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Kinematics and Dynamics Model of GH4169 Alloy for Thermal Deformation
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JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2010, 17(7): 75-78
Kinematics and Dynamics Model of GH4169 Alloy for Thermal Deformation WANG Zhong-tang'
,
ZHANG Shi-hong2,
CHENG Ming'
,
LI De-fu3,
'
YANG Xiao-hong'
(1. School of Materials Science and Engineering, Shenyang Ligong University, Shenyang 110159, Liaoning, China; 2. Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, Liaoning, China; 3. General Research Institute for Nonferrous Metals, Beijing 100088. China) Abstract: The stress-strain curves and microstructure properties of superalloy GH4169 was tested by thermal simulation experiment with different parameters, which were deformation temperature and strain rate and strain and original grain size. The influence of technology parameters on crystal grain size of dynamic recrystallization (DRC) was analyzed. The kinematics model of superalloy GH4169 was established, in which the relation between grain size of dynamic recrystallization and function 2 ( Zener-Hollomon) and parameters was described. The dynamics model of superalloy GH4169 was put forward, which described the relation between the quantity of dynamic recrystallization and function 2 and parameters. The research results showed that the grain size of dynamic recrystallization increased with increasing the temperature and decreasing the strain rate. And the grain size of DRC bore no relationship to original grain size. And the quantity of dynamic recrystallization decreased with increasing the original grain size. Key words: GH4169 superalloy: kinematics model: dynamics model; thermal deformation
GH4169 is a nickel-based superalloy, the configuration of which is body-centered cube and facecentered cube. It was strengthened by depositing and deformed at high temperature. It has high strength, high fatigue property, and fine plasticity at the temperature ranging from -325 to 650 'C. So it is widely used in many fields, such as aeronautics, astronautics, nuclear energy and petroleum, etc. Microstructure evolvement laws have much relationship with the parameters, such as deformation temperature, strain rate, strain and original grain sizeC']. T h e grain size of dynamic recrystallization for IN718 superalloy increased with increasing the temperature under the condition of low deformation and low strain rate, and the grain size increased with increasing the deformation degree under the condition of temperature of 1060 'C and strain rate of 0.01 s-"". T h e quantity of dynamic recrystallization is much related to the parameters, such as temperature, strain rate, strain, limit strain and original grain size"'. Restore and sub-dynamic recrystal-
lization
was
the
intenerate
mechanism
during
GH4169 processing, and it can improve the plasticity of GH4169 superalloyc3~.T h e kinematics model of sub-dynamic recrystallization and dynamic recrystallization of superalloy GH4169 followed a similar lad3]. In numerical simulation of microstructure evolution, it must be determined that microstructure evolution model and constitutive equation and kinematics model and dynamics model of the material proper tie^^^-^]. Because the Vickers hardness and microstructures properties of superalloy GH4169 were very sensitive to heat-processing technology parametersC6], it was necessary that the exact models of microstructure properties were established which influenced the precision of numerical simulation resultsC7'. If the microstructure properties of superalloy GH4169 were not satisfied to demand of forming, it can be improved by anneal treatmentC8'. T h e grain size of dynamic recrystallization was analyzed in the published literatures, but the mathematical model of the relation between grain size and
Foundation Item: Item Sponsored by National Natural Science Foundation of China (50834008) Biography: WANG Zhong-tang(l962-), Doctor, Professor; E-mail: ztwang@imr. ac. cn;
Received Date: February 12, 2009
*
Journal of Iron and Steel Research, International
76
technology parameters and original grain size was not established. In this paper, the kinematics model and dynamics model of dynamic recrystallization (DRC) were put forward, and the original grain size of GH4169 superalloy was considered in the model.
1
1
601
Thermal Simulation Experiment
Thermal simulation experiment was finished under different conditions of deformation temperature and strain rate and strain and original grain size by thermo-simulator Gleeble 3500. Microstructure of superalloy GH4169 was uniformed by anneal treatment. Average grain size of original microstructure was 13. 21 pm (see Fig. 1). T h e parameters of thermal simulation experiment were temperature of 900, 940, 980, 1020, 1060, and 1100 'C , respectively, the strain rate of 1, 0. 1, 0.01, and 0.001 s-' , respectively, and deformation degree of 50%.
Fig. 1
2
Vol. 17
Original microstructure
Kinematics Model of DRC
Kinematics model describes the relationship between grain size of dynamic recrystallization and function 2 and parameters, also named as grain growth model during thermal deformation. According to the results of experiment, the relationship between grain size of DRC and temperature was obtained, as shown in Fig. 2. It was found that the grain size of DRC increased with increasing the temperature and decreasing the strain rate. And the grain size of DRC had no relationship with original microstructure. The function 2 (Zener-Hollomon) was used to describe the influence of deformation temperature and strain rate on forming performancecQ1. Function 2 (Zener-Hollomon) was present in Eqn. (1).
loo0 1 050 Temperature/C
950
1100
Fig. 2 Relationship between grain size of DRC and temperature (1) where, E is strain rate, s - ' ; Q is action energy, J/mol; T is temperature, K ; and R is constant, 8.314 J/(mol K). According to the results of experiment, grain size of superalloy GH4169 grew rapidly at high temperature and low strain rate. It was put forward that the relationship between the grain size d , ( p m ) and function 2 with different value of temperature and strain rate, as shown in Fig. 3 and Fig. 4. It was found that the value of lnd. presented linearity law with the value of I n 2 at the same temperature, and the grads of the curves were near the same value at different temperature and strain rate. Kinematics model of DRC was described by Eqn. ( 2 ) and Eqn. ( 3 ) , showing the relationship between grain size ( d , ) and function Z and temperature (T)c'o-''l. lnd,=cl logz-11 150/T+cz (2) Ind. = k l InZ+O. 410gi+kz (3) According to the results of experiment, it was drawn that the curves of grain size (d.) and function 4.0 3.2 '
. 0.8
Fig. 3
14
15
16
10gz
17
18
Relationship between the grain size of DRC and function Z at different temperature
Kinematics and Dynamics Model of GH4169 Alloy for Thermal Deformation
Issue 7
0.8
30
Fig. 4
32
34
36 In2
38
40
42
CQ/ ( R T )1.
3
function 2 at different strain rate
15
logz
Dynamics Model of DRC Dynamics model of DRC describes the relationship
17
19
( a ) Relationship between l n d , + l l 150/T and logZ;
Fig. 5
1
30
35
Inz
40
( b ) Relationship between In&-0.
45 410& and InZ.
Relationship between the grain size of DRC and function Z
between the quantity of DRC and temperature, and function Z and strain rate. According to the results of experiment, the curves of quantity of DRC and temperature, and function 2 , and strain rate were obtained, as shown in Fig. 6 , Fig. 7 and Fig. 8. Based on analysis of the experiment data, it was found that the quantity of DRC increased with the increasing the temperature and decreasing the strain rate and value of 1nZ. Dynamics model of DRC was described by Avrami e q ~ a t i o n ~ ' ~a-s' ~follows: '
X=l-exp[
Relationship between the quantity of DRC and temperature at different strain rate
-k[
-1 "1
€-€,
€0. 5
(6)
where, X is the quantity of DRC, %; E is the strain; E , is the limit strain, given by Eqn. ( 7 ) ; €0.5 is strain under the condition of quantity ( X ) being 50% , given by Eqn. ( 8 ) ; do is original grain size, pm; k and n are coefficients. According to the experiment data, the limit strain cCwas determined by Eqn. (7). And the strain E ~ was . ~ determined by Eqn. (8). c e = l . 67X 10-42".247d~.154 (7)
Inz
TemperaturdV
Fig. 6
-
2 and temperature ( T ) at different parameters (see Fig. 5). And the coefficients of Eqn. (2) and Eqn. ( 3 ) were determined, which were c1 =-0.486, c2 =18. 68, k, =-0. 395, and k, = 17.45. Then, the kinematics model of DRC was given by Eqn. (4) and Eqn. (5). (4) 1nd,=-O0.4861ogZ-l1 150/T+18.68 I d , = - 0 . 3951nZ-I-0. 41ogi+17.45 (5) where, i is strain rate, s-' ; Q is action energy, J / mol; T is temperature, K ; R is constant, 8.314 J/ (mol K ) ; d , is grain size of DRC, pm; Z=;exp
Relationship between the grain size of DRC and
9.51 . 13
77
Fig. 7
Relationship between the quantity of DRC and function Z
78
J o u r n a l of Iron a n d S t e e l R e s e a r c h , International
Vol. 17
debasing the function 2. T h e quantity of dynamic recrystallization decreased with increasing the original grain size. References :
-3.0
Fig. 8
-2.0
log&
-1.0
0
Relationship between the quantity of DRC and temperature and strain rate
dg.26Zo.06 (8) Because the value of limit strain E, was much smaller than the value of E , it can be ignored in Eqn. ( 6 ) . According to the experiment data, dynamics model of DRC was obtained: E ~ . ~ = O 038 .
I) ] 1.05
X=l-exp[
-In21
€0. 5
(9)
According to Eqn. ( 8 ) and Eqn. ( 9 1 , it was found that the quantity of DRC decreased with increasing the original grain size.
4
Conclusions
1) T h e kinematics model of superalloy GH4169 was established, showing the relationship between the grain size of dynamic recrystallization and function 2 and technology parameters. 2 ) The grain size of dynamic recrystallization increased with increasing the temperature, and decreasing the strain rate. And it bore no relationship to original grain size. 3 ) T h e dynamics model of superalloy GH4169 was established, showing relationship between the quantity of dynamic recrystallization and function 2 and technology parameters. 4) The quantity of DRC increased with increasing the temperature, decreasing the strain rate and
Mirshams R A , Li Ben Q. Integration of Microstructure in a Thermo-Mechanical Processing Model [C] //Ohio Aerospace Institute. Proceedings of the 1998 HBCUs Research Conference. Cleveland: NASA Conference Publication, 1998: 38. G U O Yan-li, YAO Ze-kun, SUN Wei. Influence of Near-Isothermal Deformation Parameters on Grain Size Grade and Microstructure of GH4169 Superalloy [J]. Hot Working Technology, 2007, 36(18): 32 (in Chinese). LIU Dong, LUO Zi-jian. Mathematical Model for Microstruc ture Evolution of GH4169 alloy During Hot Working Process [J]. Transactions of Nonferrous Metals Society of China, 2003, 1 3 ( 5 ) : 1210. Liu D, Yang Y H , Geng J. Constitutive Relationship of IN718 Alloy for Thermoviscoplastic and Microstructure Evolution Coupled Analysis [J]. Acta Metallurgica Sinica: English Letters, 2007. 20(5): 373. L U Hong-jun, JIA Xin-chao, ZHANG Kai-feng. Effect of Superfine-Graining on Mechanical Properties of Superalloy GH4169 [J]. Material Science and Technology, 2002, lO(3): 268 (in Chinese). YANG Jun, LOU Song-nian, YAN Jun-min. Grain Distribution Properties of Superalloy GH4 169 Inertia Friction Welded Joint [J]. Transactions of the China Welding Institution. 2001, 2 2 ( 3 ) : 33 (in Chinese). Luo Z J , Tang H , Zeng F C. Effective Technique for Producing High Performance IN718 Forgings Using Hammers [J]. Journal of Materials Processing Technology, 1991. 28(3) : 383. Kashyap B P, Chaturvedi M C. T h e Effect of Prior Annealing on High Temperature Flow Properties of and Microstructural Evolution in S P F Grade IN718 Superalloy [J]. Materials Science and Engineering, 2007, 445-446A: 364. Sellars C M , Whiteman J A. Recrystallization and Grain Growth in Hot Rolling [J]. Metal Science, 1979, 13(3): 187. Luton M J , Sellars C M. Dynamic Recrystallization in Nickel and Nickel-Iron Alloys During High Temperature Deformation [J]. Acta Metallurgica, 1969, 17(8): 1033. Sah J P, Richardson M J , Sellars C M. Grain Size Effects During Dynamic Recrystallization of Nickel [J]. Metal Science, 1975, 8(10): 325. Sakai T, Jonas J J. Flow Stress and Substructural Change During Transient Dynamic Recrystallization of Nickel [ J 1. Acta Metallurgica, 1984, 2 ( 7 ) : 659. Stuwe H P, Ortner B. Recrystallization in Hot Working and Creep. Metal Science, 1974, 8 ( 6 ) : 161.
-?ScienceDirect -00
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~
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JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2010, 17(7): 75-78
Kinematics and Dynamics Model of GH4169 Alloy for Thermal Deformation WANG Zhong-tang'
,
ZHANG Shi-hong2,
CHENG Ming'
,
LI De-fu3,
'
YANG Xiao-hong'
(1. School of Materials Science and Engineering, Shenyang Ligong University, Shenyang 110159, Liaoning, China; 2. Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, Liaoning, China; 3. General Research Institute for Nonferrous Metals, Beijing 100088. China) Abstract: The stress-strain curves and microstructure properties of superalloy GH4169 was tested by thermal simulation experiment with different parameters, which were deformation temperature and strain rate and strain and original grain size. The influence of technology parameters on crystal grain size of dynamic recrystallization (DRC) was analyzed. The kinematics model of superalloy GH4169 was established, in which the relation between grain size of dynamic recrystallization and function 2 ( Zener-Hollomon) and parameters was described. The dynamics model of superalloy GH4169 was put forward, which described the relation between the quantity of dynamic recrystallization and function 2 and parameters. The research results showed that the grain size of dynamic recrystallization increased with increasing the temperature and decreasing the strain rate. And the grain size of DRC bore no relationship to original grain size. And the quantity of dynamic recrystallization decreased with increasing the original grain size. Key words: GH4169 superalloy: kinematics model: dynamics model; thermal deformation
GH4169 is a nickel-based superalloy, the configuration of which is body-centered cube and facecentered cube. It was strengthened by depositing and deformed at high temperature. It has high strength, high fatigue property, and fine plasticity at the temperature ranging from -325 to 650 'C. So it is widely used in many fields, such as aeronautics, astronautics, nuclear energy and petroleum, etc. Microstructure evolvement laws have much relationship with the parameters, such as deformation temperature, strain rate, strain and original grain sizeC']. T h e grain size of dynamic recrystallization for IN718 superalloy increased with increasing the temperature under the condition of low deformation and low strain rate, and the grain size increased with increasing the deformation degree under the condition of temperature of 1060 'C and strain rate of 0.01 s-"". T h e quantity of dynamic recrystallization is much related to the parameters, such as temperature, strain rate, strain, limit strain and original grain size"'. Restore and sub-dynamic recrystal-
lization
was
the
intenerate
mechanism
during
GH4169 processing, and it can improve the plasticity of GH4169 superalloyc3~.T h e kinematics model of sub-dynamic recrystallization and dynamic recrystallization of superalloy GH4169 followed a similar lad3]. In numerical simulation of microstructure evolution, it must be determined that microstructure evolution model and constitutive equation and kinematics model and dynamics model of the material proper tie^^^-^]. Because the Vickers hardness and microstructures properties of superalloy GH4169 were very sensitive to heat-processing technology parametersC6], it was necessary that the exact models of microstructure properties were established which influenced the precision of numerical simulation resultsC7'. If the microstructure properties of superalloy GH4169 were not satisfied to demand of forming, it can be improved by anneal treatmentC8'. T h e grain size of dynamic recrystallization was analyzed in the published literatures, but the mathematical model of the relation between grain size and
Foundation Item: Item Sponsored by National Natural Science Foundation of China (50834008) Biography: WANG Zhong-tang(l962-), Doctor, Professor; E-mail: ztwang@imr. ac. cn;
Received Date: February 12, 2009
*
Journal of Iron and Steel Research, International
76
technology parameters and original grain size was not established. In this paper, the kinematics model and dynamics model of dynamic recrystallization (DRC) were put forward, and the original grain size of GH4169 superalloy was considered in the model.
1
1
601
Thermal Simulation Experiment
Thermal simulation experiment was finished under different conditions of deformation temperature and strain rate and strain and original grain size by thermo-simulator Gleeble 3500. Microstructure of superalloy GH4169 was uniformed by anneal treatment. Average grain size of original microstructure was 13. 21 pm (see Fig. 1). T h e parameters of thermal simulation experiment were temperature of 900, 940, 980, 1020, 1060, and 1100 'C , respectively, the strain rate of 1, 0. 1, 0.01, and 0.001 s-' , respectively, and deformation degree of 50%.
Fig. 1
2
Vol. 17
Original microstructure
Kinematics Model of DRC
Kinematics model describes the relationship between grain size of dynamic recrystallization and function 2 and parameters, also named as grain growth model during thermal deformation. According to the results of experiment, the relationship between grain size of DRC and temperature was obtained, as shown in Fig. 2. It was found that the grain size of DRC increased with increasing the temperature and decreasing the strain rate. And the grain size of DRC had no relationship with original microstructure. The function 2 (Zener-Hollomon) was used to describe the influence of deformation temperature and strain rate on forming performancecQ1. Function 2 (Zener-Hollomon) was present in Eqn. (1).
loo0 1 050 Temperature/C
950
1100
Fig. 2 Relationship between grain size of DRC and temperature (1) where, E is strain rate, s - ' ; Q is action energy, J/mol; T is temperature, K ; and R is constant, 8.314 J/(mol K). According to the results of experiment, grain size of superalloy GH4169 grew rapidly at high temperature and low strain rate. It was put forward that the relationship between the grain size d , ( p m ) and function 2 with different value of temperature and strain rate, as shown in Fig. 3 and Fig. 4. It was found that the value of lnd. presented linearity law with the value of I n 2 at the same temperature, and the grads of the curves were near the same value at different temperature and strain rate. Kinematics model of DRC was described by Eqn. ( 2 ) and Eqn. ( 3 ) , showing the relationship between grain size ( d , ) and function Z and temperature (T)c'o-''l. lnd,=cl logz-11 150/T+cz (2) Ind. = k l InZ+O. 410gi+kz (3) According to the results of experiment, it was drawn that the curves of grain size (d.) and function 4.0 3.2 '
. 0.8
Fig. 3
14
15
16
10gz
17
18
Relationship between the grain size of DRC and function Z at different temperature
Kinematics and Dynamics Model of GH4169 Alloy for Thermal Deformation
Issue 7
0.8
30
Fig. 4
32
34
36 In2
38
40
42
CQ/ ( R T )1.
3
function 2 at different strain rate
15
logz
Dynamics Model of DRC Dynamics model of DRC describes the relationship
17
19
( a ) Relationship between l n d , + l l 150/T and logZ;
Fig. 5
1
30
35
Inz
40
( b ) Relationship between In&-0.
45 410& and InZ.
Relationship between the grain size of DRC and function Z
between the quantity of DRC and temperature, and function Z and strain rate. According to the results of experiment, the curves of quantity of DRC and temperature, and function 2 , and strain rate were obtained, as shown in Fig. 6 , Fig. 7 and Fig. 8. Based on analysis of the experiment data, it was found that the quantity of DRC increased with the increasing the temperature and decreasing the strain rate and value of 1nZ. Dynamics model of DRC was described by Avrami e q ~ a t i o n ~ ' ~a-s' ~follows: '
X=l-exp[
Relationship between the quantity of DRC and temperature at different strain rate
-k[
-1 "1
€-€,
€0. 5
(6)
where, X is the quantity of DRC, %; E is the strain; E , is the limit strain, given by Eqn. ( 7 ) ; €0.5 is strain under the condition of quantity ( X ) being 50% , given by Eqn. ( 8 ) ; do is original grain size, pm; k and n are coefficients. According to the experiment data, the limit strain cCwas determined by Eqn. (7). And the strain E ~ was . ~ determined by Eqn. (8). c e = l . 67X 10-42".247d~.154 (7)
Inz
TemperaturdV
Fig. 6
-
2 and temperature ( T ) at different parameters (see Fig. 5). And the coefficients of Eqn. (2) and Eqn. ( 3 ) were determined, which were c1 =-0.486, c2 =18. 68, k, =-0. 395, and k, = 17.45. Then, the kinematics model of DRC was given by Eqn. (4) and Eqn. (5). (4) 1nd,=-O0.4861ogZ-l1 150/T+18.68 I d , = - 0 . 3951nZ-I-0. 41ogi+17.45 (5) where, i is strain rate, s-' ; Q is action energy, J / mol; T is temperature, K ; R is constant, 8.314 J/ (mol K ) ; d , is grain size of DRC, pm; Z=;exp
Relationship between the grain size of DRC and
9.51 . 13
77
Fig. 7
Relationship between the quantity of DRC and function Z
78
J o u r n a l of Iron a n d S t e e l R e s e a r c h , International
Vol. 17
debasing the function 2. T h e quantity of dynamic recrystallization decreased with increasing the original grain size. References :
-3.0
Fig. 8
-2.0
log&
-1.0
0
Relationship between the quantity of DRC and temperature and strain rate
dg.26Zo.06 (8) Because the value of limit strain E, was much smaller than the value of E , it can be ignored in Eqn. ( 6 ) . According to the experiment data, dynamics model of DRC was obtained: E ~ . ~ = O 038 .
I) ] 1.05
X=l-exp[
-In21
€0. 5
(9)
According to Eqn. ( 8 ) and Eqn. ( 9 1 , it was found that the quantity of DRC decreased with increasing the original grain size.
4
Conclusions
1) T h e kinematics model of superalloy GH4169 was established, showing the relationship between the grain size of dynamic recrystallization and function 2 and technology parameters. 2 ) The grain size of dynamic recrystallization increased with increasing the temperature, and decreasing the strain rate. And it bore no relationship to original grain size. 3 ) T h e dynamics model of superalloy GH4169 was established, showing relationship between the quantity of dynamic recrystallization and function 2 and technology parameters. 4) The quantity of DRC increased with increasing the temperature, decreasing the strain rate and
Mirshams R A , Li Ben Q. Integration of Microstructure in a Thermo-Mechanical Processing Model [C] //Ohio Aerospace Institute. Proceedings of the 1998 HBCUs Research Conference. Cleveland: NASA Conference Publication, 1998: 38. G U O Yan-li, YAO Ze-kun, SUN Wei. Influence of Near-Isothermal Deformation Parameters on Grain Size Grade and Microstructure of GH4169 Superalloy [J]. Hot Working Technology, 2007, 36(18): 32 (in Chinese). LIU Dong, LUO Zi-jian. Mathematical Model for Microstruc ture Evolution of GH4169 alloy During Hot Working Process [J]. Transactions of Nonferrous Metals Society of China, 2003, 1 3 ( 5 ) : 1210. Liu D, Yang Y H , Geng J. Constitutive Relationship of IN718 Alloy for Thermoviscoplastic and Microstructure Evolution Coupled Analysis [J]. Acta Metallurgica Sinica: English Letters, 2007. 20(5): 373. L U Hong-jun, JIA Xin-chao, ZHANG Kai-feng. Effect of Superfine-Graining on Mechanical Properties of Superalloy GH4169 [J]. Material Science and Technology, 2002, lO(3): 268 (in Chinese). YANG Jun, LOU Song-nian, YAN Jun-min. Grain Distribution Properties of Superalloy GH4 169 Inertia Friction Welded Joint [J]. Transactions of the China Welding Institution. 2001, 2 2 ( 3 ) : 33 (in Chinese). Luo Z J , Tang H , Zeng F C. Effective Technique for Producing High Performance IN718 Forgings Using Hammers [J]. Journal of Materials Processing Technology, 1991. 28(3) : 383. Kashyap B P, Chaturvedi M C. T h e Effect of Prior Annealing on High Temperature Flow Properties of and Microstructural Evolution in S P F Grade IN718 Superalloy [J]. Materials Science and Engineering, 2007, 445-446A: 364. Sellars C M , Whiteman J A. Recrystallization and Grain Growth in Hot Rolling [J]. Metal Science, 1979, 13(3): 187. Luton M J , Sellars C M. Dynamic Recrystallization in Nickel and Nickel-Iron Alloys During High Temperature Deformation [J]. Acta Metallurgica, 1969, 17(8): 1033. Sah J P, Richardson M J , Sellars C M. Grain Size Effects During Dynamic Recrystallization of Nickel [J]. Metal Science, 1975, 8(10): 325. Sakai T, Jonas J J. Flow Stress and Substructural Change During Transient Dynamic Recrystallization of Nickel [ J 1. Acta Metallurgica, 1984, 2 ( 7 ) : 659. Stuwe H P, Ortner B. Recrystallization in Hot Working and Creep. Metal Science, 1974, 8 ( 6 ) : 161.