- Email: [email protected]
FEM Analysis of Spring-backs in Age Forming of Aluminum Alloy Plates
Chinese
Chinese Journal of Aeronautics 20(2007) 564-569
Journal of Aeronautics
www.elsevier.com/locate/cja
FEM Analysis of Spring-backs in Age Forming of Aluminum Alloy Plates Huang Lina,*, Wan Mina, Chi Cailoub, Ji Xiushengb a
Department of Aircraft Manufacturing Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China b
Technology Research Institute, Shenyang Aircraft Corporation, Shenyang 100034, China Received 21 June 2007; accepted 19 September 2007
Abstract The age forming technology, characterized by huge spring-backs, has been developed to manufacture large integral wing-skin panel parts, which necessitates devising a method of predicting spring-backs. A 7B04-T7451 aluminum alloy creep test in tension is accomplished at 155 °C, and the creep curves are obtained. The material constants of the mechanism-based creep constitutive equations are determined through experiments. The age forming process and the spring-backs of 7B04 aluminum alloy plates are analyzed using the commercial finite element software ABAQUS. The effects of plate thickness and forming time on spring-backs are researched. The spring-backs decrease with the increase of plate thickness and forming time. The test results verify the reliability of the finite element method (FEM) analysis. Keywords: aluminum alloy; age forming; constitutive equation; FEM; spring-back
1 Introduction* Since the 1980’s, the age forming technology, also termed as creep age forming or stress relaxation forming, has been developed and used in aerospace industry to manufacture panel-like parts with heightened performance at reduced costs. There are lots of research works and application examples in this respect overseas[1-9]. The occurrence of spring-backs is a key problem in age forming, so a number of numerical technical methods were devised to predict spring-backs, which enables the tool configuration to be modified to achieve the desired part surface. The aim of this paper is to build a set of creep constitutive equations for 7B04 alloy, a material widely used in aircraft manufacturing, on the base
*Corresponding author. Tel.: +86-10-82338613. E-mail address: [email protected] Foundation item: National Natural Science Foundation of China (50675010)
of experimental creep data, and then the equations are used to simulate the age forming of aluminum plates by integrating the creep constitutive equations into finite element solver. The effects of the plate thickness as well as the forming time on spring-backs are analyzed. The age forming tests are conducted to verify the reliability of the constitutive equations and the finite element method (FEM) analysis.
2 Creep Test and Constitutive Model 2.1 Creep test The creep test in tension was conducted to determine the creep constitutive model of 7B04T7451 alloy. An aluminum plate, originally 50 mm thick, was cut into pieces 3 mm thick in its thickness direction and then out of them standard creep test specimens were made in the rolling direction[10].
Huang Lin et al. / Chinese Journal of Aeronautics 20(2007) 564-569
According to the heat treatment standard for 7B04-T7451 alloy, the creep test was conducted at 155 °C and at stress levels of 240, 260, 280 and 300 MPa. With the true creep strain calculated from the experimental creep data, Fig.1 shows the creep curves.
· 565 ·
ĸ A, B characterizing the second stage of creep. ĹV0, m0 affecting the whole creep curve. 2.3 Determination of material constants In order to determine the material constants, the objective function is defined by[12] n mj
Min F ( x )
¦¦ wij (teij tcij )2
(3)
j 1i 1
Fig.1
Creep curves at 155 °C.
2.2 Creep constitutive model Uniaxial mechanism-based creep constitutive equations with three state variables were established by Kowalewski[11] in 1994 to model the primary creep hardening. The tertiary creep process in aluminum alloys contains: ķ dislocation hardening at initial stage of creep; ĸ age softening under high temperature; Ĺ softening due to cavity nucleation and growth at the grain boundary. The damage state variables can be ignored because of there being no tertiary creep in age forming. After necessary simplification and modification, the equations take the following form
H c
A sinh ª B V V 0 1 H ¬
H
h § H · ¨1 ¸ H c V m1 © H * ¹
m0
º ¼
(1) (2)
where H c is the effective creep strain rate, V the effective stress, and A, B, V0, h, H *, m0, m1 are of material constants. The rate of state variable, H, characterizing the primary stage of creep is defined by Eq.(2). According to their characteristics, these material constants can be divided into three groups: ķ h, H *, m1 characterizing the primary stage of creep.
where F(x) is the objective function, n the number of experimental creep curves, mj the number of the experimental data on the jth creep curve, wij the relative weight, and teij tcij the time difference between the ith datum on the jth experimental curve and the calculated value under the same creep strain and at the same stress level j. Based on the least-square method, the value of this objective function is in direct proportion to the area enclosed by experimental and calculated creep curves. Genetic algorithm is used to determine the material constants of the aluminum creep constitutive equations, which are numerically integrated using the fourth order Runge-Kutta method. Values of the material constants for the constitutive equations at 155 °C are listed in Table 1. Table 1 Values of the material constants of the constitutive equations at 155 °C Constant A/h
–1
Value 6×10–7
B/MPa–1
0.04
V0/MPa
300
h/MPa
200
*
H
0.3
m0
1.5
m1
0.1
A comparison between the experimental data and the calculated creep curves in the primary and the second stage of creep at four different stress levels is shown in Fig.2, which demonstrates a very close agreement between them. This creep constitutive model has been incorporated into finite element
· 566 ·
Huang Lin et al. / Chinese Journal of Aeronautics 20(2007) 564-569
solver ABAQUS to simulate the forming and the spring-backs of aluminum alloy plates by programming the user subroutine CREEP.
Fig.2
Comparison between experimental data and calculated creep curves.
3 FEM Analysis of Age Forming and Experimental Verification 3.1 Definition of model surface and plate Two tests are designed to investigate the effects of forming time and aluminum plate thickness on the spring-backs after removing all the pressure loads and constraints, as summarized in Table 2.
3.2 FEM analysis steps The procedure of age forming analysis is consisted of: (1) Fix the plate and lift the tool up by a small distance. Make the plate contact with the rigid tool thus ensuring the following computation to be successfully convergent. (2) Apply a pressure load normal to the top surface of the aluminum plate to deform until the plate gets in complete contact with the rigid tool surface. (3) Hold the pressure load for a certain period to keep the aluminum plate completely contact with the rigid tool surface allowing creep to take place, and part of elastic strain to transform into creep strain, thus relaxing the stress in the aluminum plate. (4) Remove all the pressure loads and constraints leading to a spring-back. (5) Measure the amount of the spring-back. 3.3 Definition and measure of spring-back The spring-back, shown in Fig.4, is defined by
Table 2 Test design
R
Test A: Time effects (thickness: 35.0 mm) Test No.
TA1
TA2
TA3
TA4
TA5
TA6
TA7
Time/h
5
8
10
12
15
17
20
Test B: Thickness effects (time: 15 h) Test No.
TB1
TB2
TB3
TB4
TB5
Thickness/ mm
25.0
27.5
30.0
32.5
35.0
The aluminum plate is 600 mm long and 50 mm wide. The rigid tool surface is in a cylindrical form with a radius of 3 900 mm. Fig.3 shows the FEM mesh of the analysis model.
OP' OP
(4)
R = 0 means absence of spring-back, and R = 1 means a complete spring-back of the plate. Calculated from the radius of die surface and the length of plate, OP amounts to 11.646 mm. By measuring PP' , OP' can also be calculated.
Fig.4
Definition of a spring-back.
3.4 Computational results
Fig.3
FEM model of age forming.
Taking test TA7 as an example, Fig.5 shows the effective stresses and effective creep strains in the aluminum plate on several stages of age forming. At the end of initial loading, the largest stress in plate achieves 330 MPa, which is lower than the
Huang Lin et al. / Chinese Journal of Aeronautics 20(2007) 564-569
· 567 ·
yield strength, so the whole creep deformation takes place at an elastic stress level. During the period of 20-hour-deformation, creep takes place mainly near the top and the bottom surface of the plate, where the bending stress is higher than in other areas. With a uniform distributed creep strain, the elastic stress is well relaxed while removing all the loads and constraints making the residual stress limited.
Fig.6 shows the effects of plate thickness and forming time on spring-backs. In the same forming period, the spring-back of plate linearly decreases with the increase of plate thickness, as shown in Fig.6(a). The stress at the end of initial loading in a thicker plate is larger than that in a thinner one, the creep rate is higher, and more elastic strain will transform into creep strain—all these enable a thicker plate to keep a larger amount of permanent deformation in age forming. With the same plate thickness, an identical bending stress occurs in the plates at the end of initial loading. Fig.6(b) shows that the longer forming time will cause a smaller amount of spring-back. However, because of the reduction of creep rate in the primary and the second stage of creep and also the stress relaxation, the effects of creep time on spring-backs decline in the whole forming process.
Fig.5
Fig.6
Evolution of effective stresses and effective creep strains during the forming process.
Effects of plate thickness and forming time on spring-backs.
· 568 ·
Huang Lin et al. / Chinese Journal of Aeronautics 20(2007) 564-569
3.5 Experimental verification The tests of TA2, TA5 (TB5), TA7, TB1, TB3 are performed to verify the FEM analysis. Fig.7 shows the test equipments.
neering practices, so the numerical method developed in this paper can be used in age forming to predict the spring-backs which serve as a base to modify the die surface.
4 Conclusions
Fig.7
Specimen in an electric incubator.
Fig.8 illustrates a comparison between the measured and calculated experimental spring-backs and the calculated spring-backs through FEM.
(1) Constitutive creep equations for age forming of 7B04 alloy plates are obtained based on a simplified continuum damage mechanics creep model. The material constants in the constitutive equations are determined based on the creep experimental data using the genetic algorithm. (2) The constitutive equations are used in the FEM analysis by programming the ABAQUS user subroutine. The FEM analysis of spring-backs in age forming of aluminum plates is conducted, and the results show that both the thickness of aluminum plates and the forming time have effects on the spring-backs. (3) Age forming tests of uniformly thick aluminum plates are fulfilled. The constitutive equations and the FEM analysis model are verified by comparing the experimental spring-back data to the calculated spring-backs. References [1]
Sallah M, Peddieson J, Foroudastan S. A mathematical model of autoclave age forming. Journal of Materials Processing Technology 1991; 28(1-2): 211-219.
[2]
Holman M C. Autoclave age forming large aluminum aircraft panels. Journal of Mechanical Working Technology 1989; 20(9):
Fig.8
Comparison between the experimental spring-backs and the calculated spring-backs.
The results show that all the calculated springbacks are slightly larger than the experimental ones, and their relative errors are between 5.2% and 8.8%. These errors prove to be quite steady which can be viewed as system errors. However, the effects of the differences in characteristics among different batches of aluminum material and the measuring errors of the spring-backs can not be ignored. The errors in experimental spring-backs against in calculated spring-backs are acceptable in engi-
477-488. [3]
Narimet S P, Peddieson J, Bunchanan G R. A simulation procedure for panel age forming. Journal of Engineering Materials and Technology 1998; 120(3): 183-190.
[4]
Ho K C, Lin J, Dean T A. Constitutive modelling of primary creep for age forming an aluminum alloy. Journal of Materials Processing Technology 2004; 153-154 (11): 122-127.
[5]
Ho K C, Lin J, Dean T A. Modelling of springback in creep forming thick aluminum sheets. International Journal of Plasticity 2004; 20(4): 733-751.
[6]
Foroudastan S, Peddision J, Holman M C. Application of a unified viscoplastic model of simulation of autovlave age forming. Journal of Engineering Materials and Technology 1992; 114: 71-76.
Huang Lin et al. / Chinese Journal of Aeronautics 20(2007) 564-569 [7]
Narimetl S P, Peddieson J, Bunchanan G R. A simple unified age
creep damage constitutive equations. China Mechanical Endi-
forming model. Mechanics Research Communication 2000; 27(6):
neering 2002; 13(19): 82-85. [in Chinese]
631-636. [8]
Lin J, Ho K C, Dean T A. An integrated process for modelling of precipitation hardening and springback in creep age-forming. International Journal of Machine Tools and Manufacture 2006; 46(11): 1266-1270.
[9]
Jeunechampsa P P, Ho K C, Lin J, et al. A closed form technique to predict springback in creep age-forming. International Journal of Mechanical Sciences 2006; 48(6): 621-629.
[10]
GB/T 2039-1997, Metallic materials creep and stress-rupture test in tension. Beijing: Standard Press of China, 1997. [in Chinese]
[11]
Kowalewski Z L, Hayhurst D R, Dyson B F. Mechanisms-based creep constitutive equations for an aluminum alloy. Journal of Strain Analysis 1994; 29(4): 309-316.
[12]
· 569 ·
Li B L, Lin J G, Yao X. Characteristics and optimization of unified
Biographies: Huang Lin Born in 1981, he works as a Ph.D. candidate in Beijing University of Aeronautics and Astronautics. His main research interests include age forming of panel-like parts and digital forming technique. E-mail˖[email protected] Wan Min Born in 1962, Ph.D., he works as a professor in Beijing University of Aeronautics and Astronautics. His main research interests include processing techniques and equipments for new materials and structures, digital forming techniques, processing control and vision measurement techniques. E-mail: [email protected]
Chinese Journal of Aeronautics 20(2007) 564-569
Journal of Aeronautics
www.elsevier.com/locate/cja
FEM Analysis of Spring-backs in Age Forming of Aluminum Alloy Plates Huang Lina,*, Wan Mina, Chi Cailoub, Ji Xiushengb a
Department of Aircraft Manufacturing Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China b
Technology Research Institute, Shenyang Aircraft Corporation, Shenyang 100034, China Received 21 June 2007; accepted 19 September 2007
Abstract The age forming technology, characterized by huge spring-backs, has been developed to manufacture large integral wing-skin panel parts, which necessitates devising a method of predicting spring-backs. A 7B04-T7451 aluminum alloy creep test in tension is accomplished at 155 °C, and the creep curves are obtained. The material constants of the mechanism-based creep constitutive equations are determined through experiments. The age forming process and the spring-backs of 7B04 aluminum alloy plates are analyzed using the commercial finite element software ABAQUS. The effects of plate thickness and forming time on spring-backs are researched. The spring-backs decrease with the increase of plate thickness and forming time. The test results verify the reliability of the finite element method (FEM) analysis. Keywords: aluminum alloy; age forming; constitutive equation; FEM; spring-back
1 Introduction* Since the 1980’s, the age forming technology, also termed as creep age forming or stress relaxation forming, has been developed and used in aerospace industry to manufacture panel-like parts with heightened performance at reduced costs. There are lots of research works and application examples in this respect overseas[1-9]. The occurrence of spring-backs is a key problem in age forming, so a number of numerical technical methods were devised to predict spring-backs, which enables the tool configuration to be modified to achieve the desired part surface. The aim of this paper is to build a set of creep constitutive equations for 7B04 alloy, a material widely used in aircraft manufacturing, on the base
*Corresponding author. Tel.: +86-10-82338613. E-mail address: [email protected] Foundation item: National Natural Science Foundation of China (50675010)
of experimental creep data, and then the equations are used to simulate the age forming of aluminum plates by integrating the creep constitutive equations into finite element solver. The effects of the plate thickness as well as the forming time on spring-backs are analyzed. The age forming tests are conducted to verify the reliability of the constitutive equations and the finite element method (FEM) analysis.
2 Creep Test and Constitutive Model 2.1 Creep test The creep test in tension was conducted to determine the creep constitutive model of 7B04T7451 alloy. An aluminum plate, originally 50 mm thick, was cut into pieces 3 mm thick in its thickness direction and then out of them standard creep test specimens were made in the rolling direction[10].
Huang Lin et al. / Chinese Journal of Aeronautics 20(2007) 564-569
According to the heat treatment standard for 7B04-T7451 alloy, the creep test was conducted at 155 °C and at stress levels of 240, 260, 280 and 300 MPa. With the true creep strain calculated from the experimental creep data, Fig.1 shows the creep curves.
· 565 ·
ĸ A, B characterizing the second stage of creep. ĹV0, m0 affecting the whole creep curve. 2.3 Determination of material constants In order to determine the material constants, the objective function is defined by[12] n mj
Min F ( x )
¦¦ wij (teij tcij )2
(3)
j 1i 1
Fig.1
Creep curves at 155 °C.
2.2 Creep constitutive model Uniaxial mechanism-based creep constitutive equations with three state variables were established by Kowalewski[11] in 1994 to model the primary creep hardening. The tertiary creep process in aluminum alloys contains: ķ dislocation hardening at initial stage of creep; ĸ age softening under high temperature; Ĺ softening due to cavity nucleation and growth at the grain boundary. The damage state variables can be ignored because of there being no tertiary creep in age forming. After necessary simplification and modification, the equations take the following form
H c
A sinh ª B V V 0 1 H ¬
H
h § H · ¨1 ¸ H c V m1 © H * ¹
m0
º ¼
(1) (2)
where H c is the effective creep strain rate, V the effective stress, and A, B, V0, h, H *, m0, m1 are of material constants. The rate of state variable, H, characterizing the primary stage of creep is defined by Eq.(2). According to their characteristics, these material constants can be divided into three groups: ķ h, H *, m1 characterizing the primary stage of creep.
where F(x) is the objective function, n the number of experimental creep curves, mj the number of the experimental data on the jth creep curve, wij the relative weight, and teij tcij the time difference between the ith datum on the jth experimental curve and the calculated value under the same creep strain and at the same stress level j. Based on the least-square method, the value of this objective function is in direct proportion to the area enclosed by experimental and calculated creep curves. Genetic algorithm is used to determine the material constants of the aluminum creep constitutive equations, which are numerically integrated using the fourth order Runge-Kutta method. Values of the material constants for the constitutive equations at 155 °C are listed in Table 1. Table 1 Values of the material constants of the constitutive equations at 155 °C Constant A/h
–1
Value 6×10–7
B/MPa–1
0.04
V0/MPa
300
h/MPa
200
*
H
0.3
m0
1.5
m1
0.1
A comparison between the experimental data and the calculated creep curves in the primary and the second stage of creep at four different stress levels is shown in Fig.2, which demonstrates a very close agreement between them. This creep constitutive model has been incorporated into finite element
· 566 ·
Huang Lin et al. / Chinese Journal of Aeronautics 20(2007) 564-569
solver ABAQUS to simulate the forming and the spring-backs of aluminum alloy plates by programming the user subroutine CREEP.
Fig.2
Comparison between experimental data and calculated creep curves.
3 FEM Analysis of Age Forming and Experimental Verification 3.1 Definition of model surface and plate Two tests are designed to investigate the effects of forming time and aluminum plate thickness on the spring-backs after removing all the pressure loads and constraints, as summarized in Table 2.
3.2 FEM analysis steps The procedure of age forming analysis is consisted of: (1) Fix the plate and lift the tool up by a small distance. Make the plate contact with the rigid tool thus ensuring the following computation to be successfully convergent. (2) Apply a pressure load normal to the top surface of the aluminum plate to deform until the plate gets in complete contact with the rigid tool surface. (3) Hold the pressure load for a certain period to keep the aluminum plate completely contact with the rigid tool surface allowing creep to take place, and part of elastic strain to transform into creep strain, thus relaxing the stress in the aluminum plate. (4) Remove all the pressure loads and constraints leading to a spring-back. (5) Measure the amount of the spring-back. 3.3 Definition and measure of spring-back The spring-back, shown in Fig.4, is defined by
Table 2 Test design
R
Test A: Time effects (thickness: 35.0 mm) Test No.
TA1
TA2
TA3
TA4
TA5
TA6
TA7
Time/h
5
8
10
12
15
17
20
Test B: Thickness effects (time: 15 h) Test No.
TB1
TB2
TB3
TB4
TB5
Thickness/ mm
25.0
27.5
30.0
32.5
35.0
The aluminum plate is 600 mm long and 50 mm wide. The rigid tool surface is in a cylindrical form with a radius of 3 900 mm. Fig.3 shows the FEM mesh of the analysis model.
OP' OP
(4)
R = 0 means absence of spring-back, and R = 1 means a complete spring-back of the plate. Calculated from the radius of die surface and the length of plate, OP amounts to 11.646 mm. By measuring PP' , OP' can also be calculated.
Fig.4
Definition of a spring-back.
3.4 Computational results
Fig.3
FEM model of age forming.
Taking test TA7 as an example, Fig.5 shows the effective stresses and effective creep strains in the aluminum plate on several stages of age forming. At the end of initial loading, the largest stress in plate achieves 330 MPa, which is lower than the
Huang Lin et al. / Chinese Journal of Aeronautics 20(2007) 564-569
· 567 ·
yield strength, so the whole creep deformation takes place at an elastic stress level. During the period of 20-hour-deformation, creep takes place mainly near the top and the bottom surface of the plate, where the bending stress is higher than in other areas. With a uniform distributed creep strain, the elastic stress is well relaxed while removing all the loads and constraints making the residual stress limited.
Fig.6 shows the effects of plate thickness and forming time on spring-backs. In the same forming period, the spring-back of plate linearly decreases with the increase of plate thickness, as shown in Fig.6(a). The stress at the end of initial loading in a thicker plate is larger than that in a thinner one, the creep rate is higher, and more elastic strain will transform into creep strain—all these enable a thicker plate to keep a larger amount of permanent deformation in age forming. With the same plate thickness, an identical bending stress occurs in the plates at the end of initial loading. Fig.6(b) shows that the longer forming time will cause a smaller amount of spring-back. However, because of the reduction of creep rate in the primary and the second stage of creep and also the stress relaxation, the effects of creep time on spring-backs decline in the whole forming process.
Fig.5
Fig.6
Evolution of effective stresses and effective creep strains during the forming process.
Effects of plate thickness and forming time on spring-backs.
· 568 ·
Huang Lin et al. / Chinese Journal of Aeronautics 20(2007) 564-569
3.5 Experimental verification The tests of TA2, TA5 (TB5), TA7, TB1, TB3 are performed to verify the FEM analysis. Fig.7 shows the test equipments.
neering practices, so the numerical method developed in this paper can be used in age forming to predict the spring-backs which serve as a base to modify the die surface.
4 Conclusions
Fig.7
Specimen in an electric incubator.
Fig.8 illustrates a comparison between the measured and calculated experimental spring-backs and the calculated spring-backs through FEM.
(1) Constitutive creep equations for age forming of 7B04 alloy plates are obtained based on a simplified continuum damage mechanics creep model. The material constants in the constitutive equations are determined based on the creep experimental data using the genetic algorithm. (2) The constitutive equations are used in the FEM analysis by programming the ABAQUS user subroutine. The FEM analysis of spring-backs in age forming of aluminum plates is conducted, and the results show that both the thickness of aluminum plates and the forming time have effects on the spring-backs. (3) Age forming tests of uniformly thick aluminum plates are fulfilled. The constitutive equations and the FEM analysis model are verified by comparing the experimental spring-back data to the calculated spring-backs. References [1]
Sallah M, Peddieson J, Foroudastan S. A mathematical model of autoclave age forming. Journal of Materials Processing Technology 1991; 28(1-2): 211-219.
[2]
Holman M C. Autoclave age forming large aluminum aircraft panels. Journal of Mechanical Working Technology 1989; 20(9):
Fig.8
Comparison between the experimental spring-backs and the calculated spring-backs.
The results show that all the calculated springbacks are slightly larger than the experimental ones, and their relative errors are between 5.2% and 8.8%. These errors prove to be quite steady which can be viewed as system errors. However, the effects of the differences in characteristics among different batches of aluminum material and the measuring errors of the spring-backs can not be ignored. The errors in experimental spring-backs against in calculated spring-backs are acceptable in engi-
477-488. [3]
Narimet S P, Peddieson J, Bunchanan G R. A simulation procedure for panel age forming. Journal of Engineering Materials and Technology 1998; 120(3): 183-190.
[4]
Ho K C, Lin J, Dean T A. Constitutive modelling of primary creep for age forming an aluminum alloy. Journal of Materials Processing Technology 2004; 153-154 (11): 122-127.
[5]
Ho K C, Lin J, Dean T A. Modelling of springback in creep forming thick aluminum sheets. International Journal of Plasticity 2004; 20(4): 733-751.
[6]
Foroudastan S, Peddision J, Holman M C. Application of a unified viscoplastic model of simulation of autovlave age forming. Journal of Engineering Materials and Technology 1992; 114: 71-76.
Huang Lin et al. / Chinese Journal of Aeronautics 20(2007) 564-569 [7]
Narimetl S P, Peddieson J, Bunchanan G R. A simple unified age
creep damage constitutive equations. China Mechanical Endi-
forming model. Mechanics Research Communication 2000; 27(6):
neering 2002; 13(19): 82-85. [in Chinese]
631-636. [8]
Lin J, Ho K C, Dean T A. An integrated process for modelling of precipitation hardening and springback in creep age-forming. International Journal of Machine Tools and Manufacture 2006; 46(11): 1266-1270.
[9]
Jeunechampsa P P, Ho K C, Lin J, et al. A closed form technique to predict springback in creep age-forming. International Journal of Mechanical Sciences 2006; 48(6): 621-629.
[10]
GB/T 2039-1997, Metallic materials creep and stress-rupture test in tension. Beijing: Standard Press of China, 1997. [in Chinese]
[11]
Kowalewski Z L, Hayhurst D R, Dyson B F. Mechanisms-based creep constitutive equations for an aluminum alloy. Journal of Strain Analysis 1994; 29(4): 309-316.
[12]
· 569 ·
Li B L, Lin J G, Yao X. Characteristics and optimization of unified
Biographies: Huang Lin Born in 1981, he works as a Ph.D. candidate in Beijing University of Aeronautics and Astronautics. His main research interests include age forming of panel-like parts and digital forming technique. E-mail˖[email protected] Wan Min Born in 1962, Ph.D., he works as a professor in Beijing University of Aeronautics and Astronautics. His main research interests include processing techniques and equipments for new materials and structures, digital forming techniques, processing control and vision measurement techniques. E-mail: [email protected]