at

different process parameters: (d) ε& = 10 s-1, T = 970, 1000, 1050, 1100 and 1150 ℃ and (e) T = 1150 ℃ and ε& = 0.01, 0.1,1 and 10 s-1.

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(b)

100µm (c)

100µm

TE D

M AN U

(d)

SC

(a)

100µm

100µm

AC C

EP

Fig. 18 Microstructure of region C at the temperature 1150 ℃ and the strain rates of (a) 0.01, (b) 0.1, (c) 1 and (d) 10 s-1

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Highlights (1) A constitutive Arrhenius model was successfully applied to predict flow stress. (2) The material constants under the different strains were determined.

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(3) The microstructure changes throughout the joining interface are examined.

(4) The hardness variations across the joining interface are linked to the

AC C

EP

TE D

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SC

flow behavior.