This work presents a constitutive model for metastable austenitic steels exhibiting Strain Induced Martensitic Transformation (SIMT). Based on the description of the kinetics of phase transformation proposed by Olson and Cohen [3], and later generalized to 3D by Stringfellow et al. [7] and Papatriantafillou et al. [4], this model includes the effect of temperature increase on the kinetics of SIMT and on the thermal softening of the phases. This allows capturing relevant phenomena exhibited by metastable austenitic steels when subjected to plastic deformation at high strain rates. A systematic procedure for the identification of the constitutive parameters has been proposed. The predictions of the constitutive description are compared with experiments for the austenitic steel AISI 304 provided by Rodríguez-Martínez et al. [6]. Good correlation between experiments and modelling are achieved in terms of macroscopic strain-stress curves and volume fraction of martensite formed during straining

CASADO, Alvaro

FERNANDEZ-SAEZ, José

PESCI, Raphaël

RODRIGUEZ-MARTINEZ, José Antonio

RUSINEK, Alexis

ZAERA, Ramon

English

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Ramon ZAERA, Alvaro CASADO, José Antonio RODRIGUEZ-MARTINEZ, Alexis RUSINEK,
Raphaël PESCI, José FERNANDEZ-SAEZ - Numerical simulation of the effect of adiabatic
temperature increase in martensitic transformation of austenitic steels - 2011
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Numerical simulation of the effect of adiabatic temperature increase in martensitic 
transformation of austenitic steels 
R. Zaera1, A. Casado2, J.A. Rodríguez-Martínez1, A. Rusinek3, R. Pesci4, J. Fernández-Sáez1 
1Department of Continuum Mechanics and Structural Analysis, University Carlos III of Madrid 
Avda. de la Universidad, 30. 28911 Leganés, Madrid, SPAIN 
e-mail: ramón.zaera@uc3m.es; jarmarti@ing.uc3m.es; ppfer@ing.uc3m.es 
2Andritz Hydro 
Paseo de la Castellana 163, 28046 Madrid, Spain 
e-mail: alvaro.casado@andritz.com 
3National Engineering School of Metz, Laboratory of Mechanics, Biomechanics, Polymers and Structures 
1 route d’Ars Laquenexy, 57078 Metz Cedex 3, France 
e-mail: rusinek@enim.fr 
4ENSAM-Arts et Métiers ParisTech, Laboratory of Physics and Mechanics of Materials (LPMM), FRE CNRS 3236 
4 Rue Augustin Fresnel, 57078 Metz Cedex 3, France 
e-mail: raphael.pesci@ensam.eu 
Abstract 
This work presents a constitutive model for metastable austenitic steels exhibiting Strain Induced Martensitic Transformation 
(SIMT). Based on the description of the kinetics of phase transformation proposed by Olson and Cohen [3], and later generalized to 
3D by Stringfellow et al. [7] and Papatriantafillou et al. [4], this model includes the effect of temperature increase on the kinetics of 
SIMT and on the thermal softening of the phases. This allows capturing relevant phenomena exhibited by metastable austenitic steels 
when subjected to plastic deformation at high strain rates. A systematic procedure for the identification of the constitutive parameters 
has been proposed. The predictions of the constitutive description are compared with experiments for the austenitic steel AISI 304 
provided by Rodríguez-Martínez et al. [6]. Good correlation between experiments and modelling are achieved in terms of 
macroscopic strain-stress curves and volume fraction of martensite formed during straining. 
Keywords: austenitic steel, strain induced martensitic transformation, constitutive equation, thermo-viscoplasticity, thermography, 
X-ray diffraction 
1. Introduction
Austenitic grades are the most commonly used stainless 
steels in industry. The high nickel content shifts the martensite 
start temperature to very low temperatures during cooling, 
keeping the material fully austenitic after quenching at room 
temperature. This gives excellent work hardening, high 
strength, ductility and formability, as well as good weldability. 
Some of the less highly alloyed austenitic -and yet largely used- 
grades are referred to as metastable because of their ability to 
transform from the initial austenite phase to martensite. This 
transformation may occur in different ways and one of them, 
namely Strain Induced Martensitic Transformation SIMT, takes 
place when the steel yields at a range of temperatures 
s
M σ - dM
that covers many of the in-service conditions reached by 
metastable austenitic steels in industrial applications. The 
analysis of such a process therefore presents great interest. Due 
to their ductility and work hardening ability, metastable 
austenitic steels are used for energy absorption in crash or blast 
protection. The abovementioned processes, involving high 
strain rates, are often accompanied by a rise in temperature due 
to the dissipation of plastic work. This means that the 
martensitic transformation approaches adiabaticity. Also, 
forming and machining processes, used to shape components 
made of metastable austenitic steels, take place in non-
isothermal conditions. This work presents a constitutive model 
for steels exhibiting SIMT, based on the previous works of 
Olson and Cohen [3], Stringfellow et al. [7] and 
Papatriantafillou et al. [4]. The model includes the effect of 
temperature increase on the kinetics of SIMT and on the 
thermal softening of the phases. A systematic procedure for the 
identification of the constitutive parameters is proposed. The 
predictions of the constitutive description are compared with 
dynamic experiments for the austenitic steel AISI 304 provided 
by Rodríguez-Martínez et al. [6]. Good correlation between 
experiments and modelling are achieved in terms of 
macroscopic strain-stress curves and volume fraction of 
martensite formed during straining. 
2. The constitutive description
Since the variation of temperature is intended to be 
considered in the proposed model, the equations of kinetics of 
SIMT due to Stringfellow et al. [7] have been modified with a 
new exponential law to account for the influence of temperature 
change in the thermodynamic driving force. Thermal strains are 
taken into account, contributing to the instantaneous volume 
expansion that accompanies the martensitic transformation. The 
homogenization process proposed by Ponte Castañeda [5] and 
Suquet [8], and used by Papatriantafillou et al. [4] for 
Transformation Induced Plasticity (TRIP) steels, is considered 
to obtain equivalent properties from the constitutive equations 
of austenite and martensite. A potential law is used to determine 
strain hardening, strain-rate hardening and thermal softening of 
the phases. The temperature increase during straining is 
obtained through equivalent properties. Within a corotational 
frame, the classical return mapping algorithm is proposed to 
solve the set of nonlinear rate equations in a finite deformation 
frame. An implicit scheme is used to correct the trial stress and 
to discretize every constitutive equation, and is implemented in 
ABAQUS/Explicit to reproduce the experimental results for the 
considered austenitic steel. 
3. Identification of the constitutive model
parameters
The identification procedure is split into two parts: 
Identification of the material parameters involved into the 
strain hardening/softening definition of the single phases (i. e. 
determination of the strai, rate and temperature sensitivities of 
the phases). This is supported by the experimental data reported 
in [1, 6]. 
Identification of the material parameters involved in the ki-
netics of the SIMT process. This is conducted following Iwa-
moto and Tsuta’s work [2] and based on the experimental ob-
servations reported by Rodriguez-Martinez et al. [6]. 
4. Validation of the constitutive model
In this work, results from dynamic tensile tests performed 
by the authors within the range of strain rates -1 1 -110 s 500  s−≤ ε ≤ɺ
[6] have been considered to conduct the validation. The X-ray 
diffraction technique has been used to determine the volume 
fraction of martensite in the post mortem specimens, leading to 
a good validation of the transformation kinetics [6]. Moreover, 
let us mention that the range of loading rates covered during the 
experiments agrees with that expected in engineering applica-
tions like crashworthiness, in which TRIP steels are frequently 
used. Numerical simulations of the dynamic tensile tests have 
been conducted. It has to be highlighted that considering a vis-
coplastic material model acts as a regularization method for 
solving mesh-dependent strain softening problems of plasticity. 
Rate dependent plasticity introduces implicitly a length-scale 
parameter into the boundary value problem, diffusing the locali-
zation region. It guarantees a good definition of the problem, 
avoiding pathological mesh dependency and ensuring the 
uniqueness of the numerical solution. Good correlation between 
experiments and modelling are achieved in terms of macroscop-
ic strain-stress curves and volume fraction of martensite formed 
during straining, Fig. 1. 
0
250
500
750
1000
1250
0 0,1 0,2 0,3 0,4 0,5 0,6
B
D
Tr
u
e 
st
re
ss
, 
σ
 
(M
Pa
)
True strain, ε
100 s-1
To = 293 K
Experiments [Rodríguez-Martínez et al. 2011]
Numerical simulation
Material: AISI 304
stress contour
Figure 1. Comparison between numerical predictions of 
the FE model and experiments at 100 s-1 and T0=293 K 
[6]. 
5. Conclusions
This contribution presents a constitutive model for 
describing the martensitic transformation occurring in 
metastable austenitic steels at high strain rates. The model 
extends formulations of Olson and Cohen [3], Stringfellow et al. 
[7] and Papatriantafillou et al. [4], including both the 
temperature sensitivity of the single phases and the temperature 
sensitivity of the transformation. A straightforward method for 
the model calibration has been developed. The predictions of 
the constitutive model agree with experimental results in terms 
of macroscopic stress-strain curves and volume fraction of 
martensite formed during loading.  
Acknowledgements 
The researchers of the University Carlos III of Madrid are 
indebted to the Comunidad Autónoma de Madrid (Project 
CCG08-UC3M/MAT-4464) and to the Ministerio de Ciencia e 
Innovación de España (Project DPI/2008-06408) for the finan-
cial support received which allowed conducting part of this 
work.
References 
[1] Huang G. L., Matlock D. K., Krauss G. Martensite 
formation, strain rate sensitivity, and deformation behavior 
of type 304 stainless steel sheet. Metall. Trans. A, 20ª, 
1239-1246, 1989. 
[2] Iwamoto T., Tsuta T. Computational simulation on 
deformation behaviour of CT specimens of TRIP steel 
under mode I loading for evaluation of fracture toughness. 
International Journal of Plasticity. 11, pp. 1583-1606, 
2002. 
[3] Olson, G.B., Cohen, M., Kinetics of strain-induced 
martensitic nucleation, Metallurgical Transactions A, 6A, 
pp. 791-795, 1975. 
[4] Papatriantafillou, I., Aravas, N., Haidemenopoulos, G., 
Finite element modeling of trip steels, Steel Research Int., 
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[5] Ponte Castañeda, P., New variational principles in plasticity 
and their application to composite materials, J. Mech. Phys. 
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[6] Rodríguez-Martínez J. A., Pesci R., Rusinek A. 
Experimental study on the martensitic transformation in 
AISI 304 steel sheets subjected to tension under wide ranges 
of strain rate at room temperature. Materials Science and 
Engineering A (Submitted for Publication). 
[7] Stringfellow, R.G., Parks, D.M., Olson, G.B., A constitutive 
model for transformation plasticity accompanying strain-
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[8] Suquet P., Overall properties of nonlinear composites: 
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Numerical simulation of the effect of adiabatic temperature increase in martensitic transformation of austenitic steels

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Numerical simulation of the effect of adiabatic temperature increase in martensitic transformation of austenitic steels

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