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On the evaluation of yield strength for microalloyed steels
Scripta METALLURGICA et M A T E R I A L I A
Vol.
2~, pp. 1 3 9 3 - 1 3 9 8 , 1990 P r i n t e d in the U . S . A .
P e r g a m o n P r e s s plc All r i g h t s r e s e r v e d
ON T H E E V A L U A T I O N O F YIELD S T R E N G T H FOR MICROALLOYED STEELS
I2 Jian, Sun Fuyu and Xu WenChong Central Iron and Steel Research Institute Bcijing 100081, P. R. CHINA
( R e c e i v e d M a r c h 19, 1990) ( R e v i s e d M a y iS, 1990) Introduction
For a material in which more than one strengtheningmechanisms plays an important role,its yield strengthcannot been described purely by the Hall--Perch formula and the contributionsof various strengthening mechanisms to yield strength should be taken into account. So far, the effect of individualstrengthening mechanism, such as graln--boundary strengthening, precipitationstrengtheningand dislocationstrengthening, etc.can been quantitatively estimated, neverthelessexpressing the combined effectof differentstrengtheningmechanisms is %tElan unsolved problem. Originally, the llnear--additionmethod was proposed, i.e. ~z, ~ ~. + ~ . + ~, + u, + a., + k,d-~ + . - - , (1) where, c~T is yield strength, or. the Pierls--Nabarro(P--N) force, c1,. solid solution strengthening, as precipitation strengthening, ~ dislocation strengthening, ¢~,~ subgraln strengthening, d grain size and kT the Hall--Petch ceefficicnt. Unfortunately the calculated values of yield strength were usually overestimated [ 1 ] . A current estimation method, based on the works of Koppenaal and Kuhlmann--Wilsdorf [2,3"], suggested that # --- ( ~ + d)~, (2) where cry, and (~a are two different strengthening mebanLsms, cons/dering the root mean square summation as the combined effect a. Using this principle and taking the root mean square summation of dislocation strengthening and the linear sum of the other types of strengthening, Baker [1"] attainedhis satisfyingresults. Kocks et. al [ 4 ] analysed the additive problem of various strengthening effects and classified the obstacles inhibiting dLslocation movement as two kinds, i.e. "soft" obstacles, such as solute atoms, and "hard" obstacles such as forest dislocations and precipitate particles. They considered that a dislocation line becomes curved stightiy when it meets soft obstacles and the strengthening effect can be added to lattice force. However, a glide dislocation becomes marked curved when it meets bard obstacles due to the pinning effect and the resulting strengthening effects should be expressed by a root mean square summation rather than by l/near addition [ 5 ] . Although Kocks et al took account of the different effects of soft and bard obstacles, the interaction between "hard" strengthening was still uncons/dered, and it does exist. The root mean square summation method has no physical significance. In this paper, through analysing the actions of various strengthening mechanisms existing in microalloyed steels and taking account of the interaction between the hard obstacles strengthening, we established an equation of yield strength with obvious phsyical significance for m/croaUoyed steels.
1393 0036-9748/90 $ 3 . 0 0 + .00 Copyright (¢) 1990 P e r g a m o n P r e s s
pl¢
1394
MICROALLOYED
STEELS
Experimental Procedure
Vol.
24,
No.
F'B]
A N b - bearing mioroalloyed steel was prepared by induction melting with composition of F e - 0. I°~ C 0. 037°~Nb--I. 3 2 ° ~ M n - 0. 32~Si--0. 0 8 ~ N ( w t . ). The controlled rolling, controlledcooling and coiling techniques are listed in table I. Using a MTS810--13 machine, tensiletestswere carriedout to obtain yieldstrength. The volume fractionof Nb (C,N) precipitateswas detormined by Xu's method ['7"]and the sizeof precipitatedparticlesand ferritegrain size and pcarlltevolume fractionwere measured with a LEITZ--T. A.S. image analysisdevice. The dislocationdensity in fez'ritewas determined by E M - - 4 0 0 TEM. Subgrain size and texture coefficientwere measured by Philips A P D - - i 0 X - - R a y diffractometer.
Experimental Results
The measured yield strengthc77(mca.), the Nb (C,N) precipitatevolume fraction f, and mean size D, the dislocation density p, ferrite grain size d and peariite volume fraction F corresponding to different processes are listed in table 2. The final micrcatructure obtained is ferrite -}-pearHte. X - - R a y diffraction experiments revealed that almest no textures and nor subgrains, therefore they do not play an important role in strengthening. The contribution of them to yield s~rength may be negligible. These results are agreement with those of previous studies ['8,97.
Discussion
1 • Precipitation Strengthening ap The Ashby - - Orowan model is often used for catculaflng precipitation s~engthening in mlcroaDoyed steels. ~p is expressed as 4.8~b -x/~. / ~ \ = 2 where, p is the shear modulus, b the Burgers vestor, f. the precipitate volume fraction, X the mean diameter of the precipitates on slip plane. According to the Fullman equation [i0], x
Taking ~ = 8 .
3 X 104 N / r a m : , b e 2 .
48 X 10"Tram, the calculated ap for various approaches are Listed in
table 3. 2. Dislocation Strengthening ad The results of a previous study [ 11 ] indicated that ~, = a ~ , (4) where, a is a dimensionle~ coefficient with a value of 0. 38, and p is dislocation density. The dislocation strengthening calculated by Eqn. (4) are listed in table 3.
3. G r a i n - - ~ u n d a r y Strengthening aom Based on the Hall--Peteh relation, grain--t~undary strengthening can be written as cr,j •= k J ~ ,
(5)
7
Vol.
24,
No.
7
MICROALLOYED
STEELS
1395
Usually k T is measured by experiments. Taking k,----18. 5 E5~ here, the values of cob from F_.qn. (5) arc also listed in table 3. 4. Solid Solution Strengthening e= Solid solution strengthening results from a complicated interaction between solute atoms and dislocations, which includes electrical interaction) elastic interaction, stacking fault interaction and s h o r t - - r a n g e order interaction and so on. In actual calculation, a n empirical formula is often used for solutes of Mn and SiE9~.
o-. ---- 32. 5 X ~ M ,
Jr- 84 X ~,S'i(wt. ).
(6)
The calculated c~=s are listed in table 3. S. Lattice force c% Lattice force 00, ( P - - N f o r c e ) , is in the range of 2 5 - - 7 1 N/mm2['12"~ for l o w - - a l l o y steels. In the present s t u d y , the average value of 48 N / m m - ' [ ' 1 , 5 7 was used. 6. Peaxlite Strengthening G l a d m a n et al ['13] suggested that the yield strength of microalloyed high strength steel is dominated by the ferrite matrix and the existence of a small a m o u n t of pearlite ( ~ 20°/~) has little effect. In contrast, P r e s t o n ' s research ['14"] indicated that the existence of pcarlite on ferrite grain boundary led to an increment of k r in the H a U - Perch formula, k T increases by up to 11 ~ accompanying pearlite from 0 ~ 3 0 ~ . In the present investigation, the a m o u n t s of pearllte are in the range of 1 2 ~ 1 8 ° / ~ , and the m e a n deviation ofk~ is only about 5. 5°/~, which is within the range of measured ky d a t u m , therefore pearlite strengthening is not taken into account here. 7. Complex Strengthening Little evidence exists which suggests that solid solution strengthening and precipitation strengthening should be additive. Solutes which have a substantial effect on the matrix deformation character can affect the stresses at which the precipitates become shearable. T h u s , the matrix slip character m a y significantly change the m e c h a n i s m of particle hardening. In such cases, the contributions of precipitate and solute strengthening are not likely to be strictly additive. T h u s , additional considerations must be invoked to account for the effect of solutes on v a r y i n g the nature of the dislocation--particle interaction. However in thcso cases where the solute concentration is relatively low, i . e . if the matrix deformation character does not change appreciably, the additivity of these two strengthening mechanisms appears to be simply linear [ 1 5 ] . The relation between solute strengthening and dislocation strengtherring can be considered similaxly. In the material studied here, Mn and Si contents arc s m a U , so c~= should be add to c~, linearly. There are no detailed analyses of the interaction between precipitation strengthening a n d dislocation strengthening. However, small s e c o n d - - p h a s e particles which produce strengthening must affect the distribution and movement Of dislocations as well as the deformation character of the matrix. In this case, the principal variables in dislocation strengthening, such as dislocation density and the average mean free path, would be changed. As a result, the dislocation strengthening is varied. On the other hand, precipitation strengthening is derived corresponding to a certain dislocation structure. Inversely, the change of dislocation structure would lead to the change of precipitation strengthening. So one can find that dislocation strengthening and precipitation strengthening are interrelated and interact on each other and the strengthening from them is no longer linearly additive. This problem is unsolved and is clearly worthy of further considerationr'15~. In microalloyed steels, where there is a great amount of precipitated particles, the interaction between precipitation strengthening a n d dislocation strengthening must be taken into account. The contribution of the two types of strengthening to yield strength m a y be the result of the interaction. Obviously, the geometrical mean value (apad)~ is the simplest f o r m representing the interaction with no change of individual effect. Consequently, we conclude that a formula for yield strength of microalloyed steels as
(7)
1396
MICROALLOYED
STEELS
Vol.
24,
No.
7
is reasonable and acceptable under the condition of neglecting the effects of subgrain, texture and peartite. The calculated values of yield strength from Eqn. (7) o,(cal. ) are also listedin table 3. It can be seen that there is a good agreement between o,(mea. ) and o,(cal. ). Of course, dislocationstrengthening may be present individually in a system without precipitates.
Conclusions
In estimating yield strength estimation, various strengthening mechanisms arc not likely to be strictly additive lincaxly or by means of root mean square summation. Interactions among them must be concerned, especially between dislocation strengthening and precipitation strengthening. In common miczoalloycd steels, P - - N force, solid solution strengthening and grain--boundary strengthening can be added linearly, however, the contributions of precipitation strengthening and dlsiocafion strengthening to yield strength should not be introduced into the summation J.inea~ly. A formula for the evaluation of yield strength of microaUoyed steels can be expressed as without consideration of subgrain ) texture and pearlit¢ strengthening.
References
1.
T.N.
2. 3. 4. 5. 6. 7. 8. 9.
and New York, (1983), p. 235. T. 2. KoPl~naal, 3. Appl. Phys., 35(1964), 2750. T. J. Koppcnaal, D. Kuhlmann--Wilsdorf, Appl. Phys. Lott. ) 4(1964),59. U . F . Kocks, Strength of Memb and Alloys, Vol. 3(1979), p. 1661. Sun Fuyu, Xu Wenchong, Acta Met. S|nica, 22B(1986), B23. Li 3lan, Ph. D Thes£s, Central Iron and Steel Rcasurch Inst. , Beijing, (1988). Xu Wenchong, Ma Xiang and Sun Fuyu, Iron and Steel, 20(1985), 3.34. T. Tanaka, Microalloying'75, Ed. M. Korchynsky, Union Carbide Corp. , New York, (1977), p. 195. F . B . Picketing, T. Oladman, MetaLlurgical Developments in Carbon Steel, ISI, Harrogate, (1963), p.
10. 11. 12. 13. 14. 15.
Baker, Yield, Flow and Fracture Polycrystais, Ed. T. N. Baker, Applied Science Pub. , London
10. R. L. FuUman, Trans. AIME, 197(1953), 447. A. S. Keh, Phil. Mag. , 121(1965), 97. K. Torroncn, H. Kotilainen and P. Nenonen, ibid. 4, Vet. 2(1979), p. 1437. T. Gladman, F. B. Picketing, ibid. 1, p. 141. R. R. Preston, ibid. 1, p. 199. 3. C. Williams, A. W. Thompson, Metallurgical Treatises, USA--China Bilateral Cor~erence, Eds. 2. K. Tien, 3. F. Elliott, Nov. 1 3 ~ 2 2 , (1981), Beijing, p. 487.
Vol.
2~,
No.
7
MICROALLOYED
STEELS
1397
1
TABLE
Processes of Controlled Roiling, Controlled Cooling and Coiling
Conditions
T e c h n ic a l NO.
Reheadng
Holding
Temp. ,X[~
2 3
•
Fin is h in g
TL'ne,min Temp.,'C
1200
I
Stzu~ Rolling
Cooling
Coiling
T o ta l
Temp.,I[~
Rate,'C/s
Temp,~
Red. ,~ 76.7~
60
1150
800
8
650
•
•
840
•
,
,
•
•
880
,
•
,
4
•
•
•
920
•
-
.
5
.
•
•
840
A ir Cooling
•
•
6
•
•
•
•
14
,
•
7
•
•
•
•
20
•
•
26
8
750
9 I0
•
•
•
•
•
700
•
11
•
•
•
•
•
600
•
12
•
•
•
•
•
550
.
TABLE Experimental
NO, f..%
1
2
3
4
S
2. Results
6
7
8
9
i0
11
12
0.037 0.036 0.033 0.029 0.042 0.037 0.037i0.036 0.040 0.037 0.031 0.024
D,X
100
179
218
236
220
103
87
68
227
205
91
,SO
p,cm-=X i0'
5.83
12.6
4.45
7.59
--
8. 35
5.96
6.72
7.80
9.43
8. 2,1
1.89
d,~m
7. 49
7.97
7. 59
9.60
7. 50
8. 12
8.10
7. 62
8. 43
7.42
7. 17
6.37
F,M
15.89 14.88 15. 12 12. 56 16.94 16.36 14.86 17, 83 15.46 15. 13 12.17 13.55
a,(mea. )N/ram'
398
393
382
378
381
393
388
378
363
386
416
434
1398
MICROALLOYED
STEELS
Vol.
24, No. 7
TABLE 3. Yield S~ength Evaluation NO.
~,(m~. )
~.
~=
~
~
kA-~
~,(cal. )
1
398
48
70
49
60
215
387
11
2
393
•
•
33
88
208
380
13
3
382
•
•
27
52
231
368
14
4
378
•
•
24
68
190
348
30
5
381
•
•
32
~
215
--
--
6
393
m
m
49
71
206
383
I0
7
388
s
n
54
60
207
382
6
8
3?8
n
n
62
64
213
394
--15
9
363
•
n
29
69
202
365
--2
10
386
n
•
31
76
216
382
4
11
416
m
s
48
71
220
396
20
12
434
#
n
60
108
233
431
3
note: 1) 2)
unit in N/ram2 ~----~,(mea. )--~,(c~l. )
Vol.
2~, pp. 1 3 9 3 - 1 3 9 8 , 1990 P r i n t e d in the U . S . A .
P e r g a m o n P r e s s plc All r i g h t s r e s e r v e d
ON T H E E V A L U A T I O N O F YIELD S T R E N G T H FOR MICROALLOYED STEELS
I2 Jian, Sun Fuyu and Xu WenChong Central Iron and Steel Research Institute Bcijing 100081, P. R. CHINA
( R e c e i v e d M a r c h 19, 1990) ( R e v i s e d M a y iS, 1990) Introduction
For a material in which more than one strengtheningmechanisms plays an important role,its yield strengthcannot been described purely by the Hall--Perch formula and the contributionsof various strengthening mechanisms to yield strength should be taken into account. So far, the effect of individualstrengthening mechanism, such as graln--boundary strengthening, precipitationstrengtheningand dislocationstrengthening, etc.can been quantitatively estimated, neverthelessexpressing the combined effectof differentstrengtheningmechanisms is %tElan unsolved problem. Originally, the llnear--additionmethod was proposed, i.e. ~z, ~ ~. + ~ . + ~, + u, + a., + k,d-~ + . - - , (1) where, c~T is yield strength, or. the Pierls--Nabarro(P--N) force, c1,. solid solution strengthening, as precipitation strengthening, ~ dislocation strengthening, ¢~,~ subgraln strengthening, d grain size and kT the Hall--Petch ceefficicnt. Unfortunately the calculated values of yield strength were usually overestimated [ 1 ] . A current estimation method, based on the works of Koppenaal and Kuhlmann--Wilsdorf [2,3"], suggested that # --- ( ~ + d)~, (2) where cry, and (~a are two different strengthening mebanLsms, cons/dering the root mean square summation as the combined effect a. Using this principle and taking the root mean square summation of dislocation strengthening and the linear sum of the other types of strengthening, Baker [1"] attainedhis satisfyingresults. Kocks et. al [ 4 ] analysed the additive problem of various strengthening effects and classified the obstacles inhibiting dLslocation movement as two kinds, i.e. "soft" obstacles, such as solute atoms, and "hard" obstacles such as forest dislocations and precipitate particles. They considered that a dislocation line becomes curved stightiy when it meets soft obstacles and the strengthening effect can be added to lattice force. However, a glide dislocation becomes marked curved when it meets bard obstacles due to the pinning effect and the resulting strengthening effects should be expressed by a root mean square summation rather than by l/near addition [ 5 ] . Although Kocks et al took account of the different effects of soft and bard obstacles, the interaction between "hard" strengthening was still uncons/dered, and it does exist. The root mean square summation method has no physical significance. In this paper, through analysing the actions of various strengthening mechanisms existing in microalloyed steels and taking account of the interaction between the hard obstacles strengthening, we established an equation of yield strength with obvious phsyical significance for m/croaUoyed steels.
1393 0036-9748/90 $ 3 . 0 0 + .00 Copyright (¢) 1990 P e r g a m o n P r e s s
pl¢
1394
MICROALLOYED
STEELS
Experimental Procedure
Vol.
24,
No.
F'B]
A N b - bearing mioroalloyed steel was prepared by induction melting with composition of F e - 0. I°~ C 0. 037°~Nb--I. 3 2 ° ~ M n - 0. 32~Si--0. 0 8 ~ N ( w t . ). The controlled rolling, controlledcooling and coiling techniques are listed in table I. Using a MTS810--13 machine, tensiletestswere carriedout to obtain yieldstrength. The volume fractionof Nb (C,N) precipitateswas detormined by Xu's method ['7"]and the sizeof precipitatedparticlesand ferritegrain size and pcarlltevolume fractionwere measured with a LEITZ--T. A.S. image analysisdevice. The dislocationdensity in fez'ritewas determined by E M - - 4 0 0 TEM. Subgrain size and texture coefficientwere measured by Philips A P D - - i 0 X - - R a y diffractometer.
Experimental Results
The measured yield strengthc77(mca.), the Nb (C,N) precipitatevolume fraction f, and mean size D, the dislocation density p, ferrite grain size d and peariite volume fraction F corresponding to different processes are listed in table 2. The final micrcatructure obtained is ferrite -}-pearHte. X - - R a y diffraction experiments revealed that almest no textures and nor subgrains, therefore they do not play an important role in strengthening. The contribution of them to yield s~rength may be negligible. These results are agreement with those of previous studies ['8,97.
Discussion
1 • Precipitation Strengthening ap The Ashby - - Orowan model is often used for catculaflng precipitation s~engthening in mlcroaDoyed steels. ~p is expressed as 4.8~b -x/~. / ~ \ = 2 where, p is the shear modulus, b the Burgers vestor, f. the precipitate volume fraction, X the mean diameter of the precipitates on slip plane. According to the Fullman equation [i0], x
Taking ~ = 8 .
3 X 104 N / r a m : , b e 2 .
48 X 10"Tram, the calculated ap for various approaches are Listed in
table 3. 2. Dislocation Strengthening ad The results of a previous study [ 11 ] indicated that ~, = a ~ , (4) where, a is a dimensionle~ coefficient with a value of 0. 38, and p is dislocation density. The dislocation strengthening calculated by Eqn. (4) are listed in table 3.
3. G r a i n - - ~ u n d a r y Strengthening aom Based on the Hall--Peteh relation, grain--t~undary strengthening can be written as cr,j •= k J ~ ,
(5)
7
Vol.
24,
No.
7
MICROALLOYED
STEELS
1395
Usually k T is measured by experiments. Taking k,----18. 5 E5~ here, the values of cob from F_.qn. (5) arc also listed in table 3. 4. Solid Solution Strengthening e= Solid solution strengthening results from a complicated interaction between solute atoms and dislocations, which includes electrical interaction) elastic interaction, stacking fault interaction and s h o r t - - r a n g e order interaction and so on. In actual calculation, a n empirical formula is often used for solutes of Mn and SiE9~.
o-. ---- 32. 5 X ~ M ,
Jr- 84 X ~,S'i(wt. ).
(6)
The calculated c~=s are listed in table 3. S. Lattice force c% Lattice force 00, ( P - - N f o r c e ) , is in the range of 2 5 - - 7 1 N/mm2['12"~ for l o w - - a l l o y steels. In the present s t u d y , the average value of 48 N / m m - ' [ ' 1 , 5 7 was used. 6. Peaxlite Strengthening G l a d m a n et al ['13] suggested that the yield strength of microalloyed high strength steel is dominated by the ferrite matrix and the existence of a small a m o u n t of pearlite ( ~ 20°/~) has little effect. In contrast, P r e s t o n ' s research ['14"] indicated that the existence of pcarlite on ferrite grain boundary led to an increment of k r in the H a U - Perch formula, k T increases by up to 11 ~ accompanying pearlite from 0 ~ 3 0 ~ . In the present investigation, the a m o u n t s of pearllte are in the range of 1 2 ~ 1 8 ° / ~ , and the m e a n deviation ofk~ is only about 5. 5°/~, which is within the range of measured ky d a t u m , therefore pearlite strengthening is not taken into account here. 7. Complex Strengthening Little evidence exists which suggests that solid solution strengthening and precipitation strengthening should be additive. Solutes which have a substantial effect on the matrix deformation character can affect the stresses at which the precipitates become shearable. T h u s , the matrix slip character m a y significantly change the m e c h a n i s m of particle hardening. In such cases, the contributions of precipitate and solute strengthening are not likely to be strictly additive. T h u s , additional considerations must be invoked to account for the effect of solutes on v a r y i n g the nature of the dislocation--particle interaction. However in thcso cases where the solute concentration is relatively low, i . e . if the matrix deformation character does not change appreciably, the additivity of these two strengthening mechanisms appears to be simply linear [ 1 5 ] . The relation between solute strengthening and dislocation strengtherring can be considered similaxly. In the material studied here, Mn and Si contents arc s m a U , so c~= should be add to c~, linearly. There are no detailed analyses of the interaction between precipitation strengthening a n d dislocation strengthening. However, small s e c o n d - - p h a s e particles which produce strengthening must affect the distribution and movement Of dislocations as well as the deformation character of the matrix. In this case, the principal variables in dislocation strengthening, such as dislocation density and the average mean free path, would be changed. As a result, the dislocation strengthening is varied. On the other hand, precipitation strengthening is derived corresponding to a certain dislocation structure. Inversely, the change of dislocation structure would lead to the change of precipitation strengthening. So one can find that dislocation strengthening and precipitation strengthening are interrelated and interact on each other and the strengthening from them is no longer linearly additive. This problem is unsolved and is clearly worthy of further considerationr'15~. In microalloyed steels, where there is a great amount of precipitated particles, the interaction between precipitation strengthening a n d dislocation strengthening must be taken into account. The contribution of the two types of strengthening to yield strength m a y be the result of the interaction. Obviously, the geometrical mean value (apad)~ is the simplest f o r m representing the interaction with no change of individual effect. Consequently, we conclude that a formula for yield strength of microalloyed steels as
(7)
1396
MICROALLOYED
STEELS
Vol.
24,
No.
7
is reasonable and acceptable under the condition of neglecting the effects of subgrain, texture and peartite. The calculated values of yield strength from Eqn. (7) o,(cal. ) are also listedin table 3. It can be seen that there is a good agreement between o,(mea. ) and o,(cal. ). Of course, dislocationstrengthening may be present individually in a system without precipitates.
Conclusions
In estimating yield strength estimation, various strengthening mechanisms arc not likely to be strictly additive lincaxly or by means of root mean square summation. Interactions among them must be concerned, especially between dislocation strengthening and precipitation strengthening. In common miczoalloycd steels, P - - N force, solid solution strengthening and grain--boundary strengthening can be added linearly, however, the contributions of precipitation strengthening and dlsiocafion strengthening to yield strength should not be introduced into the summation J.inea~ly. A formula for the evaluation of yield strength of microaUoyed steels can be expressed as without consideration of subgrain ) texture and pearlit¢ strengthening.
References
1.
T.N.
2. 3. 4. 5. 6. 7. 8. 9.
and New York, (1983), p. 235. T. 2. KoPl~naal, 3. Appl. Phys., 35(1964), 2750. T. J. Koppcnaal, D. Kuhlmann--Wilsdorf, Appl. Phys. Lott. ) 4(1964),59. U . F . Kocks, Strength of Memb and Alloys, Vol. 3(1979), p. 1661. Sun Fuyu, Xu Wenchong, Acta Met. S|nica, 22B(1986), B23. Li 3lan, Ph. D Thes£s, Central Iron and Steel Rcasurch Inst. , Beijing, (1988). Xu Wenchong, Ma Xiang and Sun Fuyu, Iron and Steel, 20(1985), 3.34. T. Tanaka, Microalloying'75, Ed. M. Korchynsky, Union Carbide Corp. , New York, (1977), p. 195. F . B . Picketing, T. Oladman, MetaLlurgical Developments in Carbon Steel, ISI, Harrogate, (1963), p.
10. 11. 12. 13. 14. 15.
Baker, Yield, Flow and Fracture Polycrystais, Ed. T. N. Baker, Applied Science Pub. , London
10. R. L. FuUman, Trans. AIME, 197(1953), 447. A. S. Keh, Phil. Mag. , 121(1965), 97. K. Torroncn, H. Kotilainen and P. Nenonen, ibid. 4, Vet. 2(1979), p. 1437. T. Gladman, F. B. Picketing, ibid. 1, p. 141. R. R. Preston, ibid. 1, p. 199. 3. C. Williams, A. W. Thompson, Metallurgical Treatises, USA--China Bilateral Cor~erence, Eds. 2. K. Tien, 3. F. Elliott, Nov. 1 3 ~ 2 2 , (1981), Beijing, p. 487.
Vol.
2~,
No.
7
MICROALLOYED
STEELS
1397
1
TABLE
Processes of Controlled Roiling, Controlled Cooling and Coiling
Conditions
T e c h n ic a l NO.
Reheadng
Holding
Temp. ,X[~
2 3
•
Fin is h in g
TL'ne,min Temp.,'C
1200
I
Stzu~ Rolling
Cooling
Coiling
T o ta l
Temp.,I[~
Rate,'C/s
Temp,~
Red. ,~ 76.7~
60
1150
800
8
650
•
•
840
•
,
,
•
•
880
,
•
,
4
•
•
•
920
•
-
.
5
.
•
•
840
A ir Cooling
•
•
6
•
•
•
•
14
,
•
7
•
•
•
•
20
•
•
26
8
750
9 I0
•
•
•
•
•
700
•
11
•
•
•
•
•
600
•
12
•
•
•
•
•
550
.
TABLE Experimental
NO, f..%
1
2
3
4
S
2. Results
6
7
8
9
i0
11
12
0.037 0.036 0.033 0.029 0.042 0.037 0.037i0.036 0.040 0.037 0.031 0.024
D,X
100
179
218
236
220
103
87
68
227
205
91
,SO
p,cm-=X i0'
5.83
12.6
4.45
7.59
--
8. 35
5.96
6.72
7.80
9.43
8. 2,1
1.89
d,~m
7. 49
7.97
7. 59
9.60
7. 50
8. 12
8.10
7. 62
8. 43
7.42
7. 17
6.37
F,M
15.89 14.88 15. 12 12. 56 16.94 16.36 14.86 17, 83 15.46 15. 13 12.17 13.55
a,(mea. )N/ram'
398
393
382
378
381
393
388
378
363
386
416
434
1398
MICROALLOYED
STEELS
Vol.
24, No. 7
TABLE 3. Yield S~ength Evaluation NO.
~,(m~. )
~.
~=
~
~
kA-~
~,(cal. )
1
398
48
70
49
60
215
387
11
2
393
•
•
33
88
208
380
13
3
382
•
•
27
52
231
368
14
4
378
•
•
24
68
190
348
30
5
381
•
•
32
~
215
--
--
6
393
m
m
49
71
206
383
I0
7
388
s
n
54
60
207
382
6
8
3?8
n
n
62
64
213
394
--15
9
363
•
n
29
69
202
365
--2
10
386
n
•
31
76
216
382
4
11
416
m
s
48
71
220
396
20
12
434
#
n
60
108
233
431
3
note: 1) 2)
unit in N/ram2 ~----~,(mea. )--~,(c~l. )