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Experimental and numerical analysis of rotary tube piercing process for producing thick-walled tubes of nickel-base superalloy
Journal of Materials Processing Tech. 279 (2020) 116557
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Experimental and numerical analysis of rotary tube piercing process for producing thick-walled tubes of nickel-base superalloy
T
Zhe Zhanga, Dong Liua,*, Runqiang Zhangc, Yanhui Yanga, Yuhua Pangb, Jianguo Wanga, Hai Wanga a
School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, PR China School of Metallurgical Engineering, Xi`an University of Architecture and Technology, Xi'an 710055, PR China c Xi'an Sheng Dong Forge CO., LTD, Xi'an 710072, PR China b
A R T I C LE I N FO
A B S T R A C T
Associate Editor: Z. Cui
In order to overcome the problems of existing methods for preparing thick-walled tubes of nickel-base superalloy (TWNS), the rotary tube piercing (RTP) process was proposed. For this purpose, an improved piercing mill was designed, and the influences of process parameters on strain, temperature, biting condition, lose stability of mandrel, defects control and microstructure distribution were studied by the combination of finite element model (FEM) and experiments. Based on the control variable method, the ranges of process parameters corresponding to the second biting condition and the critical condition of mandrel instability were determined by the simulation results. The experiment results indicate that the external separation layer defect (ESLD) is significantly affected by roll speed and reduction rate. The internal separation layer defect (ISLD) is mainly controlled by reduction rate. The preferred process parameters are determined as temperature 1040℃, reduction rate 13 %, roll speed 35 rpm, feed angle 8°, cross angle 15°, and plug advance against gorge 12 mm. The equiaxed grains with average grain size of 25 μm are obtained due to the complete dynamic recrystallization (DRX) process.
Keywords: Rotary tube piercing Nickel-base superalloy Thick-walled tubes FEM
1. Introduction As a billet for producing hollow structural parts, a lot of thickwalled tubes (the ratio of diameter to thickness less than 4) are demanded in aeronautics, energy power and nuclear industry as described by Huang et al. (2012). The aerospace rings, gas engine pipelines and nuclear pipelines are all hollow components, which require a large number of thick-walled tubes. Especially, Wu et al. (2014) and Mei et al. (2015) stated that the demands for thick-walled tubes of nickelbase superalloy (TWNS) are the most urgent due to its outstanding mechanical property when the temperature ranges from 253 to 700 °C. Rotary tube piercing (RTP) is an innovative process for local and incremental plastic deformation that is suitable for manufacturing seamless tubes. It was invented by Mannesmann brother according to the famous Mannesmann effect as described by Ghiotti et al. (2009). Compared with extrusion process that was reported by Bin (2014) and Guo et al. (2011); Yajing et al. (2008) considered that the RTP process has the advantages of high production efficiency, better surface quality, and small forming load. Recently, the RTP process has received considerable attention. Zhao and Mao (2014) explored the influences of ⁎
process parameters on rolling forces by FEM models. Komori and Mizuno (2009) discussed the effects of process parameters on shear deformation. Shuang et al. (2017) put forward the technology of combining RTP process with rolling process to prepare high precision tubes. Romanenko and Sizov (2014) investigated the dimension uniformity of thick-walled tubes. At the same time, Zhang et al. (2018) reported that the titanium alloy tubes were successfully manufactured by the RTP method. Ding et al. (2017) found that the magnesium alloy tubes could be produced by the RTP method. However, the reports on preparing the TWNS by RTP method are still limited. Tian (1989) made a preliminary attempt to explore the feasibility of preparing nickel-base superalloy tubes by RTP process. The results manifested that various problems are inevitable, such as biting problem (Fig. 19c), lose stability of mandrel (Fig. 15), and separating layer defects (Fig. 19a and b). The piercing process of nickel-base superalloy is much more difficult than other alloys due to its large deformation resistance, poor plasticity and narrow processing window. Therefore, it is necessary to systematically explore the influences of process parameters on the material flow. The microstructure of nickel-base superalloy is sensitive to temperature and strain rate. Extensive researches focusing on the thermal
Corresponding authors. E-mail address: [email protected] (D. Liu).
https://doi.org/10.1016/j.jmatprotec.2019.116557 Received 22 April 2019; Received in revised form 31 October 2019; Accepted 15 December 2019 Available online 17 December 2019 0924-0136/ © 2019 Elsevier B.V. All rights reserved.
Journal of Materials Processing Tech. 279 (2020) 116557
Z. Zhang, et al.
Fig. 1. The relative position of dies, (a) main view, (b) left view, (c) top view, (d) the definition of tracking points, and (e) the division of deformation region.
affected by temperature and strain rate. Zhu et al. (2014) stated that the microstructure of Inconel 718 alloy is closely related to the thermal parameters. The RTP process is a 3D plastic deformation process, accompanied by uneven distribution of strain and temperature. Therefore, it is vital to explore the preferred process parameters for obtaining the TWNS with qualified microstructures. The objective of the present work is to study the influences of process parameters on material flow and microstructure distribution of nickel-base superalloy in the RTP process, so as to obtain the preferred process parameters for manufacturing the TWNS with precise geometry, good surface quality, and qualified microstructures. The information achieved within experimental conditions can be used to guide practical production by providing precise control of process parameters.
Table 1 The composition of Inconel 718 alloy (wt%). C
Cr
Ni
Co
Mo
Al
Ti
Nb
Fe
0.03
18.1
53.8
0.25
3.15
0.52
1.04
5.23
balance
deformation behavior and microstructure evolution of nickel-based superalloy have been reported. Pu et al. (2017) considered that the nickel-base superalloy is typically characterized by large deformation resistance, poor plasticity and high sensitivity to temperature and strain rate. Wen et al. (2014) studied the hot deformation behavior of nickelbased superalloy by thermal simulation compression experiment, and the processing window was obtained. Based on the isothermal constant true strain rate compression experiments, the dynamic recrystallization (DRX) behavior of Inconel 718 alloy was discussed by Kumar et al. (2016). The results indicate that the DRX process is significantly 2
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Fig. 2. The microstructure of the as-received Inconel 718 alloy.
defined as A, which determines the biting process, as shown in Fig. 1e. The solid billet was transformed into hollow tube in the piercing region. Reduction rate is defined as:
Table 2 The mechanical and thermal properties of Inconel 718 alloy and 5CrNiMo. Simulation parameter Mechanical
Thermal
3
Density(kg/m ) Poisson ratio Young’s modulus (GPa) Heat conductivity (W/(m·°C)) Specific heat (J/(kg·°C))
Inconel 718
5CrNiMo
8240 0.3 208.46–0.094×T 12.58 + 0.016×T 361.21 + 0.326×T
7860 0.3 198 33.5 448
ε=
During the RTP process, the two rolls rotate around their axis in the same direction and the block pushes the billet forward to achieve the biting process. Under the action of roll pressure, additional tensile stress along guide plate is generated in the center of billet. If the plug is placed in the reasonable position, the solid billet can be separated into hollow tubes by the plug, as shown in Fig. 1. The angle between roll axis and rolling line in Fig. 1a denotes the cross angle β , and in Fig. 1c denotes the feed angle α . The tracking points were used to explore the evolution of filed variables, as shown in Fig. 1d. R and r represents the diameter of billet and the distance between tracking points and billet axis, respectively. T and t is the thickness of tube and the distance between tracking points and the inner surface of tube, respectively. According to the deformation characteristics, the deformation regions can be divided into four sections, which are the preparation region(Ⅰ), piercing region (Ⅱ), uniform region(Ⅲ) and rounding region(Ⅳ), as shown in Fig. 1e. In the preparation region, reduction rate before contact with plug can be expressed as:
Db − DL Db
(2)
Db
where Dg is the distance between two rolls at gorge. The rounding region and uniform region is to smooth the wall thickness and reduce the ellipticity of tube, respectively. During the RTP process, the resultant forces and moments of rolls and plug determine the piercing process. The rotation condition can be expressed as:
2. Design of the RTP process
εdq =
Db − Dg
(3)
MR = MT − MP − MI − MG
where the MR , MT , MP , MI , MG is the resultant moments, roll friction moments, positive pressure moments, inertial moments of billet and plug resistance moments, respectively. When the resultant moments are greater than zero, the rotation condition can be satisfied. The axial forward condition can be given as follows:
F = 2 × (Tx − Px ) − Q′ ≥ 0
(4)
′
where F, Tx , Px , Q is the resultant forces, axial component of driving forces, axial component of resistance forces and resistance of plug nose, respectively. When the resultant forces are greater than zero, the axial forward condition can be satisfied. The axial component of driving force, axial component of resistance force and resistance of plug nose can be determined by the following equation:
Tx = T × cos θ = pf cos θ = pbLH f cos θ = pbf (
d z εdq 2 tan α1
) 1−(
1+
dz D 2 )
fd z
(5)
(1)
where Db and DL are the billet diameter and the distance between two rolls at plug nose, respectively. The plug advance against gorge is
Px = p × sin α1 = pbLH sin α1 = pb ( 3
d z εdq 2 tan α1
)sin α1
(6)
Journal of Materials Processing Tech. 279 (2020) 116557
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Fig. 3. The experiment procedures for determining the preferred process parameters.
without plug action) should be conducted first to ensure that the piercing process can be carried out smoothly. The rotary rolling process has been described in detail in the Ref of Zhang et al. (2019).
Table 3 Configuration of the FEM model. Parameter
Value
Billet diameter (mm) Billet length (mm) Temperature (°C) Guide plate space (mm) Feed angle(°) Cross angle(°) Roll speed (rpm) Reduction rate (%) Plug advance against gorge (mm)
45 150 1100 45 8–20 9–21 20–70 8–20 5–40
Q′ = πrH 2PH
3. Material and method 3.1. Material model As the most typical nickel-base superalloy, Inconel 718 alloy was chosen as the program material, and it was provided in the form of bar with diameter of 60 mm. The chemical compositions are shown in Table 1. Microstructure of the as-received material is shown in Fig. 2. The true stress–strain curves were obtained by the isothermal compression tests, which have been described in detail in our previous research of Zhang et al. (2019). The mechanical properties parameters and thermal performance parameters are all derived from Zhu et al. (2016), as shown in Table 2. The material of roll is 5CrNiMo.
(7)
where T , θ , p , f , b , LH , α1, d z , εdq , rH , PH and D is the driving force, direction angle, mean pressure of rolls, friction factor, contact width, contact length, entrance angle of roll, diameter of tube, reduction rate before contact with the plug, diameter of plug nose, mean pressure of plug nose and roll diameter, respectively. Substituting Eqs. (5)–(7) into Eq. (4), the axial forward condition can be deduced as follows:
2 × (Tx − Px ) = pb (
d z εdq tanα1
d
) × (f ×
3.2. Experimental procedures In order to obtain the preferred process parameters for manufacturing the TWNS, the combinations of simulation and experiment were adopted, as shown in Fig. 3. Firstly, according to the simulation results of rotary rolling process (without plug action) and RTP process, the reasonable ranges of process parameters were determined. Secondly, the rotary rolling experiments were carried out to discuss the influences of process parameters on the formation of external separation layer defect (ESLD). Based on the experimental results of rotary rolling process, the experiments of RTP process were conducted to discuss the influences of process parameters on the internal separation layer defect (ISLD). The ranges of process parameters were further optimized. Finally, the influences of temperature on the surface quality and microstructure distribution of TWNS were explored, and the preferred process parameters were obtained. The obtained tubes were grinded mechanically and polished using standard metallographic techniques, and corroded by boiling 20 % H2SO4 and KMnO₄. Electron backscattered diffraction (EBSD) analyses were used to explore the DRX
2
z ⎛1 + D ⎞ 1−⎜ − sinα1) ≥ πrH 2PH fd z ⎟ ⎝ ⎠
(8) Therefore, the minimum reduction rate before contact with the plug εmin is obtained as:
π εmin =
pH r 2tanα1 p H dz
2
⎛1 + ⎞ d z b (f 1 − ⎜ fd D b⎟ − sinα1) z ⎝ ⎠
(9)
When the reduction rate before contact with the plug εdq is greater than εmin , the piercing process is completed smoothly, and vice versa. Before the RTP process, the rotary rolling process (RTP process 4
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Fig. 4. The (a) geometry model and (b) actual object of the improved piercing mill, and the (c) main view and (d) top view of mandrel position.
Fig. 5. The geometry of (a) traditional roll and (b) cone roll (Zhang et al., 2018).
5
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Fig. 6. The comparisons between experiment results and simulation results, (a) experimental process, (b) pierced tube, (c) profile of tube, (d) rolling force and (e) rolling torque.
Fig. 7. The evolution of rotary rolling process expressed by the strain field, one half ranged from 0 to 2.0, the other ranged from 0 to 4.0, and the temperature field ranged from 1050 °C to 1150 °C.
improved, as shown in Fig. 5. On the other hand, the stability of mandrel is vital for Inconel 718 alloy with large deformation resistance. Especially for thick-walled tubes, the diameter of mandrel is smaller than thin-walled tubes, so it is critical to improve the stability of mandrel. The centering devices of the improved mill are composed of three cams, which impose constraints on the mandrel in three directions, so that the stability of mandrel can be significantly improved. At the same time, the centering devices are non-uniformly distributed according to the simulation results of mandrel bending process, as shown in Fig. 4c and d. The friction condition and heat transfer
process. The ranges of process parameters for simulation are shown in Table 3. 3.3. Establishment of FEM model According to the deformation characteristics of nickel-base superalloy, an improved piercing mill was developed, as shown in Fig. 4. On the one hand, the diameter of roll increases gradually along roll axis, which is consistent with the flow law of metals. Compared with the traditional roll, the deformation uniformity can be significantly 6
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Fig. 8. The evolution of temperature and strain in rotary rolling process, (a) temperature and (b) strain.
Fig. 9. The influences of process parameters on strain distribution, (a) feed angle, (b) reduction rate, (c) roll speed, and (d) cross angle.
ranges, 0∼2 and 0∼4, respectively. The stage A is the transshipment process. It shows that the temperature is inhomogeneous, which decreases gradually from center to surface. The stage B represents the biting process. The plastic deformation gradually permeates from the surface to the center. Stage C is the steady rolling process. It is obvious that the strain gradient in the range of r/R = 0.8 to r/R = 0.95 is not conducive to the penetration of plastic deformation. The temperature filed indicates that the billet is still in hot state, even if the billet has experienced a long transport and rolling time. The evolution of strain and temperature is shown in Fig. 8. It reveals that the maximum strain is in the surface (r/R = 1) and the minimum strain is in the center (r/R = 0). Under the combined action of deformation heat, friction heat, heat dissipation, the highest temperature appears in the region of r/R = 0.8 to r/R = 0.95.
condition are consistent with our previous studies of Zhang et al. (2019). 3.4. Verification of FEM model In order to verify the accuracy of simulation results, the typical piercing process was conducted by experiment and simulation. The main process parameters are as follows: temperature 1100 °C, reduction rate 13 % and roll speed 40 rpm. The piercing process is shown in Fig. 6a–c. The comparisons of rolling force and rolling torque between simulation results and experiment results are shown in Fig. 6d and e, respectively. It indicates that the forces and torque are compatible in terms of both quality and quantity. 4. Simulation results and discussion 4.1. The distribution of temperature and strain in rotary rolling process
4.2. The influences of process parameters on strain distribution of rotary rolling process
The distribution of temperature and strain is shown in Fig. 7. In order to describe the strain more clearly, the strain field consists of two
The influences of feed angle, reduction rate, roll speed and cross angle on the strain distribution is shown in Fig. 9. It shows that 7
Journal of Materials Processing Tech. 279 (2020) 116557
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Fig. 10. The influences of process parameters on maximum temperature rise, (a) feed angle, (b) reduction rate, (c) roll speed, and (d) cross angle.
maximum strain, minimum strain and strain range decreases with the increase of feed angle. The influences of feed angle on strain are mainly related to the shear strain, whcih decreases with the increase of feed angle. The effects of reduction rate on maximum strain and minimum strain are consistent. With the increase of reduction rate, the maximum strain, minimum strain and strain range increase simultaneously. The reduction rate affects the strain distribution by changing the basic deformation and shear deformation at the same time. The effects of roll speed on maximum strain and minimum strain are opposite. With the increase of roll speed, the minimum strain decreases, but the maximum strain and the strain range increases. The cross angle has little influence on the strain distribution.
plug, and the second biting process is completed, as shown in Fig. 11b. After entering the steady piercing process, the deformation law is consistent along the billet axis, as shown in Fig. 11c. The distribution of strain and temperature is shown in Fig. 12. In the preparation region, the strain decreases gradually form the surface to the center. After entering the piercing region, the strain increases sharply under the combined action of rolls and plug. The maximum strain is in the surface (t/T = 1) and the minimum strain is in the transition layer (t/T = 0.5). The temperature reveals that the billet is still in hot state under the combined action of deformation heat, friction heat and heat conduction, and the maximum temperature rise is in the range of r/R = 0.4 to r/R = 0.8.
4.3. The influences of process parameters on temperature distribution of rotary rolling process
4.5. The influences of process parameters on the axial resistance of mandrel For the thick-walled tubes of nickel-base superalloy, the stability of mandrel is vital. The strength and stability of mandrel are determined by the axial resistance of mandrel. Therefore, the influences of process parameters on the axial resistance of mandrel are discussed systematically. The force analysis of plug is shown in Fig. 13. The axial resistance of mandrel can be expressed by the following equation.
The influences of process parameters on maximum temperature rise are shown in Fig. 10. The effects of feed angle on temperature rise are related to the combined effect of deformation heat and heat dissipation. With the increase of feed angle, both the deformation heat and heat dissipation decreases. Therefore, the effects of feed angle on temperature rise are not significant. The influences of reduction rate on maximum temperature rise are linear. With the increase of reduction rate, the deformation heat increases, leading to the increase of maximum temperature rise. Roll speed has significant effects on the maximum temperature rise. With the increase of roll speed, the friction heat increases sharply, leading to the increase of maximum temperature rise. The cross angle has little impact on the maximum temperature rise.
Q = QH + 2P0 (sinφ0 + fcosφ0)
(10)
Because the direction of friction force is not parallel to the rolling line, the axial component of contact friction force is:
Tx = P0 fcosφ0 cosθc
(11)
Therefore, the axial resistance of mandrel is modified as：
Q = QH + 2P0 (sinφ0 + fcosφ0 cosθc )
4.4. The distribution of temperature and strain in rotary tube piercing process
(12)
where the Q , QH , P0 , φ0 , Tx , θc is the axial resistance of mandrel, the resistance of plug nose, the normal pressure acting on plug, the tangent angle of plug, axial component of contact friction force and inclination angle, respectively. The resistance of plug nose is
The RTP process is shown in Fig. 11. Under the action of rolls, the billet rotates forward to achieve the first biting process, as shown in Fig. 11a. As the piercing process continues, the billet is transformed from solid bar to hollow tube under the combined action of rolls and
QH = πrH 2nH σs 8
(13)
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where rH , nH , σs is the radius of plug nose, stress state coefficient and flow stress of metal, respectively. The stress state coefficient is closely related to the transverse tensile stress in the preparation region. The critical instability force of mandrel can be expressed as follows:
Qlj =
π 2EI (μL)2
(14)
where Qlj , E , I , μ , L is the critical instability force of mandrel, elastic modulus of mandrel, moment of inertia, flexibility coefficient and the length of mandrel, respectively. Substituting Eqs. (12) and (13) into Eq. (14), the instability condition of mandrel can be deduced as follows:
Q= πrH 2nH σs + +2P0 (sinφ0 + fcosφ0 cosθc ) ≤
π 2EI = Qlj (μL)2
(15)
The influences of process parameters on the axial resistance of mandrel are shown in Fig. 14. It indicates that the axial resistance of mandrel increases with the increase of feed angle and decrease with the increase of reduction rate. The influences of feed angle on the axial resistance of mandrel are related to the strain rate. With the increase of feed angle, the strain rate increases gradually, resulting in the increase of flow stress. With the increase of reduction rate, the transverse tensile stress which can significantly reduce the resistance of plug increases. Therefore, the axial resistance of mandrel decreases with the increase of reduction rate. The effects of roll speed on the axial resistance of mandrel are determined by the comprehensive effect of strain rate and thermal effect. With the increase of roll speed, the increase of strain rate leads to the increase of flow stress. However, the temperature rise caused by the increase of roll speed reduces the flow stress. When roll speed is less than 35 rpm, axial resistance of mandrel increases with the increase of roll speed. When roll speed is greater than 35 rpm, the axial resistance of mandrel basically remains unchanged. The cross angle has little effect on the axial resistance of mandrel. The experiment results of mandrel are shown in Fig. 15. When the resistance of mandrel Q is less than the critical instability force Qlj , the piercing process can be carried out smoothly, and the TWNS with precise dimension are obtained, as shown in Fig. 15a. When the resistance of mandrel Q is approximately equal to the critical instability force Qlj , the swing of mandrel is serious, leading to the poor uniformity
Fig. 11. The piercing process of Inconel 718 alloy (indicated with strain), (a) first biting process, (b) second biting process, (c) steady piercing process.
Fig. 12. The distribution of (a) strain and (b) temperature in RTP process. 9
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Fig. 13. Force analysis of plug.
Fig. 14. The influences of (a) feed angle and reduction rate, (b) roll speed and cross angle on the axial resistance of mandrel.
Fig. 15. Experimental results of process parameters on the lose stability of mandrel, (a) good condition of mandrel, (b) swing of mandrel, (c) mandrel breaking and (d) the mandrel diagram.
5. Experiment results and discussion
of wall thickness, as shown in Fig. 15b. If the resistance of mandrel Q is greater than the critical instability force Qlj , the mandrel will be broken, and the piercing process can’t be completed, as shown in Fig. 15c. The mandrel is shown in Fig. 15d.
5.1. Experiment results of rotary rolling process and RTP process Based on the simulation results, the reasonable ranges of process 10
Journal of Materials Processing Tech. 279 (2020) 116557
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Fig. 16. The influences of reduction rate on the formation of ESLD.
Fig. 17. The influences of roll speed on the formation of ESLD.
11
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Fig. 18. The influences of reduction rate on the formation of ISLD.
Fig. 19. The experiment results of (a) ESLD (case.3), (b) ISLD (case.8), (c) rolling block and (d) successful sample.
separation layer defect (ESLD). When the crack is in the region of 0.05 ≤ t/T ≤ 0.2 (tube), it is the internal separation layer defect (ISLD). If the process parameters are unreasonable, the ESLD defects will occur in both rotary rolling process and RTP process, while the ISLD only appears in RTP process. Before the RTP process, the rotary rolling process must be guaranteed to be completed smoothly. The experiment results reveal that the formation of ESLD is greatly influenced by reduction rate, as shown in Fig. 16. When the reduction rate is less than 15 %, no defects are observed. But when the reduction
parameters are obtained as follows: feed angle 8∼20°, cross angle 9∼21°,roll speed 20∼70 rpm, reduction rate before contact plug greater than 4.5 %. The experiments are designed based on control variable method to determine the preferred process parameters. The experiment results of rotary rolling process show that the ESLD is inevitable. Yin et al. (2012) and Tian and Li (2012) described that the separation layer defect is a crack with a certain width, which is parallel to the surface of tube. When the crack appears in the region of 0.8 ≤ r/ R ≤ 0.95 (bar) or 0.8 ≤ t/T ≤ 0.95 (tube), it denotes the external 12
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Fig. 20. The TWNS of different diameters and lengths obtained by RTP process, (a) axial dimension and (b) radial dimension.
under the condition of temperature 1100 °C, reduction rate 13 %, roll speed 35 rpm, and plug advance against gorge 12 mm, but the surface quality is poor. Finally, when the temperature is 1040 °C, the piercing process is smooth, and the TWNS with better surface quality and finer grain size are obtained successfully than that in 1100 °C, as shown in Fig. 19d. Based on the preferred parameters, the TWNS with different diameters and lengths are obtained, as shown in Fig. 20a and b. The statistics of geometry dimensions are shown in Table 4. The maximum diameter difference for outer and inner diameter is 2 mm and 1.1 mm, respectively. Therefore, the preferred process parameters are reliable for preparing the TWNS with different specifications.
Table 4 The statistics of geometric dimensions for tubes with different specifications. Number
Maximum external diameter difference(mm)
Maximum internal diameter difference(mm)
No.1 No.2 No.3
1.8 1.6 2
0.8 1.1 0.8
rate increases to 15 %, the ESLD occurs, as shown in Fig. 19a. In order to predict the ESLD, the Freudenthal model proposed by Freudenthal (1950) is introduced.
∫0
εf
σdε ¯ ¯=D
(16)
5.2. The formation mechanism of ESLD and ISLD
where σ¯ , εf , D is the effective stress, fracture strain and damage. The simulation results show that the damage decreases gradually form the surface to the center, and the maximum damage is near the surface, as shown in Fig. 16. At the same time, the damage increases with the increase of reduction rate. When the damage is greater than the damage threshold, the ESLD will occur. The critical condition of ESLD is determined as roll speed 70 rpm, reduction rate 15 %. Fig. 17 indicates that the formation of ESLD is significantly affected by roll speed. When the roll speed is 70 rpm, the ESLD occurs. But as the roll speed decreases from 70 rpm to 40 rpm, the ESLD disappears. As the roll speed continues to decrease, the ESLD defect disappears and the surface quality of the rolled bar becomes better. The simulation results reveal that roll speed has little effect on the damage distribution, as shown in Fig. 17. With the increase of roll speed, the temperature rise is significant. Excessive temperature rise will lead to poor plasticity of Inconel 718 alloy and decrease the damage threshold. Therefore, the ESLD can be eliminated by selecting reasonable roll speed and reduction rate. Fig. 18 reveals that the ISLD is closely related to reduction rate. When the reduction rate is less than 18 %, no defects are observed. But as the reduction rate increase to 18 %, the ISLD appears, as shown in Fig. 19b. With the increase of reduction rate, the ISLD becomes more serious. The simulation results reveal that the radial deformation uniformity decreases with the increase of reduction rate. The non-uniform plastic deformation generates additional shear stress, which lead to the formation of ISLD. At the same time, the temperature rise caused by large deformation will also reduce the damage threshold. Therefore, reasonable control of reduction rate is vital. At the same time, the reduction rate should be greater than the critical value εmin . When the reduction rate before contact with plug is less than the critical value, the rolling block phenomenon that the billet is stuck in the middle of rolls is inevitable, and the dynamic recrystallization (DRX) may not be sufficient, as shown in Fig. 19c. Therefore, under the premise of ensuring the ESLD and ISLD doesn’t occur, the reduction rate should be selected as large as possible. The TWNS (ratio of diameter to thickness 3.5) are successfully prepared
By comparing the simulation results and experiment results, it can be found that the ESLD is mainly related to the large strain gradient and severe temperature rise in the region of r/R = 0.8∼ r/R = 0.95. On the one hand, the maximum strain gradient is consistent with the location of ESLD, as shown in Fig. 7. The maximum strain gradient caused by uneven deformation generates local shear stress. When the local shear stress is greater than the fracture strength material, the ESLD will occur. On the other hand, the maximum temperature rise is also in the range of r/R = 0.8 to r/R = 0.95, as shown in Fig. 7. Excessive temperature rise will lead to the poor plasticity of Inconel 718 alloy and decrease the damage threshold. The ISLD is controlled by reduction rate. When the reduction rate is great than critical value, the ISLD will appear. Existing evidence shows that the ISLD is related to the non-uniform plastic deformation in the piercing region. Further investigations are still necessary to provide the evidence for the formation mechanism of ISLD. 5.3. The analysis of microstructure distribution Microstructure analysis is carried out on the samples taken from the middle of tube. The corresponding process parameters are as follows: temperature 1040℃, feed angle 8°, cross angle 15°, roll speed 35 rpm, reduction rate 13 %, and plug advance against gorge 12 mm. The optical micrograph map is shown in Fig. 21a, b and c. It can be observed that the equiaxed grains with average grain size of 25 μm are obtained. Fig. 21d shows the grain boundary (GB) maps of transition layer (t/T = 0.5), in which high angle grain boundaries (the misorientations larger than 15°) and low angle grain boundaries (the misorientations lower than 15°) are represented by black lines and red lines, respectively. It reveals that high angle grain boundaries are far more than low angle grain boundaries. The formation of high angle grain boundaries is closely related to the DRX process. The statistics of misorientation angle are shown in Fig. 21h. It indicates that the average misorientation angle is 38.12°. Fig. 21e reveals the DRX maps of transition layer (t/T = 0.5), in which blue, yellow and red indicate the fully recrystallized grains, substructures and deformed grains. It is observed that the volume 13
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Fig. 21. Schematic diagram showing the microstructure of tube corresponding to Fig.18d, (a) t/T = 0.99, (b) t/T = 0.5 and (c) t/T = 0, (d) The grain boundary map, (e) dynamic recrystallization map, (f) inverse pole figure of the pierced tube, the statistics of (g) dynamic recrystallization volume proportion and (h) misorientation angle.
piercing process of nickel-base superalloy, and the effects of process parameters on the material flow and microstructure distribution were investigated by combining experiments with simulations. All the simulation and experiment results led to the following conclusions.
proportion of recrystallized grains is 96.89 %, as shown in Fig. 21g. The inverse pole figure (IPF) shows that the RTP process is a three-dimensional plastic deformation without preferred orientation. The microstructure evolution of RTP process is shown in Fig. 22. The GB map shows that the microstructure evolution includes three typical states: the coarse grains before entering the deformation region, the mixed grains in the preparation region, and the fine equiaxed grains in the uniform region and rounding region. Before entering deformation region, the coarse equiaxed grains are dominated by large number of substructures. After entering the preparation region, the mixed grains are obtained under the action of DRX process. In the piercing region, the mixed grains are transformed into fine equiaxed grains, and the DRX process is completed. The IPF map indicates that there is no significant orientation in the RTP process.
(1) The ESLD is significantly influenced by roll speed and reduction rate. The formation mechanism of ESLD is large strain gradient and severe temperature rise in the region of r/R = 0.8∼ r/R = 0.95. (2) The ISLD is mainly affected by reduction rate. For the thick-walled tube with ratio of diameter to thickness 3.5, the reduction rate is determined as 9 %–15 % to prevent the occurrence of ISLD. (3) The preferred process parameters are determined as temperature 1040 °C, reduction rate 13 %, roll speed 35 rpm, feed angle 8°, cross angle 15°, and plug advance against gorge 12 mm. The equiaxed grains with average grain size of 25 μm are obtained due to the complete DRX process. (4) In the RTP process, the microstructure evolution of nickel-base superalloy can be divided into three typical states: the coarse grains
6. Conclusions In this paper, an improved piercing mill was developed for the 14
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Fig. 22. The microstructure evolution of rolling block sample corresponding to Fig.18c, (a) rolling block sample, the GB map of (b) P-1, (c) P-2, (d) P-3, (e) P-4, the DRX map of (f) P-1, (g) P-2, (h) P-3, (i) P-4, and IPF map of (j) P-1, (k) P-2, (l) P-3, (m) P-4.
before entering the deformation region, the mixed grains in the preparation region, and the fine equiaxed grains in the uniform region and rounding region.
Ding, X., Shuang, Y., Liu, Q., Zhao, C., 2017. New rotary piercing process for an AZ31 magnesium alloy seamless tube. Mater. Sci. Technol. 0836, 1–11. Freudenthal, A.M., 1950. The Inelastic Behavior of Engineering Materials and Structures. John Wiley & Sons, New York, pp. 1–26. Ghiotti, A., Fanini, S., Bruschi, S., Bariani, P.F., 2009. Modelling of the mannesmann effect. CIRP Ann. Manuf. Technol. 58, 255–258. Guo, Q., Li, H., Li, D., Guo, S., Peng, H., Jie, H., 2011. Hot extrusion moulding process and microstructure evolution of GH625 superalloy tubes. Chin. J. Rare Met. 35, 684–689. Huang, C.C., Fan, H.Y., Hung, C.H., Hung, J.C., Lin, C.R., 2012. Three dimensional finite element analysis on neck-spinning process of thick-walled tube at an elevated temperature. Adv. Mater. Res. 579, 269–277. Komori, K., Mizuno, K., 2009. Study on plastic deformation in cone-type rotary piercing process using model piercing mill for modeling clay. J. Mater. Process. Technol. 209, 4994–5001. Kumar, S.S.S., Raghu, T., Bhattacharjee, P.P., Rao, G.A., Borah, U., 2016. Strain rate dependent microstructural evolution during hot deformation of a hot isostatically processed nickel base superalloy. J. Alloys Compd. 681, 28–42. Mei, Y., Liu, Y., Liu, C., Li, C., Yu, L., Guo, Q., Li, H., 2015. Effects of cold rolling on the precipitation kinetics and the morphology evolution of intermediate phases in Inconel 718 alloy. J. Alloys Compd. 649, 949–960. Pu, E., Zheng, W., Song, Z., Feng, H., Dong, H., 2017. Hot deformation characterization of nickel-based superalloy UNS10276 through processing map and microstructural studies. J. Alloys Compd. 694, 617–631. Romanenko, V.P., Sizov, D.V., 2014. Evaluating the adequacy of a mathematical model of the piercing of a billet into an ultra-thick-walled shell on a two-high rotary rolling mill. Metallurgist 57, 71–76. Shuang, Y., Wang, F., Wang, Q., 2017. Explorative study of tandem skew rolling process
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the Shaanxi key research and development program (2017ZDXM-GY-027), Natural Science Basic Research Plan in Shaanxi Province of China (No.2017JM5010) and Fundamental Research Funds for the Central Universities (3102019ZX004) References Bin, W., 2014. High speed hot tube extrution process of Incone1690 superalloy. RARE Met. Mater. Eng. 43, 137–142.
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Zhang, Z., Liu, D., Yang, Y., Wang, J., Zheng, Y., Zhang, F., 2019. Microstructure evolution of nickel-based superalloy with periodic thermal parameters during rotary tube piercing process. Int. J. Adv. Manuf. Technol. https://doi.org/10.1007/s00170-01904126-x. Zhang, Z., Liu, D., Yang, Y., Zheng, Y., Pang, Y., Wang, J., Wang, H., 2018. Explorative study of rotary tube piercing process for producing titanium alloy thick-walled tubes with bi-modal microstructure. Arch. Civ. Mech. Eng. 18, 1451–1463. Zhao, Y.Q., Mao, J.H., 2014. Effects of feed angle on mannesmann piercing in Drill steel production. Adv. Mater. Res. 915, 996–999. Zhu, X., Liu, D., Yang, Y., Hu, Y., Liu, G., Wang, Y., 2016. Effects of blank dimension on forming characteristics during conical-section ring rolling of Inco718 alloy. Int. J. Adv. Manuf. Technol. 84, 2707–2718. Zhu, Y.Z., Wang, S.Z., Li, B.L., Yin, Z.M., Wan, Q., Liu, P., 2014. Grain growth and microstructure evolution based mechanical property predicted by a modified Hall–Petch equation in hot worked Ni76Cr19AlTiCo alloy. Mater. Des. 55, 456–462.
and equipment for producing seamless steel tubes. J. Mech. Eng. 214, 1597–1604. Tian, D., 1989. A study on a two roll cross piercing process for GH131 alloy. Steel Pipe. 6, 34–39. Tian, D., Li, Q., 2012. Discussion on seamless steel pipe defects of separation layer and lamination. Steel Pipe 41, 51–56. Wen, D.X., Lin, Y.C., Li, H.Bin, Chen, X.M., Deng, J., Li, L.T., 2014. Hot deformation behavior and processing map of a typical Ni-based superalloy. Mater. Sci. Eng. A. 591, 183–192. Wu, L.J., Zhao, C.C., Dong, G.J., 2014. Numerical and experimental investigations on SGMF of GH3044 superalloy tube. Adv. Mater. Res. 915–916, 668–672. Yajing, X., Xianze, X., Shuqi, Z., Chao, D., Jie, Z., Mingqiang, L., 2008. TC4 titanium alloy seamless blooms made by rotary piercing. Rare Met. Lett. 27, 29–32. Yin, Y.D., Li, S.Z., Kang, Y.L., Wang, P.Z., Wang, X.D., Li, G.T., 2012. Tendency of lamination defect of thick-walled P92 pipe with large diameter elongated by 2-roll rotary rolling process. Iron Steel. 47, 52–56.
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Contents lists available at ScienceDirect
Journal of Materials Processing Tech. journal homepage: www.elsevier.com/locate/jmatprotec
Experimental and numerical analysis of rotary tube piercing process for producing thick-walled tubes of nickel-base superalloy
T
Zhe Zhanga, Dong Liua,*, Runqiang Zhangc, Yanhui Yanga, Yuhua Pangb, Jianguo Wanga, Hai Wanga a
School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, PR China School of Metallurgical Engineering, Xi`an University of Architecture and Technology, Xi'an 710055, PR China c Xi'an Sheng Dong Forge CO., LTD, Xi'an 710072, PR China b
A R T I C LE I N FO
A B S T R A C T
Associate Editor: Z. Cui
In order to overcome the problems of existing methods for preparing thick-walled tubes of nickel-base superalloy (TWNS), the rotary tube piercing (RTP) process was proposed. For this purpose, an improved piercing mill was designed, and the influences of process parameters on strain, temperature, biting condition, lose stability of mandrel, defects control and microstructure distribution were studied by the combination of finite element model (FEM) and experiments. Based on the control variable method, the ranges of process parameters corresponding to the second biting condition and the critical condition of mandrel instability were determined by the simulation results. The experiment results indicate that the external separation layer defect (ESLD) is significantly affected by roll speed and reduction rate. The internal separation layer defect (ISLD) is mainly controlled by reduction rate. The preferred process parameters are determined as temperature 1040℃, reduction rate 13 %, roll speed 35 rpm, feed angle 8°, cross angle 15°, and plug advance against gorge 12 mm. The equiaxed grains with average grain size of 25 μm are obtained due to the complete dynamic recrystallization (DRX) process.
Keywords: Rotary tube piercing Nickel-base superalloy Thick-walled tubes FEM
1. Introduction As a billet for producing hollow structural parts, a lot of thickwalled tubes (the ratio of diameter to thickness less than 4) are demanded in aeronautics, energy power and nuclear industry as described by Huang et al. (2012). The aerospace rings, gas engine pipelines and nuclear pipelines are all hollow components, which require a large number of thick-walled tubes. Especially, Wu et al. (2014) and Mei et al. (2015) stated that the demands for thick-walled tubes of nickelbase superalloy (TWNS) are the most urgent due to its outstanding mechanical property when the temperature ranges from 253 to 700 °C. Rotary tube piercing (RTP) is an innovative process for local and incremental plastic deformation that is suitable for manufacturing seamless tubes. It was invented by Mannesmann brother according to the famous Mannesmann effect as described by Ghiotti et al. (2009). Compared with extrusion process that was reported by Bin (2014) and Guo et al. (2011); Yajing et al. (2008) considered that the RTP process has the advantages of high production efficiency, better surface quality, and small forming load. Recently, the RTP process has received considerable attention. Zhao and Mao (2014) explored the influences of ⁎
process parameters on rolling forces by FEM models. Komori and Mizuno (2009) discussed the effects of process parameters on shear deformation. Shuang et al. (2017) put forward the technology of combining RTP process with rolling process to prepare high precision tubes. Romanenko and Sizov (2014) investigated the dimension uniformity of thick-walled tubes. At the same time, Zhang et al. (2018) reported that the titanium alloy tubes were successfully manufactured by the RTP method. Ding et al. (2017) found that the magnesium alloy tubes could be produced by the RTP method. However, the reports on preparing the TWNS by RTP method are still limited. Tian (1989) made a preliminary attempt to explore the feasibility of preparing nickel-base superalloy tubes by RTP process. The results manifested that various problems are inevitable, such as biting problem (Fig. 19c), lose stability of mandrel (Fig. 15), and separating layer defects (Fig. 19a and b). The piercing process of nickel-base superalloy is much more difficult than other alloys due to its large deformation resistance, poor plasticity and narrow processing window. Therefore, it is necessary to systematically explore the influences of process parameters on the material flow. The microstructure of nickel-base superalloy is sensitive to temperature and strain rate. Extensive researches focusing on the thermal
Corresponding authors. E-mail address: [email protected] (D. Liu).
https://doi.org/10.1016/j.jmatprotec.2019.116557 Received 22 April 2019; Received in revised form 31 October 2019; Accepted 15 December 2019 Available online 17 December 2019 0924-0136/ © 2019 Elsevier B.V. All rights reserved.
Journal of Materials Processing Tech. 279 (2020) 116557
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Fig. 1. The relative position of dies, (a) main view, (b) left view, (c) top view, (d) the definition of tracking points, and (e) the division of deformation region.
affected by temperature and strain rate. Zhu et al. (2014) stated that the microstructure of Inconel 718 alloy is closely related to the thermal parameters. The RTP process is a 3D plastic deformation process, accompanied by uneven distribution of strain and temperature. Therefore, it is vital to explore the preferred process parameters for obtaining the TWNS with qualified microstructures. The objective of the present work is to study the influences of process parameters on material flow and microstructure distribution of nickel-base superalloy in the RTP process, so as to obtain the preferred process parameters for manufacturing the TWNS with precise geometry, good surface quality, and qualified microstructures. The information achieved within experimental conditions can be used to guide practical production by providing precise control of process parameters.
Table 1 The composition of Inconel 718 alloy (wt%). C
Cr
Ni
Co
Mo
Al
Ti
Nb
Fe
0.03
18.1
53.8
0.25
3.15
0.52
1.04
5.23
balance
deformation behavior and microstructure evolution of nickel-based superalloy have been reported. Pu et al. (2017) considered that the nickel-base superalloy is typically characterized by large deformation resistance, poor plasticity and high sensitivity to temperature and strain rate. Wen et al. (2014) studied the hot deformation behavior of nickelbased superalloy by thermal simulation compression experiment, and the processing window was obtained. Based on the isothermal constant true strain rate compression experiments, the dynamic recrystallization (DRX) behavior of Inconel 718 alloy was discussed by Kumar et al. (2016). The results indicate that the DRX process is significantly 2
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Fig. 2. The microstructure of the as-received Inconel 718 alloy.
defined as A, which determines the biting process, as shown in Fig. 1e. The solid billet was transformed into hollow tube in the piercing region. Reduction rate is defined as:
Table 2 The mechanical and thermal properties of Inconel 718 alloy and 5CrNiMo. Simulation parameter Mechanical
Thermal
3
Density(kg/m ) Poisson ratio Young’s modulus (GPa) Heat conductivity (W/(m·°C)) Specific heat (J/(kg·°C))
Inconel 718
5CrNiMo
8240 0.3 208.46–0.094×T 12.58 + 0.016×T 361.21 + 0.326×T
7860 0.3 198 33.5 448
ε=
During the RTP process, the two rolls rotate around their axis in the same direction and the block pushes the billet forward to achieve the biting process. Under the action of roll pressure, additional tensile stress along guide plate is generated in the center of billet. If the plug is placed in the reasonable position, the solid billet can be separated into hollow tubes by the plug, as shown in Fig. 1. The angle between roll axis and rolling line in Fig. 1a denotes the cross angle β , and in Fig. 1c denotes the feed angle α . The tracking points were used to explore the evolution of filed variables, as shown in Fig. 1d. R and r represents the diameter of billet and the distance between tracking points and billet axis, respectively. T and t is the thickness of tube and the distance between tracking points and the inner surface of tube, respectively. According to the deformation characteristics, the deformation regions can be divided into four sections, which are the preparation region(Ⅰ), piercing region (Ⅱ), uniform region(Ⅲ) and rounding region(Ⅳ), as shown in Fig. 1e. In the preparation region, reduction rate before contact with plug can be expressed as:
Db − DL Db
(2)
Db
where Dg is the distance between two rolls at gorge. The rounding region and uniform region is to smooth the wall thickness and reduce the ellipticity of tube, respectively. During the RTP process, the resultant forces and moments of rolls and plug determine the piercing process. The rotation condition can be expressed as:
2. Design of the RTP process
εdq =
Db − Dg
(3)
MR = MT − MP − MI − MG
where the MR , MT , MP , MI , MG is the resultant moments, roll friction moments, positive pressure moments, inertial moments of billet and plug resistance moments, respectively. When the resultant moments are greater than zero, the rotation condition can be satisfied. The axial forward condition can be given as follows:
F = 2 × (Tx − Px ) − Q′ ≥ 0
(4)
′
where F, Tx , Px , Q is the resultant forces, axial component of driving forces, axial component of resistance forces and resistance of plug nose, respectively. When the resultant forces are greater than zero, the axial forward condition can be satisfied. The axial component of driving force, axial component of resistance force and resistance of plug nose can be determined by the following equation:
Tx = T × cos θ = pf cos θ = pbLH f cos θ = pbf (
d z εdq 2 tan α1
) 1−(
1+
dz D 2 )
fd z
(5)
(1)
where Db and DL are the billet diameter and the distance between two rolls at plug nose, respectively. The plug advance against gorge is
Px = p × sin α1 = pbLH sin α1 = pb ( 3
d z εdq 2 tan α1
)sin α1
(6)
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Fig. 3. The experiment procedures for determining the preferred process parameters.
without plug action) should be conducted first to ensure that the piercing process can be carried out smoothly. The rotary rolling process has been described in detail in the Ref of Zhang et al. (2019).
Table 3 Configuration of the FEM model. Parameter
Value
Billet diameter (mm) Billet length (mm) Temperature (°C) Guide plate space (mm) Feed angle(°) Cross angle(°) Roll speed (rpm) Reduction rate (%) Plug advance against gorge (mm)
45 150 1100 45 8–20 9–21 20–70 8–20 5–40
Q′ = πrH 2PH
3. Material and method 3.1. Material model As the most typical nickel-base superalloy, Inconel 718 alloy was chosen as the program material, and it was provided in the form of bar with diameter of 60 mm. The chemical compositions are shown in Table 1. Microstructure of the as-received material is shown in Fig. 2. The true stress–strain curves were obtained by the isothermal compression tests, which have been described in detail in our previous research of Zhang et al. (2019). The mechanical properties parameters and thermal performance parameters are all derived from Zhu et al. (2016), as shown in Table 2. The material of roll is 5CrNiMo.
(7)
where T , θ , p , f , b , LH , α1, d z , εdq , rH , PH and D is the driving force, direction angle, mean pressure of rolls, friction factor, contact width, contact length, entrance angle of roll, diameter of tube, reduction rate before contact with the plug, diameter of plug nose, mean pressure of plug nose and roll diameter, respectively. Substituting Eqs. (5)–(7) into Eq. (4), the axial forward condition can be deduced as follows:
2 × (Tx − Px ) = pb (
d z εdq tanα1
d
) × (f ×
3.2. Experimental procedures In order to obtain the preferred process parameters for manufacturing the TWNS, the combinations of simulation and experiment were adopted, as shown in Fig. 3. Firstly, according to the simulation results of rotary rolling process (without plug action) and RTP process, the reasonable ranges of process parameters were determined. Secondly, the rotary rolling experiments were carried out to discuss the influences of process parameters on the formation of external separation layer defect (ESLD). Based on the experimental results of rotary rolling process, the experiments of RTP process were conducted to discuss the influences of process parameters on the internal separation layer defect (ISLD). The ranges of process parameters were further optimized. Finally, the influences of temperature on the surface quality and microstructure distribution of TWNS were explored, and the preferred process parameters were obtained. The obtained tubes were grinded mechanically and polished using standard metallographic techniques, and corroded by boiling 20 % H2SO4 and KMnO₄. Electron backscattered diffraction (EBSD) analyses were used to explore the DRX
2
z ⎛1 + D ⎞ 1−⎜ − sinα1) ≥ πrH 2PH fd z ⎟ ⎝ ⎠
(8) Therefore, the minimum reduction rate before contact with the plug εmin is obtained as:
π εmin =
pH r 2tanα1 p H dz
2
⎛1 + ⎞ d z b (f 1 − ⎜ fd D b⎟ − sinα1) z ⎝ ⎠
(9)
When the reduction rate before contact with the plug εdq is greater than εmin , the piercing process is completed smoothly, and vice versa. Before the RTP process, the rotary rolling process (RTP process 4
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Fig. 4. The (a) geometry model and (b) actual object of the improved piercing mill, and the (c) main view and (d) top view of mandrel position.
Fig. 5. The geometry of (a) traditional roll and (b) cone roll (Zhang et al., 2018).
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Fig. 6. The comparisons between experiment results and simulation results, (a) experimental process, (b) pierced tube, (c) profile of tube, (d) rolling force and (e) rolling torque.
Fig. 7. The evolution of rotary rolling process expressed by the strain field, one half ranged from 0 to 2.0, the other ranged from 0 to 4.0, and the temperature field ranged from 1050 °C to 1150 °C.
improved, as shown in Fig. 5. On the other hand, the stability of mandrel is vital for Inconel 718 alloy with large deformation resistance. Especially for thick-walled tubes, the diameter of mandrel is smaller than thin-walled tubes, so it is critical to improve the stability of mandrel. The centering devices of the improved mill are composed of three cams, which impose constraints on the mandrel in three directions, so that the stability of mandrel can be significantly improved. At the same time, the centering devices are non-uniformly distributed according to the simulation results of mandrel bending process, as shown in Fig. 4c and d. The friction condition and heat transfer
process. The ranges of process parameters for simulation are shown in Table 3. 3.3. Establishment of FEM model According to the deformation characteristics of nickel-base superalloy, an improved piercing mill was developed, as shown in Fig. 4. On the one hand, the diameter of roll increases gradually along roll axis, which is consistent with the flow law of metals. Compared with the traditional roll, the deformation uniformity can be significantly 6
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Fig. 8. The evolution of temperature and strain in rotary rolling process, (a) temperature and (b) strain.
Fig. 9. The influences of process parameters on strain distribution, (a) feed angle, (b) reduction rate, (c) roll speed, and (d) cross angle.
ranges, 0∼2 and 0∼4, respectively. The stage A is the transshipment process. It shows that the temperature is inhomogeneous, which decreases gradually from center to surface. The stage B represents the biting process. The plastic deformation gradually permeates from the surface to the center. Stage C is the steady rolling process. It is obvious that the strain gradient in the range of r/R = 0.8 to r/R = 0.95 is not conducive to the penetration of plastic deformation. The temperature filed indicates that the billet is still in hot state, even if the billet has experienced a long transport and rolling time. The evolution of strain and temperature is shown in Fig. 8. It reveals that the maximum strain is in the surface (r/R = 1) and the minimum strain is in the center (r/R = 0). Under the combined action of deformation heat, friction heat, heat dissipation, the highest temperature appears in the region of r/R = 0.8 to r/R = 0.95.
condition are consistent with our previous studies of Zhang et al. (2019). 3.4. Verification of FEM model In order to verify the accuracy of simulation results, the typical piercing process was conducted by experiment and simulation. The main process parameters are as follows: temperature 1100 °C, reduction rate 13 % and roll speed 40 rpm. The piercing process is shown in Fig. 6a–c. The comparisons of rolling force and rolling torque between simulation results and experiment results are shown in Fig. 6d and e, respectively. It indicates that the forces and torque are compatible in terms of both quality and quantity. 4. Simulation results and discussion 4.1. The distribution of temperature and strain in rotary rolling process
4.2. The influences of process parameters on strain distribution of rotary rolling process
The distribution of temperature and strain is shown in Fig. 7. In order to describe the strain more clearly, the strain field consists of two
The influences of feed angle, reduction rate, roll speed and cross angle on the strain distribution is shown in Fig. 9. It shows that 7
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Fig. 10. The influences of process parameters on maximum temperature rise, (a) feed angle, (b) reduction rate, (c) roll speed, and (d) cross angle.
maximum strain, minimum strain and strain range decreases with the increase of feed angle. The influences of feed angle on strain are mainly related to the shear strain, whcih decreases with the increase of feed angle. The effects of reduction rate on maximum strain and minimum strain are consistent. With the increase of reduction rate, the maximum strain, minimum strain and strain range increase simultaneously. The reduction rate affects the strain distribution by changing the basic deformation and shear deformation at the same time. The effects of roll speed on maximum strain and minimum strain are opposite. With the increase of roll speed, the minimum strain decreases, but the maximum strain and the strain range increases. The cross angle has little influence on the strain distribution.
plug, and the second biting process is completed, as shown in Fig. 11b. After entering the steady piercing process, the deformation law is consistent along the billet axis, as shown in Fig. 11c. The distribution of strain and temperature is shown in Fig. 12. In the preparation region, the strain decreases gradually form the surface to the center. After entering the piercing region, the strain increases sharply under the combined action of rolls and plug. The maximum strain is in the surface (t/T = 1) and the minimum strain is in the transition layer (t/T = 0.5). The temperature reveals that the billet is still in hot state under the combined action of deformation heat, friction heat and heat conduction, and the maximum temperature rise is in the range of r/R = 0.4 to r/R = 0.8.
4.3. The influences of process parameters on temperature distribution of rotary rolling process
4.5. The influences of process parameters on the axial resistance of mandrel For the thick-walled tubes of nickel-base superalloy, the stability of mandrel is vital. The strength and stability of mandrel are determined by the axial resistance of mandrel. Therefore, the influences of process parameters on the axial resistance of mandrel are discussed systematically. The force analysis of plug is shown in Fig. 13. The axial resistance of mandrel can be expressed by the following equation.
The influences of process parameters on maximum temperature rise are shown in Fig. 10. The effects of feed angle on temperature rise are related to the combined effect of deformation heat and heat dissipation. With the increase of feed angle, both the deformation heat and heat dissipation decreases. Therefore, the effects of feed angle on temperature rise are not significant. The influences of reduction rate on maximum temperature rise are linear. With the increase of reduction rate, the deformation heat increases, leading to the increase of maximum temperature rise. Roll speed has significant effects on the maximum temperature rise. With the increase of roll speed, the friction heat increases sharply, leading to the increase of maximum temperature rise. The cross angle has little impact on the maximum temperature rise.
Q = QH + 2P0 (sinφ0 + fcosφ0)
(10)
Because the direction of friction force is not parallel to the rolling line, the axial component of contact friction force is:
Tx = P0 fcosφ0 cosθc
(11)
Therefore, the axial resistance of mandrel is modified as：
Q = QH + 2P0 (sinφ0 + fcosφ0 cosθc )
4.4. The distribution of temperature and strain in rotary tube piercing process
(12)
where the Q , QH , P0 , φ0 , Tx , θc is the axial resistance of mandrel, the resistance of plug nose, the normal pressure acting on plug, the tangent angle of plug, axial component of contact friction force and inclination angle, respectively. The resistance of plug nose is
The RTP process is shown in Fig. 11. Under the action of rolls, the billet rotates forward to achieve the first biting process, as shown in Fig. 11a. As the piercing process continues, the billet is transformed from solid bar to hollow tube under the combined action of rolls and
QH = πrH 2nH σs 8
(13)
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where rH , nH , σs is the radius of plug nose, stress state coefficient and flow stress of metal, respectively. The stress state coefficient is closely related to the transverse tensile stress in the preparation region. The critical instability force of mandrel can be expressed as follows:
Qlj =
π 2EI (μL)2
(14)
where Qlj , E , I , μ , L is the critical instability force of mandrel, elastic modulus of mandrel, moment of inertia, flexibility coefficient and the length of mandrel, respectively. Substituting Eqs. (12) and (13) into Eq. (14), the instability condition of mandrel can be deduced as follows:
Q= πrH 2nH σs + +2P0 (sinφ0 + fcosφ0 cosθc ) ≤
π 2EI = Qlj (μL)2
(15)
The influences of process parameters on the axial resistance of mandrel are shown in Fig. 14. It indicates that the axial resistance of mandrel increases with the increase of feed angle and decrease with the increase of reduction rate. The influences of feed angle on the axial resistance of mandrel are related to the strain rate. With the increase of feed angle, the strain rate increases gradually, resulting in the increase of flow stress. With the increase of reduction rate, the transverse tensile stress which can significantly reduce the resistance of plug increases. Therefore, the axial resistance of mandrel decreases with the increase of reduction rate. The effects of roll speed on the axial resistance of mandrel are determined by the comprehensive effect of strain rate and thermal effect. With the increase of roll speed, the increase of strain rate leads to the increase of flow stress. However, the temperature rise caused by the increase of roll speed reduces the flow stress. When roll speed is less than 35 rpm, axial resistance of mandrel increases with the increase of roll speed. When roll speed is greater than 35 rpm, the axial resistance of mandrel basically remains unchanged. The cross angle has little effect on the axial resistance of mandrel. The experiment results of mandrel are shown in Fig. 15. When the resistance of mandrel Q is less than the critical instability force Qlj , the piercing process can be carried out smoothly, and the TWNS with precise dimension are obtained, as shown in Fig. 15a. When the resistance of mandrel Q is approximately equal to the critical instability force Qlj , the swing of mandrel is serious, leading to the poor uniformity
Fig. 11. The piercing process of Inconel 718 alloy (indicated with strain), (a) first biting process, (b) second biting process, (c) steady piercing process.
Fig. 12. The distribution of (a) strain and (b) temperature in RTP process. 9
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Fig. 13. Force analysis of plug.
Fig. 14. The influences of (a) feed angle and reduction rate, (b) roll speed and cross angle on the axial resistance of mandrel.
Fig. 15. Experimental results of process parameters on the lose stability of mandrel, (a) good condition of mandrel, (b) swing of mandrel, (c) mandrel breaking and (d) the mandrel diagram.
5. Experiment results and discussion
of wall thickness, as shown in Fig. 15b. If the resistance of mandrel Q is greater than the critical instability force Qlj , the mandrel will be broken, and the piercing process can’t be completed, as shown in Fig. 15c. The mandrel is shown in Fig. 15d.
5.1. Experiment results of rotary rolling process and RTP process Based on the simulation results, the reasonable ranges of process 10
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Fig. 16. The influences of reduction rate on the formation of ESLD.
Fig. 17. The influences of roll speed on the formation of ESLD.
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Fig. 18. The influences of reduction rate on the formation of ISLD.
Fig. 19. The experiment results of (a) ESLD (case.3), (b) ISLD (case.8), (c) rolling block and (d) successful sample.
separation layer defect (ESLD). When the crack is in the region of 0.05 ≤ t/T ≤ 0.2 (tube), it is the internal separation layer defect (ISLD). If the process parameters are unreasonable, the ESLD defects will occur in both rotary rolling process and RTP process, while the ISLD only appears in RTP process. Before the RTP process, the rotary rolling process must be guaranteed to be completed smoothly. The experiment results reveal that the formation of ESLD is greatly influenced by reduction rate, as shown in Fig. 16. When the reduction rate is less than 15 %, no defects are observed. But when the reduction
parameters are obtained as follows: feed angle 8∼20°, cross angle 9∼21°,roll speed 20∼70 rpm, reduction rate before contact plug greater than 4.5 %. The experiments are designed based on control variable method to determine the preferred process parameters. The experiment results of rotary rolling process show that the ESLD is inevitable. Yin et al. (2012) and Tian and Li (2012) described that the separation layer defect is a crack with a certain width, which is parallel to the surface of tube. When the crack appears in the region of 0.8 ≤ r/ R ≤ 0.95 (bar) or 0.8 ≤ t/T ≤ 0.95 (tube), it denotes the external 12
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Fig. 20. The TWNS of different diameters and lengths obtained by RTP process, (a) axial dimension and (b) radial dimension.
under the condition of temperature 1100 °C, reduction rate 13 %, roll speed 35 rpm, and plug advance against gorge 12 mm, but the surface quality is poor. Finally, when the temperature is 1040 °C, the piercing process is smooth, and the TWNS with better surface quality and finer grain size are obtained successfully than that in 1100 °C, as shown in Fig. 19d. Based on the preferred parameters, the TWNS with different diameters and lengths are obtained, as shown in Fig. 20a and b. The statistics of geometry dimensions are shown in Table 4. The maximum diameter difference for outer and inner diameter is 2 mm and 1.1 mm, respectively. Therefore, the preferred process parameters are reliable for preparing the TWNS with different specifications.
Table 4 The statistics of geometric dimensions for tubes with different specifications. Number
Maximum external diameter difference(mm)
Maximum internal diameter difference(mm)
No.1 No.2 No.3
1.8 1.6 2
0.8 1.1 0.8
rate increases to 15 %, the ESLD occurs, as shown in Fig. 19a. In order to predict the ESLD, the Freudenthal model proposed by Freudenthal (1950) is introduced.
∫0
εf
σdε ¯ ¯=D
(16)
5.2. The formation mechanism of ESLD and ISLD
where σ¯ , εf , D is the effective stress, fracture strain and damage. The simulation results show that the damage decreases gradually form the surface to the center, and the maximum damage is near the surface, as shown in Fig. 16. At the same time, the damage increases with the increase of reduction rate. When the damage is greater than the damage threshold, the ESLD will occur. The critical condition of ESLD is determined as roll speed 70 rpm, reduction rate 15 %. Fig. 17 indicates that the formation of ESLD is significantly affected by roll speed. When the roll speed is 70 rpm, the ESLD occurs. But as the roll speed decreases from 70 rpm to 40 rpm, the ESLD disappears. As the roll speed continues to decrease, the ESLD defect disappears and the surface quality of the rolled bar becomes better. The simulation results reveal that roll speed has little effect on the damage distribution, as shown in Fig. 17. With the increase of roll speed, the temperature rise is significant. Excessive temperature rise will lead to poor plasticity of Inconel 718 alloy and decrease the damage threshold. Therefore, the ESLD can be eliminated by selecting reasonable roll speed and reduction rate. Fig. 18 reveals that the ISLD is closely related to reduction rate. When the reduction rate is less than 18 %, no defects are observed. But as the reduction rate increase to 18 %, the ISLD appears, as shown in Fig. 19b. With the increase of reduction rate, the ISLD becomes more serious. The simulation results reveal that the radial deformation uniformity decreases with the increase of reduction rate. The non-uniform plastic deformation generates additional shear stress, which lead to the formation of ISLD. At the same time, the temperature rise caused by large deformation will also reduce the damage threshold. Therefore, reasonable control of reduction rate is vital. At the same time, the reduction rate should be greater than the critical value εmin . When the reduction rate before contact with plug is less than the critical value, the rolling block phenomenon that the billet is stuck in the middle of rolls is inevitable, and the dynamic recrystallization (DRX) may not be sufficient, as shown in Fig. 19c. Therefore, under the premise of ensuring the ESLD and ISLD doesn’t occur, the reduction rate should be selected as large as possible. The TWNS (ratio of diameter to thickness 3.5) are successfully prepared
By comparing the simulation results and experiment results, it can be found that the ESLD is mainly related to the large strain gradient and severe temperature rise in the region of r/R = 0.8∼ r/R = 0.95. On the one hand, the maximum strain gradient is consistent with the location of ESLD, as shown in Fig. 7. The maximum strain gradient caused by uneven deformation generates local shear stress. When the local shear stress is greater than the fracture strength material, the ESLD will occur. On the other hand, the maximum temperature rise is also in the range of r/R = 0.8 to r/R = 0.95, as shown in Fig. 7. Excessive temperature rise will lead to the poor plasticity of Inconel 718 alloy and decrease the damage threshold. The ISLD is controlled by reduction rate. When the reduction rate is great than critical value, the ISLD will appear. Existing evidence shows that the ISLD is related to the non-uniform plastic deformation in the piercing region. Further investigations are still necessary to provide the evidence for the formation mechanism of ISLD. 5.3. The analysis of microstructure distribution Microstructure analysis is carried out on the samples taken from the middle of tube. The corresponding process parameters are as follows: temperature 1040℃, feed angle 8°, cross angle 15°, roll speed 35 rpm, reduction rate 13 %, and plug advance against gorge 12 mm. The optical micrograph map is shown in Fig. 21a, b and c. It can be observed that the equiaxed grains with average grain size of 25 μm are obtained. Fig. 21d shows the grain boundary (GB) maps of transition layer (t/T = 0.5), in which high angle grain boundaries (the misorientations larger than 15°) and low angle grain boundaries (the misorientations lower than 15°) are represented by black lines and red lines, respectively. It reveals that high angle grain boundaries are far more than low angle grain boundaries. The formation of high angle grain boundaries is closely related to the DRX process. The statistics of misorientation angle are shown in Fig. 21h. It indicates that the average misorientation angle is 38.12°. Fig. 21e reveals the DRX maps of transition layer (t/T = 0.5), in which blue, yellow and red indicate the fully recrystallized grains, substructures and deformed grains. It is observed that the volume 13
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Fig. 21. Schematic diagram showing the microstructure of tube corresponding to Fig.18d, (a) t/T = 0.99, (b) t/T = 0.5 and (c) t/T = 0, (d) The grain boundary map, (e) dynamic recrystallization map, (f) inverse pole figure of the pierced tube, the statistics of (g) dynamic recrystallization volume proportion and (h) misorientation angle.
piercing process of nickel-base superalloy, and the effects of process parameters on the material flow and microstructure distribution were investigated by combining experiments with simulations. All the simulation and experiment results led to the following conclusions.
proportion of recrystallized grains is 96.89 %, as shown in Fig. 21g. The inverse pole figure (IPF) shows that the RTP process is a three-dimensional plastic deformation without preferred orientation. The microstructure evolution of RTP process is shown in Fig. 22. The GB map shows that the microstructure evolution includes three typical states: the coarse grains before entering the deformation region, the mixed grains in the preparation region, and the fine equiaxed grains in the uniform region and rounding region. Before entering deformation region, the coarse equiaxed grains are dominated by large number of substructures. After entering the preparation region, the mixed grains are obtained under the action of DRX process. In the piercing region, the mixed grains are transformed into fine equiaxed grains, and the DRX process is completed. The IPF map indicates that there is no significant orientation in the RTP process.
(1) The ESLD is significantly influenced by roll speed and reduction rate. The formation mechanism of ESLD is large strain gradient and severe temperature rise in the region of r/R = 0.8∼ r/R = 0.95. (2) The ISLD is mainly affected by reduction rate. For the thick-walled tube with ratio of diameter to thickness 3.5, the reduction rate is determined as 9 %–15 % to prevent the occurrence of ISLD. (3) The preferred process parameters are determined as temperature 1040 °C, reduction rate 13 %, roll speed 35 rpm, feed angle 8°, cross angle 15°, and plug advance against gorge 12 mm. The equiaxed grains with average grain size of 25 μm are obtained due to the complete DRX process. (4) In the RTP process, the microstructure evolution of nickel-base superalloy can be divided into three typical states: the coarse grains
6. Conclusions In this paper, an improved piercing mill was developed for the 14
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Fig. 22. The microstructure evolution of rolling block sample corresponding to Fig.18c, (a) rolling block sample, the GB map of (b) P-1, (c) P-2, (d) P-3, (e) P-4, the DRX map of (f) P-1, (g) P-2, (h) P-3, (i) P-4, and IPF map of (j) P-1, (k) P-2, (l) P-3, (m) P-4.
before entering the deformation region, the mixed grains in the preparation region, and the fine equiaxed grains in the uniform region and rounding region.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the Shaanxi key research and development program (2017ZDXM-GY-027), Natural Science Basic Research Plan in Shaanxi Province of China (No.2017JM5010) and Fundamental Research Funds for the Central Universities (3102019ZX004) References Bin, W., 2014. High speed hot tube extrution process of Incone1690 superalloy. RARE Met. Mater. Eng. 43, 137–142.
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