- Email: [email protected]
High Temperature Deformation Behavior of Fe-9Ni-C Alloy
Available online at www.sciencedirect.com -"@0
Y0ScienceDirect JOURNAL OF IRON AND SITEL RESEARCH, INTEFWYMONAL. 2012, 19(5): 58-62
High Temperature Deformation Behavior of Fe-9Ni-C Alloy ZHANG Kun,
W U Hui-bin,
TANG Di
(Engineering Research Institute, University of Science and Technology Beijing , Beijing 100083, China)
Abstract: The high temperature deformation behavior of the 9Ni steel has been studied by the Gleeble-3500 tester. The relationship between deformation resistance and deformation degree, deformation temperature and deformation rate was revealed. The results show that when the deformation degree is less than 0.2, the deformation resistance increases by about 70 to 200 MPa, while the deformation degree varied between 0. 2 and 0 . 4 , the deformation resistance increases by about 30-40 MPa, when the deformation degree is larger than 0.4, the deformation resistance increases slowly, some become stable gradually. The influence of deformation temperature on deformation resistance is larger, and deformation resistance at higher temperature is about 160 MPa smaller than at lower temperature. Higher deformation rate leads to larger deformation resistance. The deformation resistance increases about 70 to 110 MPa with the increase of the deformation rate. A new and highly accurate mathematical model of the steel was established to describe the deformation behavior during rolling. Key words: 9Ni steel; high temperature deformation resistance; mathematical model
Liquefied natural gas ( L N G ) is known as a clean energy source which is commonly used as domestic and industrial fuel for its abundance, versatility, and clean burning nature"]. It is reportedCz3 that the consumption will almost be double in size between 2005 and 2010, delivering around 40% of global gas supply growth. T h e LNG is a mixture composed mostly of methane and a small quantity of ethane propane, nitrogen and other minor components. Fe-9Ni-C alloy or 9Ni steel, simply referred to as 9Ni steel, is known as a cryogenic structural material applied for L N G t a n k e r and pipelineC3]. The microstructure of 9Ni steel is martensite along with a small quantity of retained austenite. The morphology and crystallography of martensite in F e N i alloy had been studiedc"-?]. T h e reversed austenite which plays key role in enhancing the cryogenic toughness of the steel had been researched by scholar^^^-^^. Heat treatment especially the quenching, lamellarizing and tempering (QLT) was studied in recent years and the QLT-processed 9Ni steel showed better cryogenic toughness and strength which meet the requirement of the steel working at or below 111 Kc'o-'zl. But for now only little research on the hot deformation of the 9Ni
steel has been made. T h e precision of mathematical model for hot deformation resistance needs to be further improved, thus, further research on hot deformation behavior of 9Ni steel is extremely urgent. In this paper, the effect of different deformation conditions on hot deformation resistance of 9Ni steel was studied via thermal simulation experiment. It is hoped that it could provide the actual production application of 9Ni steel with some references.
1
Materials and Experiment
T h e chemical composition of the steel used in this paper is showed in Table 1. According to the experimental requirement, the experimental materials were cut and machined into pieces of cylindrical specimens of 10 mmX 15 mm. T h e experimental equipment, Gleeble-3500 thermal simulation machine, is used in this paper. In order to describe a more accurate high temperature behavior of the steel, overall consideration should be given to interactions between deformation resistance and deformation parameters including deformation degree, temperature and rate etc. T h e simulation experiment was performed according to the process as shown in Fig. 1.
Fonndation Item: Item Sponsored by National Key Technology Research and Development Program in 11th Fiveyears Plan of China (2006BAEO3.406) Biography:ZHANG Kun(1982-),
Male, Doctor Candidate;
E-mail: wuhbanercar. ustb. edu. cn;
Reeeived Date: May 5 , 2011
Issue 5
High Temperature Deformation Behavior of FeSNi-C Alloy
Table 1 Chemical composition of test steel (mass percent,
%>
C
Si
Mn
Ni
Mo
P
S
0.036
0.10
0.70
9.02
0.096
0.0068
0.005
59
1-
300
'E
8 1M 4
I
/
6C/s\
Y W &=lo
Temperature
strain
0
I/
u's
\
Time
Fig. 1 Schematic diagram of hot deformation
The experimental specimens were heated up to 1200 "C at a rate of 10 C / s , holding 120 s, then cooled down to deformation temperatures at a rate of 5 C/s. In order to eliminate the temperature gradient, the specimens were kept at the temperature for 30 s before deformation. The specimens were then deformed at the temperatures of 1loo, 1050, 1000, 950, 900, 850, 800 and 750 'C , respectively. The reduction rate was 66. 7 % and the deformation rates were 0.1, 1.0, 5.0 and 10 s-l respectively. The specimens were air-cooled after deformation. In the deformation process, argon was used as protection gas to prevent oxidation of the specimen. At the same time, in order to keep the temperature uniformity during the heating and compression processes, and to reduce the friction between the specimens and the press head, tantalum sheets were affixed on the surfaces of the specimen contacting with press head, and lubricant was applied on the 2 ends of the specimen (the compositions of the lubricants by mass fraction are: 75% graphite+2O% No. 46 engine oil-l-5 % nitrate trimethylbenzene resin).
2
0.2
0.4
0.6
0.8
Deformation degree
s-1
1.0
Ng. 2 Relation of deformation degree and deformation resistance
plays a leading role in the deformation processC133. For example, when the deformation temperature is 750 'C , the deformation resistance mounted from 50 to 250 MPa, about 200 MPa addition formed in the range of deformation degree of 0 to 0.2. While deformation degree varies between 0. 2 and 0.4, the increase of deformation resistance value tends to slow down, and the dynamic recovery action is in30 to 40 MPa increase creased g r a d ~ a l l y ~ "nearly ~, in deformation resistance at overall temperatures. When the deformation degree is higher than 0.4, the deformation resistance value stable gradually because that the work-hardening and the dynamicsoftening reach a balance at this p ~ i n t ~ ~ ~ - ' ~ ] .
2 . 2 Effect of deformation temperature on deformation resistance As shown in Fig. 3 , the changing rule of the deformation resistance along with the deformation temperature under different deformation rates is given. It can be seen from Fig. 3 that under the same deformation rate and deformation degree, the deforma-
Results and Discussion
2.1 Effect of deformation degree on deformation resistance As shown in Fig. 2 , the effects of the deformation degree on the deformation resistance under different deformation temperatures and same deformation rates are studied. It can be seen that when the deformation degree is less than 0.2, the deformation resistance increased rapidly with the increase of deformation degree due to the work-hardening which
700 760
860
960
1060
Deformation temperature/9:
111
Fig. 3 Relation of deformation temperature and deformation resistance
Journal of Iron and Steel Research, International
60
tion resistance is apparently reduced along with the increasing of the deformation temperature. For example, when the deformation rate is 1 s-' , the deformation resistance value at 1100 'C is 85 MPa, on the other hand, under the same deformation rate, the deformation resistance value is increased to 250 MPa when the deformation temperature is reduced to 750 %. It is universally acknowledged that the deformation temperature is the most significant factor among all the facts affecting the deformation resistance valueCl7'. The reason why the deformation temperature influenced the deformation resistance so greatly, is that when the deformation temperature increases, the energy for thermal motion of the atoms is increased, which will generate new slip system and create conditions for simultaneous functioning of various plastic deformation mechanisms of different dispersion patterns, thus make the plastic deformation easier to achieve. Meanwhile, higher temperature facilitates easier development of the recovery and recrystallization process, and softening can be realized during the deformation. All above conditions will result in increase of the plasticity. Moreover, the rise of the temperature facilitates easier dislocation glide and climb, eliminates part of the dislocation pileup due to the deformation, and result in dynamic recovery under high temperature, abates the workhardening owing to the plastic deformation and thus reduced the deformation resistance.
2.3 Effect of deformation rate on deformation resistance The effect of the deformation rate on deformation resistance is indicated in Fig. 4. From the curves it can be seen that the deformation resistance is increased along with the increase of the deformation rate. As shown in Fig. 4, when the deformation rate 760 'c
800
850
900
960 loo0 1060 1 100
0
Fig. 4
2
6 8 strain W s - '
4
10
12
VOl. 19
varied from 0. 1 to 1 s-l, the deformation resistance increased rapidly, moreover, when the deformation rate is higher than 1 s-' , the deformation resistance inclined to mount slowly. It is noticeable that the deformation resistance at higher temperature is smaller than that of lower temperature under the same deformation rate and deformation degree. Take temperatures of 750 and 1100 'C for example, the deformation resistance is about 260 MPa at 750 'C under strain rate of 1 s-' , while the deformation resistance equals to about 100 MPa at 1100 'C as demonstrated in Fig. 4. When the metallic material is deformed at a relatively faster strain rate, the increase of deformation rate aggravates the work-hardening as the available time for dislocation to glide and climb which resulted in softening is limited. The effect of temperature on the deformation resistance had been discussed in Section 2. 2 , as higher temperature will facilitate the dislocation to move, eliminates part of dislocation pileup due to the deformation, and resulted in dynamic recovery under higher temperature, eases the work-hardening so as to reduce the deformation resistance.
2.4 Establishment of mathematical model for deformation resistance The deformation resistance value of the material plays a vital role in the safe operation of equipment and in choosing the right parameters during practical rolling. So, the study of rules of the deformation resistance has direction instruction function in determining rolling parameters in industrial production. In order to describe the effects of the deformation resistance in details, many studies about the mathematical models have been carried out by the researchers in the world. In order to establish a simple and practical mathematical model for the deformation resistance for 9Ni steel, some of the existing mathematical models for the deformation resistance are referred to. With reference to the regression analysis of those models and the analysis of residuals and correlation coefficients, it has been determined to use the following model in the study for the best matching effect. The mathematical model for the deformation re: sistance is shown in Eqn. (1)c'81
I
Relation of strain rate and deformation resistance
(1) where, t is deformation temperature, % ; T = ( t +
Issue 5
High Temperature Deformation Behavior of Fe-9Ni-C Alloy
273)/1000, K ; i is deformation rate, s - l ; uo is reference deformation resistance value, i. e. the deformation resistance value under the conditions of t = 1000 ' C , E=O. 4 and E=10 s-l, MPa; and al, - * , a6 are regression coefficients, the values are determined based on the steel grades. Based on the experimental data, various parameters in equation were regressed using the SPSS programmingC'gl. The results are shown in Table 2.
adopted due to various deformation temperatures, strain rates and strain degrees, relevant data was indicated in Table 3. The result of FO. 025 (6, 273)< FO. 025 (6, 120) = 2.52<22 273 was available looking up F distribution table, so the equation was highly significant at level of 0.025, and the value R is 0.991 5 , which verified that the regression equation fitted the curve very well. According to the regression theory, the forecast accuracy of the regression equation can be measured by residual standard deviation which is expressed in Eqn. (3).
Modulus table of deformation resistance
Table 2
,
m/MPa
a1
az
a3
ad
169
-2.129
2.721
0.271
-0.193
a5
a6
0.299
1.184
where, Q = sum of squares of residual deviations; and fQ=degree of freedom of sum of squares of residual deviations. to. 05, 273
The mathematical model for the deformation resistance is established as shown in Eqn. (2). u= 169 X exp( -2.129T-I-2.721) 0.299
[I. 1841 I
-0.184
I I
J
lie,
-
I
-
oe4I
0.271T-0.193
,
1
(2)
!
T h e F distribution function was employed for the regression significance test of the multi-variable nonlinear equation. All 279 experimental dots had been Table 3
61
Analysis table of regression model
Resource
Sum of square
Degree of freedom
Mean square deviation
Regression Residua1 Total
8 163 091.931 16 675.201 980 220.254
6 273 278
1 360 515
0.2
Fig. 5
0.4
0.6
0.8
1.0
931/6=22273 F = 8163091. 16 675.201/273
61.081
1.2
0.2
Deformationdegree
0.4
F distribution
0.6
0.8
1.0
Comparison of deformation resistance between calculation value and measured value with different strain rates
Journal of Iron and Steel R e search, International
62
lated values are similar to the experimental results. Therefore it can be said that the model has higher matching precision.
c41
3 Conclusions 1) When the deformation degree is less than 0.2, the deformation resistance increases rapidly with the increase of deformation degree with increase in range of 70 to 200 MPa; when the deformation degree reaches 0. 2 to 0.4, the deformation resistance increases slowly with increase of 30 to 40 MPa, when the deformation degree is larger than 0.4, the deformation resistance increased even slower and some becomes stable gradually. 2) T h e influence of deformation temperature on deformation resistance is large, deformation resistance at higher temperature is about 160 MPa smaller than at lower temperature at all strain rates in this paper. Meanwhile, at the same deformation temperature, the deformation resistance at strain rate of 10 s-l is 60 to 90 MPa higher than that at 0. 1 s-'. 3 1 T h e deformation resistance increases about 70 to 110 MPa with the increase of the strain rate, at the same strain rate, deformation resistance at higher temperature is about 160 MPa smaller than that at lower temperature. 4) T h e mathematical model of deformation resistance of Fe-9Ni-C alloy was established, a=169 X exp(-2.129T+2.721)
,
io,
0.271T-0.193
-
[1.184[
$1
0.299
-
[ of41
0. 184 - ] and the calculated values were compared
with the experimental values; from the result it is known that the calculated values match the experimental values very well, which demonstrates that the precision of this mathematical model is higher. References : [l]
[2]
[3]
WANG Xiu-li. The Stateof-theArt in Natural Gas Production [J]. Journal of Natural Gas Science and Engineering, 2009 ( 1) : 14. Mario Miana, Rafael del Hoyo, Vega Rodrigalvarez, et al. Calculation Models for Prediction of Liquefied Natural Gas (LNG) Ageing During Ship Transportation [J]. Applied Energy, 2010, 87: 1687. Nobuo Nakada, Junaidi Syarif, Toshihiro Tsuchigama, et al. Improvement of Strength-Ductility Balance by Copper Addition in 9%Ni Steel [J]. Materials and Science and Engineering,
Cgl
VOl. 19
2004, 374 A: 137. Zhang L , Takahito Ohmura, Akinobu Shibata. et al. Characterization of Local Deformation Behavior of F e N i Lenticular Martensite by Nanoindentation [J]. Materials Science and Engineering, 2010, 527A: 1869. Hiromoto Kitahara, Rintaro Ueji, Masato Ueda, et d Crystallographic Analysis of Plate Martensite in Fe28. 5at%Ni by FESEM/EBSD [J]. Materials Characterization, 2005, 54: 378. Hiromoto Kitahara, Rintaro Ueji, Nobuhiro Tsuji, et al. Crystallographic Features of Lath Martensite in Low-Carbon Steel [J]. Acta Materialia, 2006, 54: 1279. Danil'chenko V E , Sagaradze V V, I'Heritier Ph. Martensite Crystal Structure of Nickel Steel at Cryogenic Temperatures [J]. Materials Science and Engineering, 2003, 358A: 26. Emadoddin E, Akbarzadeh A , Daneshi Gh. Effect of Intercritical Annealing on Retained Austenite Characterization in Textured TRIP-Assisted Steel Sheet [J]. Materials Characterization, 2006, 57: 408. ZHAO X Q, Pan T, WANG Q F, et al. Effect of Intercritical Quenching on Reversed Austenite Formation and Cryogenic Toughness in QLT-Processed 9%Ni Steel [J]. Journal of Iron and Steel Research, International, 2007, 14(Supplement 1): 240. Lee C H , Lee S W , Yo0 J Y, et al. Enhancement of Low Temperature Toughness of Nickel Steel by Intercritical Quenching Treatment [C] [Proceedings of the Second Pacific Rim International Conference on Advanced Materials and Processing. Kyongju: [s. n. ], 1995: 2035. Ahn Yeon-Sang, Kim I-long-Deok, Byun Thak-Sang, et al. Application of Intercritical Heat Treatment to Improve Toughness of SA508C1. 3 Reactor Pressure Vessel Steel [J]. Nuclear Engineering and Design, 1999, 194: 161. ZHANG Chunling, CAI Dayong, LIAO Bo, et al. A Study on the Dual-Phase Treatment of Weathering Steel O9CuPCrNi [J]. Materials Letters, 2004, 58: 1524. YANG Jing-hong, LIU Qing-you, SUN Dong-hai, et al. R e crystallization Behavior of Deformed Austenite in High Strength Microalloyed Pipeline Steel [J]. J Iron Steel Res, Int, 2009, 16(1): 75. Sun Z Q, Yang W Y, Qi J J , et al. Deformation Enhanced Transformation and Dynamic Recrystallization of Ferrite in a Low Carbon Steel During Multipass Hot Deformation [J]. Mater Sci Eng, 2002, 334A: 201. Anbuselvan S, Ramanathan S. Hot Deformation and Processing Maps of Extruded ZE41A Magnesium Alloy [J]. Mater Des, 2010, 31: 2319. Eghbali B, Abdollan-zadeh A. The Influence of Thermome chanical Parameters in Ferrite Grain Refinement in a Low Carbon Nb-Microalloyed Steel [J]. Scripta Mater, 2005, 53: 41. Calvo J , Jung I H , Elwazri A M, et al. Influence of the Chemical Composition on Transformation Behavior of Low Carbon Microalloyed Steels [J]. Mater Sci Eng, 2009, 520A: 90. ZHOU Ji-hua , GUAN Kezhi. Plastic Deformation Resistance of Metal [MI. Beijing: Mechanic Industry Publishing Company, 1989 (in Chinese). CHEN Ping-yan. SPSS 13. 0 Statictical Software Application Tutorials [MI. Beijing: People's Medic Publishing House, 2005.
Y0ScienceDirect JOURNAL OF IRON AND SITEL RESEARCH, INTEFWYMONAL. 2012, 19(5): 58-62
High Temperature Deformation Behavior of Fe-9Ni-C Alloy ZHANG Kun,
W U Hui-bin,
TANG Di
(Engineering Research Institute, University of Science and Technology Beijing , Beijing 100083, China)
Abstract: The high temperature deformation behavior of the 9Ni steel has been studied by the Gleeble-3500 tester. The relationship between deformation resistance and deformation degree, deformation temperature and deformation rate was revealed. The results show that when the deformation degree is less than 0.2, the deformation resistance increases by about 70 to 200 MPa, while the deformation degree varied between 0. 2 and 0 . 4 , the deformation resistance increases by about 30-40 MPa, when the deformation degree is larger than 0.4, the deformation resistance increases slowly, some become stable gradually. The influence of deformation temperature on deformation resistance is larger, and deformation resistance at higher temperature is about 160 MPa smaller than at lower temperature. Higher deformation rate leads to larger deformation resistance. The deformation resistance increases about 70 to 110 MPa with the increase of the deformation rate. A new and highly accurate mathematical model of the steel was established to describe the deformation behavior during rolling. Key words: 9Ni steel; high temperature deformation resistance; mathematical model
Liquefied natural gas ( L N G ) is known as a clean energy source which is commonly used as domestic and industrial fuel for its abundance, versatility, and clean burning nature"]. It is reportedCz3 that the consumption will almost be double in size between 2005 and 2010, delivering around 40% of global gas supply growth. T h e LNG is a mixture composed mostly of methane and a small quantity of ethane propane, nitrogen and other minor components. Fe-9Ni-C alloy or 9Ni steel, simply referred to as 9Ni steel, is known as a cryogenic structural material applied for L N G t a n k e r and pipelineC3]. The microstructure of 9Ni steel is martensite along with a small quantity of retained austenite. The morphology and crystallography of martensite in F e N i alloy had been studiedc"-?]. T h e reversed austenite which plays key role in enhancing the cryogenic toughness of the steel had been researched by scholar^^^-^^. Heat treatment especially the quenching, lamellarizing and tempering (QLT) was studied in recent years and the QLT-processed 9Ni steel showed better cryogenic toughness and strength which meet the requirement of the steel working at or below 111 Kc'o-'zl. But for now only little research on the hot deformation of the 9Ni
steel has been made. T h e precision of mathematical model for hot deformation resistance needs to be further improved, thus, further research on hot deformation behavior of 9Ni steel is extremely urgent. In this paper, the effect of different deformation conditions on hot deformation resistance of 9Ni steel was studied via thermal simulation experiment. It is hoped that it could provide the actual production application of 9Ni steel with some references.
1
Materials and Experiment
T h e chemical composition of the steel used in this paper is showed in Table 1. According to the experimental requirement, the experimental materials were cut and machined into pieces of cylindrical specimens of 10 mmX 15 mm. T h e experimental equipment, Gleeble-3500 thermal simulation machine, is used in this paper. In order to describe a more accurate high temperature behavior of the steel, overall consideration should be given to interactions between deformation resistance and deformation parameters including deformation degree, temperature and rate etc. T h e simulation experiment was performed according to the process as shown in Fig. 1.
Fonndation Item: Item Sponsored by National Key Technology Research and Development Program in 11th Fiveyears Plan of China (2006BAEO3.406) Biography:ZHANG Kun(1982-),
Male, Doctor Candidate;
E-mail: wuhbanercar. ustb. edu. cn;
Reeeived Date: May 5 , 2011
Issue 5
High Temperature Deformation Behavior of FeSNi-C Alloy
Table 1 Chemical composition of test steel (mass percent,
%>
C
Si
Mn
Ni
Mo
P
S
0.036
0.10
0.70
9.02
0.096
0.0068
0.005
59
1-
300
'E
8 1M 4
I
/
6C/s\
Y W &=lo
Temperature
strain
0
I/
u's
\
Time
Fig. 1 Schematic diagram of hot deformation
The experimental specimens were heated up to 1200 "C at a rate of 10 C / s , holding 120 s, then cooled down to deformation temperatures at a rate of 5 C/s. In order to eliminate the temperature gradient, the specimens were kept at the temperature for 30 s before deformation. The specimens were then deformed at the temperatures of 1loo, 1050, 1000, 950, 900, 850, 800 and 750 'C , respectively. The reduction rate was 66. 7 % and the deformation rates were 0.1, 1.0, 5.0 and 10 s-l respectively. The specimens were air-cooled after deformation. In the deformation process, argon was used as protection gas to prevent oxidation of the specimen. At the same time, in order to keep the temperature uniformity during the heating and compression processes, and to reduce the friction between the specimens and the press head, tantalum sheets were affixed on the surfaces of the specimen contacting with press head, and lubricant was applied on the 2 ends of the specimen (the compositions of the lubricants by mass fraction are: 75% graphite+2O% No. 46 engine oil-l-5 % nitrate trimethylbenzene resin).
2
0.2
0.4
0.6
0.8
Deformation degree
s-1
1.0
Ng. 2 Relation of deformation degree and deformation resistance
plays a leading role in the deformation processC133. For example, when the deformation temperature is 750 'C , the deformation resistance mounted from 50 to 250 MPa, about 200 MPa addition formed in the range of deformation degree of 0 to 0.2. While deformation degree varies between 0. 2 and 0.4, the increase of deformation resistance value tends to slow down, and the dynamic recovery action is in30 to 40 MPa increase creased g r a d ~ a l l y ~ "nearly ~, in deformation resistance at overall temperatures. When the deformation degree is higher than 0.4, the deformation resistance value stable gradually because that the work-hardening and the dynamicsoftening reach a balance at this p ~ i n t ~ ~ ~ - ' ~ ] .
2 . 2 Effect of deformation temperature on deformation resistance As shown in Fig. 3 , the changing rule of the deformation resistance along with the deformation temperature under different deformation rates is given. It can be seen from Fig. 3 that under the same deformation rate and deformation degree, the deforma-
Results and Discussion
2.1 Effect of deformation degree on deformation resistance As shown in Fig. 2 , the effects of the deformation degree on the deformation resistance under different deformation temperatures and same deformation rates are studied. It can be seen that when the deformation degree is less than 0.2, the deformation resistance increased rapidly with the increase of deformation degree due to the work-hardening which
700 760
860
960
1060
Deformation temperature/9:
111
Fig. 3 Relation of deformation temperature and deformation resistance
Journal of Iron and Steel Research, International
60
tion resistance is apparently reduced along with the increasing of the deformation temperature. For example, when the deformation rate is 1 s-' , the deformation resistance value at 1100 'C is 85 MPa, on the other hand, under the same deformation rate, the deformation resistance value is increased to 250 MPa when the deformation temperature is reduced to 750 %. It is universally acknowledged that the deformation temperature is the most significant factor among all the facts affecting the deformation resistance valueCl7'. The reason why the deformation temperature influenced the deformation resistance so greatly, is that when the deformation temperature increases, the energy for thermal motion of the atoms is increased, which will generate new slip system and create conditions for simultaneous functioning of various plastic deformation mechanisms of different dispersion patterns, thus make the plastic deformation easier to achieve. Meanwhile, higher temperature facilitates easier development of the recovery and recrystallization process, and softening can be realized during the deformation. All above conditions will result in increase of the plasticity. Moreover, the rise of the temperature facilitates easier dislocation glide and climb, eliminates part of the dislocation pileup due to the deformation, and result in dynamic recovery under high temperature, abates the workhardening owing to the plastic deformation and thus reduced the deformation resistance.
2.3 Effect of deformation rate on deformation resistance The effect of the deformation rate on deformation resistance is indicated in Fig. 4. From the curves it can be seen that the deformation resistance is increased along with the increase of the deformation rate. As shown in Fig. 4, when the deformation rate 760 'c
800
850
900
960 loo0 1060 1 100
0
Fig. 4
2
6 8 strain W s - '
4
10
12
VOl. 19
varied from 0. 1 to 1 s-l, the deformation resistance increased rapidly, moreover, when the deformation rate is higher than 1 s-' , the deformation resistance inclined to mount slowly. It is noticeable that the deformation resistance at higher temperature is smaller than that of lower temperature under the same deformation rate and deformation degree. Take temperatures of 750 and 1100 'C for example, the deformation resistance is about 260 MPa at 750 'C under strain rate of 1 s-' , while the deformation resistance equals to about 100 MPa at 1100 'C as demonstrated in Fig. 4. When the metallic material is deformed at a relatively faster strain rate, the increase of deformation rate aggravates the work-hardening as the available time for dislocation to glide and climb which resulted in softening is limited. The effect of temperature on the deformation resistance had been discussed in Section 2. 2 , as higher temperature will facilitate the dislocation to move, eliminates part of dislocation pileup due to the deformation, and resulted in dynamic recovery under higher temperature, eases the work-hardening so as to reduce the deformation resistance.
2.4 Establishment of mathematical model for deformation resistance The deformation resistance value of the material plays a vital role in the safe operation of equipment and in choosing the right parameters during practical rolling. So, the study of rules of the deformation resistance has direction instruction function in determining rolling parameters in industrial production. In order to describe the effects of the deformation resistance in details, many studies about the mathematical models have been carried out by the researchers in the world. In order to establish a simple and practical mathematical model for the deformation resistance for 9Ni steel, some of the existing mathematical models for the deformation resistance are referred to. With reference to the regression analysis of those models and the analysis of residuals and correlation coefficients, it has been determined to use the following model in the study for the best matching effect. The mathematical model for the deformation re: sistance is shown in Eqn. (1)c'81
I
Relation of strain rate and deformation resistance
(1) where, t is deformation temperature, % ; T = ( t +
Issue 5
High Temperature Deformation Behavior of Fe-9Ni-C Alloy
273)/1000, K ; i is deformation rate, s - l ; uo is reference deformation resistance value, i. e. the deformation resistance value under the conditions of t = 1000 ' C , E=O. 4 and E=10 s-l, MPa; and al, - * , a6 are regression coefficients, the values are determined based on the steel grades. Based on the experimental data, various parameters in equation were regressed using the SPSS programmingC'gl. The results are shown in Table 2.
adopted due to various deformation temperatures, strain rates and strain degrees, relevant data was indicated in Table 3. The result of FO. 025 (6, 273)< FO. 025 (6, 120) = 2.52<22 273 was available looking up F distribution table, so the equation was highly significant at level of 0.025, and the value R is 0.991 5 , which verified that the regression equation fitted the curve very well. According to the regression theory, the forecast accuracy of the regression equation can be measured by residual standard deviation which is expressed in Eqn. (3).
Modulus table of deformation resistance
Table 2
,
m/MPa
a1
az
a3
ad
169
-2.129
2.721
0.271
-0.193
a5
a6
0.299
1.184
where, Q = sum of squares of residual deviations; and fQ=degree of freedom of sum of squares of residual deviations. to. 05, 273
The mathematical model for the deformation resistance is established as shown in Eqn. (2). u= 169 X exp( -2.129T-I-2.721) 0.299
[I. 1841 I
-0.184
I I
J
lie,
-
I
-
oe4I
0.271T-0.193
,
1
(2)
!
T h e F distribution function was employed for the regression significance test of the multi-variable nonlinear equation. All 279 experimental dots had been Table 3
61
Analysis table of regression model
Resource
Sum of square
Degree of freedom
Mean square deviation
Regression Residua1 Total
8 163 091.931 16 675.201 980 220.254
6 273 278
1 360 515
0.2
Fig. 5
0.4
0.6
0.8
1.0
931/6=22273 F = 8163091. 16 675.201/273
61.081
1.2
0.2
Deformationdegree
0.4
F distribution
0.6
0.8
1.0
Comparison of deformation resistance between calculation value and measured value with different strain rates
Journal of Iron and Steel R e search, International
62
lated values are similar to the experimental results. Therefore it can be said that the model has higher matching precision.
c41
3 Conclusions 1) When the deformation degree is less than 0.2, the deformation resistance increases rapidly with the increase of deformation degree with increase in range of 70 to 200 MPa; when the deformation degree reaches 0. 2 to 0.4, the deformation resistance increases slowly with increase of 30 to 40 MPa, when the deformation degree is larger than 0.4, the deformation resistance increased even slower and some becomes stable gradually. 2) T h e influence of deformation temperature on deformation resistance is large, deformation resistance at higher temperature is about 160 MPa smaller than at lower temperature at all strain rates in this paper. Meanwhile, at the same deformation temperature, the deformation resistance at strain rate of 10 s-l is 60 to 90 MPa higher than that at 0. 1 s-'. 3 1 T h e deformation resistance increases about 70 to 110 MPa with the increase of the strain rate, at the same strain rate, deformation resistance at higher temperature is about 160 MPa smaller than that at lower temperature. 4) T h e mathematical model of deformation resistance of Fe-9Ni-C alloy was established, a=169 X exp(-2.129T+2.721)
,
io,
0.271T-0.193
-
[1.184[
$1
0.299
-
[ of41
0. 184 - ] and the calculated values were compared
with the experimental values; from the result it is known that the calculated values match the experimental values very well, which demonstrates that the precision of this mathematical model is higher. References : [l]
[2]
[3]
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