1. No category

SIMULATION OF THE STATIC MECHANICAL BEHAVIOUR OF TRIP
STEELS BY MICRO-MECHANICAL MODELLING
J. Bouquerel1, K. Verbeken1, 2, *, P. Verleysen3 and Y. Houbaert1
1
Department of Metallurgy and Materials Science, Ghent University, Technologiepark 903, B-9052
Ghent (Zwijnaarde), Belgium
2
Microstructure Physics, Max-Planck-Institut für Eisenforschung, Max-Planck-Strasse 1, 40237
Düsseldorf, Germany
3
Department of Mechanical construction and Production, Ghent University, Sint-Pieternieuwstraat 41,
B-9000 Ghent, Belgium
* Postdoctoral Fellow with the Fund for Scientific Research – Flanders (Belgium) (FWO-Vlaanderen)
ABSTRACT
TRIP (TRansformation-Induced Plasticity) steels display a composite behaviour originating from the
different constituent phases present in these steels: polygonal ferrite, bainitic ferrite, and
martensite/austenite. This behaviour results in an excellent combination of a large uniform elongation
and high strength. In order to understand the composite behaviour of the different phases, the
constituents were prepared as separate alloys. The stress–strain relationships of these alloys were
simulated by physically based micro-mechanical models based on the Mecking–Kocks theory.
Physical properties such as the microstructural parameters, the dislocation density and the chemical
composition of the different phases were taken into account. The influence of the transformation of the
metastable austenite was included by using a generalized form of the Olson–Cohen law. The static
stress–strain properties of the multiphase steels were modelled by the successive application of
Gladman-type mixture laws. Besides the simulation of the stress-strain curves, the model also
generates detailed information of stress and strain partitioning between the different phases during a
static tensile test.
1. INTRODUCTION
In literature, various models have been proposed to simulate the stress-strain curves for different
types of steels (ferritic, martensitic, pearlitic, dual phase). A majority of these models is based on
standard Hollomon and/or Ludwig-type laws [1-10] and some models are physically-based [13-25].
However, only a limited amount of work was carried out on TRIP steels [13-15].
The increasing demands, especially for the automotive industry, to combine an increased formability
with a weight reduction have largely contributed to the development of TRIP-aided ferrous alloys [26,
27]. The fine microstructure of these steels is obtained by a two step annealing cycle and consists of
different constituents, namely polygonal ferrite, bainitic ferrite and retained austenite. The particular
feature of this material is the presence of retained austenite, which is metastable and which displays a
strain induced martensitic transformation upon deforming.
The ductility of TRIP steels is a very complex matter since that various and often coupled parameters
influence the stability of the dispersed retained austenite under mechanical loading [14]. The main
parameters are the chemical composition, the grain size and the stress state. The optimization of the
mechanical properties of such complex multiphase steels requires a detailed understanding of the
microstructural characteristics of this material. The present study aims to predict the macroscopic
mechanical behaviour of the TRIP steels by making use of a physically based model, taking into
account the composition, morphology and the behaviour of each constituent.
The presented model for multiphase high strength low alloy TRIP steels will have two major
advantages: the model parameters are physically meaningful and their value was determined by fitting
to experimentally determined properties of the isolated phases, which was done by preparing the
constituents as separate alloys. The transformation kinetics for retained austenite were determined
experimentally, taking the temperature and the compositional effects into account, and integrated in
the Olson – Cohen [28] equation. The properties of the TRIP steel were predicted by combining the
features of the different constituents by means of the successive application of mixture laws for twophase steels. This model allows for a detailed description of the behaviour of each phase separately
within the multiphase microstructure during a tensile test, including stress-strain partitioning between
the different phases.
2. MODEL
Figure 1 schematically describes how the stress – strain curve of a TRIP steel is simulated in the
present model. The stress-strain behaviour of TRIP steel is based on the behaviour of the isolated
constituent phases, with a successive application of a mixture law for two-phase steels. The TRIP
steel consists of two main constituents: polygonal ferrite and bainite. The bainitic constituent can, in
turn, be decomposed into bainitic ferrite and the M/A constituent. Finally, the M/A constituent is a twophase mixture of retained austenite and martensite. In order to model the TRIP behaviour, a
deformation model was first developed for each constituent and correlated with experimental results
for this constituent. The obtained data for a single constituent were combined in three successive
stages making use of a Gladman-type mixture law for two-phase steels [29]. A brief description of the
model is given here, more details can be found elsewhere [30].
TRIP
Stress mixture law
Polygonal
Ferrite
Bainite
Mecking – Kocks
model
Stress mixture law
Bainitic
Ferrite
Martensite / Austenite
constituent
Mecking – Kocks
model
Stress mixture law
Retained
Austenite
Mecking – Kocks
model
Strain induced
Martensite
Mecking – Kocks model +
Olson Cohen (kinetics)
Figure 1: Comparison of the complex TRIP microstructure decomposed into its various
constituents in the present work
2.1 DESCRIPTION OF THE MODEL
During tension, the macroscopic stress σ and strain ε can be calculated from the shear stress for the
current microstructural state,τ and the amount of crystallographic slip, γ as follows:
σ = M .τ , ε = γ / M
(1)
where M, the Taylor factor, is independent of the grain size. The shear stress τ can be decomposed
into components related to the lattice friction, and to the interaction between dislocations:
τ =τ0 +α µb ρ
(2)
In this equation, b is the magnitude of the Burgers vector, ρ is the dislocation density and α is a
numerical factor that characterizes the dislocation-dislocation interaction.
Equation 2 relates the shear stress variation
deformation
dτ
to the evolution of the dislocation density with
dγ
dρ
. According to the Mecking-Kocks theory, this evolution is the result of the competition
dγ
−
+
dρ
between the rate of production of dislocations, dρ , and the annihilation rate of dislocations,
dγ
dγ
,[24, 31-38].
The strain hardening, which is due to the accumulation of dislocations, depends on the mean distance
λ that a dislocation can glide before it encounters an obstacle. This is generally expressed as:
dρ
dγ
+
=
1
λb
(3)
In case of materials that deform by dislocation glide, these obstacles are mainly the grain boundaries
and the distance between dislocations:
1
λ
=
1
+k ρ
d
(4)
where k is a constant and d the grain size.
−
dρ
term, which is the dislocation annihilation term, corresponds to dynamic recovery: two
dγ
dislocations, with opposed burgers vectors and close to each other, will attract each other and
annihilate. This term strongly depends on the dislocation density and can be expressed as:
The
dρ
dγ
−
=−f ρ
(5)
Where f is dislocation annihilation constant.
The resulting equation is frequently [24, 31-38] written in the following form:
dρ
1
k
=
+
ρ−fρ
M .dε λ b b
(6)
When modelling the stress-strain curves of TRIP constituents, equation (6) was mainly used together
with Equation (1) and Equation (2). k and f are fitting parameters, b is the amplitude of the burgers
vector and λ is the grain diameter.
2.2 MODEL FOR THE M/A CONSTITUENT
The particular features of the M/A constituent during cold deformation, i.e. the strain induced
martensitic transformation, requires a specific model. Since the retained austenite transforms to a
martensite/austenite (M/A) constituent, the separate behaviour of the martensite and the austenite
constituents was considered and coupled to a strain-dependent evolution of the phase ratio in the M/A
constituent. Several hypotheses, which are summarized here and which are given in more detail
elsewhere [30], were made for the description of the M/A microstructure.
The volume fraction of martensite, fα’ was determined by using an Olson-Cohen [28] law:
n
f α ' = 1 − exp − β [1 − exp( −αε ) ]
(7)
(
)
In this equation α is related to the volume fraction of shear bands and β is related to the probability
that a shear band intersection will lead to the formation of a martensite nucleus. The value of n is
related with the number of shear band intersections per unit of volume austenite. Samek et al. [28]
found that n=2 for TRIP steels.
Both the austenite and the martensite were assumed to have a spherical shape. In the description of
the M/A behaviour, it was also assumed that only one martensitic grain grew inside an austenitic
island during straining. The size of each constituent was considered to change during straining; this
results in a strain dependent grain size for the retained austenite described by the following equation:
d γ (ε ) = d γ init .3 1 − f α '
(8)
where dγ init is the initial grain size of the austenite.
The stress-strain curve of the austenitic constituent was modelled by the Mecking - Kocks law.
The strength of the martensite results from several different strengthening mechanisms: the solid
solution strengthening effect of the carbon and other alloying elements, the lath size, the dislocation
density and carbide particles. The stress-strain curve of martensite in static tensile test condition is
well described by the model that was developed by Rodriguez et al. [17]. The yield strength of
martensite was determined by Krauss [39]
In order to obtain the true behaviour of the M/A constituent, the stress-strain curves for the remaining
austenite and the martensite were combined, using a two-phase mixture rule, as is commonly done to
describe multiphase material behaviour [2, 3, 16]. In the present case, the approach was to use of a
Gladman-type [29] power law for the M/A constituent, as expressed in Equation 9.
σ M / A = σ γ .(1 − f αn'' ) + σ α ' . f αn''
(9)
In this equation, fα’ is the fraction of martensite. σγ and σα' are the stress in the austenite and
martensite, respectively.
The same type of Gladman-type mixture law was successively used to describe the stress-strain
curves of the TRIP steels. The values of n’ were determined by fitting calculated stress-strain curves
to experimental data.
3. EXPERIMENTAL PROCEDURE
Two TRIP steels, a CMnSi TRIP and a CMnAl TRIP steel, were laboratory processed. The different
constituents were prepared separately in order to study them separately. Polygonal ferrite, the bainite
and the M/A constituent were made as bulk alloys with compositions corresponding to those of the
constituents in the TRIP steel. These alloys could be obtained simply by varying the carbon content as
can be seen in Table 1. All the materials were cast under argon atmosphere in a vacuum induction
furnace. After hot rolling and pickling, the materials, except the austenitic alloy, were cold rolled to a
final thickness of 1 mm. The TRIP steel microstructure was obtained after a two step thermal
treatment involving intercritical annealing and austempering. The microstructure consisted typically of
50% ferrite, 35% bainite and 15% M/A.
Table 1: Chemical composition (%wt) for the laboratory cast materials.
C
Si
Al
Mn
P
Cγγret
% γret
CMnSi TRIP
0.24
1.45
0.03
1.61
0.006
1.79
14
CMnAl TRIP
0.24
0.09
1.54
1.61
0.006
2.16
9
CMnAl Ferrite
0.025
0.07
1.63
1.78
0.016
---
---
CMnAl Bainite
0.37
0.02
1.49
1.50
0.011
2.1
14
CMnAl Austenite
1.6
0.02
1.57
1.64
0.012
---
---
CMnSi Ferrite
0.02
1.25
0.06
1.60
0.013
---
---
CMnSi Bainite
0.34
1.32
0.03
1.49
0.012
1.6
11
CMnSi Austenite
1.87
1.57
0.04
1.53
0.018
---
---
The resulting microstructures of the non-strained materials were observed with Light Optical
Microscopy (LOM) using Lepera etching [40]. Figures 2 and 3 show the micrographs of each alloy for
the corresponding CMnAl and CMnSi TRIP steels. The high carbon austenitic alloy microstructure
contained an appreciable volume fraction of athermal martensite (cf. Fig. 3.c). The stress-strain
behaviour obtained for that alloy did not correspond to that of a fully austenitic structure. In order to
obtain meaningful model parameters for the austenite phase, two austenitic stainless steels were
studied (Table 2). The alloy 304L had a “stable” austenitic microstructure, whereas the 301LN was
metastable and transformed to martensite during straining.
Figure 2: Microstructures of the different CMnAl alloys (a) ferrite (b) bainite (c) austenite (d)
TRIP
The static mechanical properties were determined by tensile tests on an Instron 5569 tensile testing
machine. All tensile specimens were machined in the rolling direction from the annealed sheets, which
were temper rolled (1%) before testing in order to avoid discontinuous yielding. The specimen
geometry, with 80mm of gauge length, was according to the European Standard EN 10002-1
specification. The initial crosshead speed of 10-4 s-1 was increased to 10-3 s-1 at a strain of 3.38%. The
mechanical properties were characterized by means of the yield stress (YS), the ultimate tensile
strength (UTS), the uniform elongation (UE) and the total elongation (TE).
Figure 3: Microstructures of the different CMnSi alloys (a) ferrite (b) bainite (c) austenite (d)
TRIP
Table 2: Chemical composition (% wt) for the two austenitic stainless steels
C
Si
Mn
Cr
Ni
304 L
0.025
0.6
1.5
18.5
10.2
301 LN
0.025
0.5
1.5
17.5
6.6
N
0.11
4. SIMULATION OF THE TRIP STRESS-STRAIN CURVES
The Mecking-Kocks model [31, 32] was used to model the mechanical behaviour of the different
phases in TRIP steels. In the present work, the following constants were used: α = 0.4; M=3 (Taylor
factor); Gα = 78500 MPa (Shear modulus for BCC); Gγ = 72000 MPa (Shear modulus for FCC); and bα
= 2.48 10-10 m (Burgers vector in α-Fe), b=2.58 10-10 m (Burgers vector in γ-Fe).
4.1 POLYGONAL FERRITE
According to Antoine [41], the initial dislocation density of the polygonal ferrite is 3.1012 m-2. The grain
sizes of the CMnAl and CMnSi polygonal ferrite were determined by optical microscopy and were 17.5
µm and 20 µm, respectively. Three parameters were obtained by fitting the model to experimental
data: the k factor, the annihilation coefficient f and the initial flow stress σ 0 . Table 3 presents in the
columns with the heading ‘ferrite’ the parameters, which were obtained by fitting the experimentally
obtained data of the ferritic alloys to the Mecking-Kocks Model.
Figure 4 represents the experimental and model stress-strain curves for the CMnSi polygonal ferrite. A
similar result was obtained for the CMnAl material. It is demonstrated that the results of the MeckingKocks model corresponds very well with the behaviour of the bulk polygonal ferrite phase that was
observed during the static tensile test.
Table 3: values of the fitting parameters considering the different alloys
4.2 BAINITE
4.2.1 BAINITIC FERRITE
As shown previously [30], the bainitic alloy contains retained austenite both as a film between the
bainite laths and as a larger blocky phase. The amount of retained austenite was determined by
means of X-Ray diffraction and is together with the carbon content of the retained austenite given in
Table 1. Since the bainitic alloy is actually a three phase composite, containing both bainitic ferrite and
the M/A constituent, this alloy could not be used directly as a reference material to obtain the
parameters of the Mecking-Kocks model by fitting the experimental stress-strain curve. As shown
above, the behaviour of a single constituent, such as the polygonal ferrite, can be modelled
accurately. The values of the different constants in the Mecking-Kocks model for polygonal ferrite were
therefore also considered to be applicable to the bainitic ferrite taking into account the small lath size
and the higher dislocation density. According to De Meyer et al. [42], the initial dislocation density was
chosen at 1013 m-2. The lath size for the bainitic ferrite, which was determined to be between 2 and 4
µm, was used instead of the grain size.
Figure 4 Experimental and modelled stress strain curves for the CMnSi ferritic alloy
4.2.2 MARTENSITE / AUSTENITE CONSTITUENT
Figure 2c and 3c showed that the austenitic alloys contained some athermal martensite. These alloys
could therefore not be used in order to model the behaviour of the M/A constituent directly. Instead the
behaviour of two austenitic stainless steels, 304L and 301LN, was studied to obtain model parameters
values. The first steel (304L) displays a stable austenite microstructure that does not transform during
straining. The second one (301 LN) was used to study the TRIP effect, since a strain induced
martensitic transformation occurs during the tensile test.
- Stable austenitic steel (304L)
The Mecking-Kocks model was applied to 304L steel. The average grain size of this material was
determined to be 15 µm. The initial dislocation density was assumed to be 1012 m-2, in accordance with
the work of Yoshie et al. [43]. The measured yield stress was 270 MPa. An overview of the model
parameters is also given in Table 3.
As shown in earlier work [30], the experimental and model stress-strain curves for the 304 L steel. The
model presents a good fit to the data. Compared to the ferritic phase, the fitting parameter f is
remarkably lower. This can be related to the lower SFE (Stacking Fault Energy) for FCC materials,
since a high SFE implies that dynamic recovery takes place more easily.
- Metastable austenitic steel (301LN)
During the strain induced martensitic transformation, two mechanisms affect the austenite behaviour:
on the one hand, the volume of retained austenite decreases and the mean free path of the
dislocations in austenite is therefore reduced during straining. On the other hand, the amount of
martensite increases with straining.
XRD analysis was carried out to determine the parameters of the Olson-Cohen law for the 301LN
steel, which were determined to be α=6.527, β=0.9 and n=3, and to find an equation for the evolution
of the volume fraction of martensite, fα’ during straining. From this volume fraction, using Equation (8),
the equivalent grain size of austenite and martensite was calculated as a function of the strain. It was
found that the equivalent austenitic grain size decreases whereas the martensite grain enlarges with
increasing strain.
The stress-strain curve of both the austenitic and the martensitic constituent of the 301LN stainless
steel were predicted. These curves are shown in Figure 5a, while the corresponding fitting parameters
are given in Table 3. From Figure 5a it is clear that martensite is the hard phase with a flow plastic
stress varying from 1900 to 2400 MPa.
The stress-strain curve of the 301 LN steel, was simulated by applying a mixture law in order to
combine the two curves of Figure 5b., A Gladman-type mixture law was used with n=2. As shown in
Figure 5b, a good correspondence was observed between the modelled and experimental curve.
1200
True Stress, MPa
True Stress, MPa
2500
2000
1500
301 LN
martensite
austenite
1000
500
0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
True Strain
(a)c)
1000
800
600
400
200
Austenite 301 LN
experiment
model
0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
True Strain
(b)d)
Figure 5: (a) Simulated stress-strain curve for the martensitic and austenitic constituent of the
301LN steel. (b) Experimental and modelled stress-strain curves for the 301LN austenitic
stainless steel.
When the fitting parameters of the stable 304L and the metastable 301LN stainless steel are
compared, it is clear that the annihilation parameter f of the Mecking-Kocks model is far more
important in the latter case.
The experimental results of the CMnSi bainitic and the CMnAl bainitic alloy could not be used in order
to model the bainitic ferrite constituent in section 4.2.1, because of the presence of retained austenite
in the microstructure. However, if the fitting parameters of section 4.2.1 are combined with those
obtained for the 301LN metastable stainless steel, it becomes possible to model the data reliably. The
Olson-Cohen parameters, which depend on the chemical composition of the two steels were
determined using equations proposed by Samek et al. [28] for low alloyed TRIP steel. The carbon
content of the retained austenite (Table 1) was calculated from XRD results, by using the temperature
and carbon dependence of the austenite lattice parameter proposed by Onink et al. [44].
The Olson-Cohen parameters for the retained austenite transformation kinetics were α = 10.11, β =
1.34 and n=2 for the CMnAl alloy and α = 30.53, β = 1.67 and n=2 for the CMnSi bainitic alloy,
respectively. From these data, the kinetics of the martensitic transformation during straining were
determined.
The evolution of the austenitic and martensitic equivalent grain size was calculated for the CMnSi
bainitic steel using these data. In Figure 6a, the behaviour of the M/A constituent present in the bainitic
alloy is obtained by making use of a power mixture law with n=2.
4.2.3 BAINITE
The last step consists in combining the behaviour of the M/A constituent and the bainitic ferrite.
The exponent of the mixture law was again considered to be 2. In both cases, the model gave a good
correspondence with the experimental data (Figure 6b).
1200
True Stress, MPa
True Stress, MPa
2500
2000
1500
1000
austenite
martensite
M/A constituent
500
0
0.00
0.05
0.10
0.15
True Strain
1000
800
600
400
expriment
model
200
0
0.00
0.20
0.05
0.10
True Strain
(a)c)
0.15
0.20
(b) d)
Figure 6: (a) Estimated stress-strain curve for the M/A constituent (b) Experimental and
modelled stress - strain curves for the CMnSi Bainite
4.3 TRIP STEEL
As mentioned before, two types of TRIP steel, namely a CMnAl and a CMnSi steel, were studied in
the course of the present work. The results discussed in the previous sections were combined in order
to model the stress-strain curves of the TRIP steels. The numerical parameters for both steels are
summarised in Table 3, while more detail will be given about the results of the CMnSi TRIP steel. The
Olson – Cohen parameters were determined, similarly to bainitic alloys in order to take into account
the behaviour of the M/A constituent. These values were found: α = 11.27, β = 1.45 and n=2 for the
CMnAl TRIP steel and α = 33.22, β = 1.73 and n=2 for the CMnSi TRIP steel, respectively.
The behaviour of the three TRIP constituents, polygonal ferrite, bainite, M/A constituent and the
experimentally obtained TRIP stress-strain curves were taken into account. It is self-evident that the
grain size of the various constituents differs from the grain sizes that were measured when the
constituents were studied separately. This feature was found to have a large influence on the value of
the fitting parameters. Therefore, different model parameters were found when fitting the calculated
stress-strain curves to the experimental data.
The stress-strain curves of TRIP steels are shown in Figure 7. An excellent match was obtained
between the experimental results and the model calculations. The input parameters for both TRIP
steels are reported in Table 3 and the model stress-strain curve is plotted with reference to the
experimental results.
True Stress, MPa
1200
1000
800
600
CMnSi TRIP experiment
400
model
CMnAl TRIP experiment
200
0
0.00
model
0.05
0.10
0.15
0.20
True Strain
0.25
0.30
e)
Figure 7: Stress - strain curves for the CMnSi and CMnAl TRIP (experimental and predicted)
5 EVALUATION OF THE MODEL
5.1 INFLUENCE OF THE DIFFERENT CONSTITUENTS ON THE BEHAVIOUR OF THE TRIP
STEEL
In the previous section, the stress-strain curve of two TRIP steels was predicted by combining the
behaviour of the different constituents of the TRIP microstructure. The partitioning of the stress and
strain between the polygonal ferrite and the bainitic constituent, implies that any point (σ,ε) on the
TRIP stress-strain curve corresponds to two points, one on the stress-strain curve for the bainitic
constituent, which consists of the bainitic ferrite and the M/A constituent, and one on the stress-strain
curve for the polygonal ferrite. The stress-strain curve of the CMnSi TRIP steel and the corresponding
polygonal ferrite and bainite points are shown in Figure 8a. The evolution of the parameter q, as
defined in Equation 6, is shown in the Figure 8b.
σ − σα
(10)
q = αB
ε αB − ε α
1000
800
600
400
Bainite
Ferrite
TRIP CMnSi
200
0
0.00
0.05
0.10
True Strain
q parameter
True Stress, MPa
1200
100000
10000
0.00
0.15
a)
0.05
True Strain
0.10
b)
Figure 8: (a) Stress and strain partitioning between the polygonal ferrite and the bainitic
constituent in the CMnSi TRIP steel (b) Evolution of the q parameter for the CMnSi TRIP steel
The evolution of the ratios ε αB/εα and σ αB/σα with straining is given in Figure 9. When the value of q is
maximal, the iso-strain condition, i.e. the same amount of the total strain is accommodated by both
constituents, is approached. The stress ratio is rather invariant with stress, this behaviour is similar to
that observed for Dual Phase, duplex and spheroidized high carbon steels by Cho et al. [4]. The strain
ratio presents mainly two domains which are related to the kinetics of the strain induced martensitic
transformation: in a first stage, the strain ratio decreases drastically: only the soft ferrite deforms
plastically, the bainitic constituent does not deform plastically as a result of the austenite to martensite
transformation. In a second stage, the two constituents deform plastically, the stress ratio increases
and tends to a constant value. When the amount of deformation increases, the softest phase, i.e.
polygonal ferrite, absorbs more strain, whereas the hardest, i.e. the bainitic constituent, carries most of
the stress. This result presents a good correspondence with the behaviour of the ferritic and bainitic
alloys, and also indicates the importance of the presence of soft and hard phases in the TRIP
microstructure for formability applications. Similar results were observed by Furnémont [45] in the
case of two CMnSi TRIP steels. The evolution and the range of the q parameters approaches the
values that were found for Dual Phase steels [16], where the partitioning occurs between polygonal
ferrite and lath martensite islands.
0.9
2.0
εbainite/ε ferrite
0.7
1.5
0.6
0.5
1.0
0.4
0.3
εbainite/εferrite
0.2
0.5
kinetics
0.1
0.0
0.00
σ bainite/σ ferrite
0.8
σbainite/σferrite
0.05
0.10
0.0
εTRIP
Figure 9: Evolution of the stress and strain partitioning between the polygonal ferrite and the
bainitic constituent during the deformation of the CMnSi TRIP
5.2 INFLUENCE OF THE CHEMICAL COMPOSITION AND MICROSTRUCTURE
Two types of TRIP steel have been studied, namely a CMnSi and a CMnAl TRIP steel. The impact of
the composition on the kinetics of the strain-induced transformation of retained austenite to martensite
was observed by Samek et al. [28]. By modelling the stress-strain curves of these steels, the influence
of the most important alloying elements, i.e. aluminium and silicon, on the k, f and σ0 fitting parameters
could be examined.
The evolution of these parameters is reported in Table 3. The influence of the different constituent
(polygonal ferrite, bainitic ferrite, M/A constituent) is shown in the same table. The solid solution
strengthening effect of silicon and aluminium is known to be different (Al: 41 MPa/wt-%, Si: 88
MPa/wt-%) [46], so a difference in σ0 is expected. The parameter σ0 of the individual phases in the
multiphase steels is always higher than the value of σ0 determined for the bulk phase. This is very
likely related to the interaction between the different phases during deformation.
The aim of the present research was to keep the value of the fitting parameters (k and f) used for
separate constituent and use them for that phase in the multiphase TRIP steel. It could easily be
achieved for CMnSi alloys but seemed to not be entirely applicable to CMnAl alloys.
The k and f values for the single ferrite phase are not composition dependent. In bainite k and f have
slight composition dependence: Al addition results in reduction of k and f.
In the case of multiphase CMnSi TRIP steel, the values of k and f obtained for the single phase ferrite
and bainite are applicable. This not the case for the multiphase CMnAl TRIP where there is a strong
reduction of k and f values in the ferrite phase. The k/f ratio for ferrite is the same for the single phase
ferrite and the ferrite phase in the CMnSi and CMnAl TRIP.
In addition the values of k, f and σ0 have a pronounced grain size dependence in both cases.
The sensitivity of the model to each of the fitting parameter was also investigated. The specific range
of the k and f parameters is given for the CMnSi alloys in Table 3. Generally the range is small in case
of ferrite and bainite constituent. In case of the M/A constituent the range is more important, the model
is then more sensitive to the transformation parameters than to the changes in the values of k and f.
6 CONCLUSIONS
The behaviour of multiphase TRIP steels was modelled by means of a micromechanical model
based on the Mecking-Kocks theory, and the successive application of a two-phase power mixture
law. The model presented in this work is straightforward and has the advantage of being physically
meaningful by including the contribution of each microstructural constituent on the flow stress and the
strain hardening of multiphase steel.
The main conclusions of the model calculations are the following:
1. In comparison with empirical laws, the model combines physically meaningful parameters in order
to describe the stress-strain curve of a complex multiphase microstructure. This model was validated
by making comparison with experimental results of TRIP steel and isolated phases.
2. The strain-induced martensitic transformation was studied in detail by considering the behaviour of
a metastable 301LN austenitic stainless steel.
3. The behaviour of the TRIP steels was modelled by successively combining the behaviour of single
phase constituents using two-phase power mixture laws.
4. The stress and strain partitioning for the TRIP steels could be studied in detail with this model. It
was found that the presence of the bainitic constituent, consisting of bainitic ferrite + M/A constituent,
permits to the TRIP steel to keep a high hardening potential, which retarded the onset of necking.
5. A clear influence of the alloying elements, aluminium and silicon was observed for the different
fitting parameters: σ0, k and f. These parameters depend on the chemical composition. k and f were
also found to depend on the grain size and the microstructure. σ0 could be related to solid solution
hardening and f to SFE.
ACKNOWLEDGEMENT
The authors would like to thank the Fonds voor Wetenschappelijk Onderzoek – Vlaanderen (Fund for
Scientific Research – Flanders) for its support.
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