Modelling of Transformations in TRIP Steels · steel research int. 75 (2004) No. 11 739 ......

Materials Technology – TRIP Steels

steel research int. 75 (2004) No. 11 739

Introduction

The increased demand of the automotive industry forsteel grades exhibiting high strength and formability hasbeen the main incentive for the advent of new, multi-phasesteel families, such as the low-alloy DP and TRIP steels [1].The mechanical behaviour of TRIP steels in particular isunique among the Fe-based alloys, since they manage tocombine high strength (typical tensile strengths 600–1000MPa) and formability (typical uniform elongations20–25%) [2]. This excellent combination of mechanicalproperties of TRIP steels is largely attributed to their com-plex microstructure, consisting of dispersed retainedaustenite (γR) and bainite in a ferritic matrix, figure 1.

Under the effect of stress and/or plastic deformation, γR

transforms to martensite (α′), thus contributing to an in-crease in strain-hardening rate (static hardening), while si-multaneously the transformation acts as a deformationmechanism (dynamic softening). The combined effect ofstatic hardening and dynamic softening promotes the stabi-lization of plastic flow [3].

The γR dispersion in the microstructure is produced by atwo-stage heat-treatment, i.e. an Intercritical Annealing(IA) followed by a Bainitic Isothermal Treatment (BIT),figure 2. The major factor influencing the mechanical be-haviour of low-alloy TRIP steels is the stability of the γR

dispersion, which in turn is affected by chemical composi-tion, particle size and stress-state. These parameters areusually coupled, thus making optimisation of the mi-crostructure and properties of TRIP steels a rather complextask and creating a necessity for the application of model-ing and simulation methods, in order to understand the var-ious mechanisms involved [4,5].

The aim of the present work is to demonstrate the useful-ness of simple computational models, by which the heat-

Modelling of Transformations in TRIP SteelsAntonis I. Katsamas, Gregory N. Haidemenopoulos, Nikolaos Aravas

Dept. of Mechanical & Industrial Engineering, University of Thessaly, Volos/Greece

Industrial processing of low-alloy Transformation Induced Plasticity (TRIP) steels involves various stages of heat-treating, such as Intercrit-ical Annealing (IA) and Bainitic Isothermal Treatment (BIT), in order to produce a dispersion of retained austenite (γR) particles and bainite(αB) in a ferritic matrix (α). Retained austenite then transforms to martensite (α′) during forming processes undergone by the steel. In thepresent work an effort was made to model these stages of processing, i.e. IA, BIT and the γR→α′ strain-induced transformation. Simulationof heat-treatment stages was implemented using computational kinetics methods. Investigation of the strain-induced γR→α′ transformationkinetics was performed by means of a simple analytical model. Simulation of IA and comparison with available experimental data showedthat the amount of austenite (γ) forming during IA reaches the values predicted by thermodynamic equilibrium only at high annealing tem-peratures (>825oC). It was also observed that kinetic and thermodynamic predictions set a lower and an upper limit, respectively, within whichthe actual amount of austenite experimentally observed is contained. Results from the simulation of the BIT indicated considerable carbonenrichment, and thus stabilization of γR, in agreement with recent experimental observations. As regards the strain-induced γR→α′ transfor-mation, the analytical model employed in the present work was fitted to available experimental results, showing reasonably good adaptationto the kinetic behaviour of the microstructure during plastic deformation.

Keywords: low-alloy TRIP steels, phase-transformations, simulation, modeling, intercritical annealing, bainitic isothermal treatment, retainedaustenite, strain-induced transformation.

Figure 1. Typical microstructure of a low-alloy TRIP steel.

Figure 2. Typical heat-treatment sequence of low-alloy TRIP steels(A: austenite, B: bainite, F: ferrite).

treatment stages (IA and BIT) can be simulated, and also topresent an analytical model, which can be used to estimatethe kinetics of γR→α′ transformation during uniaxial ten-sion of TRIP steels.

Intercritical Annealing (IA)

The starting microstructure of low-alloy TRIP steels con-sists of proeutectoid ferrite and pearlite. It is well estab-lished that austenite (γ ) formation during heating of fer-rite/pearlite microstructures proceeds in two steps [6]. Thefirst step is relatively rapid and involves the formation ofhigh-C γ from pearlite. The second step is substantiallyslower and involves the growth of γ in expense of proeu-tectoid ferrite (α). Therefore, in the simple IA model em-ployed here, the assumption was that pearlite transforma-tion to austenite is completed in a negligible amount oftime. The conditions at the end of the first step (i.e. vol.fractions and compositions of phases) were considered asinitial conditions for the second step. Consequently, the sys-tem was considered to initially consist of a high-C γ region(formed from pearlite) with width Lγ , and a proeutectoid αregion with width Lα , figure 3.

Under these conditions, simulation of γ formation withinthe intercritical range (α+γ ) can be performed by solvingthe coupled diffusion equations in the two phases involved.Details on the mathematical formulation of the model canbe found in [7]. The resulting 1-D moving-boundary diffu-sion problem can be solved by a numerical method for thesolution of coupled diffusion equations developed byÅgren, which is incorporated in the DICTRA computation-al kinetics software [8]. Determination of various necessarythermodynamic quantities for the simulation was imple-mented with the use of CALPHAD methodology, throughThermo-Calc computational alloy thermodynamics soft-ware [9]. Simulations of IA were performed for the threelaboratory-produced low-alloy TRIP steels shown intable 1, for which experimental measurements of vol.% γas a function of annealing temperature and time were avail-able [10]. Annealing temperatures tested ranged between780-960°C.

Figures 4a-c depict a comparison between calculated bythe model (full lines), experimentally measured (squaresymbols) and equilibrium values as calculated by Thermo-Calc (dotted lines), of vol.% γ as a function of annealingtemperature, for an annealing time of 90 sec. Despite thesimplicity of the model, a reasonable agreement can be ob-served. At low annealing temperatures (780–810°C) exper-imental and model results agree quite well, whereas at high-er annealing temperatures the amount of γ is slightly un-derestimated by the model. This could be attributed to theactivation of high-diffusivity paths, such as grain-bound-aries, which accelerate the rate of transformation at highertemperatures, but cannot be taken into account by the mod-el.

It is also interesting to compare model and experimentalresults with the ones predicted by thermodynamic equilibri-um. As regards the kinetically calculated and equilibriumvalues, it seems that for all the steels and annealing temper-


740 steel research int. 75 (2004) No. 11

Figure 3. Schematic representation of the one-dimensional movingboundary diffusion model for IA simulation [7].

(a)

Figure 4. Experimental, equilibrium and kinetic model results ofvol.% austenite as a function of IA temperature for the low-alloyTRIP steels of Table 1. a) Steel 1, b) Steel 2 and c) Steel 3.

(b)

(c)

atures considered, kinetics predict significantly less γ thanthermodynamics. It can be observed that the experimental-ly measured vol.% γ lies between the kinetically and ther-modynamically calculated curves. Thus, kinetics and ther-modynamics set a lower and an upper limit, respectively,within which the experimental results are contained. In fact,equilibration has proven to require substantially greater an-nealing times in order to be achieved [7].

Bainitic Isothermal Treatment (BIT)

The stage of BIT is of great importance for the formationof a stable γR dispersion in the microstructure. Bainitegrowth is accompanied by the rejection of C in austenite,thus increasing the stability of the final γR dispersion. Re-cent measurements of C-content within individual γR parti-cles in various low-alloy TRIP steels, using sophisticatedtechniques such as PEELS, have shown considerable C en-richment of γR after the BIT stage, with concentrationsreaching as high as 1.25–1.40 mass % C [11,12].

In order to investigate C enrichment of γR a simple kinet-ic model was employed, which was based on an idea origi-nally developed by Hillert et al. [13]. To adapt this idea forthe case of low-alloy TRIP steels, some initial considera-tions had to be made:

i) Austenite (γ ) enters the BIT stage with an initial com-position determined by thermodynamic equilibrium at theIA temperature.

ii) High Si or Si+Al content of low-alloy TRIP steels sup-presses carbide precipitation. Thus only bainitic ferrite (αB)forms during the BIT stage.

iii) αB grows in ‘‘parabolic cylinder’’ plates, figure 5, inan edge-wise manner [14].

iv) Growth rate is rapid enough, so that solute species (C,Mn, Si) initially become entrapped inside αB. Thus, αB ini-tially inherits the chemical composition of γ .

v) The initial supersaturation of αB is then eliminated byside-wise diffusion of the solute species out of the αB plateand into the adjacent γR, figure 6. The purpose of the proposed kinetic model is to simulatethe side-wise rejection of solute species out of the αB platesand not their growth rate. In order to do so, a ‘‘two-cells’’approach was employed for the geometry of the model. Twocells, separated by an immobile interface allowing the dif-fusional exchange of mass, were used; one assigned to αB

and the other to γR. The width of the αB cell is associated tothe half-thickness of the plate (W/2), whereas the width ofthe γ cell is associated to the austenite grain size. The ini-tial chemical composition of the γR cell is determined bythermodynamic equilibrium at the IA temperature and, asexplained above, this is also the initial composition for theαB cell.

The model was then applied for simulating the BIT treat-ment of a 0.20C-1.65Mn-1.60Si (mass %) industrially pro-duced low-alloy TRIP steel. The initial composition of γR

was calculated by Thermo-Calc at 775°C (i.e. at the IA tem-perature corresponding to a 50%-50% γ /α mixture), andwas found to be 0.38C-2.30Mn-1.42Si (mass %). Variouscell sizes (0.2 - 5 µm), as well as BIT temperatures (250-400oC) and holding times (up to 600 sec) were examined in

the simulations, which were performed by using the DIC-TRA computational alloy kinetics software.

A series of interesting results can be drawn from the sim-ulations. Figure 7 depicts the variation of C concentrationprofiles within a γR particle at various BIT holding times,for treatment at 300°C and 400°C. As shown, significant C-enrichment of γR occurs, which is more pronounced at theinterface with αB (right-hand end of the diagram). Increas-ing BIT temperature seems to have an effect on the rate ofC migration and homogenisation of the particle, but not onthe total amount of C entering the particle. This is better il-lustrated in figure 8, which depicts the total C-concentra-tion of the γR particle of figure 7 as a function of the squareroot of BIT time. It should also be observed in figure 8 thatat the end of BIT, the C-content of the γR particle has in-creased by a factor of 2 with respect to the initial value.



Table 1. Chemical composition (in mass%) of TRIP steels employedin IA simulations.

Material C Mn Si

Steel 1 0.142 1.35 1.31

Steel 2 0.176 1.41 1.45

Steel 3 0.146 1.33 1.28

Figure 5. Parabolic cylinder model for the bainitic ferrite plates.

Figure 6. Edge-wise growth and side-wise rejection of C from abainitic ferrite plate.

It should however be noted that the levels of C-enrich-ment calculated by the model are solely dependent on thecell sizes, which were selected arbitrarily for the sake of thesimulations. In order to get more realistic results, the cellsizes have to be related to the actual αB plate thickness andγ grain size. Additionally, the limitations imposed by the To

line have to be taken into account, in order to determine themaximum amount of C that can be accommodated by γR.The To line can be readily determined by thermodynamics.For the alloy examined here the To line was calculated byThermo-Calc and is presented in figure 9. The dotted verti-cal line represents the chemical composition of γ at the endof the IA stage.

Simulation results were quite different for the substitu-tional species of the alloy (Mn, Si), for which no significantmass transfer between the two phases was calculated. Thisis illustrated in figure 10, which depicts the total Mn-con-tent of a γR particle as a function of square root BIT timefor treatment at 300°C and 400°C. There seems to be a netflow of Mn out of the γR particle towards αB during thetreatment, but in very small quantities. The same outcomewas also valid for Si. These results indicate that the processpossibly takes place under paraequilibrium conditions withrespect to C.

The usefulness of such a relatively simple kinetic modelfor the BIT lies in the information it can provide regardingγR stability. For example, the simplest expression of austen-ite stability is the Ms temperature, which can be calculatedby using simple empirical laws, such as the well-known An-drews equation [15]. For the steel analysed with the presentmodel, Andrews equation yields an Ms temperature of308°C for γR at the beginning of the BIT, while after thetreatment this reduces to 152°C.

Furthermore, as a result of the formation of a C concen-tration gradient within the γR particles (figure 7), it wouldbe reasonable to expect that a stability gradient should alsoexist inside each γR particle. Such an example is presentedin the diagram of figure 11, which shows the calculated Mσ

stemperature, using an analytical model proposed by Haide-menopoulos et al. [16], as a function of distance from thecentre of the particle. It should be reminded at this point thatthe characteristic Mσ

s is a measure of the stability of γR dis-persions against mechanically induced transformation. Asexpected, Mσ

s in figure 11 is low in the vicinity of the γR/αB

interface (i.e. retained austenite is very stable there) and in-creases towards the centre of the particle. On straining ofthe steel, this could lead to the formation of martensitic‘‘cores’’ surrounded by very stable retained austenite‘‘rims’’. Actually, a similar though reverse morphology(martensitic rims surrounding austenite particles) has beenobserved by Speich et al. [17], in intercritically annealedand then slowly cooled DP steels.

Strain-Induced Transformation of RetainedAustenite to Martensite

Transformation induced plasticity can occur by two dis-tinct mechanisms, i.e. stress-assisted and strain-inducedγR→α′ transformation. In the stress-assisted regime α′



Figure 7. C-concentration profiles in a γR particle as a function ofBIT time at 300oC and 400oC.

Figure 8. Total C-content in a γR particle (cell size 1µm) as a func-tion of BIT time at 300oC and 400oC.

Figure 9. Calculated To line for the Fe – C – 2.30Mn – 1.42Si alloysystem.

forms on pre-existing nucleation sites. In contrast, in thestrain-induced regime, new and more potent nucleationsites are created by plastic deformation of the parent phase.As the steel is stressed and deformed, γR will transform toα′ by the simultaneous operation of both mechanisms. Thestress-assisted mechanism dominates at stresses lower thanthe yield-strength of γR, whereas the strain-induced mecha-nism prevails after the yield-strength has been surpassed.The total volume fraction of γR transforming to martensite,f, could then be expressed in the following form:

f = f (σ )stress + f (σ, ε)strain (1)

where f(σ )stress and f(σ ,ε)strain denote the contributions ofthe stress-assisted and strain-induced mechanisms, respec-tively.

According to the mechanism for heterogeneous marten-sitic nucleation proposed by Olson et al. [18,19], formationof a martensitic nucleus can occur by the dissociation of anexisting defect, which serves as a nucleation site for thetransformation. Dissociation of such a defect creates a fault-ed structure or martensitic embryo, the growth of which isdetermined by the energy change accompanying the disso-ciation. The energy per unit area of an embryo with thick-ness of n crystal planes, γf(n), is given by equation:

γ f (n) = n · d · (gch + gel + w f) + 2γs (2)

in which ∆gch is the chemical driving force for the transfor-mation, gel the elastic strain energy, associated with distor-tions in the embryo/matrix interface, wf the frictional workof interfacial motion, γs the specific embryo/matrix interfa-cial energy and d the close-packed interplanar spacing inthe martensitic embryo. The potency of a nucleation site(defect) can be expressed in terms of the thickness n (ex-pressed in number of crystal planes) of the nucleus, whichcan be formed from barrierless dissociation of the defect.The critical value of n, for nucleation at a given chemicaldriving force per unit volume, is then given by:

n = − 2γs

(ch + gel + w f ) · d(3)

Based on this theory, the cumulative defect-potency dis-tribution has been derived [20], using results from the well-known Cech and Turnbull small-particle experiments in Fe-30Ni alloys [21]:

Nv = N ov · exp(−α · n) ⇒

⇒ Nv = N ov · exp

[2α · γs

(gch + gel + w f ) · d

](4)

where Nv denotes the number density of nucleation sitesrandomly distributed throughout the volume, N o

v the totalnumber density of nucleation sites of all potencies and α isa constant.

In the case of transformation induced plasticity, the po-tency distribution of pre-existing nucleation sites in thestress-assisted region, is given by:

N stressv = N o

v · exp

(2α · γs

A · d

)(5)

where A = ∆gch+(1/3)∆gσ,max+gel+wf. Here, N stressv is the

number density of pre-existing nucleation sites and N 0v the

number density of pre-existing nucleation sites of all poten-cies. Comparing equation (5) to equation (4), the formercontains an extra term, ∆gσ,max, which stands for the me-chanical contribution to the driving force. The mechanicaldriving force contribution term has been determined by Pa-tel and Cohen [22]:

gσ,max = −1

2

(σ

√γ 2

o + ε2o + σ · εo

)(6)

where γo and εo are the transformation shear and normalstrains, respectively.



Figure 10. Total Mn-content of a γR particle (cell size 1µm) as afunction of BIT time at 300oC and 400oC.

Figure 11. Variation of temperature in a γR particle of size 0.5 µm,after BIT at 400oC for 60 sec.

A similar expression can be used to describe the potencydistribution of the new, strain-induced nucleation sites:

N strainv = N o

v (ε) · exp

[2α · γs

B · d

](7)

in which B = ∆gch+∆gσ,max+gel+wf. All parameters in equa-tion (7) represent the same physical quantities as explainedfor equation (5). It should, however, be emphasized that incontrast to equation (5), the total strain-induced nucleationsites density up to plastic strain ε, N 0

v (ε) , is in this case afunction of plastic strain ε. The number density of all nu-cleation sites is equal to the sum of equations (5) and (7):

Nv = N stressv + N strain

v ⇒Nv = N o

v · exp(−αstress · nstress) + ...

... + N ov (ε) · exp(−αstrain · nstrain)

(8)

Parameters nstress and nstrain are given by:

nstress = −(

2γs

A · d

)(9)

for the stress-assisted and

nstrain = −(

2γs

B · d

)(10)

for the strained-induced regime of the transformation, re-spectively.

Assuming that the nucleating defects are randomly dis-tributed, the vol. fraction γR transforming to α′ is given by:

f = 1 − exp(−Nv · Vp

)(11)

where Vp is the particle volume. Combined with equations(8), (9) and (10), equation (11) gives:

f = 1 − exp

{−Vp ·

[N o

v · exp

(2γs · αstress

A · d

)+ ...

... + N ov (ε) · exp

(2γs · αstrain

B · d

)]} (12)

An expression for the total strain-induced nucleation sitesdensity up to a specific plastic strain ε, N 0

v (ε) , has beenproposed by Kuroda [23]:

N ov (ε) = N · [1 − exp

(−k · εn)]

(13)

where N represents the overall number density of nucleationsites that is possible to be induced by plastic strain, while kand n are dimensionless constants. Introducing equation(13) into (12) the later becomes:

f = 1 − exp{−Vp · [N ov · exp(

2γs · αstress

A · d) + ..

.. + N · [1 − exp(−k · εn)] · exp(2γs · αstrain

B · d)]}

(14)

Equation (14) establishes a relation between vol. fractionγR transformed to α′, f, and true plastic strain, ε. It is, there-fore, possible to predict the kinetics of the transformation atcertain amounts of plastic strain, provided that some valuesfor the rest of the parameters in equation (14) are given. Theanalytical kinetics model described above was used in orderto calculate the f-ε behaviour in uniaxial tension of two lab-oratory-produced low-alloy TRIP steels, for which experi-mental f-ε kinetic data where available in literature [2].Table 2 presents the chemical composition of these steels.

Appropriate values for the parameters employed in equa-tion (14) were found in literature [1,2,23]. Equation (14)was then subjected to a non-linear curve fitting procedure,in order to best fit the experimental results. This was ac-complished by varying parameters N 0

V and N.Figure 12 depicts experimental (symbols) and calculated

(lines) f-ε results for the two steels examined. The diagramsalso show the BIT conditions applied to the steels. Asshown, the model manages to describe fairly well the sig-moidal variation of the transformation product with respectto plastic strain. One should also note the substantial frac-tion of the transformation, which occurs in the elastic re-gion (ε = 0), under the operation of solely the stress-assist-ed nucleation mechanism. Comparing the f-ε behaviour ofthe two steels, the existence of Nb in steel TRIP 2 does notseem to produce any significant differences in the kineticsof the strain-induced part of the transformation. However,Nb seems to promote the stress-assisted transformation ofγR, since a greater fraction of γR has transformed in theelastic region for the Nb containing steel (TRIP 2).



Figure 12. Experimental and model f - ε results for steels TRIP 1and TRIP 2 of table 2.

Table 2. Chemical composition (in mass%) of the low-alloy TRIPsteels with available f – ε kinetics experimental data.

Steel C Mn Si Al Nb

TRIP 1 0.20 1.40 0.50 0.70 -----

TRIP 2 0.20 1.40 0.50 0.70 0.03

Conclusions

Modern metallurgical methods, such as computational al-loy thermodynamics and kinetics, can be used in order tosimulate the phase transformations involved during theheat-treatment stages of low-alloy TRIP steels, i.e. intercrit-ical annealing and bainitic isothermal transformation. Theuse of relatively simple models allows for the simulation ofthese heat-treatments, which in turn can provide useful in-formation regarding microstructural characteristics such asvolume fraction and stability of the γR dispersion in TRIPsteels. In addition, prediction of the evolution of the mi-crostructure during plastic deformation of TRIP steels, byemploying a suitable analytical model, can be used in orderto optimise the final microstructure of the steel and, thus, itsmechanical behaviour. The main concluding remarks of thepresent work can be summarized in the following points:

i) Simulation of IA annealing and comparison to availableexperimental results showed good agreement at lower an-nealing temperatures (<825°C). At higher IA temperaturesthe experimental results reach better agreement with pre-dictions obtained by equilibrium calculations. In any case,kinetics and thermodynamics set a lower and upper limit,respectively, within which the experimental results are ob-tained.

ii) Considerable C-enrichment and, thus, stabilisation ofγR particles was calculated by the simulation of the BITtreatment. In contrast, negligible exchange of substitutionalelements, such as Mn and Si, seems to take place betweenγR and αB during the BIT. As a consequence of a C-con-centration gradient within γR particles a stability gradientshould also exist.

iii) The analytical model used for the analysis of theγR→α′ deformation induced transformation kinetics dis-played good adaptation to available experimental data.

Acknowledgement

This work has been partly supported by the EuropeanCoal and Steel Community (ECSC) through the 7210-PR-370 project ‘‘Control and exploitation of the bake-harden-ing effect in multi-phase high-strength steels’’.

(A2004086)

Contact: Prof. Dr.-Ing. G. N. HaidemenopoulosDepartment of Mechanical and Industrial EngineeringUniversity of ThessalyVolos, Greece

References

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