ESOMAT 2009, 06016 (2009)
DOI:10.1051/esomat/200906016
© Owned by the authors, published by EDP Sciences, 2009
Mechanical Behavior of a Metastable Austenitic Stainless Steel
3+DXãLOG1,a, P. Pilvin2 DQG0.DUOtN1
1
Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of
Materials, Trojanova 13, 120 00 Praha 2, Czech Republic
2
8QLYHUVLWp GH %UHWDJQH-Sud, /DERUDWRLUH G¶,QJpQLHULH GHV 0DWpULDX[ GH %UHWDJQH 5XH GH 6DLQW-0DXGp %3
92116, 56321 Lorient, France
Abstract. The mechanical properties of metastable austenitic steel corresponding to the AISI301 were characterized
by means of tensile testing and cupping tests. High sensitivity to the strain rate was observed. The fracture
mechanism in tensile specimens changed from the combination of cleavage and ductile dimpled rupture at lower
strain rates to entire ductile dimpled rupture at higher strain rates. Fracture mechanisms were very different in deep
drawn cups. After deep drawing tests, delayed cracking occurred. Main fractographic feature observed in cracked
deep drawn cups was the intergranular decohesion.
The mechanical behavior was described by a two-phase model incorporating the martensitic transformation.
Identification of parameters was carried out on complex loading paths (tensile test, shear test, cyclic loading-
unloading).
1. Introduction
Austenitic stainless steels have an excellent corrosion resistance, good mechanical properties and are widely
used for cold forming (deep-drawing) at room temperature. Increasing need for conserving the strategic elements
such as nickel and chromium impel the steel-makers to lower the content of these elements in stainless steels.
However, the low nickel content can lead during the forming process to the plastic deformation-induced phase
transformation of face-FHQWHUHG FXELF IFF Ȗ DXVWHQLWH WR ERG\-centered cXELF EFF Į¶ PDUWHQVLWH >-4]. High
internal stresses are generated due to an incompatible transformation strain accompanying the martensitic
transformation. The residual stresses together with the internal stresses induced by martensitic transformation
can lead after deep-drawing to the phenomenon of delayed cracking. Several authors mentioned the role of
hydrogen in delayed cracking phenomena [5-7], e.g., increasing Į¶ martensite content was found to have a huge
effect on the hydrogen embrittlement susceptibility a cathodically charged AISI 304 austenitic stainless steel [5].
The aim of this paper is to characterize the influence of martensitic transformation on the mechanical
properties of metastable austenitic steels and to propose numerical modeling of the material behavior in order to
assess the local stress-strain field arising in each phase during plastic deformation.
2. Experimental results
The material chosen for this study was austenitic steel corresponding to the AISI301. The chemical composition
is given in Table 1. The low nickel and chromium content situates the steel at the limit of the austenite field in
the phase diagram. The material was provided as cold rolled sheets of 0.68 mm thickness in the bright annealed
state.
Table 1. Chemical composition of AISI301 steel (in wt.%).
C Cr Ni Si Mn Mo
nominal Max 0.12 16-18 6.5-9 <1.5 <2 <0.8
0.05 17 7 0.5 1.5 0.1
a
e-mail: petr.hausild@fjfi.cvut.cz
This is an Open Access article distributed under the terms of the Creative Commons Attribution-Noncommercial License
(http://creativecommons.org/licenses/by-nc/3.0/), which permits unrestricted use, distribution, and reproduction in any
noncommercial medium, provided the original work is properly cited.
Article available at http://www.esomat.org or http://dx.doi.org/10.1051/esomat/200906016
ESOMAT 2009
The tensile tests were carried out on an INSPEKT 100kN testing machine at room temperature
imposing various strain rates ranging from H =5.10-5 s-1 to H =5.10-2 s-1. Temperature increase during tests was
measured by a thermocouple. Cup drawing tests were carried out on a 500kN INSTRON testing machine using
punch diameter 100 mm and different drawing ratios.
Fractured tensile specimens and cracked cups were examined in the Scanning Electron Microscope
(SEM) JSM 5510LV. The martensite volume fraction was characterized by EBSD in SEM FEI Quanta 200 FEG
HTXLSSHGZLWKD76/(%6'DQDO\]HU$FTXLUHGGDWDZHUHHYDOXDWHGE\2,0VRIWZDUH
2.1 Tensile tests
Results of tensile tests (in the rolling direction - RD) at room temperature with strain rates ranging from
H =5.10-5 s-1 to H =5.10-2 s-1 are shown in Fig.1. The shape of stress-strain curves is strongly dependent on strain
rate. With increasing strain rate yield stress increases, fracture stress and elongation to fracture have a maximum
at H =5.10-3 s-1. During the tensile tests at higher strain rates ( H =5.10-3 s-1 and H =5.10-2 s-1), the heating of
specimens occurred (temperature increase up to 50qC).
Fracture surfaces of tensile specimens tested at the strain rates H =5.10-5 s-1 and H =5.10-4 s-1, were
oriented in perpendicular to the loading axis whereas the fracture surfaces of tensile specimens tested at the
strain rates H =5.10-3 s-1 and H =5.10-2 s-1ZHUHLQFOLQHGRIDERXW
Fractographic analysis of specimens broken at the strain rate H =5.10-5 s-1 and H =5.10-4 s-1 revealed
several transgranular cleavage facets connected by ductile dimpled rupture (Fig. 2a). Several slip bands can be
found on cleavage facets which indicate that the cleavage facets were formed before the final ductile fracture. On
the other hand, the fracture surfaces of tensile specimens tested at the strain rates H =5.10-3 s-1 and H =5.10-2 s-1,
are completely covered by ductile dimples (Fig. 2b).
a) b)
Fig. 1. Stress-strain curves of AISI301 steel tested at room temperature at different strain rates (a), evolution of
martensite volume fraction in the specimen tested at H =5.10-4 s-1.
a) b)
Fig. 2. Fracture surfaces of tensile specimens tested at room temperature at H =5.10-4 s-1 (a), and H =5.10-3 s-1 (b).
06016-p.2
ESOMAT 2009
2.1 Cupping tests
Delayed fracture occurred in the cups (Fig.3) after deep drawing tests with drawing ratios DR > 1.5. On the
lateral face several more or less equidistant arrested cracks can be observed. Cracks arrested in the cup wall at
about the same height as the height of cup with initial drawing ratio DR ~ 1.4.
Lateral faces and cracks in the cups issued from deep drawing tests were analyzed in SEM. Cracks
propagated by the mechanism of diffused damage - several microcracks were found in proximity of principal
crack lips and ahead of the crack tips (Fig.4a). On the fracture surfaces of opened cracks, the main feature
observed was the intergranular decohesion (Fig.4b).
Fig. 3. Delayed cracking after deep drawing test in cups with different drawing ratios.
Martensite
a) b)
Fig. 4. Crack propagation on the lateral face of the cup (a), intergranular decohesion on the fracture surface of the cup
cracked after deep drawing test (b).
3. Numerical modeling
Constitutive equations for two-phase material have already been detailed in [8] and are only summarized here.
The aim of this model is to characterize the behavior of the steel at a macroscopic scale by taking into account
the individual behavior and the volume fraction of each phase (martensite: fM and austenite:1±fM). In this work, a
self-consistent approach is used and it assumes that each phase is embedded in a homogeneous equivalent
medium. The representative volume element is constituted here of two phases, i.e., austenite and martensite, and
it is assumed that both phases have the same isotropic elastic behavior.
AISI 301 austenitic stainless steel undergoes a martensitic phase transformation induced by plastic deformation.
The description of this transformation must be incorporated in the model in addition to the behavior of austenitic
and martensitic phases.
3.1 Constitutive equations for austenite
In the initial state, the steel is 100% austenitic. Due to the orthotropic symmetry of the sheet, the austenite
behavior is modeled as orthotropic, whereas the martensite behavior is described using isotropic behavior.
The yield stress function f for austenite is expressed in the form:
06016-p.3
ESOMAT 2009
f V a , X a , Ra V ad X a : Ʃ : V ad X a Roa Ra (1)
where Vad is the deviatoric part of the stress tensor in austenite. Xa is the second order tensor of kinematic work-
hardening and Ra is the term of isotropic work-hardening. The initial yield stress Roa is equal to the yield stress
in tension along the RD and H is the fourth-order Hill's tensor. The coefficients of H can be deduced from the 6
parameters F, G, H, L, M and N of the quadratic Hill's criterion. The condition on the initial yield stress along
the RD allows to impose the relation G + H = 1.
The viscoplastic strain follows a flow rule derived from a viscoplastic potential which is a power function of the
yield function:
n
dH pa § f · wf (2)
¨¨ ¸¸
dt © K ¹ wV
where n is the strain rate sensitivity coefficient, K a weighting coefficient of the viscous part of the stress and f+
the positive part of f , i.e., f+=max(0, f). Hence, the behavior is elastic if f < 0.
The evolution of the isotropic work-hardening is associated to the dislocation density U in austenite:
Ra = MTDPb U with dU M T dp a § 1 · (3)
¨ k U bGU ¸
dt b dt © / ¹
where MT is the Taylor factor, D is a constant of the order of one, P is the elastic shear modulus, b is the
PDJQLWXGHRI%XUJHU¶VYHFWRU and pa is cumulative plastic strain in austenite. The first two terms in the bracket of
eq.(3) represent the storage of dislocations in the microstructure, which may be interfered by obstacles as grain
boundaries and/or by the average spacing between the forest dislocations. The third term in the bracket of eq.(3)
takes into account the dynamical recovery process (annihilation of screw dislocations) assumed to be linear with
ȡ and characterized by a recovery coefficient G.
The kinematic hardening rule is similar to the well know Armstrong-Frederick law with the addition of a linear
term:
a
2 [CaDa+ aHa ] with dD dp a § wf · (4)
Xa p ¨ * aD a ¸
3 dt dt © wV ¹
where parameters Ca and *a control the intensity of work-hardening and + a is the slope of the linear part of the
kinematic work-hardening.
3.2 Constitutive equations for martensite
The martensite behavior is described using a simple elastoplastic model (von Mises criterion with a Voce law for
isotropic work-hardening). The yield stress function g for martensite is expressed in the form:
1
3 d
g V m , Rm
2
>
V m : V md Rom Q m 1 - exp(-b m p m ) @ 2 (5)
where Vmd is the deviatoric part of the stress tensor in martensite. Rmo, Qm, and bm are hardening material
parameters and pm is cumulative plastic strain in martensite.
3.3 Austenite-martensite transformation
In this work, the evolution of the volume fraction of martensite is given by the Shin et al. law [10], in which the
martensitic transformation is considered as a continual relaxation of the internal strain energy accumulated
during the plastic deformation. This volume fraction depends on the cumulative plastic strain in the austenite (pa)
and not on the macroscopic strain. Furthermore, it is clearly established that the kinetic of the martensitic
transformation depends on the temperature and stress path [9].
In order to take into account the transformation dependence on the stress path, the evolution of the austenite-
martensite transformation depends on the stress triaxiality ratio in austenite (Ta). This ratio is equal to 0 in shear,
06016-p.4
ESOMAT 2009
f
1/3 in tension. The evolution law of the martensite volume fraction fM is expressed in eq.(6) where fM is the
value of the saturation of the martensite volume fraction. In the evolution rate of the transformation, the
dependence of the stress triaxiality ratio is introduced with linear functions: fMf(Ta) and E(Ta).
df M dp a f a
dt dt
>
f M (T ) f M E (T a ) N p a
( N 1)
@ (6)
In equation (6) the value of the exponent N is about 2 according to [10].
3.4 Parameters identification
Parameters were identified using identification software SiDoLo based on a Levenberg±Marquardt
minimization algorithm [11]. The experimental database consists of monotonic shear tests and tensile tests
(along rolling and transverse directions) at room temperature with different strain rates (Fig.5a). Cyclic shear
tests are used to identify the kinematic hardening parameters (Fig.5b). Identified model of material behavior is in
good agreement with monotonic tensile and/or shear test and cyclic shear test results (Fig.5) as well as with
austenite to martensite transformation kinetics during tensile and shear tests (Fig.6).
1250 1000
simulation
experimental 750
Tensile
1000
500
Shear stress (MPa)
True stress (MPa)
Shear
250
750
500
-250
-500
250
simulation
-750
experimental
0 -1000
0.0 0.1 0.2 0.3 0.4 0.5 0.6 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75
Logarithmic strain HJ Logarithmic strain J
a) b)
Fig. 5. Identification of material behavior on monotonic tensile and shear tests (a) and cyclic shear tests (b).
0.7
0.6
Volume fraction of martensite
0.5
0.4
0.3
0.2
identified on tensile test
0.1 identified on shear test
experimental
0.0
0.0 0.1 0.2 0.3 0.4
Equivalent plastic strain
Fig. 6. Identification of austenite to martensite transformation kinetics on monotonic tensile and shear tests.
4. Summary
Mechanical response of AISI301 steel is very sensitive to the strain rate due to the coupling of thermo-
mechanical behaviors. Fracture mechanism in tensile specimens at the strain rate lower than H =5.10-3 s-1 is the
combination of cleavage and ductile dimpled rupture. At the strain rate higher than H =5.10-3 s-1 fracture
mechanism changes to entire ductile dimpled rupture.
06016-p.5
ESOMAT 2009
Fracture mechanisms are very different in tensile specimens and deep drawn cups. In cracked deep drawn cups,
the intergranular decohesion was main fractographic feature.
Delayed cracking occurred only in deep drawn cups but not in tensile specimens. This is probably due to the
necessity of the synergy effect between macroscopic (residual) stresses and internal stresses provoked by
martensitic transformation.
The mechanical behavior was described by a two-phase model incorporating the individual behavior and the
volume fraction of each phase. Identification of model parameters was successfully carried out on complex
loading paths (monotonic tensile and shear test, cyclic shear test).
In the following research, the model will be implemented in a finite element method code and used for the
simulation of cupping test.
Acknowledgement
Authors wish to thank the Arcelor-Mittal group for supplying the material. This work was supported by the Ministry of
Education, Youth and Sports of the Czech Republic in the frame of the research project MSM 6840770021. Authors are
deeply grateful to Dr S. Bouvier (LPMTM, Villetaneuse) who kindly provided experimental data for cyclic shear tests.
References
[1] L. Mangonon Jr., G. Thomas, Met. Trans. 1 (1970) 1577±1586.
[2] T. Suzuki, H. Kojima, K. Suzuki, T. Hashimoto, M. Ichihara, Acta Met. 25 (1977) 1151±1162.
[3] J.W. Brooks, M.H. Loretto, R.E. Smallman, Acta Met. 27 (1979) 1839±1847.
[4] M. Humbert, B. Petit, B. Bolle, N. Gey, Mater. Sci. Eng. A 454±455 (2007) 508±517.
[5] H. Hanninen, T. Hakarainer, Corrosion 36 (1980), 47-51.
[6] J.A. Brooks, A.J. West, Metall. Trans. A 12 (1981), 213-223.
[7] C. Pan, W.Y. Chu, Z.B. Li, D.T. Liang, et al., Mater. Sci. Eng. A351 (2003) 293-298.
[8] 6*DOOpH3<0DQDFK33LOYLQ67KXLOOLHU*/RYDWR0DWpULDX[HW7HFKQLTXHV-4, (2003) 1-10
[9] A.A. Lebedev, V.V. Kosarchuk, International Journal of Plasticity, 16, (2000) 749-767.
[10] H.C. Shin, T.K. Ha, Y.W. Chang, Scripta Materialia, 45, (2001) 823-829.
[11] Ph. Pilvin, in: 3URFRI0pFD0DW, C. Oytana et al editors (1988) 155-164.
06016-p.6
