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Materials Science and Engineering A 483–484 (2008) 184–187

Influence of addition elements on the stacking-fault energyand mechanical properties of an austenitic Fe–Mn–C steel

A. Dumay a,∗, J.-P. Chateau a, S. Allain b, S. Migot a, O. Bouaziz b

a Laboratoire de Physique des Mat´ eriaux, Ecole des Mines, Parc de Saurupt, CS 14234, F-54042 Nancy cedex, Franceb Arcelor Research SA, Voie Romaine, BP 30320, F-57283 Maizieres-les-Metz cedex, France

Received 6 June 2006; received in revised form 2 October 2006; accepted 7 December 2006

Abstract

We present a thermochemical model of the stacking-fault energy (SFE) in the Fe–Mn–C systemwith few percent of Cu,Cr, Al and Si in addition.Aluminium strongly increases the SFE, contrary to chromium, while the effect of silicon is more complex. Copper also increases the SFE, but

strongly decreases the Neel temperature. The SFE is the relevant parameter that controls mechanical twinning, which is known to be at the origin

of the excellent mechanical properties of these steels. Using this model, copper containing Fe–Mn–C grades were elaborated with SFE below

18 mJ/m2, in the range where -martensite platelets forminstead of microtwins duringplastic deformation. This substitution of deformation modes,

confirmed by X-ray diffraction, does not significantly damage the mechanical properties, as long as the SFE is greater than 12 mJ/m2, which avoids

the formation of  -martensite.

© 2007 Elsevier B.V. All rights reserved.

Keywords:   Fe–Mn–C; Stacking-fault energy; Martensitic transformation; Strain hardening

1. Introduction

The Fe22Mn0.6C fcc steel developed by Arcelor exhibits

mechanical twinning in addition to dislocation gliding when

deformed at room temperature  [1–3].   The fine microtwins

formed along with plastic deformation act as strong obstacles,

such as grain boundaries, and lead to a “dynamical Hall and

Petch effect”, a high strain hardening rate and consequently

both excellent elongation to fracture (>50%)andultimate tensile

strength (>900 MPa). The relevant parameter for twinning is the

stacking-fault energy (SFE) which depends on temperature and

composition.

The best hardening rate is obtained at room temperature in

this steel, where its SFE is intermediate (≈20 mJ/m2)  [1,3].

At higher values, twinning tends to disappear, while below18 mJ/m2 microtwins are replaced by hcp-martensite platelets.

In an alloy design approach, it is necessary to predict the tem-

perature and composition dependence of the SFE, in order to

adjust an alloy’s grade to its forming or service conditions.

∗ Corresponding author. Tel.: +33 3 8358 4143; fax: +33 3 8358 4344.

 E-mail address:  dumay@mines.inpl-nancy.fr (A. Dumay).

We first present a thermochemical model based on the one

previously developed for the Fe–Mn–C system, in order to pre-dict the effect of adding few percents of copper, chromium,

aluminium or silicon on the SFE. An example of the influ-

ence of the SFE on the mechanical properties and deformation

microstructure, in connection with the model’s prediction, is

presented in the second part in the case of copper.

2. Thermochemical modelling of the stacking-fault

energy

In fcc structures, twinning is due to stacking faults (SFs)

extending in parallel adjacent dense planes. Extending them

every twoplanes leads to the formationof -martensite. A stack-

ing fault can be modelled by two atomic layers of  ε-martensitewithin the dense planes. This allows to write the SFE as [4]:

Γ   = 2ρ Gγ →ε+ 2σ γ  / ε (1)

with   Gγ →ε, the free molar enthalpy of the transformation

γ → ε, ρ the molar surface density of atoms in the {1 1 1} planes

and σ γ  / ε =8mJ/m2 [1] the energy per surface unit of a  {1 1 1}interface between γ  and ε.

Accordingto thesimplifiedprevious model for theFe–Mn–C

system [3], the free molar enthalpy of martensite formation can

0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.msea.2006.12.170

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 A. Dumay et al. / Materials Science and Engineering A 483–484 (2008) 184–187    185

be written as follow:

Gγ →ε= G

γ →εFeMnX + xc G

γ →εFeMnX/C +Gγ →ε

mg   (2)

Using the regular and subregular solution model,  Gγ →εFeMnX is

the chemical contribution of all the elements in substitution in

the fcc lattice. The Fe–Mn excess term is taken into account but

the others involving the addition elements are neglected becauseof the little quantities considered, except for silicon:

Gγ →εFeMnX  =

i

xi Gγ →εi   + xFexMn[C + D(xFe − xMn)]

+xFexSi[E + F (xFe − xSi)] (3a)

Gγ →εi   = Ai + BiT, i = Fe, Mn, Cu, Cr, Al, Si (3b)

with x i the molar fraction of element i, T  the temperature and

{ Ai}, { Bi}, C , D, E  and F  fitting parameters.

Carbon in insertion is simply introduced as a disturbance of 

the former fcc solid solution [5]. An empirical law has beenimproved since [3], to account for an increasing carbon effect

with manganese content:

Gγ →εFeMnX/C  =

a

xC(1− e−bxC )+ cxMn   (4)

where a, b and c are fitting parameters according to Ref. [1].

Gγ →εmg   is a magnetic term, due to the Neel transition (para-

magnetic to antiferromagnetic) of each phase ϕ:

Gγ →εmg   = Gε

m − Gγ m   (5a)

where

Gϕm  = RT  ln

1+βϕ

µB

f   T 

T ϕN

, ϕ = γ, ε   (5b)

with  βϕ and  T ϕN , respectively, the magnetic moment and Neel

temperature of phase ϕ, µB the Bohr magneton and f  a polyno-

mial function which expression can be found in Ref. [6].

ρ, Gγ →εFe   , G

γ →εMn   and T εN are unchanged compared to Ref.

[3].   βγ ,  βε have been improved in Ref. [1]  to take the effect

of carbon into account (additional elements in substitution are

neglected):

βγ = β

γ FexFe + β

γ MnxMn − β

γ FeMnxFexMn − βCxC   (6a)

βε= βε

MnxMn − βCxC   (6b)

with   βϕi   the contribution of element  i  in phase   ϕ and   β

ϕij   the

excess i– j term. An empirical expression of  T γ N has been fitted

to data of literatures [7–10] and measurementsconductedon our

FeMnCuC alloys. T εN is given in Ref. [3]:

T γ N  = 250 ln(xMn)− 4750xCxMn − 222xCu

−2.6xCr − 6.2xAl − 13xSi + 720 (K) (7a)

T εN  = 580xMn (K) (7b)

A current assumption  [11,12]   is that the   -martensitic (and

the reverse austenitic) thermal transformations occurs when

Table 1

Summarised parameters of the model from Refs. [1,3] and the present work for

addition elements (T  in K)

ρ   2.94× 10−5 molm−2 [3]

σ γ  / ε 8mJm−2 [1]

Gγ →εFe   −2243.38+ 4.309T Jmol−1 [3]

Gγ →εMn   −1000.00+ 1.123T Jmol−1 [3]

G

γ →ε

FeMn   C =2873Jmol

−1

; D =−

717Jmol

−1

[1]Gγ →ε

FeMnX/C   a =1246Jmol−1; b = 24.29 J mol−1; c =−17,175 J mol−1 [1]

βγ  / µB   0.7 x Fe + 0.62 x Mn −0.64 x Fe x Mn −4 x C   [1]

βε / µB   0.62 x Mn −4 x C   [1]

Gγ →ε

Al   2800+5T Jmol−1

Gγ →ε

Cr   1370−10T Jmol−1

Gγ →ε

Cu   2273J mol−1

Gγ →ε

Si   −560− 8T Jmol−1

Gγ →ε

FeSi  E = 2850J mol−1; F =3520Jmol−1

Gγ →ε≈−100 J/mol (respectively, +100 J/mol; we find that

+80 J/mol gives better results). The parameters for FeMnC have

beenobtainedfirst[1]. Then,the parametersconcerning theaddi-

tion elements are fitted to give the best accordance with 120transformation temperatures of different compositions with less

than 5 wt.% of alloying elements. All data have been found in

Refs. [6,7,11,13–23]. The set of parameters which give the best

estimation of the transformation temperatures over the whole

database is summarised in Table 1 (results from Refs. [3,1] and

the present paper).

Fig. 1 shows the result when adding each element to the

Fe22Mn0.6C steel. Petrov measured the SFE by loss-energy

method and deduced the influence of chromium [23], which

is rather weak; our model is in good agreement with his results.

Copper and even more aluminium increase the SFE, contrary

to chromium. Copper is shown to strongly decrease  T N. Sili-

con have a complex effect on SFE, increasing SFE for small

quantities and decreasing it at higher ones. Previous studies on

silicon effect showed that Si decreases the SFE but their range

of validity is over 4wt.% [21,24].

Fig. 1. Predicted influence of alloying elements on the SFE of the Fe22Mn0.6C

reference.

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186   A. Dumay et al. / Materials Science and Engineering A 483–484 (2008) 184–187 

Fig. 2. (a) Strain hardening rate n = ε / σ  dσ  /dε and SFE predicted for samples A–D. (b) X-ray patterns (θ , 2θ ) of deformed samples.

This model is used to predict the SFE in accordance with

the deformation modes activated in copper containing alloys

presented in the following part.

3. Mechanical properties of a low SFE austenitic steel

The effect of the SFE on the mechanical properties was stud-ied in the Fe22Mn0.6C alloy by changing the temperature of the

tensile tests [1,3]. The decrease of the elongation to fracture and

hardening rate below room temperature was attributed to the

occurrence of  -martensitic transformation instead of twinning

at lower SFE values (below 18 mJ/m2 [3]). However, disloca-

tion glide also depends on temperature: dislocation pinning by

carbon atoms is strongly thermally activated below room tem-

perature.

In order to discriminate between martensitic transformation

and thermal activation of glide, the SFE value was varied this

time by using different grades elaborated by Arcelor and all

tested at room temperature. The grades tested are four ironbase alloys containing 0.6 wt.% C, 2 wt.% Cu and increasing

Mn amounts (from 10 up to 20 wt.%). Our model predicts a

SFE increasing with the Mn content: 10, 12, 15 and 17mJ/m2,

labelled A, B, C and D, respectively, well in the  -martensitic

transformation range. The SFE of the Fe22Mn0.6C reference is

23 mJ/m2.

Samples were cut out from 4 mm thick sheets obtained by hot

rolling. Metallography and X-ray analyses show that they are

100% austenitic, fully recrystallised with equal average grain

sizes of 6m. Static uniaxial tensile tests were performed up to

fracture at room temperature. Samples are analysed after tensile

testing by X-ray diffraction (θ , 2θ  method) to detect the pres-

ence of  -martensite and simply tested with a magnet to detectthepresence of -martensite (bodycentred tetragonal structure,

ferromagnetic).

The mechanical characteristics of each alloy are shown in

Table 2. The evolutions of the strain hardening rate with true

strain are shown in Fig. 2(a) and the X-ray diffraction patterns

after deformation in Fig. 2(b). They confirm the presence of 

-martensite in all samples. Samples A and B with the lowest

valuesof theSFE(austenitestronglyunstable)are ferromagnetic

after deformation, thus containing  -martensite.

Except for alloy A, the homogeneous elongation ends at

the Considere’s criterion n = ε, leading to high elongations to

fractureandultimatetensile strengths, as forthe Fe22Mn0.6Cref-

Table 2

Yield stress (YS), ultimate tensile strength (UTS), elongation at fracture (EF)

and phases observed after tensile testing on A, B, C and D Cu-containing grades

YS (MPa) UTS (MPa) EF (%) Phases observed after testing

A 337 825 37.7   γ , ε, α

B 343 914 64.4   γ , ε, α

C 345 908 62.7   γ , εD 351 883 68   γ , ε

erencesteel. Inall samples ofsteel A,and somesamples ofB,the

nucleation of  -martensite, which is a hard phase, at the inter-

sections of two variants of  -martensite platelets promotes pre-

mature fracture before this criterion by concentrating stresses.

4. Conclusion

Based on experimental measurements and numerous

bibliographic data of Neel temperatures and -martensite trans-

formation temperatures, we extend the SFE prediction modelfor the Fe–Mn–C system to alloys containing Cu, Cr, Al and

Si in addition. Except for the more complex case of silicon, the

results are in good agreement with other experimental results.

Chromium is the only element decreasing the SFE. All elements

decrease the Neel temperature, especially copper which has a

strongeffect. Themodelwas successfullyused in analloydesign

approach to elaborate steels containing copper with SFEs below

the lower limit of 18 mJ/m2 for the activation of mechanical

twinning.

The prediction is in good agreement with the observation of 

-martensite in these steels after tensile testing at room tem-

perature. The substitution of mechanical twinning by athermal

-martensite transformation does not significantly damage the

mechanical properties of Fe–Mn–C steels. The sequential acti-

vation of two  -martensite variants also leads to a “dynamical

Hall and Petch effect”, by reducing the mean free path of the

dislocations, and consequently a high hardening rate. However,

attention must be paid to the formation of  -martensite, which

occurs for SFEs below 12mJ/m2 and reduces ductility.

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