m. humbert; b. gardiola; c. esling; g. flemming; k.e. hensger -- modelling of the variant selection...

8/12/2019 M. Humbert; B. Gardiola; C. Esling; G. Flemming; K.E. Hensger -- Modelling of the Variant Selection Mechanism in

1/7

Acta Materialia 50 (2002) 17411747 www.actamat-journals.com

Modelling of the variant selection mechanism in the phasetransformation of HSLA steel produced by compact strip

production

M. Humbert a,*, B. Gardiola a, C. Esling a, G. Flemming b, K.E. Hensger b

a

Laboratoire dEtude des Textures et Applications aux Materiaux LETAM, CNRS UMR 7078, ISGMP, Universite de Metz, F-57045 Metz Cedex 01, France

b SMS Demag AG, Postfach 230 229, Dusseldorf 40088, Germany

Received 20 September 2001; received in revised form 20 December 2001; accepted 31 December 2001

Abstract

The ferrite and residual austenite textures of a microalloyed steel (HSLA) produced by Compact Strip Production(CSP) were determined by X-ray diffraction. At the same time, the individual orientations of neighbouring inheritedferrite grains and austenite grains were measured by EBSD. Orientation relations between the parent austenite and theinherited ferrite have been assessed. Knowing these orientation relations and the parent austenite texture, the simulation

of the texture of the inherited ferrite texture has been performed without variant selection. The comparison of thiscalculated texture with the experimental ferrite texture shows differences due to a variant selection mechanism occurringduring the phase transformation at cooling.

A modelling of a variant selection mechanism based on the elastic anisotropy of the parent austenite leads to asimulated inherited texture with the main characteristics of the experimental ferrite texture. 2002 Acta MaterialiaInc. Published by Elsevier Science Ltd. All rights reserved.

Keywords: Texture; Phase transformations; Variant selection

1. Introduction

The process for the production of hot strip froma continuous cast thin slab has been described insome previous contributions [1,2]. This processallows the production of HSLA grades. Their roomtemperature states and notably their textures,

* Corresponding author. Fax: +33-03873-15377.E-mail address: [email protected]

(M. Humbert).

1359-6454/02/$22.00 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

PII: S1359-6454(02)00023-X

inherited by phase transformation from high tem-

perature austenitic states which can be stronglyinfluenced by the chosen hot rolling routes, deter-mine their mechanical behaviour. Therefore, thestudy of the texture changes and of the variantselection mechanisms is of great interest toimprove the steel properties. In a previous work[2], the texture of the ferrite phase of an HSLAsheet was determined and the parent austenite tex-ture was evaluated from the residual austenite atroom temperature. The analysis of these textures,using texture transformation modelling without


2/7

1742 M. Humbert et al. / Acta Materialia 50 (2002) 17411747

variant selection showed that the texture change

occurred with a variant selection which was not

further investigated at the time. In this contri-

bution, a modelling of texture change by phasetransformation, giving the main features of the

inherited textures, is presented and discussed. Thismodelling takes into account a variant selectionmechanism related to the elastic strain workimposed on the polycrystal by nucleation of the

variants.

2. Microstructures and textures of the sample

In this section only some essential informationabout the investigated sample is referred to.

2.1. Description of the sample

For information only, the levels of somealloying elements of the investigated HSLA grade

are given in Table 1.

The cooling down of the austenite phase of thisinvestigated HSLA grade was chosen to lead to an

incomplete bainitic phase transformation. Conse-quently, residual austenite is present in the final

product. The ferritic microstructure obtained afterphase transformation of the work hardened austen-ite is characterised by a small grain size (3.54.5m) and by elongated grain shapes (see Fig. 1).

2.2. Texture of the ferrite

Experimental details of these texture determi-nations and texture characteristic descriptions can

be found in [2]. The textures presented in the fol-

lowing were measured at the mid section of the

sheet. All the texture functions (ODFs) were calcu-lated with the harmonic method [3,4], considering

Table 1

Illustrative composition of the investigated HSLA steel

Alloying C Si Mn V Ti

element

Composition 0.05 0.5 1.6 0.12 0.002

(wt%)

Fig. 1. Optical micrograph (mid-thickness) of the ferrite

obtained after phase transformation of the work hardenedaustenite. The microstructure shows small and elongated grains.

that the rolling process had induced a macroscopicorthorhombic symmetry. The ODF of the ferrite is

not very sharp with a texture index ofJ 3.9. Fig.

2 displays the ODF sections plotted at j1constant.This texture is often described in the literature by

RD fibre (110//RD) and TD fibre(110//TD) [5].

2.3. Texture of the austenite

The texture of the ferrite phase is related to the

texture of the parent high temperature austenite

phase whose determination is not possible. Conse-quently, the texture of this latter phase has been

evaluated by considering the texture of the residual

austenite or by reconstructing the texture of theparent phase from the ferrite texture thanks to a

model recently developed by the authors [6]. Thetexture of the residual austenite is itself not easy

Fig. 2. ODF of the ferrite (mid-section), plotted inj1sections

(maximum=6.9 times random).


3/7

1743M. Humbert et al. / Acta Materialia 50 (2002) 17411747

Fig. 3. ODF of the minor residual austenite (mid-section),

plotted in j1 sections (maximum=17.3 times random).

to determine accurately because the proportion ofthe residual austenite is very small. For thesereasons, the textures of residual austenite can only

be interpreted in a qualitative way (Fig. 3). Thistexture can be characterised by components such as

strong {110}112 (brass), {110}001 (Goss)and {112}111 (copper) components as usually

in rolled FCC metals.

Fig. 4 shows the ODF sections of the austenitetexture, evaluated from the ferrite texture, using the

orientation relations of NishiyamaWassermann(NW). This latter reconstructed texture whichreproduces the main features of the residual austen-

ite texture is assumed as the texture of the parent

austenite texture.

3. Orientation relations between the austenite

and ferrite phases

Local orientations have been determined byEBSD, using a LEO440 SEM operating at 200kV. A 60 m square area, scanned with steps of

0.2 m gave an orientation map, on which the

Fig. 4. ODF of the austenite(mid-section), reconstructed from

the ODF of the ferrite, plotted in 1 sections (maximum=13.

times random).

orientations and phases (ferrite or austenite) were

determined by automatic indexing of Kikuchi pat-

terns. Thus, important information on the phase

transformation induced by cooling has beenobtained. The detailed results will be published

soon [7].

The microstructure mainly displays equi-axed

grains. Some of the largest ferrite grains showed

subgrain boundaries. These latter grains are charac-

terised by misorientations (up to 5) from one

extremity to the other. Few residual austenite

grains have been detected. Their size is lower than

2m. Fig. 5 presents a map containing an austenite

grain (A) surrounded by ferrite grains (F1, F2 and

F3) whose orientations are homogeneous withineach grain. The orientation relations between dif-

ferent residual austenite grains and their neigh-

bouring ferrite grains have been determined. As a

result, the orientation relations are, within some

spread, close to the orientation relations of Nishi-

yamaWassermann (NW): (111) // (110) and211//110, or to KurdjumovSachs (KS):(111)// (110) and 110g //111. None of

these relations is strictly fulfilled. Thus, it was notpossible to decide which one of these orientation

relations best describes the experimental ones.

Fig. 5. Orientation map showing a residual austenite grain

(A), surrounded by ferrite grains (F1, F2, F3).


4/7


4. Modelling of the phase transformation

without variant selection

Assuming that the austenite to ferrite phasetransformation occurred without variant selection,

it is possible to simulate the inherited ferrite texturef2(g) from the texture of the parent texture f1(g)thanks to the relation [3]:

f2(g) W(g1)f1(g11 g)dg1 (1)provided that the orientation transformation func-

tionW(g1) be known. This function takes the mut-

ual orientation relation g0 between both lattices

into account [for example NishiyamaWassermann(NW) or KurdjumovSachs (KS)].

The simulated ferrite texture, calculated accord-ing to Eq. (1), in which each function has been

expanded in series of spherical harmonics up to arankl 22 and using NW orientation relationship

are shown in Fig. 6.

In each ODF section, the localisation of the mainpeaks of the simulated textures is in good agree-

ment with the main peaks of the experimental tex-

tures whatever the orientation relation used. Never-

theless, a detailed comparison shows somedifferences between the calculated and experi-

mental textures. For example, in the ODF sectionsof the simulated textures some intensities which

build up a partial fibre (see orientations j1 6090 for 30 and j2 22.5) are very weakin the experimental ferrite texture. Moreover the

experimental texture is sharper than the simulated

one, as the magnitudes of corresponding peaksshow. Calculating with KS orientation relations

Fig. 6. ODF of the ferrite, simulated without variant selection

from the reconstructed ODF of austenite, plotted in j1sections


leads, in this case, to the same conclusion. These

facts indicate that the transformation occurred with

a variant selection mechanism which is efficient

enough to erase peaks of medium magnitudes.

5. Modelling of the variant selection

To analyse the texture changes occurring during

cooling, we have modelled and checked differentmechanisms of variant selection. The modelling we

explain in this contribution is able to give the mean

trends of the inherited texture. We assumed thatthe variant selection was mainly related to the very

beginning of the transformation by selection of theferrite nuclei within each parent grain. According

to the elastic polycrystal anisotropy, the nucleation

of possible initial ferrite volumes within the aus-tenite requires different energy magnitudes. There-

from the initial ferrite volumes favoured at the very

beginning of the transformation are those whichimpose the minimal elastic strain work to the

polycrystal. After the selection of the nuclei ineach parent grain, the polycrystal keeps on trans-forming by growth of the initial ferrite volumes

which constitute the selected inherited variants

until the transformation is completed. These differ-ent hypotheses have been introduced in the texture

transformation modelling, according to the follow-

ing assumptions and remarks:

1. The lattice of an initial BCC ferrite volume

(nucleus) is deduced from the FCC austenite lat-tice by a modification of the FCC parametercell. A contraction ratio of

h3 aBCC

aFCC

into the Z direction of the body centred tetra-

gonal (BCT) cell of the austenite and an expan-sion ratio of

h1

aBCC2aFCC

in the X and Y leads to the BCC ferrite struc-ture as shown in Fig. 7. This change is called

Bain distorsion.


5/7


Fig. 7. Lattice correspondence between FCC () and BCC ()

cells.

The corresponding deformation tensor,

expressed in the FCC reference frame of theaustenite reads:

[eBij]

h11

h11

h31 eB (2)

WithaFCC 3.591A andaBCC 2.875A, thecontraction deformation is approx. 20% and the

expansion deformation is approx. 13%).2.The orientation relations between the parent

FCC and the transformed BCC lattices are, on

average, close to NW orientation relation. Thenucleation of the ferrite variant whose orien-

tation is related to the austenite by the relation:

(111)FCC/ / (011)BCC

[112]FCC/ / [011]BCCinvolves a Bain defor-

mation Eq. (2) which ensures short paths in the

atom displacement. One is led to the same con-clusion by calculating with the phenomenologi-cal theory of the transformation [8,9]. This

orientation relation corresponds to the rotation

gNW. Thus if the FCC crystal orientation ischaracterised by the rotation g, the considered

variant orientation is characterised by the

rotation gNWg. For this specific orientationrelation, gNW corresponds to Euler angles

(135.0, 9.73, 180.0).Taking into account the 24

rotational symmetry elements of the FCC lat-tice, one theoretically obtains 24 variants which

reduce to 12 distinct variants in the case of NWorientation relation for only three differentBain deformations.

3. The nucleation of a variant requires a certain

energy per volume unit. The nucleus can be

considered as an non-homogeneity within thepolycrystal of austenite considered as a homo-

geneous equivalent medium. A part of this

energy is the elastic strain work required to

deform the matrix. This work per volume unitto form a ferrite nucleus at the very beginning

of the transformation is assumed, in firstapproximation, to be equal to:

W 1

2eBCeB (3)

In this relation C* is the effective elastic con-stant tensor of the parent medium (austenite),whereas eB is the Bain deformation required in

a parent austenite grain to give rise to a variant.The Bain deformation tensor is expressed in the

polycrystal reference frame:

eBij(Sp.g) aik(Sp.g)ajl(Sp.g)eBkl (4)

In this relation the aik(Sp.g) are direction cosines

of one among the 24 reference frames describ-ing the parent grain orientation, p is one among

the 24 variants whereas Sp is one among the 24

rotations of the FCC point symmetry group. Inthis condition, the corresponding elastic strain

work required for the nucleation of the variant,

oriented gNWSp.g, reads:

W(Sp.g) 12eBij(Sp.g)C

ijkleBkl(Sp.g) (5)

4. The effective elastic constant tensor C* is

assumed to be equal toCHill, i.e. the mean valueofCReuss and CVoigt. These quantities are calcu-lated as in [3] to take the anisotropy of the aus-

tenite crystal and the texture into account. This

calculation requires the elastic constants of theaustenite single crystal which are difficult tomeasure experimentally. Therefore the data


6/7


have been drawn from ab initio calculations,available in the literature [1012]. The elasticconstants reported by different authors neverthe-

less reflect the same elastic anisotropy and leadto similar results of the elastic energy per vol-

ume unit. It is also notable that the evaluatedelastic constants of the FCC iron show the samehierarchy as for the BCC iron. For this contri-bution, the data of [10] were used (C11

1.54, C12 1.22, C44 0.77 in 105 MPa).

5. The variant selection is assumed to be linked tothe elastic strain work. Among all the potential

variants which can be inherited from a given

austenite parent grain, only those for which the

elastic strain works are the lowest are formed.In our simulation, for a parent crystal in one

orientation characterised by rotation g the 24elastic strain works W*Sp.g(p 1, 2,...24) are

calculated as well as the mean valueW, the stan-dard deviation s, the maximum Wmax and the

minimumWminvalues. A thresholdWThbetween

the maximum and the minimum is chosen (forinstance, the mean value, the mean value plus

a fraction of the standard deviation). The vari-ants with W(Sp.g) less than WTh are selected.The orientation of one selected variant is

gNWSp.g and its weight is equal to f1(g) /Nvwhere f1(g) is the value of the ODF at g and Nvthe number of variants, selected according to the

threshold criterion.

6. The inherited ODF is calculated according topoint 5 from a discretisation of the parent aus-

tenite ODF. In this paper, the Euler space of the

parent texture was discretised into 15552 boxesof equal volume.

Fig. 8 displays the sections of the ferrite ODF,

simulated with a threshold WTh equal to W.This simulated ferrite texture reproduces the

trends of the experimental texture. The peaklocations are respected. Some particular peaks,

foreseen by the modelling without variant selectionare erased (see orientations j1 6090 for 30 and j2 22.5), the other peaks being

correspondingly reinforced. By progressively

increasing WTh, the erased peaks are reintroduced,the other being softened. For WTh equal to Wmax,

there is no longer variant selection. Even if the

Fig. 8. ODF of the ferrite, simulated with variant selection

from the reconstructed ODF of austenite, plotted in j1sections


results of the simulation are in good agreement

with the experimental texture, some differencesremain. The simulated texture is sharper than the

experimental one. This can be due to the evaluatedaustenite texture which could be smoother along

with the fact that orientation relation is strict in the

modelling although Section 3 shows that, in fact,it is not strict. Moreover the modelling does not

take into account the local conditions of the trans-

formation linked to the grain boundaries, the grainshapes. The grain interactions within the polycrys-

tal are seen as the simplified interactions betweenan inhomogeneous inclusion embedded in an

anisotropic homogeneous medium. Further thevariant selection rules apply in the same mannerwhatever the difference betweenWmaxand Wminis.

It is a static modelling which takes only the state

prior to the transformation into account. Neverthe-less, using basic assumptions, this modelling is

able to give the main trends of the experimental

texture.

6. Conclusion

We have shown thanks to analysis of local

orientations in the ferrite phase that the lattices ofthe parent austenite and inherited ferrite phases are

not related by strict orientation relations like thoseof NishiyamaWassermann or KurdjumovSachsas observed in martensitic transformation. In fact,

the orientation relations present some spread

around these strict orientations. Knowing in meanthese orientation relations, the ferrite texture has

been simulated without variant selection from the


7/7


texture of the austenite. The comparison between

the experimental and simulated textures shows that

the texture change by phase transformation

occurred with variant selection. The variant selec-tion appears efficient enough to erase peaks ofmedium magnitudes and to enhance higher peaks.Among numerous mechanisms of variant selectionwe have modelled and tested, we have presentedassumptions and a modelling able to give all the

main trends of the inherited ferrite texture.

References

[1] Flemming HG, Hensger K-E. In: Proceedings of Mech.

Working and Steel Processing Conference, Pittsburgh,

PA, 1998.

[2] Gardiola B, Humbert M, Esling C, Flemming G, Hensger

KE. Mater Sci Engng A 2000;303:60.

[3] Bunge HJ. Texture analysis in materials science. London:

Butterworths, 1982.

[4] Wagner F, Humbert M. Text Microstruct 1987;7:115.

[5] Butron-Guillen MP, Jonas JJ, Ray RK. Acta Metall

Mater 1994;42:3615.

[6] Humbert M, Gey N, Gardiola B, Esling C. Acta Mater

2001;49:445.

[7] Gardiola B. et al. to be published.

[8] Wechsler MS, Liebermann DS, Read TA. Trans AIME

1953;197:1503.

[9] Wayman CM. Introduction to the crystallography of mar-

tensitic transformations. New York: Macmillan, 1964.

[10] Svennson EC, Brockhouse BN, Rowe JM. Phys Rev

1967;155:619.

[11] Johnson RA. Phys Rev 1965;145:423.

[12] Guo GY, Wang HH. Chin J Phys 2000;38:949.

m. humbert; b. gardiola; c. esling; g. flemming; k.e. hensger -- modelling of the variant selection...

Documents