A simplified model of martensitic transformation in stainless steels at cryogenic temperatures is proposed. The constitutive modeling of plastic flow under cryogenic conditions is based on the assumption of small strains (⩽0.2). The hardening law for the biphase material (α martensite platelets embedded in the γ austenite matrix) has been obtained from the Mori-Tanaka homogenization. A mixed hardening with combined isotropic and kinematic contributions is proposed. The constitutive model, containing a reasonable number of parameters, has been numerically implemented and checked with respect to experimental data. Finally, the model is applied to compute the martensite evolution in thin-walled corrugated shells designed for cryogenic temperatures (mechanical compensation system of the Large Hadron Collider at CERN).

1.
Morris
,
J. W.
,
Chan
,
J. W.
, and
Mei
,
Z.
,
1992
, “
The Influence of Deformation-Induced Martensite on the Cryogenic Behavior of 300-Series Stainless Steels
,”
Cryogenics
,
32
, pp.
78
85
.
2.
Suzuki, K., Fukakura, J., and Kashiwaya, H., 1988, Cryogenic Fatigue Properties of 304L and 316L Stainless Steels Compared to Mechanical Strength and Increasing Magnetic Permeability, American Society for Testing and Materials, pp. 190–197.
3.
Olson
,
G. B.
, and
Cohen
,
M.
,
1975
, “
Kinetics of Strain-Induced Martensitic Nucleation
,”
Metall. Trans. A
,
6A
, Apr., pp.
791
795
.
4.
Narutani
,
T.
,
Olson
,
G. B.
, and
Cohen
,
M.
,
1982
, “
Constitutive Flow Relations for Austenitic Steels During Strain-Induced Martensitic Transformation
,”
J. de Phys., Colloque C4
, Supple´ment au No. 12,
43
, pp.
429
434
.
5.
Stringfellow
,
R. G.
,
Parks
,
D. M.
, and
Olson
,
G. B.
,
1992
, “
Constitutive Model for Transformation Plasticity Accompanying Strain-Induced Martensitic Transformations in Metastable Austenitic Steels
,”
Acta Metall. Mater.
,
40
(
7
), pp.
1703
1716
.
6.
Angel
,
T.
,
1954
, “
Formation of Martensite in Austenitic Stainless Steel
,”
J. Iron Steel Inst.
,
177
, pp.
165
174
.
7.
Levitas
,
V. I.
,
Idesman
,
A. V.
, and
Olson
,
G. B.
,
1999
, “
Continuum Modeling of Strain-Induced Martensitic Transformation at Shear Band Intersections
,”
Acta Mater.
,
47
(
1
), pp.
219
233
.
8.
Lebedev
,
A. A.
, and
Kosarchuk
,
V. V.
,
2000
, “
Influence of Phase Transformation on the Mechanical Properties of Austenitic Stainless Steels
,”
Int. J. Plast.
,
16
, pp.
749
767
.
9.
Fisher
,
F. D.
,
Reisner
,
G.
,
Werner
,
E.
,
Tanaka
,
K.
,
Cailletaud
,
G.
, and
Antretter
,
T.
,
2000
, “
A New View on Transformation Induced Plasticity (TRIP)
,”
Intl. J. Plasticity
,
16
, pp.
723
748
.
10.
Cherkaoui
,
M.
,
Berveiller
,
M.
, and
Lemoine
,
X.
,
2000
, “
Couplings Between Plasticity and Martensitic Phase Transformation: Overall Behavior of Polycrystalline TRIP Steels
,”
Intl. J. Plasticity
,
16
, pp.
1215
1241
.
11.
Tomita
,
Y.
, and
Iwamoto
,
T.
,
2001
, “
Computational Prediction of Deformation Behavior of TRIP Steels Under Cycling Loading
,”
Int. J. Mech. Sci.
,
43
, pp.
2017
2034
.
12.
Reed, R. P., “Martensitic phase transformations,” Material at Low Temperatures, American Society for Metals.
13.
Tomita
,
Y.
, and
Iwamoto
,
T.
,
1995
, “
Constitutive Modeling of TRIP Steel and Its Application to the Improvement of Mechanical Properties
,”
Int. J. Mech. Sci.
,
37
(
12
), pp.
1295
1305
.
14.
Bornert, M., Bretheau, T., and Gilormini, P., 2001, Homoge´ne´isation en me´canique des mate´riaux 1: Mate´riaux ale´atoires e´lastiques et milieux pe´riodiques, Herme`s, Paris.
15.
Mori
,
T.
, and
Tanaka
,
K.
,
1973
, “
Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions
,”
Acta Metall. Mater.
,
21
, pp.
597
629
.
16.
Chaboche
,
J.-L.
,
1993
, “
Cyclic Viscoplastic Constitutive Equations, Part I: A Thermodynamically Consistent Formulation
,”
ASME J. Appl. Mech.
,
60
, pp.
813
828
.
17.
Sadough-Vanini, A., and Lehr, P., 1994, “Comportement en fatigue oligocyclique de l’acier inoxydable Z3CN18-10 a` 20 et −196°C,” La revue de me´tallurgie-CIT/Science et Ge´nie des mate´riaux, May, pp. 781–788.
18.
Zyczkowski, M., 1981, Combined Loadings in the Theory of Plasticity, Scientific Publication, Warsaw.
19.
Wilkins
,
M. L.
,
1964
, “
Calculation of Elastic-Plastic Flow
,”
Methods Comput. Phys.
,
3
, pp.
211
263
.
20.
Ortiz
,
M.
, and
Simo
,
J. C.
,
1986
, “
An Analysis of a New Class of Integration Algorithms for Elastoplastic Constitutive Equations
,”
Int. J. Numer. Methods Eng.
,
23
, pp.
1353
1366
.
21.
Iwamoto
,
T.
,
Tsuta
,
T.
, and
Tomita
,
Y.
,
1998
, “
Investigation on Deformation Mode Dependence of Strain-Induced Martensitic Transformation in TRIP Steels and Modeling of Transformation Kinetics
,”
Int. J. Mech. Sci.
,
40
(
2–3
), pp.
173
182
.
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