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Microstructure Homogeneity Evaluation for TC11 Blisk Forging Using Loss Function Based on Taguchi Method
Rare Metal Materials and Engineering Volume 40, Issue 4, April 2011 Online English edition of the Chinese language journal
Cite this article as: Rare Metal Materials and Engineering, 2011, 40(4): 0565-0570.
ARTICLE
Microstructure Homogeneity Evaluation for TC11 Blisk Forging Using Loss Function Based on Taguchi Method Yang Yanhui,
Liu Dong,
Luo Zijian
Northwestern Polytechnical University, Xi’an 710072, China
Abstract: The word “blisk” means that all the blades are integrated with a disk. The application of the blisk is a key technology for improving performance of aero-engines. High quality of the blisk conduces to expand its application. Because of a strong influence of microstructure homogeneity on the quality of blisk, the author gives attention to it. In this paper, a loss function (LF) referring to the concept of Taguchi method was proposed. In the proposed LF, the distribution homogeneity of thermomechanical parameters was employed to evaluate the microstructure homogeneity of TC11 blisk forging. Then, the forging process of the TC11 alloy blisk was analyzed using FEM technique. Based on the FEM simulation results, the microstructure homogeneity of TC11 blisk forging was evaluated. Experiment was performed to verify the proposed method. Key words: blisk; numerical simulation; loss function; microstructure homogeneity; Taguchi method
A blisk is an integrated engine component comprising a rotor disc and blades, also known as an integrally bladed rotor (IBR). Due to the elimination of the need to mount the blades on the disk (via screws, bolts, etc.), the number of components within the compressor is decreased, leading to the increase in the efficiency of air compressors. In addition, a common source for crack initiation and subsequent propagation could be eliminated by removing the dovetail joint of traditional turbine blades. Therefore, it is an inevitable tendency to apply the blisk to the modern aeroengine with high thrust-weight ratio[1]. However, the blisk is difficult to manufacture, because it is often made of hard deformed materials, such as nickel-base and titanium alloys, and its geometric shape is more complicated involving many semi-enclosed, twisted and 3D surfaces. Additionally, several common processes including machining from a solid piece of material and welding individual blades to the rotor disc have some disadvantages: low materials utilization, discontinuous flowlines, inconsistent properties of weld joint, etc[2]. Thus, the bulk forming is widely used to produce such a kind of aerospace components due to high productivity, manufacturing of for-
gings with continuous flowlines and the fibre orientation conforming to stress orientation. For example, combining isothermal forging with numerical simulation techniques, a TC17 compressor blisk with high tensile strength and ductility at room temperature could be produced[2-4]. Even so, the homogeneity of the microstructure and mechanical properties, a common requirement for a variety of aerospace forgings, is still hard to achieve because the geometric shapes, thermomechanical parameters and history are fairly different between the disc and blades of a blisk. Since 1970s many researches[5-9] have been devoted to the numerical simulation of microstructure evolutions for steel, superalloy, titanium alloy, etc. For TC11 alloy, several models were set up to describe the microstructure evolutions through experiments and systematic metallographic analysis under prescribed conditions[10-16]. The above work laid the foundation for the microstructure predictions of products to a certain extent. However, it’s rare to be used directly to evaluate microstructure homogeneity because various metallurgical processes such as phase transformation ( β → α + β for conventional α / β titanium alloys), dynamic recrystallization (DRX), metadynamic recrystallization
Received date: April 26, 2010 Corresponding author: Yang Yanhui, Candidate for Ph. D., School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, P. R. China, Tel: 0086-29-88460530, E-mail: [email protected] Copyright © 2011, Northwest Institute for Nonferrous Metal Research. Published by Elsevier BV. All rights reserved.
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Yang Yanhui et al. / Rare Metal Materials and Engineering, 2011,40(4): 0565−0570
(MDRX), static recrystallization (SRX), etc may occur during hot forming processes of TC11 alloy. With the development of FEM technique, it is convinced to reveal the evolutions of thermomechanical parameters (equivalent strain ε , equivalent strain rate ε& and temperature T) within forging with high accuracy[17]. The published research works indicated that the microstructures within forgings of hard deformed materials are mainly related to thermomechanical parameters and their history during forging processes[5-9,18]. In the present study, the thermomechanical parameters determined by FEM simulation are directly used to evaluate the microstructure homogeneity of TC11 blisk forging. Referring to the concept of loss function in Taguchi method, a loss function (LF) for the microstructure homogeneity evaluation was proposed. On the basis of the numerical analysis of the forging process, four cases were discussed using different LF for TC11 alloy blisk. Finally, an experiment was performed and the results were compared with the calculated results to verify the proposed method.
1
Design of LF for the Microstructure Homogeneity Evaluation
According to Taguchi method[19,20], three stages are included in a process development: system design, parametric design and tolerance design. In the third stage, a loss function (LF) is developed to determine the cost-optimal way for tolerance selection on controllable design variables while maintaining or improving of the product quality is defined by the customer. Taguchi’s loss function is classified into three types: nominal-is-best (NB), lower-is-better (LB) and greater-is-better (GB). In this paper, the LB loss function is employed, in which the lower the value of LF is, the better the microstructure homogeneity is. The procedures of establishing the LF for evaluation of microstructure homogeneity are expressed as follows: Step 1, the thermomechanical parameter of the element i, denoted as X(i), is normalized by: X (i ) − X avg X ' (i) = (1)
σF
where σF represents variance in statistics and Xavg denotes the volume-averaged value of thermomechanical parameter. Xavg and σF are given by the following formulae: N
X avg =
∑ X (i ) ⋅ vi
e
i =1
N
(2)
∑ vi
e
i =1
N
σF =
2
e ∑ X (i ) − X avg ⋅ vi i =1
N
∑ vi
e
(3)
defined as follows: 0 < X '(i) < 1 X ' = 0 , here X (i ) = X avg X '(i) ≥1
⎧ X '(i ) ⎪
λi = ⎨ 0 ⎪ 1 ⎩
(4)
When the normalized thermomechanical parameter X′ for an element at certain increment step is equal to Xavg, λ=0, which means that the element i has no contribution to LF, otherwise, 0<λ≤1 is to weight the contribution of the element i to LF. Step 3, the LF for the element i is defined as follows: K ⎧∑ ⎫ & ⎪ k =1 λi ⋅ (σ i ⋅ ε i ) Δtk ⎪ LF(i) = ⎨ K ⎬ ⎪ ∑ (σ i ⋅ ε&i ) Δtk ⎪ ⎩ k =1 ⎭
2
(5)
where K is the total number of increment steps for the numerical simulation, Δt k is the time increment for step k, σ i and ε&i are the equivalent stress and equivalent strain rate of the element i, respectively. The LF for the entire workpiece domain can be defined as follows: N
LF =
∑ LF(i ) ⋅ vi
e
i =1
N
(6)
∑ vi
e
i =1
The value of the LF given by Eq.(6) will lie in the interval [0,1]. The loss function is of the type of “lower-is-better”.
2
Simulation of TC11 Blisk Forging Process
Fig.1 gives the sketch map of the blisk forging which is integrated by 15 twisted blades and a disk. The shape of the disk is complicated and characterized by large diameter, varying thickness and geometric asymmetry. It is required that the difference of microstructure grading between the blades and the disk should be less than one grade according to grading diagrams of HB 5264-83. Numerical simulation of the TC11 blisk forging process was carried out with the aid of commercial code DEFORM 3D, where an integrated subroutine code was used to describe the characteristics of clutch screw press[21]. Additionally, Eqs.(3)-(6) were incorporated into DEFORM 3D as the subroutine codes to evaluate the microstructure homogeneity. The high sensitivity of flow behavior to thermomechanical parameters was taken into consideration by the flow stress data obtained during the compression test of the isothermal constant strain rate. The flow stress curves at temperatures of 900 and 1000 °C are shown in Fig.2. The process conditions for FEM simulation are summarized in Table 1. a
b
i =1
where N is the total number of the elements in workpiece, and vie is the volume of the element i. Step 2, weighted coefficient for element i, denoted as λi, is
Fig.1 Sketch map of the blisk forging
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Yang Yanhui et al. / Rare Metal Materials and Engineering, 2011,40(4): 0565−0570
Table 2 Results of microstructure homogeneity evaluation
Flow Stress/MPa
350 50 s
300
10 s
1.0 s-1
200
0.1 s-1
150 100
0.01 s-1 0.001 s-1
50 0.1
0.2
0.3
Flow Stress/MPa
120
0.5
0.6 b
-1
10 s
100
1.0 s-1
80 60 40 0 0.0
0.4 50 s-1
140
20
Case 1 Case 2 Case 3 Case 4
-1
250
0.0
a
-1
0.001 s-1 0.1
0.2
0.1 s-1 0.01 s-1 0.3
0.4
0.5
0.6
Strain Fig.2 Flow stress curves at different temperatures: (a) 900 °C and (b) 1000 °C Table 1 Processing conditions for FEM simulation Initial temperature/°C Transfer time/s Dwell time/s Friction factor Heat transfer coefficient between workpiece and dies/N·(mm·K)-1 Convection coefficient to environment/N·(mm·K)-1 Number of heat Number of blows in each heat Energy grade for each blow in every heat
3
980 (workpiece); 260 (dies) 20 4 0.25 (shear type) 20 (during deformation); 2 (during dwell) 0.018 3 5 0.45，0.75，0.75，0.85, 0.9
Evaluation of Microstructure Homogeneity of the TC11 Blisk Forging
Supposing that λε , λT and λε& are the weighted coefficient defined by Eqs.(1)-(4) corresponding to the distributions of equivalent strain, temperature and strain rate, respectively. The microstructure homogeneities for four cases of the above blisk forging were evaluated using Eqs.(5, 6) and are listed in Table 2. In the four cases λε , λT , λε& and (λε + λT + λε& ) / 3 are taken as weighted coefficient, respectively. It is found that the values of LF are close to each other and the maximal difference is only 0.07. In addition, the value of LF for case 4 is equal to the average LF value of the other three cases. Fig.3 shows the distribution of thermomechanical parameters within the finish blisk forging. For the convenience to reveal the characteristics of the cross-section, 1/4 of the forg-
λ λε λT λε& λε + λT + λε& / 3
(
)
Value of LF 0.5 0.46 0.43 0.46
ing is shown. It can be seen that the forging is completely deformed with large flashes. Fig.4 and Fig.5 show the distribution of λ and LF value in the finished blisk forging for different cases. It can be seen from Fig.4a that the regions with larger λε ( λε = 0.75 -1 ) for case 1 are in the flash, the center of the disk as well as the rim of the disk, where the equivalent strain is far greater or lower than the volume-averaged value ε avg = 1.25 (see Fig.3a). On the contrary, the values of equivalent strain in the hub of the disk are close to ε avg (see Fig.3a), and λε are in the range of 0-0.3. In summary, the distribution of λε mainly depends on the equivalent strain distribution and the calculated ε avg . Similarly, it is obvious that the temperatures in the flash (1010-1030 °C) and surfaces (880-930 °C) in contact with the dies are fairly different from Tavg (966.5 °C). Thus, high values of λT lie in the both regions (see Fig.4b). Additionally, the values of λT in most parts of the forging are relatively low (bellow 0.375) since the temperature are correspondingly in the range of 950-970 °C. For case 3 (see Fig.5c), it is found that high λε& is mainly concentrated in the areas adjacent to the flash where the materials flow acutely at the end of the forging process as mentioned above. λ for case 4 is determined by the average of λε , λT and λε& . The distribution of λ for this case (Fig.4d) may be considered as the comprehensive weighted coefficient to LF. It is found that the higher weighted coefficients are mainly concentrated in the flash and the surfaces in contact with the bottom die. It is known from Eqs. (5,6) that value of LF is dependent on both λ and the processing history. It can be validated by the fact that the distribution of value of LF is not necessary in agreement with that of λ (see Fig.4 and Fig.5). In summary, the values of LF in most parts of the blisk forging are very low (below 0.3) except the flash, the region adjacent to the center and the hub of disk (see Fig.5a), the edges of the blades and the surfaces in contact with the bottom die (see Fig.5b, Fig.5c and Fig.5d). Fig.6 gives the curves of LF values vs increment number for different cases. As shown in the figure, the values of LF increase continuously for case 1 and case 3 due to the fact that the homogeneities of the equivalent strain and the strain rate become worse as the process proceeds and the material flows acutely. The sharp increase of LF in the first heat is attributed to relative large deformation. However, for case 2, large value of LF occurs at the beginning of each heat due to the inhomogeneous distribution of temperature resulting from heat loss in
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Yang Yanhui et al. / Rare Metal Materials and Engineering, 2011,40(4): 0565−0570
b
a
c
Fig.3 Distribution of thermomechanical parameters in the finished blisk forging: (a) equivalent strain, (b) equivalent temperature, and (c) equivalent strain rate a
b
c
d
Fig.4 Distribution of weighted coefficient for the loss in the finished blisk forging: (a) case 1, λ= λε , (b) case 2, λ=λT, (c) case 3, λ= λε& , and (d) case 4, λ=( λε +λT+ λε& )/3 a
b
c
d
Fig.5 Distribution of value of LF within the finish blisk forging: (a) case 1, λ = λε , (b) case 2, λ=λT, (c) case 3, λ= λε& , and (d) case 4, λ=( λε +λT+ λε& )/3
a
0.6
b
Value of LF
0.5 0.4 0.3
Case 1 Case 2 Case 3 Case 4
0.2 0.1 0.0
Heat 1 100
Heat 2 200
20 μm
Heat 3 300
400
Fig.7 Initial structures of TC11 alloy billet: (a) microstructures 500
and (b) macrostructures
Increment Number Fig.6 LF value-step curves of the forging process
transfer. Thanks to the heat generation from deformation and friction, the value of LF decreases in subsequent deformation process in this case. For case 4, the variation in value of LF is the comprehensive embodiment of the other three cases.
4
Comparisons between Experiment and Simulation Results
An experiment was conducted on the clutch screw press with nominal load of 112 mN under the processing conditions shown in Table 1. The initial structures of TC11 alloy billet are shown in Fig.7. The following heat treatments after forging process were conducted: (1) heating to 1223 K, holding for 1 h, and air-cooling to room temperature; (2) heating to 803 K, holding for 3 h and air-cooling to room temperature.
Fig.8a shows the picture of the blisk forging after flash cutting and sand blasting in experiment. Compared with the simulation result (Fig.8b), the similarity of the geometry between the experiment and the simulation result is apparent. The microstructure homogeneity of the forging was analyzed by the microscopic examination, in which eight measured points were observed. The locations and the optical micrographs of these measured points are shown in Fig.9 and a
b
Fig.8 Geometries of the blisk forgings via experiment (a) and simulation (b)
568
Fig.10, respectively. It can be found that the microstructures of all measured points consist of equiaxed α in a transformed β matrix with α-grain size about 15 μm and the percentage of equiaxed (or primary) α about 40%-50%. It is clear that the microstructures in both blades (see point No.1, point No.2, point No.7 and point No.8) and disk (see point No.3, point No.4, point No.5 and point No.6) are almost similar and can be graded as 3rd grade according to the grading diagrams in HB 5264-83. Fig.11 gives the comparison of LF values for the measured points. In the four cases, the LF values of the measured points are close and almost in the range of 0.33-0.44, especially in case 2 (refer to the dash dotted curves in Fig.11). However, it can be found that the LF values vary in a relatively large range in case 1 and the LF value of point No.5 reaches 0.68. In fact, the microstructure of point No.5 doesn’t change obviously
Fig.9 Locations of the measured points within the forging a
b
c
d
e
f
Value of LF
Yang Yanhui et al. / Rare Metal Materials and Engineering, 2011,40(4): 0565−0570
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Case 1 Case 2 Case 3 Case 4
1
2
3
4
5
6
7
8
Number of Measured Points Fig.11 Comparison of LF values for the measured points
(see Fig.10e). It can be explained as follows. The size of α-grain and the percentage of primary α are almost stable when the deformation reaches an extent such as 70% ( ε =1.2) according to Ref. [16]. From the FEM results, the value of the equivalent strain for point No.5 is 1.28. In addition, it is found that the LF value of the measured point located in the flash with a distance of 23 mm away from the edge of the forging is relatively high, which indicates that the microstructure homogeneity is bad in this region. For example, the LF value of this point is 0.68 in case 2 and is higher than that of the measured points in Fig.9. The optical micrograph of this measured point in the flash is shown in Fig.12. It can be found that the percentage of α decreases and a small amount of lamellar α-grain exists in the microstructure comparing to the micrographs in Fig.10. This may be attributed to undergoing deformation above the β transus during forging process and transformation of β phase in subsequent heat treatment, which is validated from the temperature-time curve of this point shown in Fig.13. To sum up, the LF in case 2 is more adequate to evaluate
20 μm
g
h
20 μm Fig.10 Optical micrographs of the measured points in Fig.9: (a) No.1, (b) No.2, (c) No.3, (d) No.4, (e) No.5, (f) No.6, (g) No.7, and (h) No.8
Temperature/℃
Fig.12 Optical micrograph of the measured point in the flash 1030 1020 1010 1000 990 980 970 960
Solvus temperature
0
20
40
60
80
100
Time/s Fig.13 Temperature vs time curve for the measured point in the flash
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Yang Yanhui et al. / Rare Metal Materials and Engineering, 2011,40(4): 0565−0570
the microstructure homogeneity of the TC11 blisk forging.
5 Conclusions 1) The proposed method based on loss function and finite element method may pave a way to evaluate the microstructure homogeneity of hard-deformed materials forgings using FEM simulation results. 2) For TC11 alloy blisk forging, the LF in case 2 can more appropriately evaluate the microstructure homogeneity. 3) If LF values are in the range of 0.33-0.44 using the LF in case 2, the TC11 blisk forging with desired microstructure homogeneity can be obtained.
References 1 Huang, Chunfeng. Aeronautical Manufacturing Technology, 2006(4): 94 2 Zhou, Y. G.; Zeng, W. D.; Yu, H. Q. Materials Science and Engineering, 2005, A393: 204 3 Meng, Qingtong; Pang, Kechang; Wang, Xiaoying. Shanghai Steel & Iron Research, 2006(2): 16 4 Wu, Ruiheng; Pang, Kechang; Xu, Zuyao. Baosteel Technology, 2005(5): 47 5 Sellars, C. M.; Whiteman, J. A. Metal Science, 1979, 13(3-4): 187 6 Yada, H.; Senuma, T. J. JSTP, 1986, 27: 33 7 KoPP, R.; Karnhausen, K.; de Souza M M. J. Metal., 1991, 20: 351 8 Shen, G. S.; Semiatin, S. L.; Shivpuri, R. Metallurgical and Ma-
9 Ding, R.; Guo, Z. X. Computational Materials Science, 2002, 23: 209 10 Humphreys, F. J.; Hatherly, M. Recystallization and Related Annealing Phenomena. Oxford: Elsevier, 2004 11 McQueen, H. J.; Evangelista, E.; Ryan, N. D. Recrystallization’90. Warrendale: TMS-AIME, 1990, 89 12 Doherty, R. D.; Humphreys, F. J. Materials Science and Engineering, 1997, A238: 219 13 McQueen, H. J. Materials Science and Engineering, 2004, A387-389: 203 14 Sun, Xinjun; Bai, Bingzhe; Gu, Jialin. Rare Metals, 2000, 19(2): 101 15 Chen, Huiqin; Deng, Wenbin. Chinese Journal of Rare Metals, 2009, 33(2): 147 16 Chen, Huiqin; Lin, Haozhuan; Guo, Ling. Journal of Aeronautical Material, 2007, 27(3): 1 17 Lü, Cheng; Zhang, Liwen; Mu, Zhengjun. Journal of Materials Processing Technology, 2008, 198(1-3): 463 18 Liu, Dong; Luo, Zijian. The Chinese Journal of Nonferrous Metals, 2003, 13(5): 1211 19 Wickand, C.; Veilleux, R. F. Tool and Manufacturing Engineers Handbook 4: Quality Control and Assembly. Dearborn, Mich.: SME, 1987 20 Srinivasan, R. J.; Chardhary, A. JOM, 1990, 42(2): 22 21 Yang, Yanhui; Liu, Dong; Luo, Zijian. Acta Aeronautica et Astronautica Sinica, 2009, 30(7): 1346 22 Semiatin, S. L. ASM Metals Handbook: Forming and Forging. OH: ASM International, 1989
terials Transactions, 1995, 26A: 1795
570
Cite this article as: Rare Metal Materials and Engineering, 2011, 40(4): 0565-0570.
ARTICLE
Microstructure Homogeneity Evaluation for TC11 Blisk Forging Using Loss Function Based on Taguchi Method Yang Yanhui,
Liu Dong,
Luo Zijian
Northwestern Polytechnical University, Xi’an 710072, China
Abstract: The word “blisk” means that all the blades are integrated with a disk. The application of the blisk is a key technology for improving performance of aero-engines. High quality of the blisk conduces to expand its application. Because of a strong influence of microstructure homogeneity on the quality of blisk, the author gives attention to it. In this paper, a loss function (LF) referring to the concept of Taguchi method was proposed. In the proposed LF, the distribution homogeneity of thermomechanical parameters was employed to evaluate the microstructure homogeneity of TC11 blisk forging. Then, the forging process of the TC11 alloy blisk was analyzed using FEM technique. Based on the FEM simulation results, the microstructure homogeneity of TC11 blisk forging was evaluated. Experiment was performed to verify the proposed method. Key words: blisk; numerical simulation; loss function; microstructure homogeneity; Taguchi method
A blisk is an integrated engine component comprising a rotor disc and blades, also known as an integrally bladed rotor (IBR). Due to the elimination of the need to mount the blades on the disk (via screws, bolts, etc.), the number of components within the compressor is decreased, leading to the increase in the efficiency of air compressors. In addition, a common source for crack initiation and subsequent propagation could be eliminated by removing the dovetail joint of traditional turbine blades. Therefore, it is an inevitable tendency to apply the blisk to the modern aeroengine with high thrust-weight ratio[1]. However, the blisk is difficult to manufacture, because it is often made of hard deformed materials, such as nickel-base and titanium alloys, and its geometric shape is more complicated involving many semi-enclosed, twisted and 3D surfaces. Additionally, several common processes including machining from a solid piece of material and welding individual blades to the rotor disc have some disadvantages: low materials utilization, discontinuous flowlines, inconsistent properties of weld joint, etc[2]. Thus, the bulk forming is widely used to produce such a kind of aerospace components due to high productivity, manufacturing of for-
gings with continuous flowlines and the fibre orientation conforming to stress orientation. For example, combining isothermal forging with numerical simulation techniques, a TC17 compressor blisk with high tensile strength and ductility at room temperature could be produced[2-4]. Even so, the homogeneity of the microstructure and mechanical properties, a common requirement for a variety of aerospace forgings, is still hard to achieve because the geometric shapes, thermomechanical parameters and history are fairly different between the disc and blades of a blisk. Since 1970s many researches[5-9] have been devoted to the numerical simulation of microstructure evolutions for steel, superalloy, titanium alloy, etc. For TC11 alloy, several models were set up to describe the microstructure evolutions through experiments and systematic metallographic analysis under prescribed conditions[10-16]. The above work laid the foundation for the microstructure predictions of products to a certain extent. However, it’s rare to be used directly to evaluate microstructure homogeneity because various metallurgical processes such as phase transformation ( β → α + β for conventional α / β titanium alloys), dynamic recrystallization (DRX), metadynamic recrystallization
Received date: April 26, 2010 Corresponding author: Yang Yanhui, Candidate for Ph. D., School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, P. R. China, Tel: 0086-29-88460530, E-mail: [email protected] Copyright © 2011, Northwest Institute for Nonferrous Metal Research. Published by Elsevier BV. All rights reserved.
565
Yang Yanhui et al. / Rare Metal Materials and Engineering, 2011,40(4): 0565−0570
(MDRX), static recrystallization (SRX), etc may occur during hot forming processes of TC11 alloy. With the development of FEM technique, it is convinced to reveal the evolutions of thermomechanical parameters (equivalent strain ε , equivalent strain rate ε& and temperature T) within forging with high accuracy[17]. The published research works indicated that the microstructures within forgings of hard deformed materials are mainly related to thermomechanical parameters and their history during forging processes[5-9,18]. In the present study, the thermomechanical parameters determined by FEM simulation are directly used to evaluate the microstructure homogeneity of TC11 blisk forging. Referring to the concept of loss function in Taguchi method, a loss function (LF) for the microstructure homogeneity evaluation was proposed. On the basis of the numerical analysis of the forging process, four cases were discussed using different LF for TC11 alloy blisk. Finally, an experiment was performed and the results were compared with the calculated results to verify the proposed method.
1
Design of LF for the Microstructure Homogeneity Evaluation
According to Taguchi method[19,20], three stages are included in a process development: system design, parametric design and tolerance design. In the third stage, a loss function (LF) is developed to determine the cost-optimal way for tolerance selection on controllable design variables while maintaining or improving of the product quality is defined by the customer. Taguchi’s loss function is classified into three types: nominal-is-best (NB), lower-is-better (LB) and greater-is-better (GB). In this paper, the LB loss function is employed, in which the lower the value of LF is, the better the microstructure homogeneity is. The procedures of establishing the LF for evaluation of microstructure homogeneity are expressed as follows: Step 1, the thermomechanical parameter of the element i, denoted as X(i), is normalized by: X (i ) − X avg X ' (i) = (1)
σF
where σF represents variance in statistics and Xavg denotes the volume-averaged value of thermomechanical parameter. Xavg and σF are given by the following formulae: N
X avg =
∑ X (i ) ⋅ vi
e
i =1
N
(2)
∑ vi
e
i =1
N
σF =
2
e ∑ X (i ) − X avg ⋅ vi i =1
N
∑ vi
e
(3)
defined as follows: 0 < X '(i) < 1 X ' = 0 , here X (i ) = X avg X '(i) ≥1
⎧ X '(i ) ⎪
λi = ⎨ 0 ⎪ 1 ⎩
(4)
When the normalized thermomechanical parameter X′ for an element at certain increment step is equal to Xavg, λ=0, which means that the element i has no contribution to LF, otherwise, 0<λ≤1 is to weight the contribution of the element i to LF. Step 3, the LF for the element i is defined as follows: K ⎧∑ ⎫ & ⎪ k =1 λi ⋅ (σ i ⋅ ε i ) Δtk ⎪ LF(i) = ⎨ K ⎬ ⎪ ∑ (σ i ⋅ ε&i ) Δtk ⎪ ⎩ k =1 ⎭
2
(5)
where K is the total number of increment steps for the numerical simulation, Δt k is the time increment for step k, σ i and ε&i are the equivalent stress and equivalent strain rate of the element i, respectively. The LF for the entire workpiece domain can be defined as follows: N
LF =
∑ LF(i ) ⋅ vi
e
i =1
N
(6)
∑ vi
e
i =1
The value of the LF given by Eq.(6) will lie in the interval [0,1]. The loss function is of the type of “lower-is-better”.
2
Simulation of TC11 Blisk Forging Process
Fig.1 gives the sketch map of the blisk forging which is integrated by 15 twisted blades and a disk. The shape of the disk is complicated and characterized by large diameter, varying thickness and geometric asymmetry. It is required that the difference of microstructure grading between the blades and the disk should be less than one grade according to grading diagrams of HB 5264-83. Numerical simulation of the TC11 blisk forging process was carried out with the aid of commercial code DEFORM 3D, where an integrated subroutine code was used to describe the characteristics of clutch screw press[21]. Additionally, Eqs.(3)-(6) were incorporated into DEFORM 3D as the subroutine codes to evaluate the microstructure homogeneity. The high sensitivity of flow behavior to thermomechanical parameters was taken into consideration by the flow stress data obtained during the compression test of the isothermal constant strain rate. The flow stress curves at temperatures of 900 and 1000 °C are shown in Fig.2. The process conditions for FEM simulation are summarized in Table 1. a
b
i =1
where N is the total number of the elements in workpiece, and vie is the volume of the element i. Step 2, weighted coefficient for element i, denoted as λi, is
Fig.1 Sketch map of the blisk forging
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Yang Yanhui et al. / Rare Metal Materials and Engineering, 2011,40(4): 0565−0570
Table 2 Results of microstructure homogeneity evaluation
Flow Stress/MPa
350 50 s
300
10 s
1.0 s-1
200
0.1 s-1
150 100
0.01 s-1 0.001 s-1
50 0.1
0.2
0.3
Flow Stress/MPa
120
0.5
0.6 b
-1
10 s
100
1.0 s-1
80 60 40 0 0.0
0.4 50 s-1
140
20
Case 1 Case 2 Case 3 Case 4
-1
250
0.0
a
-1
0.001 s-1 0.1
0.2
0.1 s-1 0.01 s-1 0.3
0.4
0.5
0.6
Strain Fig.2 Flow stress curves at different temperatures: (a) 900 °C and (b) 1000 °C Table 1 Processing conditions for FEM simulation Initial temperature/°C Transfer time/s Dwell time/s Friction factor Heat transfer coefficient between workpiece and dies/N·(mm·K)-1 Convection coefficient to environment/N·(mm·K)-1 Number of heat Number of blows in each heat Energy grade for each blow in every heat
3
980 (workpiece); 260 (dies) 20 4 0.25 (shear type) 20 (during deformation); 2 (during dwell) 0.018 3 5 0.45，0.75，0.75，0.85, 0.9
Evaluation of Microstructure Homogeneity of the TC11 Blisk Forging
Supposing that λε , λT and λε& are the weighted coefficient defined by Eqs.(1)-(4) corresponding to the distributions of equivalent strain, temperature and strain rate, respectively. The microstructure homogeneities for four cases of the above blisk forging were evaluated using Eqs.(5, 6) and are listed in Table 2. In the four cases λε , λT , λε& and (λε + λT + λε& ) / 3 are taken as weighted coefficient, respectively. It is found that the values of LF are close to each other and the maximal difference is only 0.07. In addition, the value of LF for case 4 is equal to the average LF value of the other three cases. Fig.3 shows the distribution of thermomechanical parameters within the finish blisk forging. For the convenience to reveal the characteristics of the cross-section, 1/4 of the forg-
λ λε λT λε& λε + λT + λε& / 3
(
)
Value of LF 0.5 0.46 0.43 0.46
ing is shown. It can be seen that the forging is completely deformed with large flashes. Fig.4 and Fig.5 show the distribution of λ and LF value in the finished blisk forging for different cases. It can be seen from Fig.4a that the regions with larger λε ( λε = 0.75 -1 ) for case 1 are in the flash, the center of the disk as well as the rim of the disk, where the equivalent strain is far greater or lower than the volume-averaged value ε avg = 1.25 (see Fig.3a). On the contrary, the values of equivalent strain in the hub of the disk are close to ε avg (see Fig.3a), and λε are in the range of 0-0.3. In summary, the distribution of λε mainly depends on the equivalent strain distribution and the calculated ε avg . Similarly, it is obvious that the temperatures in the flash (1010-1030 °C) and surfaces (880-930 °C) in contact with the dies are fairly different from Tavg (966.5 °C). Thus, high values of λT lie in the both regions (see Fig.4b). Additionally, the values of λT in most parts of the forging are relatively low (bellow 0.375) since the temperature are correspondingly in the range of 950-970 °C. For case 3 (see Fig.5c), it is found that high λε& is mainly concentrated in the areas adjacent to the flash where the materials flow acutely at the end of the forging process as mentioned above. λ for case 4 is determined by the average of λε , λT and λε& . The distribution of λ for this case (Fig.4d) may be considered as the comprehensive weighted coefficient to LF. It is found that the higher weighted coefficients are mainly concentrated in the flash and the surfaces in contact with the bottom die. It is known from Eqs. (5,6) that value of LF is dependent on both λ and the processing history. It can be validated by the fact that the distribution of value of LF is not necessary in agreement with that of λ (see Fig.4 and Fig.5). In summary, the values of LF in most parts of the blisk forging are very low (below 0.3) except the flash, the region adjacent to the center and the hub of disk (see Fig.5a), the edges of the blades and the surfaces in contact with the bottom die (see Fig.5b, Fig.5c and Fig.5d). Fig.6 gives the curves of LF values vs increment number for different cases. As shown in the figure, the values of LF increase continuously for case 1 and case 3 due to the fact that the homogeneities of the equivalent strain and the strain rate become worse as the process proceeds and the material flows acutely. The sharp increase of LF in the first heat is attributed to relative large deformation. However, for case 2, large value of LF occurs at the beginning of each heat due to the inhomogeneous distribution of temperature resulting from heat loss in
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b
a
c
Fig.3 Distribution of thermomechanical parameters in the finished blisk forging: (a) equivalent strain, (b) equivalent temperature, and (c) equivalent strain rate a
b
c
d
Fig.4 Distribution of weighted coefficient for the loss in the finished blisk forging: (a) case 1, λ= λε , (b) case 2, λ=λT, (c) case 3, λ= λε& , and (d) case 4, λ=( λε +λT+ λε& )/3 a
b
c
d
Fig.5 Distribution of value of LF within the finish blisk forging: (a) case 1, λ = λε , (b) case 2, λ=λT, (c) case 3, λ= λε& , and (d) case 4, λ=( λε +λT+ λε& )/3
a
0.6
b
Value of LF
0.5 0.4 0.3
Case 1 Case 2 Case 3 Case 4
0.2 0.1 0.0
Heat 1 100
Heat 2 200
20 μm
Heat 3 300
400
Fig.7 Initial structures of TC11 alloy billet: (a) microstructures 500
and (b) macrostructures
Increment Number Fig.6 LF value-step curves of the forging process
transfer. Thanks to the heat generation from deformation and friction, the value of LF decreases in subsequent deformation process in this case. For case 4, the variation in value of LF is the comprehensive embodiment of the other three cases.
4
Comparisons between Experiment and Simulation Results
An experiment was conducted on the clutch screw press with nominal load of 112 mN under the processing conditions shown in Table 1. The initial structures of TC11 alloy billet are shown in Fig.7. The following heat treatments after forging process were conducted: (1) heating to 1223 K, holding for 1 h, and air-cooling to room temperature; (2) heating to 803 K, holding for 3 h and air-cooling to room temperature.
Fig.8a shows the picture of the blisk forging after flash cutting and sand blasting in experiment. Compared with the simulation result (Fig.8b), the similarity of the geometry between the experiment and the simulation result is apparent. The microstructure homogeneity of the forging was analyzed by the microscopic examination, in which eight measured points were observed. The locations and the optical micrographs of these measured points are shown in Fig.9 and a
b
Fig.8 Geometries of the blisk forgings via experiment (a) and simulation (b)
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Fig.10, respectively. It can be found that the microstructures of all measured points consist of equiaxed α in a transformed β matrix with α-grain size about 15 μm and the percentage of equiaxed (or primary) α about 40%-50%. It is clear that the microstructures in both blades (see point No.1, point No.2, point No.7 and point No.8) and disk (see point No.3, point No.4, point No.5 and point No.6) are almost similar and can be graded as 3rd grade according to the grading diagrams in HB 5264-83. Fig.11 gives the comparison of LF values for the measured points. In the four cases, the LF values of the measured points are close and almost in the range of 0.33-0.44, especially in case 2 (refer to the dash dotted curves in Fig.11). However, it can be found that the LF values vary in a relatively large range in case 1 and the LF value of point No.5 reaches 0.68. In fact, the microstructure of point No.5 doesn’t change obviously
Fig.9 Locations of the measured points within the forging a
b
c
d
e
f
Value of LF
Yang Yanhui et al. / Rare Metal Materials and Engineering, 2011,40(4): 0565−0570
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Case 1 Case 2 Case 3 Case 4
1
2
3
4
5
6
7
8
Number of Measured Points Fig.11 Comparison of LF values for the measured points
(see Fig.10e). It can be explained as follows. The size of α-grain and the percentage of primary α are almost stable when the deformation reaches an extent such as 70% ( ε =1.2) according to Ref. [16]. From the FEM results, the value of the equivalent strain for point No.5 is 1.28. In addition, it is found that the LF value of the measured point located in the flash with a distance of 23 mm away from the edge of the forging is relatively high, which indicates that the microstructure homogeneity is bad in this region. For example, the LF value of this point is 0.68 in case 2 and is higher than that of the measured points in Fig.9. The optical micrograph of this measured point in the flash is shown in Fig.12. It can be found that the percentage of α decreases and a small amount of lamellar α-grain exists in the microstructure comparing to the micrographs in Fig.10. This may be attributed to undergoing deformation above the β transus during forging process and transformation of β phase in subsequent heat treatment, which is validated from the temperature-time curve of this point shown in Fig.13. To sum up, the LF in case 2 is more adequate to evaluate
20 μm
g
h
20 μm Fig.10 Optical micrographs of the measured points in Fig.9: (a) No.1, (b) No.2, (c) No.3, (d) No.4, (e) No.5, (f) No.6, (g) No.7, and (h) No.8
Temperature/℃
Fig.12 Optical micrograph of the measured point in the flash 1030 1020 1010 1000 990 980 970 960
Solvus temperature
0
20
40
60
80
100
Time/s Fig.13 Temperature vs time curve for the measured point in the flash
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the microstructure homogeneity of the TC11 blisk forging.
5 Conclusions 1) The proposed method based on loss function and finite element method may pave a way to evaluate the microstructure homogeneity of hard-deformed materials forgings using FEM simulation results. 2) For TC11 alloy blisk forging, the LF in case 2 can more appropriately evaluate the microstructure homogeneity. 3) If LF values are in the range of 0.33-0.44 using the LF in case 2, the TC11 blisk forging with desired microstructure homogeneity can be obtained.
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