Abstract

Quenching is an important part of the production chain of steel components. The final properties of the product are largely determined during this stage, and this renders quenching as one of the most critical stages of production, requiring design and optimization specific to the product. The simulation of quenching requires the solution of a multi-scale/multi-physics problem with complex boundary conditions because of the simultaneously occurring heat transfer, phase transformation, and mechanical interactions. The aim of this paper is to provide an updated review of research studies on the simulation of quenching. The subject is covered from the pioneering work up to very recent advances in the field, with special emphasis on future research needs for improving the industrial usage of heat treatment simulations.

References

1.
Zoch
,
H.-W.
, “
From Single Production Step to Entire Process Chain—The Global Approach of Distortion Engineering
,”
Materialwiss. Werkstofftech.
, Vol.
37
,
2006
, pp.
6
10
. https://doi.org/10.1002/mawe.200500958
2.
Gür
,
C. H.
and
Tekkaya
,
A. E.
, “
Finite Element Simulation of Quench Hardening
,”
Steel Res.
, Vol.
67
,
1996
, pp.
298
306
.
3.
Inoue
,
T.
and
Wang
,
Z.
, “
Coupling between Stress, Temperature, and Metallic Structures during Processes Involving Phase Transformations
,”
Mater. Sci. Technol.
, Vol.
1
,
1984
, pp.
845
850
. https://doi.org/10.1179/026708385790124080
4.
Sjöström
,
S.
,
1982
, “
Calculation of Quench Stresses in Steel
,” Ph.D. thesis,
University of Linköping
, Sweden.
5.
Denis
,
S.
,
Farias
,
D.
, and
Simon
,
A.
, “
Mathematical-model Coupling Phase-transformations and Temperature Evolutions in Steels
,”
ISIJ Int.
, Vol.
32
,
1992
, pp.
316
325
. https://doi.org/10.2355/isijinternational.32.316
6.
Embury
,
J. D.
,
Deschamps
,
A.
, and
Brechet
,
Y.
, “
The Interaction of Plasticity and Diffusion Controlled Precipitation Reactions
,”
Scr. Mater.
, Vol.
49
,
2003
, pp.
927
932
. https://doi.org/10.1016/S1359-6462(03)00479-2
7.
Şimşir
,
C.
and
Gür
,
C. H.
, “
Simulation of Quenching
,”
Thermal Process Modeling of Steels
,
Gür
C. H.
, and
Pan
J. S.
, Eds.,
CRC Press
,
New York
,
2010
, pp.
341
425
.
8.
Inoue
,
T.
,
Haraguchi
,
K.
, and
Kimura
,
S.
, “
Analysis of Stresses due to Quenching and Tempering of Steel
,”
Trans. Iron Steel Inst. Jpn.
, Vol.
18
,
1978
, pp.
11
15
.
9.
Inoue
,
T.
and
Tanaka
,
K.
, “
Elastic-plastic Stress Analysis of Quenching When Considering a Transformation
,”
Int. J. Mech. Sci.
, Vol.
17
,
1975
, pp.
361
367
. https://doi.org/10.1016/0020-7403(75)90028-4
10.
Kobasko
,
N. I.
, “
Methods of Overcoming Self-deformation and Cracking during Quenching of Metal Parts
,”
Metal Science and Heat Treatment
, Vol.
17
,
1975
, pp.
287
290
. https://doi.org/10.1007/BF00663385
11.
Kobasko
,
N. I.
, “
Computer-Analysis of Thermal Processes during Quenching of Steel
,”
Metal Science and Heat Treatment
, Vol.
18
,
1976
, pp.
846
852
. https://doi.org/10.1007/BF00705187
12.
Liscic
,
B.
, “
Influence of Some Cooling Parameters on Depth of Hardening and Possibility of Measuring Quenching Intensity during Steel Hardening
,”
Strojarstvo
, Vol.
19
,
1977
, pp.
189
201
.
13.
Inoue
,
T.
and
Raniecki
,
B.
, “
Determination of Thermal-hardening Stress in Steels by Use of Thermoplasticity Theory
,”
J. Mech. Phys. Solids
, Vol.
26
,
1978
, pp.
187
212
. https://doi.org/10.1016/0022-5096(78)90008-X
14.
Kobasko
,
N. I.
, “
Effect of Pressure on Quenching of Steel
,”
Metal Science and Heat Treatment
, Vol.
20
,
1978
, pp.
31
35
. https://doi.org/10.1007/BF00670438
15.
Inoue
,
T.
,
Nagaki
,
S.
, and
Kawate
,
T.
, “
Successive Deformation of a Viscoelastic-plastic Tube Subjected to Internal-Pressure under Temperature Cycling
,”
J. Therm. Stresses
, Vol.
3
,
1980
, pp.
185
198
. https://doi.org/10.1080/01495738008926962
16.
Inoue
,
T.
,
Nagaki
,
S.
,
Kishino
,
T.
, and
Monkawa
,
M.
, “
Description of Transformation Kinetics, Heat-Conduction and Elastic-plastic Stress in the Course of Quenching and Tempering of Some Steels
,”
Ing.-Arch.
, Vol.
50
,
1981
, pp.
315
327
. https://doi.org/10.1007/BF00778427
17.
Gergely
,
M.
,
Tardy
,
P.
,
Buza
,
G.
, and
Reti
,
T.
, “
Prediction of Transformation Characteristics and Microstructure of Case-hardened Components
,”
Heat Treat. Met.
, Vol.
11
,
1984
, pp.
67
74
.
18.
Sjöström
,
S.
, “
Interactions and Constitutive Models for Calculating Quench Stresses in Steel
,”
Mater. Sci. Technol.
, Vol.
1
,
1984
, pp.
823
829
. https://doi.org/10.1179/026708385790124099
19.
Fernandes
,
F. B. M.
,
Denis
,
S.
, and
Simon
,
A.
, “
Mathematical Model Coupling Phase Transformation and Temperature Evolution during Quenching of Steels
,”
Mater. Sci. Technol.
, Vol.
1
,
1985
, pp.
838
844
. https://doi.org/10.1179/026708385790123991
20.
Inoue
,
T.
and
Wang
,
Z. G.
, “
Coupling between Stress, Temperature, and Metallic Structures during Processes Involving Phase-Transformations
,”
Mater. Sci. Technol.
, Vol.
1
,
1985
, pp.
845
850
. https://doi.org/10.1179/026708385790124080
21.
Leblond
,
J. B.
,
Mottet
,
G.
,
Devaux
,
J.
, and
Devaux
,
J. C.
, “
Mathematical-Models of Anisothermal Phase-Transformations in Steels, and Predicted Plastic Behavior
,”
Mater. Sci. Technol.
, Vol.
1
,
1985
, pp.
815
822
. https://doi.org/10.1179/026708385790124017
22.
Leblond
,
J. B.
,
Mottet
,
G.
, and
Devaux
,
J. C.
, “
A Theoretical and Numerical Approach to the Plastic Behavior of Steels during Phase-Transformations
,”
J. Mech. Phys. Solids
, Vol.
34
,
1986
, pp.
395
409
. https://doi.org/10.1016/0022-5096(86)90009-8
23.
Denis
,
S.
,
Gautier
,
E.
,
Sjostrom
,
S.
, and
Simon
,
A.
, “
Influence of Stresses on the Kinetics of Pearlitic Transformation during Continuous Cooling
,”
Acta Metall.
, Vol.
35
,
1987
, pp.
1621
1632
. https://doi.org/10.1016/0001-6160(87)90109-X
24.
Denis
,
S.
,
Sjostrom
,
S.
, and
Simon
,
A.
, “
Coupled Temperature, Stress, Phase-transformation Calculation Model Numerical Illustration of the Internal-stresses Evolution during Cooling of a Eutectoid Carbon-steel Cylinder
,”
Metall. Trans. A
, Vol.
18
,
1987
, pp.
1203
1212
. https://doi.org/10.1007/BF02647190
25.
Gautier
,
E.
,
Simon
,
A.
, and
Beck
,
G.
, “
Transformation Plasticity during the Pearlitic Transformation of an Eutectoid Steel
,”
Acta Metall.
, Vol.
35
,
1987
, pp.
1367
1375
. https://doi.org/10.1016/0001-6160(87)90019-8
26.
Liscic
,
B.
and
Filetin
,
T.
, “
Computer-aided Determination of the Process Data for Hardening and Tempering of Structural Steels
,”
Neue Hutte
, Vol.
33
,
1988
, pp.
257
262
.
27.
Reti
,
T.
,
Gergely
,
M.
, and
Tardy
,
P.
, “
Mathematical Treatment of Nonisothermal Transformations
,”
Mater. Sci. Technol.
, Vol.
3
,
1987
, pp.
365
371
. https://doi.org/10.1179/026708387790122611
28.
Gautier
,
E.
and
Simon
,
A.
, “
Transformation Plasticity Mechanisms for Martensitic Transformation of Ferrous Alloys
,”
Phase Transformation
, Vol.
87
,
1988
, pp.
285
287
.
29.
Leblond
,
J. B.
, “
Mathematical-Modeling of Transformation Plasticity in Steels: 2. Coupling with Strain-hardening Phenomena
,”
Int. J. Plast.
, Vol.
5
,
1989
, pp.
573
591
. https://doi.org/10.1016/0749-6419(89)90002-8
30.
Leblond
,
J. B.
,
Devaux
,
J.
, and
Devaux
,
J. C.
, “
Mathematical-Modeling of Transformation Plasticity in Steels: 1. Case of Ideal-plastic Phases
,”
Int. J. Plast.
, Vol.
5
,
1989
, pp.
551
572
. https://doi.org/10.1016/0749-6419(89)90001-6
31.
Tensi
,
H. M.
and
Kunzel
,
T.
, “
Importance of the Different Boiling Phases for the Cooling of Parts by Immersion—Numerical-Simulation and Experimental Revision
,”
Neue Hutte
, Vol.
32
,
1987
, pp.
354
359
.
32.
Bates
,
C. E.
and
Totten
,
G. E.
, “
Procedure for Quenching Media Selection to Maximize Tensile Properties and Minimize Distortion in Aluminum-alloy Parts
,”
Heat Treat. Met.
, Vol.
15
,
1988
, pp.
89
97
.
33.
Kobasko
,
N. I.
, “
Increasing the Service Life and Reliability of Components through the Use of New Steel Quenching Technology
,”
Metal Science and Heat Treatment
, Vol.
31
,
1989
, pp.
645
653
. https://doi.org/10.1007/BF00717481
34.
Reti
,
T.
and
Gergely
,
M.
, “
Computerized Process Planning in Heat-treatment Practice Using Personal Computers
,”
Heat Treat. Met.
, Vol.
18
,
1991
, pp.
117
121
.
35.
Saunders
,
N.
, “
Computer Modeling of Phase-Diagrams
,”
Mater. Sci. Technol.
, Vol.
8
,
1992
, pp.
112
113
. https://doi.org/10.1179/026708392790170379
36.
Stringfellow
,
R. G.
,
Parks
,
D. M.
, and
Olson
,
G. B.
, “
A Constitutive Model for Transformation Plasticity Accompanying Strain-induced Martensitic Transformations in Metastable Austenitic Steels
,”
Acta Metall. Mater.
, Vol.
40
,
1992
, pp.
1703
1716
. https://doi.org/10.1016/0956-7151(92)90114-T
37.
Umemoto
,
M.
,
Hiramatsu
,
A.
,
Moriya
,
A.
,
Watanabe
,
T.
,
Nanba
,
S.
,
Nakajima
,
N.
,
Anan
,
G.
, and
Higo
,
Y.
, “
Computer Modelling of Phase Transformation from Work-hardened Austenite
,”
ISIJ Int.
, Vol.
32
,
1992
, pp.
306
315
. https://doi.org/10.2355/isijinternational.32.306
38.
Mujahid
,
S. A.
and
Bhadeshia
,
H.
, “
Coupled Diffusional Displacive Transformations—Effect of Carbon Concentration
,”
Acta Metall. Mater.
, Vol.
41
,
1993
, pp.
967
973
. https://doi.org/10.1016/0956-7151(93)90031-M
39.
Besserdich
,
G.
,
Scholtes
,
B.
,
Muller
,
H.
, and
Macherauch
,
E.
, “
Consequences of Transformation Plasticity on the Development of Residual-stresses and Distortions during Martensitic Hardening of SAE 4140 Steel Cylinders
,”
Steel Res.
, Vol.
65
,
1994
, pp.
41
46
.
40.
Sjöström
,
S.
,
Ganghoffer
,
J. F.
,
Denis
,
S.
,
Gautier
,
E.
, and
Simon
,
A.
, “
Finite-element Calculation of the Micromechanics of a Diffusional Transformation: 2. Influence of Stress Level, Stress History and Stress Multiaxiality
,”
Eur. J. Mech. A/Solids
, Vol.
13
,
1994
, pp.
803
817
.
41.
Fischer
,
F. D.
,
Oberaigner
,
E. R.
,
Tanaka
,
K.
, and
Nishimura
,
F.
, “
Transformation Induced Plasticity Revised an Updated Formulation
,”
Int. J. Solids Struct.
, Vol.
35
,
1998
, pp.
2209
2227
. https://doi.org/10.1016/S0020-7683(97)00134-0
42.
Marketz
,
F.
and
Fischer
,
F. D.
, “
A Mesoscale Study on the Thermodynamic Effect of Stress on Martensitic-Transformation
,”
Metall. Mater. Trans. A
, Vol.
26
,
1995
, pp.
267
278
. https://doi.org/10.1007/BF02664665
43.
Shipway
,
P. H.
and
Bhadeshia
,
H.
, “
Mechanical Stabilisation of Bainite
,”
Mater. Sci. Technol.
, Vol.
11
,
1995
, pp.
1116
1128
. https://doi.org/10.1179/026708395790164526
44.
Chang
,
L. C.
and
Bhadeshia
,
H.
, “
Stress-affected Transformation to Lower Bainite
,”
J. Mater. Sci.
, Vol.
31
,
1996
, pp.
2145
2148
. https://doi.org/10.1007/BF00356638
45.
Fischer
,
F. D.
,
Sun
,
Q. P.
, and
Tanaka
,
K.
, “
Transformation-induced Plasticity
,”
Appl. Mech. Rev.
, Vol.
49
,
1996
, pp.
317
364
. https://doi.org/10.1115/1.3101930
46.
Marketz
,
F.
,
Fischer
,
F. D.
, and
Tanaka
,
K.
, “
Micromechanics of Transformation-induced Plasticity and Variant Coalescence
,”
J. Phys. IV
, Vol.
6
,
1996
, pp.
445
454
. https://doi.org/10.1051/jp4:1996143
47.
Tanaka
,
K.
,
Nishimura
,
F.
,
Fischer
,
F. D.
, and
Oberaigner
,
E. R.
, “
Transformation Thermomechanics of Alloy Materials in the Process of Martensitic Transformation: A Unified Theory
,”
J. Phys. IV
, Vol.
6
,
1996
, pp.
455
463
. https://doi.org/10.1051/jp4:1996144
48.
Bhadeshia
,
H.
, “
Martensite and Bainite in Steels: Transformation Mechanism & Mechanical Properties
,”
J. Phys. IV
, Vol.
7
,
1997
, pp.
367
376
. https://doi.org/10.1051/jp4:1997558
49.
Chen
,
J. R.
,
Tao
,
Y. Q.
, and
Wang
,
H. G.
, “
A Study on Heat Conduction with Variable Phase Transformation Composition during Quench Hardening
,”
J. Mater. Process. Technol.
, Vol.
63
,
1997
, pp.
554
558
. https://doi.org/10.1016/S0924-0136(96)02682-9
50.
Jones
,
S. J.
and
Bhadeshia
,
H.
, “
Kinetics of the Simultaneous Decomposition of Austenite into Several Transformation Products
,”
Acta Mater.
, Vol.
45
,
1997
, pp.
2911
2920
. https://doi.org/10.1016/S1359-6454(96)00392-8
51.
Lusk
,
M.
and
Jou
,
H. J.
, “
On the Rule of Additivity in Phase Transformation Kinetics
,”
Metall. Mater. Trans. A
, Vol.
28
,
1997
, pp.
287
291
. https://doi.org/10.1007/s11661-997-0131-5
52.
Reti
,
T.
,
Horvath
,
L.
, and
Felde
,
I.
, “
A Comparative Study of Methods Used for the Prediction of Nonisothermal Austenite Decomposition
,”
J. Mater. Eng. Perform.
, Vol.
6
,
1997
, pp.
433
442
. https://doi.org/10.1007/s11665-997-0113-1
53.
Reisner
,
G.
,
Werner
,
E. A.
,
Kerschbaummayr
,
P.
,
Papst
,
I.
, and
Fischer
,
F. D.
, “
The Modeling of Retained Austenite in Low-alloyed TRIP Steels
,”
JOM
, Vol.
49
,
1997
, pp.
62
65
. https://doi.org/10.1007/BF02914354
54.
Starink
,
M. J.
, “
Kinetic Equations for Diffusion-controlled Precipitation Reactions
,”
J. Mater. Sci.
, Vol.
32
,
1997
, pp.
4061
4070
. https://doi.org/10.1023/A:1018649823542
55.
Cherkaoui
,
M.
,
Berveiller
,
M.
, and
Sabar
,
H.
, “
Micromechanical Modeling of Martensitic Transformation Induced Plasticity in Austenitic Single Crystals
,”
Int. J. Plast.
, Vol.
14
,
1998
, pp.
597
626
. https://doi.org/10.1016/S0749-6419(99)80000-X
56.
Liu
,
C. C.
,
Liu
,
Z.
,
Xu
,
X. J.
,
Chen
,
G. X.
, and
Wu
,
J. Z.
, “
Effect of Stress on Transformation and Prediction of Residual Stresses
,”
Mater. Sci. Technol.
, Vol.
14
,
1998
, pp.
747
750
. https://doi.org/10.1179/026708398790300990
57.
Reisner
,
G.
,
Werner
,
E. A.
, and
Fischer
,
F. D.
, “
Micromechanical Modeling of Martensitic Transformation in Random Microstructures
,”
Int. J. Solids Struct.
, Vol.
35
,
1998
, pp.
2457
2473
. https://doi.org/10.1016/S0020-7683(97)00149-2
58.
Todinov
,
M. T.
, “
Alternative Approach to the Problem of Additivity
,”
Metall. Mater. Trans. B
, Vol.
29
,
1998
, pp.
269
273
. https://doi.org/10.1007/s11663-998-0030-1
59.
Lee
,
Y. K.
and
Lusk
,
M. T.
, “
Thermodynamic Prediction of the Eutectoid Transformation Temperatures of Low-alloy Steels
,”
Metall. Mater. Trans. A
, Vol.
30
,
1999
, pp.
2325
2330
. https://doi.org/10.1007/s11661-999-0241-3
60.
Lusk
,
M. T.
, “
A Phase-field Paradigm for Grain Growth and Recrystallization
,”
Proc. R. Soc.
London
, Vol.
455
,
1999
, pp.
677
700
.
61.
Lusk
,
M. T.
and
Lee
,
Y.-K.
, “
A Global Material Model for Simulating the Transformation Kinetics of Low Alloy Steels
,”
Proceedings of the 7th International Seminar of the IFHTSE
,
IFHT
,
Budapest, Hungary
,
1999
, pp.
273
282
.
62.
Reti
,
T.
and
Felde
,
I.
, “
A Non-linear Extension of the Additivity Rule
,”
Comput. Mater. Sci.
, Vol.
15
,
1999
, pp.
466
482
. https://doi.org/10.1016/S0927-0256(99)00035-X
63.
Bates
,
C. E.
and
Totten
,
G. E.
, “
Quantifying Quench-oil Cooling Characteristics
,”
Advanced Materials and Processes
, Vol.
139
,
1991
, pp.
25
28
.
64.
Kobasko
,
N. I.
, “
Technological Aspects of Quenching (Review)
,”
Metal Science and Heat Treatment
, Vol.
33
,
1991
, pp.
253
263
. https://doi.org/10.1007/BF00776430
65.
Bates
,
C. E.
and
Totten
,
G. E.
, “
Quench Severity Effects on the As-quenched Hardness of Selected Alloy-steels
,”
Heat Treat. Met.
, Vol.
19
,
1992
, pp.
45
48
.
66.
Kobasko
,
N. I.
, “
Basics of Intensive Quenching
,”
Advanced Materials and Processes
, Vol.
148
,
1995
, pp.
42W
42Y
.
67.
Reti
,
T.
,
Felde
,
I.
,
Horvath
,
L.
,
Kohlheb
,
R.
, and
Bell
,
T.
, “
Quenchant Performance Analysis Using Computer Simulation
,”
Heat Treat. Met.
, Vol.
23
,
1996
, pp.
11
14
.
68.
Sverdlin
,
A. V.
,
Totten
,
G. E.
,
Bates
,
C.
, and
Jarvis
,
L. M.
, “
Use of the Quenching Factor for Predicting the Properties of Polymer Quenching Media
,”
Metal Science and Heat Treatment
, Vol.
38
,
1996
, pp.
248
251
. https://doi.org/10.1007/BF01395823
69.
Totten
,
G. E.
,
Webster
,
G. M.
,
Blackwood
,
R. R.
,
Jarvis
,
L. M.
, and
Narumi
,
T.
, “
Chute Quench Recommendations for Continuous Furnace Applications with Aqueous Polymer Quenchants
,”
Heat Treat. Met.
, Vol.
23
,
1996
, pp.
36
39
.
70.
Totten
,
G. E.
,
Webster
,
G. M.
, and
Gopinath
,
N.
, “
Quenching Fundamentals: Effect of Agitation
,”
Advanced Materials and Processes
, Vol.
149
,
1996
, pp.
73
76
.
71.
Archambault
,
P.
,
Denis
,
S.
, and
Azim
,
A.
, “
Inverse Resolution of the Heat-transfer Equation with Internal Heat Source: Application to the Quenching of Steels with Phase Transformations
,”
J. Mater. Eng. Perform.
, Vol.
6
,
1997
, pp.
240
246
. https://doi.org/10.1007/s11665-997-0020-5
72.
Liscic
,
B.
and
Totten
,
G. E.
, “
Benefits of Delayed Quenching
,”
Advanced Materials and Processes
, Vol.
152
,
1997
, pp.
180
184
.
73.
Totten
,
G. E.
,
Webster
,
G. M.
,
Tensi
,
H. M.
, and
Liscic
,
B.
, “
Standards for Cooling Curve Analysis
,”
Advanced Materials and Processes
, Vol.
151
,
1997
, pp.
68LL
68OO
.
74.
Kobasko
,
N. I.
, “
Basics of Intensive Quenching
,”
Advanced Materials and Processes
, Vol.
156
,
1999
, pp.
H31
H33
.
75.
Totten
,
G. E.
,
Tensi
,
H. M.
, and
Lainer
,
K.
, “
Performance of Vegetable Oils as a Cooling Medium in Comparison to a Standard Mineral Oil
,”
J. Mater. Eng. Perform.
, Vol.
8
,
1999
, pp.
409
416
. https://doi.org/10.1361/105994999770346693
76.
Totten
,
G. E.
and
Webster
,
G. M.
, “
Stability & Drag-out of Polymers
,”
Advanced Materials and Processes
, Vol.
155
,
1999
, pp.
H63
H66
.
77.
Lübben
,
T.
,
Rath
,
J.
,
Krause
,
F.
,
Hoffmann
,
F.
,
Fritsching
,
U.
, and
Zoch
,
H.-W.
, “
Determination of Heat Transfer Coefficient during High-speed Water Quenching
,”
15th International Metallurgy and Materials Congress
,
Chamber of Turkish Metallurgical and Materials Engineers
,
Istanbul, Turkey
, Nov 11–13,
2010
.
78.
Stratton
,
P. F.
and
Ho
,
D.
, “
Individual Component Gas Quenching
,”
Heat Treat. Met.
, Vol.
27
,
2000
, pp.
65
68
.
79.
Stratton
,
P. F.
, “
Modelling Gas Quenching of a Carburised Gear
,”
Heat Treat. Met.
, Vol.
29
,
2002
, pp.
29
32
.
80.
Stratton
,
P. F.
and
Richardson
,
A.
, “
Validation of a Single Component Gas Quenching Model
,”
J. Phys. IV
, Vol.
120
,
2004
, pp.
537
543
.
81.
Pietzsch
,
R.
,
Brzoza
,
M.
,
Kaymak
,
Y.
,
Specht
,
E.
, and
Bertram
,
A.
, “
Minimizing the Distortion of Steel Profiles by Controlled Cooling
,”
Steel Research International
, Vol.
76
,
2005
, pp.
399
407
.
82.
Brzoza
,
M.
,
Specht
,
E.
,
Ohland
,
J.
,
Belkessam
,
O.
,
Lubben
,
T.
, and
Fritsching
,
U.
, “
Minimizing Stress and Distortion for Shafts and Discs by Controlled Quenching in a Field of Nozzles
,”
Materialwiss. Werkstofftech.
, Vol.
37
,
2006
, pp.
97
102
. https://doi.org/10.1002/mawe.200500970
83.
Li
,
H.
,
Zhao
,
G.
,
Huang
,
C.
, and
Niu
,
S.
, “
Technological Parameters Evaluation of Gas Quenching Based on the Finite Element Method
,”
Comput. Mater. Sci.
, Vol.
40
,
2007
, pp.
282
291
. https://doi.org/10.1016/j.commatsci.2006.12.010
84.
Wang
,
J.
,
Gu
,
J.
,
Shan
,
X.
,
Hao
,
X.
,
Chen
,
N.
, and
Zhang
,
W.
, “
Numerical Simulation of High Pressure Gas Quenching of H13 Steel
,”
J. Mater. Process. Technol.
, Vol.
202
,
2008
, pp.
188
194
. https://doi.org/10.1016/j.jmatprotec.2007.08.059
85.
Dhir
,
V. K.
, “
Numerical Simulations of Pool-boiling Heat Transfer
,”
AIChE J.
, Vol.
47
,
2001
, pp.
813
834
. https://doi.org/10.1002/aic.690470407
86.
Krause
,
F.
,
Shüttenberg
,
S.
, and
Fritsching
,
U.
, “
Modeling and Simulation of Flow Boiling Heat Transfer
,”
Int. J. Numer. Methods Heat Fluid Flow
, Vol.
20
,
2010
, pp.
312
331
. https://doi.org/10.1108/09615531011024066
87.
Cherkaoui
,
M.
, “
Transformation Induced Plasticity: Mechanisms and Modeling
,”
J. Eng. Mater. Technol.
, Vol.
124
,
2002
, pp.
55
61
. https://doi.org/10.1115/1.1421051
88.
Cherkaoui
,
M.
,
Berveiller
,
M.
, and
Lemoine
,
X.
, “
Couplings between Plasticity and Martensitic Phase Transformation: Overall Behavior of Polycrystalline Trip Steels
,”
Int. J. Plast.
, Vol.
16
,
2000
, pp.
1215
1241
. https://doi.org/10.1016/S0749-6419(00)00008-5
89.
Fischer
,
F. D.
,
Reisner
,
G.
,
Werner
,
E.
,
Tanaka
,
K.
,
Cailletaud
,
G.
, and
Antretter
,
T.
, “
A New View on Transformation Induced Plasticity
,”
Int. J. Plast.
, Vol.
16
,
2000
, pp.
723
748
. https://doi.org/10.1016/S0749-6419(99)00078-9
90.
Oberste-Brandenburg
,
C.
and
Bruhns
,
O. T.
, “
Tensorial Description of the Transformation Kinetics during Phase Transitions
,”
Z. Angew. Math. Mech.
, Vol.
80
,
2000
, pp.
197
200
.
91.
Taleb
,
L.
,
Cavallo
,
N.
, and
Waeckel
,
F.
, “
Experimental Analysis of Transformation Plasticity
,”
Int. J. Plast.
, Vol.
17
,
2001
, pp.
1
20
. https://doi.org/10.1016/S0749-6419(99)00090-X
92.
Antretter
,
T.
,
Fischer
,
F. D.
,
Tanaka
,
K.
, and
Cailletaud
,
G.
, “
Theory, Experiments and Numerical Modelling of Phase Transformations with Emphasis on TRIP
,”
Steel Res.
, Vol.
73
,
2002
, pp.
366
366
.
93.
Levitas
,
V. I.
and
Cherkaoui
,
M.
, “
Special Issue on Micromechanics of Martensitic Phase Transformations
,”
Int. J. Plast.
, Vol.
18
,
2002
, pp.
1425
1425
. https://doi.org/10.1016/S0749-6419(02)00023-2
94.
Taleb
,
L.
and
Sidoroff
,
F.
, “
A Micromechanical Modeling of the Greenwood-Johnson Mechanism in Transformation Induced Plasticity
,”
Int. J. Plast.
, Vol.
19
,
2003
, pp.
1821
1842
. https://doi.org/10.1016/S0749-6419(03)00020-2
95.
Antretter
,
T.
,
Fischer
,
F. D.
, and
Cailletaud
,
G.
, “
A Numerical Model for Transformation Induced Plasticity
,”
J. Phys. IV
, Vol.
115
,
2004
, pp.
233
241
.
96.
Oberste-Brandenburg
,
C.
and
Bruhns
,
O. T.
, “
A Tensorial Description of the Transformation Kinetics of the Martensitic Phase Transformation
,”
Int. J. Plast.
, Vol.
20
,
2004
, pp.
2083
2109
. https://doi.org/10.1016/j.ijplas.2004.01.002
97.
Turteltaub
,
S.
and
Suiker
,
A. S. J.
, “
Transformation-induced Plasticity in Ferrous Alloys
,”
J. Mech. Phys. Solids
, Vol.
53
,
2005
, pp.
1747
1788
. https://doi.org/10.1016/j.jmps.2005.03.004
98.
Taleb
,
L.
and
Petit
,
S.
, “
New Investigations on Transformation Induced Plasticity and Its Interaction with Classical Plasticity
,”
Int. J. Plast.
, Vol.
22
,
2006
, pp.
110
130
. https://doi.org/10.1016/j.ijplas.2005.03.012
99.
Tjahjanto
,
D. D.
,
Turteltaub
,
S.
,
Suiker
,
A. S. J.
, and
van der Zwaag
,
S.
, “
Modelling of the Effects of Grain Orientation on Transformation-induced Plasticity in Multiphase Carbon Steels
,”
Modell. Simul. Mater. Sci. Eng.
, Vol.
14
,
2006
, pp.
617
636
. https://doi.org/10.1088/0965-0393/14/4/006
100.
Turteltaub
,
S.
and
Suiker
,
A. S. J.
, “
Grain Size Effects in Multiphase Steels Assisted by Transformation-induced Plasticity
,”
Int. J. Solids Struct.
, Vol.
43
,
2006
, pp.
7322
7336
. https://doi.org/10.1016/j.ijsolstr.2006.06.017
101.
Turteltaub
,
S.
and
Suiker
,
A. S. J.
, “
A Multiscale Thermomechanical Model for Cubic to Tetragonal Martensitic Phase Transformations
,”
Int. J. Solids Struct.
, Vol.
43
,
2006
, pp.
4509
4545
. https://doi.org/10.1016/j.ijsolstr.2005.06.065
102.
Wolff
,
M.
,
Bohm
,
M.
, and
Schmidt
,
A.
, “
Modelling of Steel Phenomena and Their Interactions—An Internal Variable Approach
,”
Materialwiss. Werkstofftech.
, Vol.
37
,
2006
, pp.
147
151
. https://doi.org/10.1002/mawe.200500979
103.
Meftah
,
S.
,
Barbe
,
F.
,
Taleb
,
L.
, and
Sidoroff
,
F.
, “
Parametric Numerical Simulations of TRIP and Its Interaction with Classical Plasticity in Martensitic Transformation
,”
Eur. J. Mech. A/Solids
, Vol.
26
,
2007
, pp.
688
700
. https://doi.org/10.1016/j.euromechsol.2006.10.004
104.
Hunkel
,
M.
,
Hoffmann
,
F.
, and
Zoch
,
H.-W.
, “
Distortion Due to Segregations of Components of a Low Alloy SAE 5120 Steel after Blank and Case Hardening
,”
HTM Journal of Heat Treatment and Materials
, Vol.
62
,
2007
, pp.
144
149
.
105.
Şimşir
,
C.
,
Eisbrecher
,
I.
,
Hunkel
,
M.
, et al
, “
The Prediction of Distortion of Blank-Hardened Gear Blanks by Considering the Effect of Prior Manufacturing Operations
,” Steel Research International : Special Issue for ICTP’2011 (
2011
), pp.
386
391
.
106.
Şimşir
,
C.
,
Hunkel
,
M.
, et al
, “
Process Chain Simulation for Prediction of the Distortion of Case-Hardened Gear Blanks
,”
2012, Materialwissenschaft und Werkstofftechnik
, Vol.
43
(1),
2012
, pp.
163
170
.
107.
Taleb
,
L.
,
Cavallo
,
N.
, and
Waeckel
,
F.
, “
Experimental Analysis of Transformation Plasticity
,”
Int. J. Plast.
, Vol.
17
,
2001
, pp.
1
20
. https://doi.org/10.1016/S0749-6419(99)00090-X
108.
Luiggi
,
N. J.
, “
Comments on the Analysis of Experimental Data in Nonisothermal Kinetics
,”
Metall. Mater. Trans. A
, Vol.
34
,
2003
, pp.
2679
2681
. https://doi.org/10.1007/s11661-003-0027-y
109.
Tszeng
,
T. C.
and
Shi
,
G.
, “
A Global Optimization Technique to Identify Overall Transformation Kinetics Using Dilatometry Data—Applications to Austenitization of Steels
,”
Mater. Sci. Eng. A
, Vol.
380
,
2004
, pp.
123
136
. https://doi.org/10.1016/j.msea.2004.03.040
110.
Wolff
,
M.
,
Bohm
,
M.
,
Lowisch
,
G.
, and
Schmidt
,
A.
, “
Modelling and Testing of Transformation-induced Plasticity and Stress-dependent Phase Transformations in Steel via Simple Experiments
,”
Comput. Mater. Sci.
, Vol.
32
,
2005
, pp.
604
610
. https://doi.org/10.1016/j.commatsci.2004.09.003
111.
Wolff
,
M.
,
Bohm
,
M.
,
Dalgic
,
M.
,
Lowisch
,
G.
,
Lysenko
,
N.
, and
Rath
,
J.
, “
Parameter Identification for a Trip Model with Backstress
,”
Comput. Mater. Sci.
, Vol.
37
,
2006
, pp.
37
41
. https://doi.org/10.1016/j.commatsci.2005.12.007
112.
Wolff
,
M.
,
Bohm
,
M.
,
Dalgic
,
M.
, and
Lowisch
,
G.
, “
Validation of a Trip Model with Backstress for the Pearlitic Transformation of the Steel 100cr6 under Step-wise Loads
,”
Comput. Mater. Sci.
, Vol.
39
,
2007
, pp.
49
54
. https://doi.org/10.1016/j.commatsci.2006.01.025
113.
Funatani
,
K.
, “
Modeling and Simulation Technology for the Advancement of Materials Processing Technology
,”
J. Phys. IV
, Vol.
120
,
2004
, pp.
737
742
.
114.
Inoue
,
T.
and
Okamura
,
K.
, “
Material Database for Simulation of Metallo-thermo-mechanical field
,”
ASM International
, Vol.
2
,
2000
, pp.
753
760
.
115.
Houghton
,
R. L.
, “
Heat Treating Technology Roadmap Update 2006, Part I: Process and Materials Technology
,”
Heat Treating Progress
, Vol.
6
,
2006
, pp.
54
57
.
116.
Majorek
,
A.
,
Scholtes
,
B.
,
Muller
,
H.
, and
Macherauch
,
E.
, “
Influence of Heat-transfer on the Development of Residual Stresses in Quenched Steel Cylinders
,”
Steel Res.
, Vol.
65
,
1994
, pp.
146
151
.
117.
Totten
,
G. E.
,
Tensi
,
H. M.
, and
Canale
,
L. C. F.
, “
Chemistry of Quenching: Part I—Fundamental Interfacial Chemical Processes Involved in Quenching
,”
Proceedings of the 22nd Heat Treating Society Conference and 2nd International Surface Engineering Congress
,
ASM International
,
Indianapolis, IN
,
2003
, pp.
141
147
.
118.
Totten
,
G. E.
,
Tensi
,
H. M.
, and
Canale
,
L. C. F.
, “
Chemistry of Quenching: Part II—Fundamental Thermophysical Processes Involved in Quenching
,”
Proceedings of 22nd Heat Treating Society Conference and the 2nd International Surface Engineering Congress
,
ASM International
,
Indianapolis, IN
,
2003
, pp.
148
154
.
119.
Bhadeshia
,
H.
, “
Thermodynamic Analysis of Isothermal Transformation Diagrams
,”
Met. Sci.
, Vol.
16
,
1982
, pp.
159
165
. https://doi.org/10.1179/030634582790427217
120.
Kirkaldy
,
J. S.
and
Baganis
,
E. A.
, “
Thermodynamic Prediction of Ae3 Temperature of Steels with Additions of Mn, Si, Ni, Cr, Mo, Cu
,”
Metall. Trans. A
, Vol.
9
,
1978
, pp.
495
501
. https://doi.org/10.1007/BF02646405
121.
Kirkaldy
,
J. S.
,
Hashiguchi
,
K.
, and
Purdy
,
G. R.
, “
Prediction of TTT and CCT Curves for Low-alloy Steels
,”
CIM Bulletin
, Vol.
75
,
1982
, pp.
123
128
.
122.
Kirkaldy
,
J. S.
and
Sharma
,
R. C.
, “
New Phenomenology for Steel IT and CCT Curves
,”
Scr. Metall.
, Vol.
16
,
1982
, pp.
1193
1198
. https://doi.org/10.1016/0036-9748(82)90095-3
123.
Watt
,
D. F.
,
Coon
,
L.
,
Bibby
,
M.
,
Goldak
,
J.
, and
Henwood
,
C.
, “
An Algorithm for Modeling Microstructural Development in Weld Heat-affected Zones A. Reaction-kinetics
,”
Acta Metall.
, Vol.
36
,
1988
, pp.
3029
3035
. https://doi.org/10.1016/0001-6160(88)90185-X
124.
Geijselaers
,
H. J. M.
,
2003
, “
Numerical Simulation of Stresses due to Solid State Transformations
,” Ph.D. thesis,
University of Twente
, Twente, The Netherlands.
125.
Gaude-Fugarolas
,
D.
and
Bhadeshia
,
H. K. D. H.
, “
A Model for Austenitization of Hypoeutectoid Steels
,”
J. Mater. Sci.
, Vol.
38
,
2003
, pp.
1195
1201
. https://doi.org/10.1023/A:1022805719924
126.
Avrami
,
M.
, “
Kinetics of Phase Change: I. General Theory
,”
J. Chem. Phys.
, Vol.
7
,
1939
, pp.
1103
1112
. https://doi.org/10.1063/1.1750380
127.
Scheil
,
E.
, “
Incubation time of Austenite Transformation
,”
Arch. Eisenhuettenwes
,
1935
, pp.
565
567
.
128.
Cahn
,
J. W.
, “
Transformation Kinetics during Continuous Cooling
,”
Acta Metall.
, Vol.
4
,
1956
, pp.
572
575
. https://doi.org/10.1016/0001-6160(56)90158-4
129.
Christian
,
J. W.
,
The Theory of Transformations in Metals and Alloys
,
Pergamon Press
,
Oxford, England
,
1975
.
130.
Mecozzi
,
M. G.
,
Sietsma
,
J.
, and
van der Swaag
,
S.
, “
Phase Field Modelling of the Interfacial Condition at the Moving Interphase during the Austenite-ferrite Transformation in C–Mn Steels
,”
Comput. Mater. Sci.
, Vol.
34
,
2006
, pp.
207
290
.
131.
Iwamoto
,
T.
,
Cherkaoui
,
M.
, and
Busso
,
E.
, “
A Finite Element-based Level-set Method of an Interface Motion Driven by a Diffusion Field: Application to a Phase Transformation Problem
,”
Comput. Mater. Sci.
, Vol.
44
,
2008
, pp.
792
801
. https://doi.org/10.1016/j.commatsci.2008.05.030
132.
Ammar
,
K.
,
Appolaire
,
B.
,
Cailletaud
,
G.
, and
Forest
,
S.
, “
Combining Phase Field Approach and Homogenization Methods for Modelling Phase Transformation in Elastoplastic Media
,”
European Journal of Computational Mechanics
, Vol.
18
,
2009
, pp.
485
523
.
133.
Lan
,
Y.
,
Xiao
,
N.
,
Li
,
D.
, and
Li
,
Y.
, “
Mesoscale Simulation of Deformed Austenite Decomposition into Ferrite by Coupling a Cellular Automaton Method with a Crystal Plasticity Finite Element Model
,”
Acta Mater.
, Vol.
53
,
2005
, pp.
991
1003
. https://doi.org/10.1016/j.actamat.2004.10.045
134.
Koistinen
,
D. P.
and
Marburger
,
R. E.
, “
A General Equation Prescribing the Extent of the Austenite-martensite Transformation in Pure Iron-carbon Alloys and Plain Carbon Steels
,”
Acta Metall.
, Vol.
7
,
1959
, pp.
59
60
. https://doi.org/10.1016/0001-6160(59)90170-1
135.
Magee
,
C. L.
,
1966
, “
Transformation Kinetics, Micro-plasticity and Ageing of Martensite in Fe-31Ni
,” Ph.D. thesis,
Carnegie Institute of Technology
, Pittsburgh, PA.
136.
Kastner
,
O.
and
Ackland
,
G. J.
, “
Mesoscale Kinetics Produces Martensitic Microstructure
,”
J. Mech. Phys. Solids
, Vol.
57
,
2009
, pp.
109
121
. https://doi.org/10.1016/j.jmps.2008.09.016
137.
Kundin
,
J.
,
Raabe
,
D.
, and
Emmerich
,
H.
, “
A Phase-field Model for Incoherent Martensitic Transformations Including Plastic Accommodation Processes in the Austenite
,”
J. Mech. Phys. Solids
, Vol.
59
,
2011
, pp.
2082
2102
. https://doi.org/10.1016/j.jmps.2011.07.001
138.
Denis
,
S.
,
Boufoussi
,
M.
,
Chevrier
,
J. C.
, and
Simon
,
A.
, “
Analysis of the Development of Residual Stresses for Surface Hardening of Steels by Numerical Simulation: Effect of ProcessParameters
,”
International Conference on Residual Stresses (ICRS4)
,
Baltimore, Maryland (USA)
, June
1994
, pp.
513
519
.
139.
Rammerstorfer
,
F. G.
,
Fischer
,
D. F.
,
Mitter
,
W.
,
Bathe
,
K. J.
, and
Snyder
,
M. D.
, “
On Thermo-elastic-plastic Analysis of Heat-treatment Processes Including Creep and Phase Changes
,”
Comput. Struct.
, Vol.
13
,
1981
, pp.
771
779
. https://doi.org/10.1016/0045-7949(81)90040-7
140.
Zandona
,
M.
,
Mey
,
A.
,
Boufoussi
,
M.
,
Denis
,
S.
, and
Simon
,
A.
, “
Calculation of Internal Stresses during Surface Heat Treatment of Steels
,”
Residual Stresses
, Vol.
1
,
Hauk
V.
,
Hougardy
H. P.
,
Macherauch
E.
, and
Tietz
H. D.
, Eds.,
DEM Information mBH
,
Oberursel (Germany)
,
1993
, pp.
1011
1020
.
141.
Şimşir
,
C.
,
Dalgiç
,
M.
,
Lübben
,
T.
,
Irretier
,
A.
,
Wolff
,
M.
, and
Zoch
,
H.-W.
, “
The Bauschinger Effect in the Supercooled Austenite of SAE 52100 Steel
,”
Acta Mater.
, Vol.
58
,
2010
, pp.
4478
4491
. https://doi.org/10.1016/j.actamat.2010.04.044
142.
Wolff
,
M.
,
Suhr
,
B.
, and
Şimşir
,
C.
, “
Parameter Identification for an Armstrong–Frederick Hardening Law for Supercooled Austenite of SAE 52100 Steel
,”
Comput. Mater. Sci.
, Vol.
50
,
2010
, pp.
487
495
. https://doi.org/10.1016/j.commatsci.2010.09.009
143.
Rammerstorfer
,
F. G.
,
Fischer
,
F. D.
,
Till
,
E. T.
,
Mitter
,
W.
, and
Grundler
,
O.
, “
The Influence of Creep and Transformation Plasticity in the Analysis of Stresses due to Heat Treatment
,”
Numerical Methods in Heat Transfer
, Vol.
2
,
1983
, pp.
447
460
.
144.
Colonna
,
F.
,
Massoni
,
E.
,
Denis
,
S.
,
Chenot
,
J. L.
,
Wendenbaum
,
J.
, and
Gauthier
,
E.
, “
On Thermo-elastic-viscoplastic Analysis of Cooling Processes Including Phases Changes
,”
J. Mater. Process. Technol.
, Vol.
34
,
1992
, pp.
525
532
. https://doi.org/10.1016/0924-0136(92)90150-Q
145.
Gür
,
C. H.
and
Tekkaya
,
A. E.
, “
Numerical Investigation of Non-homogeneous Plastic Deformation in Quenching Process
,”
Mater. Sci. Eng. A
, Vol.
319
,
2001
, pp.
164
169
. https://doi.org/10.1016/S0921-5093(01)01064-4
146.
Iyer
,
J.
,
Brimacombe
,
J. K.
, and
Hawbolt
,
E. B.
, “
Development of a Mathematical-Model to Predict the Structure and Mechanical-Properties of Control-cooled Eutectoid Steel Rods
,”
J. Met.
, Vol.
35
,
1983
, pp.
87
95
.
147.
Sjöström
,
S.
, “
Interactions and Constitutive Models for Calculating Quench Stresses in Steel
,”
Mater. Sci. Technol.
, Vol.
1
,
1984
, pp.
823
829
. https://doi.org/10.1179/026708385790124099
148.
Denis
,
S.
,
Gautier
,
E.
,
Simon
,
A.
, and
Beck
,
G.
, “
Stress-phase-transformation Interactions—Basic Principles, Modelling, and Calculation of Internal Stresses
,”
Mater. Sci. Technol.
, Vol.
1
,
1984
, pp.
805
814
. https://doi.org/10.1179/026708385790124071
149.
Todinov
,
M. T.
, “
Mechanism for Formation of the Residual Stresses from Quenching
,”
Modell. Simul. Mater. Sci. Eng.
, Vol.
6
,
1998
, pp.
273
291
. https://doi.org/10.1088/0965-0393/6/3/006
150.
Denis
,
S.
,
Sjöström
,
S.
, and
Simon
,
A.
, “
Coupled Temperature, Stress, Phase Transformation Calculation; Model Numerical Illustration of the Internal Stresses Evolution during Cooling of a Eutectoid Carbon Steel Cylinder
,”
Metall. Trans. A
, Vol.
18
,
1987
, pp.
1203
1212
. https://doi.org/10.1007/BF02647190
151.
Denis
,
S.
,
Gautier
,
E.
,
Sjostrom
,
S.
, and
Simon
,
A.
, “
Influence of Stresses on the Kinetics of Pearlitic Transformation during Continuous Cooling
,”
Acta Metall.
, Vol.
35
,
1987
, pp.
1621
1632
. https://doi.org/10.1016/0001-6160(87)90109-X
152.
Jahanian
,
S.
and
Mosleh
,
M.
, “
The Mathematical Modeling of Phase Transformation of Steel during Quenching
,”
J. Mater. Eng. Perform.
, Vol.
8
,
1999
, pp.
75
82
. https://doi.org/10.1361/105994999770347197
153.
Ahrens
,
U.
,
Maier
,
H. J.
, and
Maksoud
,
A. E. M.
, “
Stress Affected Transformation in Low Alloy Steels—Factors Limiting Prediction of Plastic Strains
,”
J. Phys. IV
, Vol.
120
,
2004
, pp.
615
623
.
154.
Antretter
,
T.
,
Fischer
,
F. D.
,
Cailletaud
,
G.
, and
Ortner
,
B.
, “
On the Algorithmic Implementation of a Material Model Accounting for the Effects of Martensitic Transformation
,”
Steel Research International
, Vol.
77
,
2006
, pp.
733
740
.
155.
Liu
,
C. C.
,
Yao
,
K. F.
,
Lu
,
Z.
, and
Gao
,
G. F.
, “
Study of the Effects of Stress and Strain on Martensite Transformation: Kinetics and Transformation Plasticity
,”
J. Comput.-Aided Mater. Des.
, Vol.
7
,
2000
, pp.
63
69
. https://doi.org/10.1023/A:1008779710225
156.
Liu
,
C. C.
,
Yao
,
K. F.
,
Xu
,
X. J.
, and
Liu
,
Z.
, “
Models for Transformation Plasticity in Loaded Steels Subjected to Bainitic and Martensitic Transformation
,”
Mater. Sci. Technol.
, Vol.
17
,
2001
, pp.
983
988
.
157.
Maalekian
,
M.
,
Kozeschnik
,
E.
,
Chatterjee
,
S.
, and
Bhadeshia
,
H.
, “
Mechanical Stabilisation of Eutectoid Steel
,”
Mater. Sci. Technol.
, Vol.
23
,
2007
, pp.
610
612
. https://doi.org/10.1179/174328407X158686
158.
Todinov
,
M. T.
, “
Mechanism for Formation of the Residual Stresses from Quenching
,”
Modell. Simul. Mater. Sci. Eng.
, Vol.
6
,
1998
, pp.
273
291
. https://doi.org/10.1088/0965-0393/6/3/006
159.
Bhadeshia
,
H.
, “
Thermodynamic Analysis of Isothermal Transformation Diagrams
,”
Met. Sci.
, Vol.
16
,
1982
, pp.
159
165
. https://doi.org/10.1179/030634582790427217
160.
Babu
,
S. S.
and
Bhadeshia
,
H.
, “
Mechanism of the Transition from Bainite to Acicular Ferrite
,”
Mater. Trans., JIM
, Vol.
32
,
1991
, pp.
679
688
.
161.
Babu
,
S. S.
and
Bhadeshia
,
H.
, “
Stress and the Acicular Ferrite Transformation
,”
Mater. Sci. Eng. A
, Vol.
156
,
1992
, pp.
1
9
. https://doi.org/10.1016/0921-5093(92)90410-3
162.
Bhadeshia
,
H.
,
David
,
S. A.
,
Vitek
,
J. M.
, and
Reed
,
R. W.
, “
Stress-induced Transformation to Bainite in Fe-Cr-Mo-C Pressure Vessel Steel
,”
Mater. Sci. Technol.
, Vol.
7
,
1991
, pp.
686
698
. https://doi.org/10.1179/026708391790184915
163.
Matsuzaki
,
A.
,
Bhadeshia
,
H.
, and
Harada
,
H.
, “
Stress Affected Bainitic Transformation in a Fe-C-Si-Mn Alloy
,”
Acta Metall. Mater.
, Vol.
42
,
1994
, pp.
1081
1090
. https://doi.org/10.1016/0956-7151(94)90125-2
164.
Denis
,
S.
,
Gautier
,
E.
,
Sjostrom
,
S.
, and
Simon
,
A.
, “
Influence of Stresses on the Kinetics of Pearlitic Transformation during Continuous Cooling
,”
Acta Metall.
, Vol.
35
,
1987
, pp.
1621
1632
. https://doi.org/10.1016/0001-6160(87)90109-X
165.
Chang
,
L. C.
and
Bhadeshia
,
H.
, “
Stress-affected Transformation to Lower Bainite
,”
J. Mater. Sci.
, Vol.
31
,
1996
, pp.
2145
2148
. https://doi.org/10.1007/BF00356638
166.
Liu
,
C. C.
,
Liu
,
Z.
,
Xu
,
X. J.
,
Chen
,
G. X.
, and
Wu
,
J. Z.
, “
Effect of Stress on Transformation and Prediction of Residual Stresses
,”
Mater. Sci. Technol.
, Vol.
14
,
1998
, pp.
747
750
. https://doi.org/10.1179/026708398790300990
167.
Denis
,
S.
,
Archambault
,
P.
,
Gautier
,
E.
,
Simon
,
A.
, and
Beck
,
G.
, “
Prediction of Residual Stress and Distortion of Ferrous and Non-ferrous Metals: Current Status and Future Developments
,”
J. Mater. Eng. Perform.
, Vol.
11
,
2002
, pp.
92
102
. https://doi.org/10.1007/s11665-002-0014-2
168.
Liu
,
C. C.
,
Ju
,
D. Y.
,
Yao
,
K. F.
,
Liu
,
Z.
, and
Xu
,
X. J.
, “
Bainitic Transformation Kinetics and Stress Assisted Transformation
,”
Mater. Sci. Technol.
, Vol.
17
,
2001
, pp.
1229
1237
.
169.
Maier
,
H. J.
and
Ahrens
,
U.
, “
Isothermal Bainitic Transformation in Low Alloy Steels: Factors Limiting Prediction of the Resulting Material’s Properties
,”
Z. Metallkd.
, Vol.
93
,
2002
, pp.
712
718
.
170.
Meng
,
Q. P.
,
Rong
,
Y. H.
, and
Hsu
,
T. Y.
, “
Effect of Internal Stress on Autocatalytic Nucleation of Martensitic Transformation
,”
Metall. Mater. Trans. A
, Vol.
37
,
2006
, pp.
1405
1411
. https://doi.org/10.1007/s11661-006-0085-z
171.
Hsu
,
T. Y.
, “
Additivity Hypothesis and Effects of Stress on Phase Transformations in Steel
,”
Curr. Opin. Solid State Mater. Sci.
, Vol.
9
,
2005
, pp.
256
268
. https://doi.org/10.1016/j.cossms.2006.02.011
172.
Veaux
,
M.
,
Denis
,
S.
, and
Archambault
,
P.
, “
Modelling and Experimental Study of the Bainitic Transformation, Residual Stresses and Deformations in the Quenching Process of Middle Alloyed Steel Parts
,”
J. Phys. IV
, Vol.
120
,
2004
, pp.
719
726
.
173.
Veaux
,
M.
,
Louin
,
J. C.
,
Houin
,
J. P.
,
Denis
,
S.
,
Archambault
,
P.
, and
Aeby-Gautier
,
E.
, “
Bainitic Transformation under Stress in Medium Alloyed Steels
,”
J. Phys. IV
, Vol.
11
,
2001
, pp.
181
188
. https://doi.org/10.1051/jp4:2001423
174.
Tszeng
,
T. C.
, “
Autocatalysis in Bainite Transformations
,”
Mater. Sci. Eng. A
, Vol.
293
,
2000
, pp.
185
190
. https://doi.org/10.1016/S0921-5093(00)01221-1
175.
Loshkarev
,
V. E.
, “
Mathematical Modeling of the Hardening Process with Allowance for the Effect of Stresses on Structural Transformations in Steel
,”
Metal Science and Heat Treatment
, Vol.
28
,
1986
, pp.
3
9
. https://doi.org/10.1007/BF00735537
176.
Hsu
,
T. Y.
, “
Martensitic Transformation under Stress
,”
Mater. Sci. Eng. A
, Vol.
438
,
2006
, pp.
64
68
. https://doi.org/10.1016/j.msea.2006.02.111
177.
Liu
,
C. C.
,
Yao
,
K. F.
, and
Liu
,
Z.
, “
Quantitative Research on Effects of Stresses and Strains on Bainitic Transformation Kinetics and Transformation Plasticity
,”
Mater. Sci. Technol.
, Vol.
16
,
2000
, pp.
643
647
.
178.
Patel
,
J. R.
and
Cohen
,
M.
, “
Criterion for the Action of Applied Stress in the Martensitic Transformation
,”
Acta Metall.
, Vol.
1
,
1953
, pp.
531
538
. https://doi.org/10.1016/0001-6160(53)90083-2
179.
Rees
,
G. I.
and
Bhadeshia
,
H.
, “
Bainite Transformation Kinetics: 1. Modified Model
,”
Mater. Sci. Technol.
, Vol.
8
,
1992
, pp.
985
993
. https://doi.org/10.1179/026708392790409842
180.
Rees
,
G. I.
and
Bhadeshia
,
K. D. H.
, “
Bainite Transformation Kinetics: 2. Non-uniform Distribution of Carbon
,”
Mater. Sci. Technol.
, Vol.
8
,
1992
, pp.
994
996
. https://doi.org/10.1179/026708392790409815
181.
Greenwood
,
G. W.
and
Johnson
,
R. H.
, “
The Deformation of Metals under Small Stresses during Phase Transformations
,”
Proc. R. Soc.
London
, Vol.
283
,
1965
, pp.
403
422
.
182.
Abrassart
,
F.
, “
Stress-induced Gamma-alpha Martensitic Transformation in Two Carbon Stainless-steels—Application to Trip Steels
,”
Metall. Trans.
, Vol.
4
,
1973
, pp.
2205
2216
. https://doi.org/10.1007/BF02643289
183.
Fischer
,
F. D.
and
Schlogl
,
S. M.
, “
The Influence of Material Anisotropy on Transformation-induced Plasticity in Steel Subject to Martensitic-Transformation
,”
Mech. Mater.
, Vol.
21
,
1995
, pp.
1
23
. https://doi.org/10.1016/0167-6636(94)00070-0
184.
Cherkaoui
,
M.
and
Berveiller
,
M.
, “
Mechanics of Martensitic Phase Transformation in SMA and TRIP Steels
,”
Int. J. Plast.
, Vol.
16
,
2000
, pp.
1133
1134
. https://doi.org/10.1016/S0749-6419(00)00003-6
185.
Taleb
,
L.
,
Cavallo
,
N.
, and
Waeckel
,
F.
, “
Experimental Analysis of Transformation Plasticity
,”
Int. J. Plast.
, Vol.
17
,
2001
, pp.
1
20
. https://doi.org/10.1016/S0749-6419(01)00002-X
186.
Jacques
,
P.
,
Furnemont
,
Q.
,
Mertens
,
A.
, and
Delannay
,
F.
, “
On the Sources of Work Hardening in Multiphase Steels Assisted by Transformation-induced Plasticity
,”
Philos. Mag. A
, Vol.
81
,
2001
, pp.
1789
1812
. https://doi.org/10.1080/01418610108216637
187.
Taleb
,
L.
and
Petit-Grostabussiat
,
S.
, “
Elastoplasticity and Phase Transformations in Ferrous Alloys: Some Discrepancies between Experiments and Modeling
,”
J. Phys. IV
, Vol.
12
,
2002
, pp.
187
194
.
188.
Suiker
,
A. S. J.
and
Turteltaub
,
S.
, “
Computational Modelling of Plasticity Induced by Martensitic Phase Transformations
,”
Int. J. Numer. Methods Eng.
, Vol.
63
,
2005
, pp.
1655
1693
. https://doi.org/10.1002/nme.1327
189.
De Jong
,
M.
and
Rathenau
,
G. W.
, “
Mechanical Properties of Iron and Some Iron Alloys while Undergoing Allotropic Transformation
,”
Acta Metall.
, Vol.
7
,
1959
, pp.
246
253
. https://doi.org/10.1016/0001-6160(59)90017-3
190.
Leblond
,
J. B.
,
Devaux
,
J.
, and
Devaux
,
J. C.
, “
Mathematical Modelling of Transformation Plasticity in Steels: I. Case of Ideal-plastic Phases
,”
Int. J. Plast.
, Vol.
5
,
1989
, pp.
551
572
. https://doi.org/10.1016/0749-6419(89)90001-6
191.
Wolff
,
M.
,
Böhm
,
M.
, and
Suhr
,
B.
, “
Comparison of Different Approaches to Transformation-induced Plasticity in Steel
,”
Materialwiss. Werkstofftech.
, Vol.
40
,
2009
, pp.
454
459
. https://doi.org/10.1002/mawe.200900476
192.
Tanaka
,
K.
,
Terasaki
,
T.
,
Goto
,
S.
,
Antretter
,
T.
,
Fischer
,
F. D.
, and
Cailletaud
,
G.
, “
Effect of Back Stress Evolution due to Martensitic Transformation on Iso-volume Fraction Lines in a Cr-Ni-Mo-Al-Ti Maraging Steel
,”
Mater. Sci. Eng. A
, Vol.
341
,
2003
, pp.
189
196
. https://doi.org/10.1016/S0921-5093(02)00202-2
193.
Jaramillo
,
R. A.
,
Lusk
,
M. T.
, and
Mataya
,
M. C.
, “
Dimensional Anisotropy during Phase Transformations in a Chemically Banded 5140 Steel. Part I: Experimental Investigation
,”
Acta Mater.
, Vol.
52
,
2004
, pp.
851
858
. https://doi.org/10.1016/j.actamat.2003.11.017
194.
Cui
,
C.
,
Schulz
,
A.
,
Fritsching
,
U.
, and
Kohlmann
,
R.
, “
Spray Forming of Homogeneous 20MnCr5 Steel of Low Distortion Potential
,”
Materialwiss. Werkstofftech.
, Vol.
37
,
2006
, pp.
34
39
. https://doi.org/10.1002/mawe.200500977
195.
Wei
,
J.
,
Kessler
,
O.
,
Hunkel
,
M.
,
Hoffmann
,
F.
, and
Mayr
,
P.
, “
Anisotropic Phase Transformation Strain in Forged D2 Tool Steel
,”
Mater. Sci. Technol.
, Vol.
20
,
2004
, pp.
909
914
. https://doi.org/10.1179/026708304225019641
196.
Mola
,
J.
,
Chae
,
D.
, and
de Cooman
,
B.
, “
Dilatometric Analysis of Anisotropic Dimensional Changes in a 16 pct Cr Stainless Steel with a Planar Banded Structure
,”
Metall. Mater. Trans. A
, Vol.
41
A,
2010
, pp.
1429
1440
. https://doi.org/10.1007/s11661-010-0206-6
197.
Hunkel
,
M.
,
Dalgic
,
M.
, and
Hoffmann
,
F.
, “
Plasticity of the Low Alloy Steel SAE 5120 during Heating and Austenitizing
,”
BHM Berg- und Hüttenmännische Monatshefte
, Vol.
155
,
2010
, pp.
125
128
. https://doi.org/10.1007/s00501-010-0548-9
198.
Şimşir
,
C.
,
Lübben
,
T.
,
Clausen
,
B.
,
Hoffmann
,
F.
, and
Zoch
,
H.-W.
, “
Anisotropic Transformation Strain and Its Consequences in Coupling of Prior Forming Operations with Heat Treatment Simulation
,”
Proceedings of the International Metallurgy and Materials Congress (IMMC 2010)
,
Chamber of Turkish Metallurgical and Materials Engineers
,
Istanbul, Turkey
, November 11–13,
2010
.
199.
Schuh
,
C.
and
Dunand
,
D. C.
, “
Non-isothermal Transformation-mismatch Plasticity: Modeling and Experiments on Ti-6Al-4V
,”
Acta Mater.
, Vol.
49
,
2001
, pp.
199
210
. https://doi.org/10.1016/S1359-6454(00)00318-9
200.
Jaramillo
,
R. A.
and
Lusk
,
M. T.
, “
Dimensional Anisotropy during Phase Transformations in a Chemically Banded 5140 Steel. Part II: Modeling
,”
Acta Mater.
, Vol.
52
,
2004
, pp.
859
867
. https://doi.org/10.1016/j.actamat.2003.10.020
201.
Hunkel
,
M.
, “
Anisotropic Transformation Strain and Transformation Plasticity: Two Corresponding Effects
,”
Materialwiss. Werkstofftech.
, Vol.
40
,
2009
, pp.
466
472
. https://doi.org/10.1002/mawe.200900478
202.
Zwigl
,
P.
and
Dunand
,
D. C.
, “
A Non-linear Model for Internal Stress Superplasticity
,”
Acta Mater.
, Vol.
45
,
1997
, pp.
5285
5294
. https://doi.org/10.1016/S1359-6454(97)00186-9
203.
Han
,
H. N.
and
Lee
,
J. K.
, “
A Constitutive Model for Transformation Superplasticity under External Stress during Phase Transformation of Steels
,”
ISIJ Int.
, Vol.
42
,
2002
, pp.
200
205
. https://doi.org/10.2355/isijinternational.42.200
204.
Rees
,
G. I.
and
Shipway
,
R. H.
, “
Modelling Transformation Plasticity during the Growth of Bainite under Stress
,”
Mater. Sci. Eng.
, Vol.
223
,
1997
, pp.
168
178
. https://doi.org/10.1016/S0921-5093(96)10478-0
205.
Han
,
H. N.
and
Suh
,
D.-W.
, “
A Model for A Model for Transformation Plasticity during Bainite Transformation of Steel under External Stress
,”
Acta Mater.
, Vol.
51
,
2003
, pp.
4907
4917
. https://doi.org/10.1016/S1359-6454(03)00333-1
206.
Han
,
H. N.
,
Lee
,
C. G.
,
Oh
,
C.-S.
,
Lee
,
T.-H.
, and
Kim
,
S.-J.
, “
A Model for Deformation Behavior and Mechanically Induced Martensitic Transformation of Metastable Austenitic Steel
,”
Acta Mater.
, Vol.
52
,
2004
, pp.
5203
5214
. https://doi.org/10.1016/j.actamat.2004.07.031
207.
Lee
,
M.-G.
,
Kim
,
S.-J.
,
Han
,
H. N.
, and
Jeong
,
W. C.
, “
Implicit Finite Element Formulations for Multi-phase Transformation in High Carbon Steel
,”
Int. J. Plast.
, Vol.
25
,
2009
, pp.
1726
1758
. https://doi.org/10.1016/j.ijplas.2008.11.010
208.
Mahnken
,
R.
,
Schneidt
,
A.
, and
Antretter
,
T.
, “
Macro Modelling and Homogenization for Transformation Induced Plasticity of a Low-alloy Steel
,”
Int. J. Plast.
, Vol.
25
,
2009
, pp.
183
204
. https://doi.org/10.1016/j.ijplas.2008.03.005
209.
Wolff
,
M.
,
Böhm
,
M.
, and
Suhr
,
B.
, “
Comparison of Different Approaches to Transformation-induced Plasticity in Steel
,”
Materialwiss. Werkstofftech.
, Vol.
40
,
2009
, pp.
454
459
. https://doi.org/10.1002/mawe.200900476
210.
Diani
,
J. M.
,
Saber
,
H.
, and
Berveiller
,
M.
, “
Micromechanical Modeling of the Martensitic Transformation Induced Plasticity Phenomenon in Steels
,”
Int. J. Eng. Sci.
, Vol.
33
,
1995
, pp.
1921
1934
. https://doi.org/10.1016/0020-7225(95)00045-Y
211.
Fischer
,
F. D.
,
Sun
,
Q.-P.
, and
Tanaka
,
K.
, “
Transformation-induced Plasticity
,”
Appl. Mech. Rev.
, Vol.
49
,
1996
, pp.
317
364
. https://doi.org/10.1115/1.3101930
212.
Fischer
,
F. D.
,
Reisner
,
G.
,
Werner
,
E.
,
Tanaka
,
K.
,
Cailletaud
,
G.
, and
Antretter
,
T.
, “
A New View on Transformation-induced Plasticity
,”
Int. J. Plast.
, Vol.
16
,
2000
, pp.
723
748
. https://doi.org/10.1016/S0749-6419(99)00078-9
213.
Cherkaoui
,
M.
,
Berveiller
,
M.
, and
Sabar
,
H.
, “
Micromechanical Modeling of Martensitic Transformation Induced Plasticity in Austenitic Single Crystal
,”
Int. J. Plast.
, Vol.
14
,
1998
, pp.
597
626
. https://doi.org/10.1016/S0749-6419(99)80000-X
214.
Cherkaoui
,
M.
,
Berveiller
,
M.
, and
Lemoine
,
X.
, “
Couplings between Plasticity and Martensitic Phase Transformation: Overall Behavior of Polycrystalline TRIP Steels
,”
Int. J. Plast.
, Vol.
16
,
2000
, pp.
1215
1241
. https://doi.org/10.1016/S0749-6419(00)00008-5
215.
Iwamoto
,
T.
, “
Multiscale Computational Simulation of Deformation Behavior of TRIP Steel with Growth of Martensitic Particles in Unit Cell by Asymptotic Homogenization Method
,”
Int. J. Plast.
, Vol.
20
,
2004
, pp.
841
869
. https://doi.org/10.1016/j.ijplas.2003.05.002
216.
Levitas
,
V. I.
and
Ozsoy
,
I. B.
, “
Micromechanical Modeling of Stress-induced Phase Transformations. Part 2. Computational Algorithms and Examples
,”
Int. J. Plast.
, Vol.
25
,
2009
, pp.
546
583
. https://doi.org/10.1016/j.ijplas.2008.02.005
217.
Apel
,
M.
,
Benke
,
S.
, and
Steinbach
,
I.
, “
Virtual Dilatometer Curves and Effective Young’s Modulus of a 3D Multiphase Structure Calculated by the Phase-field Method
,”
Comput. Mater. Sci.
, Vol.
45
,
2009
, pp.
589
592
. https://doi.org/10.1016/j.commatsci.2008.07.007
218.
Manchiraju
,
S.
and
Anderson
,
P.
, “
Coupling between Martensitic Phase Transformations and Plasticity: A Microstructure-based Finite Element Model
,”
Int. J. Plast.
, Vol.
26
,
2010
, pp.
1508
1526
. https://doi.org/10.1016/j.ijplas.2010.01.009
219.
Lee
,
M.-G.
,
Kim
,
S.-J.
, and
Han
,
H. N.
, “
Crystal Plasticity Finite Element Modeling of Mechanically Induced Martensitic Transformation in Metastable Austenite
,”
Int. J. Plast.
, Vol.
26
,
2010
, pp.
688
710
. https://doi.org/10.1016/j.ijplas.2009.10.001
220.
Barbe
,
F.
,
Quey
,
R.
,
Taleb
,
L.
, and
Souza de Cursi
,
E.
, “
Numerical Modelling of the Plasticity Induced during Diffusive Transformation. An Ensemble Averaging Approach for the Case of Random Arrays of Nuclei
,”
Eur. J. Mech. A/Solids
, Vol.
27
,
2008
, pp.
1121
1139
. https://doi.org/10.1016/j.euromechsol.2008.01.005
221.
Hoang
,
H.
,
Barbe
,
F.
,
Quey
,
R.
, and
Taleb
,
L.
, “
FE Determination of the Plasticity Induced during Diffusive Transformation in the Case of Nucleation at Random Locations and Instants
,”
Comput. Mater. Sci.
, Vol.
43
,
2007
, pp.
101
107
. https://doi.org/10.1016/j.commatsci.2007.07.032
222.
Quey
,
R.
,
Hoang
,
H.
,
Barbe
,
F.
, and
Taleb
,
L.
,
2010
, “
Effect of the Random Spatial Distribution of Nuclei on the Transformation Plasticity in a Diffusively Transforming Steel
,”
International Journal of Microstructure and Materials Properties
, Vol.
5
,
2010
, pp.
354
364
. https://doi.org/10.1504/IJMMP.2010.037612
223.
Barbe
,
F.
and
Quey
,
R.
, “
A Numerical Modelling of 3D Polycrystal-to-polycrystal Diffusive Phase Transformations Involving Crystal Plasticity
,”
Int. J. Plast.
, Vol.
27
,
2011
, pp.
823
840
. https://doi.org/10.1016/j.ijplas.2010.09.008
224.
Boudiaf
,
A.
,
Taleb
,
L.
, and
Belouchrani
,
M. A.
, “
Experimental Analysis of the Correlation between Martensitic Transformation Plasticity and the Austenitic Grain Size in Steels
,”
Eur. J. Mech. A/Solids
, Vol.
30
,
2011
, pp.
326
335
. https://doi.org/10.1016/j.euromechsol.2010.12.004
225.
Stringfellow
,
R. G.
and
Parks
,
D. M.
, “
A Self-consistent Model of Isotropic Viscoplastic Behavior in Multiphase Materials
,”
Int. J. Plast.
, Vol.
7
,
1991
, pp.
529
547
. https://doi.org/10.1016/0749-6419(91)90043-X
226.
Simsir
,
C.
and
Gur
,
C. H.
, “
3-D FEM Simulation of Steel Quenching and Investigation of the Effect of Asymmetric Geometry on Residual Stress Distribution
,”
J. Mater. Process. Technol.
, Vol.
207
,
2008
, pp.
211
221
. https://doi.org/10.1016/j.jmatprotec.2007.12.074
This content is only available via PDF.
You do not currently have access to this content.