Abstract

This paper is devoted to theoretical analysis of the critical cooling rate necessary to suppress the diffusional transformation of austenite. The transition from isothermal conditions to continuous cooling conditions was accomplished in two ways: by means of the traditional integral of Scheil and Steinberg (often called the additivity rule), and via direct integration of the Avrami equation. The resulting equations for both the cooling rate and a coefficient in Grange and Kiefer’s formula are presented. It was found that the theoretical value of the Grange–Kiefer coefficient almost never reached the value of 1.5 that they proposed. A method for determining the parameters in kinetic equations describing isothermal and continuous cooling transformations from an experimental time-temperature transformation diagram is also outlined.

Issue Section:
Research Papers
Keywords:
austenite transformation, continuous cooling transformation, TTT diagram, Grange–Kiefer formula, Scheil–Steinberg integral, Avrami equation, critical cooling rate

References

1.
ASM International
,
ASM Handbook Volume 4: Heat Treating
,
ASM International
,
Materials Park, OH
,
1991
.
2.
Totten
,
G. E.
,
Steel Heat Treatment: Metallurgy and Technologies
,
Taylor and Francis
,
London
,
2007
.
3.
Blanter
,
M. E.
,
Theory of Heat Treatment
,
Metallurgiya
,
Moscow
,
1984
(in Russian).
4.
Smirnov
,
M. A.
,
Schastlivtsev
,
V. M.
, and
Zhuravlev
,
L. G.
,
Fundamentals of Heat Treatment of Steel
,
Ural Branch of RAS
,
Ekaterinburg
,
1999
; Nauka i Tekhnologii, Moscow,
2002
(in Russian).
5.
Christian
,
J. W.
,
The Theory of Transformations in Metals and Alloys
,
Elsevier Science
,
New York, Amsterdam
,
2002
.
6.
Scheil
,
E.
, “
Anlaufzeit der Austenitumwandlung [Start Time of Austenite Transformation]
,”
Arch. Eisenhüttenwes.
, Vol.
8
, No.
12
, 1934/1935, pp.
565
–
567
.
Crossref
Search ADS
 
7.
Steinberg
,
S. S.
, “
On the Relation between Cooling Rate, Transformation Rate, Degree of Supercooling and Critical Rate of Quenching
,”
Metallurg
, No.
1
,
1938
, pp.
7
–
12
(in Russian).
8.
Mirzaev
,
D. A.
,
Okishev
,
K. Yu.
,
Schastlivtsev
,
V. M.
,
Mirzoev
,
A. A.
,
Yakovleva
,
I. L.
, and
Karzunov
,
S. E.
, “
Kinetics of Ferrite Formation from Austenite in Fe–9%Cr Alloys with Various Concentrations of Interstitial Impurities
,”
Phys. Met. Metallogr.
, Vol.
86
, No.
6
,
1998
, pp.
590
–
600
.
9.
Lyubov
,
B. Ya.
,
Kinetic Theory of Phase Transformations
,
Metallurgiya
,
Moscow
,
1969
(in Russian).
10.
Kurdyumov
,
G. V.
,
Utevskii
,
L. M.
, and
Entin
,
R. I.
,
Transformations in Iron and Steel
,
Nauka
,
Moscow
,
1977
(in Russian).
11.
Grange
,
R. A.
 and
Kiefer
,
J. M.
, “
Transformation of Austenite on Continuous Cooling and Its Relation to Transformation at Constant Temperature
,”
Trans. Am. Soc. Met.
, Vol.
29
, No.
1
,
1941
, pp.
85
–
114
.
12.
Mirzaev
,
D. A.
,
Karzunov
,
S. E.
,
Schastlivtsev
,
V. M.
,
Yakovleva
,
I. L.
, and
Kharitonova
,
E. V.
, “
The Gamma → Alpha Transformation in Low-Carbon Fe-Cr Alloys
,”
Phys. Met. Metallogr.
, Vol.
61
,
1986
, p. 114.
13.
Prudnikov
,
A. P.
,
Brychkov
,
Yu. A.
, and
Marichev
,
O. I.
,
Integrals and Series. Elementary Functions
,
Nauka
,
Moscow
,
1981
(in Russian).
14.
Jahnke
,
E.
,
Emde
,
F.
, and
Lösch
,
F.
,
Tafeln höherer Funktionen [Tables of Higher Functions]
,
B.G. Teubner Verlagsgesellschaft
,
Stuttgart, Germany
,
1960
.
15.
Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables
,
M.
 
Abramowitz
 and
I. A.
 
Stegun
, Eds.,
National Bureau of Standards
,
1964
.
16.
Umemoto
,
M.
,
Nishioka
,
N.
, and
Tamura
,
I.
, “
Prediction of Hardenability from Isothermal Transformation Diagrams
,”
Trans. Iron Steel Inst. Jpn.
, Vol.
22
, No.
8
,
1982
, pp.
629
–
636
. https://doi.org/10.2355/isijinternational1966.22.629
Google Scholar
Crossref
Search ADS
 
17.
Zener
,
C.
, “
Kinetics of the Decomposition of Austenite
,”
Trans. AIME
, Vol.
167
,
1946
, pp.
550
–
583
.
18.
Hillert
,
M.
, “
Solid State Phase Transformations
,”
Jernkontorets Ann.
, Vol.
141
, No.
11
,
1957
, pp.
757
–
790
.
19.
Hillert
,
M.
, “
The Role of Interfaces in Phase Transformations
,”
The Mechanism of Phase Transformations in Crystalline Solids
,
The Institute of Metals
,
London
,
1969
, pp.
231
–
247
.
20.
Whiting
,
M. J.
, “
A Reappraisal of Kinetic Data for the Growth of Pearlite in High Purity Fe–C Eutectoid Alloys
,”
Scr. Mater.
, Vol.
47
, No.
11
,
2000
, pp.
969
–
975
. https://doi.org/10.1016/S1359-6462(00)00464-4
Google Scholar
Crossref
Search ADS
 
21.
Umemoto
,
M.
,
Komatsubara
,
N.
, and
Tamura
,
I.
, “
Effect of Austenite Grain Size on the Hardenability of Eutectoid Steel
,”
J. Iron Steel Inst. Jpn.
, Vol.
66
, No.
3
,
1980
, pp.
400
–
409
.
Google Scholar
Crossref
Search ADS
 
22.
Popova
,
L. E.
 and
Popov
,
A. A.
,
Diagrams of Transformation of Austenite in Steels and Beta Solution in Titanium Alloys
,
Metallurgiya
,
Moscow
,
1991
(in Russian).
23.
Mirkin
,
I. L.
, “
Study of Eutectoid Crystallization of Steel
,”
Structure and Properties of Steels and Alloys: 18th Collected Papers of Moscow Institute of Steel
,
Oborongiz
,
Moscow
,
1941
, pp. 5–158 (in Russian).
24.
Russev
,
K.
,
Budurov
,
S.
,
Danailov
,
D.
, and
Lazarowa
,
T.
, “
Über die Kinetik der perlitischen Umwandlung eines eutektoiden Stahles bei kontinuierlicher Abkühlung [On the Kinetics of Pearlite Transformation of a Eutectoid Steel on Continuous Cooling]
,”
Z. Metallkd.
, Vol.
65
, No.
11
,
1974
, pp.
686
–
691
.
25.
Wever
,
F.
,
Rose
,
A.
,
Peter
,
W.
,
Strassburg
,
W.
, and
Rademacher
,
L.
,
Atlas zur Wärmebehandlung der Stähle [Atlas for Heat Treatment of Steels]
,
Verlag Stahleisen m.b.H.
,
Düsseldorf, Germany
,
1961
(in German).
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