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Prediction of blow forming profile of spherical titanium tank
Journal of Materials Processing Technology 187–188 (2007) 463–466
Prediction of blow forming profile of spherical titanium tank J.H. Yoon a,∗ , H.S. Lee a , Y.M. Yi b , Y.S. Jang a a
Structures and Materials Department, Korea Aerospace Research Institute, Deajeon 305-335, Republic of Korea b KSLV Technology Division, Korea Aerospace Research Institute, Deajeon 305-335, Republic of Korea
Abstract When manufacturing spherical titanium tank by superplastic blow forming, it is important to obtain uniform thickness distribution of the tank in terms of performance. In the current study, the optimization of thickness distribution of diffusion bonded initial blank and the prediction of the thickness at final forming stage have been carried out by using theoretical equations available in reference and finite element methods for superplastic blow forming process. The analysis has been carried out for each case of using uniform blank, profiled one, and optimized blank without boss. The optimized blank resulted in almost uniform thickness of final product, however, slight thinning phenomena near the boss was observed because of large size of boss. Also, the final thickness deviated a bit from the target thickness. This resulted from that the equation employed for the current study was driven without considering the boss diameter, and the difference of boundary condition. Therefore, since the region near boss is a region where stress concentration occurred under internal pressure loading, more improved theoretical or empirical optimization should be followed to prevent from thinning near boss and to maximize the performance of the tank. © 2006 Elsevier B.V. All rights reserved. Keywords: Superplastic blow forming; Diffusion bonding; Thickness; Boss; Optimization
1. Introduction
2. Optimization of thickness distribution of blank
Titanium tanks in aerospace field have been used for storing liquid or gaseous propellant because of its high specific strength. The tanks are manufactured by a process method properly chosen under the consideration of the quantity and formability. Superplastic blow forming using diffusion bonded blank is one of the appropriate process to manufacture tanks for aerospace purpose. When superplastic blow forming method is applied for manufacturing spherical tank, it is well known that the process variables should be carefully controlled to obtain uniform thickness coincident with the requirement. Thus, the thickness distribution of initial blank should be predicted properly and researchers have been trying to optimize the blank theoretically or numerically [1,2]. In the current study, the optimization of thickness distribution of diffusion bonded initial blank and the prediction of the wall thickness distribution of final formed tank have been carried out throughout theoretical equations and forming analysis using finite element methods.
Thickness distribution of initial blank was optimized by using the equations proposed by Dutta [1] and the optimized result was summarized in Table 1. Eq. (1) can be numerically solved by Simpson’s rule, and then the thickness profile of initial blank is calculated by substituting the obtained (s0 )p into Eq. (2). Fig. 1 shows the meaning of symbols expressed in the equations.
∗ Corresponding author at: Structures and Materials Department, Korea Aerospace Research Institute, 45 Eoeun-Dong, Yuseong-Gu, Deajeon 305-333, Republic of Korea. Tel.: +82 42 860 2049; fax: +82 42 860 2233. E-mail address: [email protected] (J.H. Yoon).
0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.11.187
π/2 (s ) Xθ 0 p
0
1/m
(s0 )p (s0 )θ = s s
Kθ =
sin(2θ) dθ = 2.
s
Xθ =
/Yθ
X1/m /Yθ θ
.
3 1 + Kθ + Kθ2 2 + Kθ
(1)
(2)
,
2 Yθ = √ 3
1 + Kθ + Kθ2 1 + Kθ
ln[π cos θ/{tan−1 (2 cot θ cos ecθ)(1 + cos2 θ)}] . 2 + Kθ
. (3)
(4)
464
J.H. Yoon et al. / Journal of Materials Processing Technology 187–188 (2007) 463–466
Table 1 Optimized result of initial blank (unit: mm) Radial Pos. Thickness
0.00 7.00
9.88 6.93
19.63 6.74
30.49 6.46
40.86 6.17
50.59 5.93
60.57 5.71
70.24 5.54
80.19 5.39
90.00 5.27
Fig. 2. Analysis geometry in case of uniform blank. Fig. 1. Schematic description of formed hemisphere from profiled thickness blank [1].
3. FE simulation of axi-symmetric superplastic blow forming of Ti–6Al–4V tank 3.1. Analysis condition Finite element simulation has been carried out by using superplastic forming module of MARC. The deformation is assumed to be axi-symmetric, and forming pressure is imposed on nondiffusion bonded area and inner wall of gas inlet hole. The material properties used in the analysis and initial configuration of tool and workpiece are shown in Table 2 and Fig. 2, respectively. In Fig. 2, diffusion bonded area generates such boundary condition that the displacement in axial direction should be constrained. The analysis cases were summarized in Table 3. 3.2. Analysis results Fig. 3 shows the equivalent strain rate distributions in deformed shape at t = 1100 s for case 1 and case 2. In case of uniform blank, the maximum equivalent strain rate occurred in Table 2 Analysis condition Material Flow stress equation (MPa) Optimal strain rate (s−1 ) Friction model Friction coefficient Initial diameter of initial blank (mm) Target thickness (mm) Limit of maximum pressure (MPa)
Ti–6Al–4V ELI σf = 450ε0.4 eq 5.0 × 10−4 Coulomb model 0.3 90.0 3.5 4.0
Fig. 3. Equivalent strain rate distribution at t = 1100 s; (a) uniform blank and (b) optimized blank.
J.H. Yoon et al. / Journal of Materials Processing Technology 187–188 (2007) 463–466
465
Table 3 Summary of analysis cases Case
Initial blank thickness (mm)
Workpiece construction
Case 1 Case 2 Case 3
6.0 7.0–5.27 (optimized) 7.0–5.27 (optimized)
Blank with boss Blank with boss Blank without boss
knuckle zone and the gradient was observed in the deformed blank. On the other hand, optimized blank shows that it maintains uniform deformation in spite of higher strain rate than uniform blank. Fig. 4 shows the total equivalent strain distributions at final forming step. Uniform thickness of initial blank resulted in serious thinning phenomena in knuckle zone, while relatively uniform strain distribution in the final shape can be observed in case of using optimized blank. The pressure profile according to forming time, which has Nconfiguration, was shown in Fig. 5. Case 1 predicted the longest forming time, about 3500 s, while the optimized blank without boss showed the shortest duration (about 2440 s). Also, forming pressure drastically increased according to approaching the
Fig. 4. Total equivalent strain distributions at final step; (a) uniform blank, t = 3500 s and (b) optimized blank, t = 2760s.
Fig. 5. Pressure profile according to forming time.
final shape in all cases. It is thought that there are two main reasons. Firstly, knuckle zone and diffusion bonded zone are the latest areas to be formed. It means that the material was trapped, thus it is difficult for the material corresponding to this zone to flow. This deformation mode induced the forming pressure to increase. Secondly, the increase of contact nodes causes the increase of pressure. In case of the blank without boss, the pressure increased only due to the trapped material in the diffusion bonded zone. The wall thickness distributions of formed tank were summarized in Fig. 6, where it seemed that the boss affects both the thickness uniformity and the thickness deviation from the case 3. But it is estimated that the effect of friction on thickness uniformity cannot be also ignored. The equations employed in the current study were proposed for hemisphere bulging process. In this process, there is no boss and the flange that is an exterior region of blank is constrained by blank holder. As a result, the boundary condition in equatorial region constrained by the holder becomes a fixed displacement in all directions. However, the current case allows the radial displacement of diffusion bonded zone. Thus, it is thought that the difference of boundary condition caused a thinner thickness profile of initial blank, and it resulted in the deviation from the target thickness.
Fig. 6. Thickness distribution on formed tank shell.
466
J.H. Yoon et al. / Journal of Materials Processing Technology 187–188 (2007) 463–466
4. Conclusion
References
Throughout the current study, although there is a bit difference between the simulation results and target thickness, it is construed that the equations introduced by Dutta [1] is able to drive a qualitatively uniform wall thickness of formed tank. In the future, if the effect of boss size and boundary condition in the diffusion bonded zone of initial blank is considered in the equations, a quantitatively satisfactory result can be obtained.
[1] A. Dutta, Thickness-profiliing of initial blank for superplastic forming of uniformly thick domes, J. Mater. Process. Technol. A371 (2004) 79–81. [2] J.M. Lee, S.S. Hong, Y.H. Kim, Blank design for optimized thickness distribution for axi-symmetric blow forming, Trans. Mater. Process. V8 (1) (1999) 92–100.
Prediction of blow forming profile of spherical titanium tank J.H. Yoon a,∗ , H.S. Lee a , Y.M. Yi b , Y.S. Jang a a
Structures and Materials Department, Korea Aerospace Research Institute, Deajeon 305-335, Republic of Korea b KSLV Technology Division, Korea Aerospace Research Institute, Deajeon 305-335, Republic of Korea
Abstract When manufacturing spherical titanium tank by superplastic blow forming, it is important to obtain uniform thickness distribution of the tank in terms of performance. In the current study, the optimization of thickness distribution of diffusion bonded initial blank and the prediction of the thickness at final forming stage have been carried out by using theoretical equations available in reference and finite element methods for superplastic blow forming process. The analysis has been carried out for each case of using uniform blank, profiled one, and optimized blank without boss. The optimized blank resulted in almost uniform thickness of final product, however, slight thinning phenomena near the boss was observed because of large size of boss. Also, the final thickness deviated a bit from the target thickness. This resulted from that the equation employed for the current study was driven without considering the boss diameter, and the difference of boundary condition. Therefore, since the region near boss is a region where stress concentration occurred under internal pressure loading, more improved theoretical or empirical optimization should be followed to prevent from thinning near boss and to maximize the performance of the tank. © 2006 Elsevier B.V. All rights reserved. Keywords: Superplastic blow forming; Diffusion bonding; Thickness; Boss; Optimization
1. Introduction
2. Optimization of thickness distribution of blank
Titanium tanks in aerospace field have been used for storing liquid or gaseous propellant because of its high specific strength. The tanks are manufactured by a process method properly chosen under the consideration of the quantity and formability. Superplastic blow forming using diffusion bonded blank is one of the appropriate process to manufacture tanks for aerospace purpose. When superplastic blow forming method is applied for manufacturing spherical tank, it is well known that the process variables should be carefully controlled to obtain uniform thickness coincident with the requirement. Thus, the thickness distribution of initial blank should be predicted properly and researchers have been trying to optimize the blank theoretically or numerically [1,2]. In the current study, the optimization of thickness distribution of diffusion bonded initial blank and the prediction of the wall thickness distribution of final formed tank have been carried out throughout theoretical equations and forming analysis using finite element methods.
Thickness distribution of initial blank was optimized by using the equations proposed by Dutta [1] and the optimized result was summarized in Table 1. Eq. (1) can be numerically solved by Simpson’s rule, and then the thickness profile of initial blank is calculated by substituting the obtained (s0 )p into Eq. (2). Fig. 1 shows the meaning of symbols expressed in the equations.
∗ Corresponding author at: Structures and Materials Department, Korea Aerospace Research Institute, 45 Eoeun-Dong, Yuseong-Gu, Deajeon 305-333, Republic of Korea. Tel.: +82 42 860 2049; fax: +82 42 860 2233. E-mail address: [email protected] (J.H. Yoon).
0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.11.187
π/2 (s ) Xθ 0 p
0
1/m
(s0 )p (s0 )θ = s s
Kθ =
sin(2θ) dθ = 2.
s
Xθ =
/Yθ
X1/m /Yθ θ
.
3 1 + Kθ + Kθ2 2 + Kθ
(1)
(2)
,
2 Yθ = √ 3
1 + Kθ + Kθ2 1 + Kθ
ln[π cos θ/{tan−1 (2 cot θ cos ecθ)(1 + cos2 θ)}] . 2 + Kθ
. (3)
(4)
464
J.H. Yoon et al. / Journal of Materials Processing Technology 187–188 (2007) 463–466
Table 1 Optimized result of initial blank (unit: mm) Radial Pos. Thickness
0.00 7.00
9.88 6.93
19.63 6.74
30.49 6.46
40.86 6.17
50.59 5.93
60.57 5.71
70.24 5.54
80.19 5.39
90.00 5.27
Fig. 2. Analysis geometry in case of uniform blank. Fig. 1. Schematic description of formed hemisphere from profiled thickness blank [1].
3. FE simulation of axi-symmetric superplastic blow forming of Ti–6Al–4V tank 3.1. Analysis condition Finite element simulation has been carried out by using superplastic forming module of MARC. The deformation is assumed to be axi-symmetric, and forming pressure is imposed on nondiffusion bonded area and inner wall of gas inlet hole. The material properties used in the analysis and initial configuration of tool and workpiece are shown in Table 2 and Fig. 2, respectively. In Fig. 2, diffusion bonded area generates such boundary condition that the displacement in axial direction should be constrained. The analysis cases were summarized in Table 3. 3.2. Analysis results Fig. 3 shows the equivalent strain rate distributions in deformed shape at t = 1100 s for case 1 and case 2. In case of uniform blank, the maximum equivalent strain rate occurred in Table 2 Analysis condition Material Flow stress equation (MPa) Optimal strain rate (s−1 ) Friction model Friction coefficient Initial diameter of initial blank (mm) Target thickness (mm) Limit of maximum pressure (MPa)
Ti–6Al–4V ELI σf = 450ε0.4 eq 5.0 × 10−4 Coulomb model 0.3 90.0 3.5 4.0
Fig. 3. Equivalent strain rate distribution at t = 1100 s; (a) uniform blank and (b) optimized blank.
J.H. Yoon et al. / Journal of Materials Processing Technology 187–188 (2007) 463–466
465
Table 3 Summary of analysis cases Case
Initial blank thickness (mm)
Workpiece construction
Case 1 Case 2 Case 3
6.0 7.0–5.27 (optimized) 7.0–5.27 (optimized)
Blank with boss Blank with boss Blank without boss
knuckle zone and the gradient was observed in the deformed blank. On the other hand, optimized blank shows that it maintains uniform deformation in spite of higher strain rate than uniform blank. Fig. 4 shows the total equivalent strain distributions at final forming step. Uniform thickness of initial blank resulted in serious thinning phenomena in knuckle zone, while relatively uniform strain distribution in the final shape can be observed in case of using optimized blank. The pressure profile according to forming time, which has Nconfiguration, was shown in Fig. 5. Case 1 predicted the longest forming time, about 3500 s, while the optimized blank without boss showed the shortest duration (about 2440 s). Also, forming pressure drastically increased according to approaching the
Fig. 4. Total equivalent strain distributions at final step; (a) uniform blank, t = 3500 s and (b) optimized blank, t = 2760s.
Fig. 5. Pressure profile according to forming time.
final shape in all cases. It is thought that there are two main reasons. Firstly, knuckle zone and diffusion bonded zone are the latest areas to be formed. It means that the material was trapped, thus it is difficult for the material corresponding to this zone to flow. This deformation mode induced the forming pressure to increase. Secondly, the increase of contact nodes causes the increase of pressure. In case of the blank without boss, the pressure increased only due to the trapped material in the diffusion bonded zone. The wall thickness distributions of formed tank were summarized in Fig. 6, where it seemed that the boss affects both the thickness uniformity and the thickness deviation from the case 3. But it is estimated that the effect of friction on thickness uniformity cannot be also ignored. The equations employed in the current study were proposed for hemisphere bulging process. In this process, there is no boss and the flange that is an exterior region of blank is constrained by blank holder. As a result, the boundary condition in equatorial region constrained by the holder becomes a fixed displacement in all directions. However, the current case allows the radial displacement of diffusion bonded zone. Thus, it is thought that the difference of boundary condition caused a thinner thickness profile of initial blank, and it resulted in the deviation from the target thickness.
Fig. 6. Thickness distribution on formed tank shell.
466
J.H. Yoon et al. / Journal of Materials Processing Technology 187–188 (2007) 463–466
4. Conclusion
References
Throughout the current study, although there is a bit difference between the simulation results and target thickness, it is construed that the equations introduced by Dutta [1] is able to drive a qualitatively uniform wall thickness of formed tank. In the future, if the effect of boss size and boundary condition in the diffusion bonded zone of initial blank is considered in the equations, a quantitatively satisfactory result can be obtained.
[1] A. Dutta, Thickness-profiliing of initial blank for superplastic forming of uniformly thick domes, J. Mater. Process. Technol. A371 (2004) 79–81. [2] J.M. Lee, S.S. Hong, Y.H. Kim, Blank design for optimized thickness distribution for axi-symmetric blow forming, Trans. Mater. Process. V8 (1) (1999) 92–100.