Interaction between recrystallization and phase transformation during intercritical annealing in a

14 Pages·2014·2.07 MB·English

by  Chengwu Zheng

Available onlineat www.sciencedirect.com
ActaMaterialia61(2013)5504–5517
www.elsevier.com/locate/actamat
Interaction between recrystallization and phase transformation
during intercritical annealing in a cold-rolled dual-phase steel:
A cellular automaton model
Chengwu Zhenga,b,⇑, Dierk Raabeb,⇑
aInstituteofMetalResearch,ChineseAcademyofSciences,WenhuaRoad72,Shenyang110016,China
bMax-PlanckInstitutfu¨rEisenforschung,Max-Planck-Strabe1,Du¨sseldorf40237,Germany
Received13December2012;receivedinrevisedform30May2013;accepted30May2013
Availableonline24June2013
Abstract
Theconcurrentferriterecrystallizationandaustenitictransformationduringintercriticalannealingofcold-rolledDPsteelsisinves-
tigatedbycellularautomaton(CA)modeling.Thesimulationsprovideinsightintothemicrostructuralphenomenathatresultfromthe
interactionofprimaryrecrystallizationandphasetransformation.Wefindthattheinteractionbetweenferriterecrystallizationandaus-
teniteformationaffectsnotonlythetransformationkineticsbutalsothemorphologyandspatialdistributionoftheaustenite.Fromthis
wecan interpret experimentaldataofthe observed temperature-dependent hardness anditsdependenceon the twometallurgical pro-
cesses.Theinfluenceoftheinitialheatingrateonsubsequentisothermaltransformationkineticsandthemicrostructureevolutionisalso
obtained bythe model.
(cid:2)2013ActaMaterialia Inc. PublishedbyElsevier Ltd. All rightsreserved.
Keywords: Intercriticalannealing;Ferriterecrystallization;Austenitization;Cellularautomaton;Mesoscopicmodeling
1. Introduction DP microstructure [8]. During this process, microstructure
formation isdetermined by a numberof interacting metal-
Owing to a favorable combination of high strength and lurgical phenomena, of which ferrite recrystallization, aus-
good formability, dual-phase (DP) steels are currently tenite formation and carbon diffusion are the most
receiving high interest in the automotive industry for low important. What makes the prediction of DP microstruc-
energy consumption vehicle design through weight reduc- tureschallengingisthefactthatthesephenomenamaypro-
tion [1–6]. The microstructure of DP steel is characterized ceed consecutively or simultaneously, i.e. complex local
by hard martensite islands dispersed in a soft and ductile interactions between the metallurgical diffusion and trans-
ferrite matrix [7]. To generate DP microstructures, a con- formation phenomena occur. The nonlinear character of
tinuous annealing process that includes reheating of a the phenomena involved minor changes in these interac-
cold-rolled ferrite/pearlite microstructure followed by tions,andthismayhaveaprofoundinfluenceontheresult-
intercritical annealing is implemented to form an austen- ing microstructure. On the other hand, from a theoretical
ite/ferrite mixture, which after final quenching results in a point of view, it is also an essential challenge to quantita-
tively understand and evaluate the interdependence and
⇑ Correspondingauthors.Address:InstituteofMetalResearch,Chinese competition between these two metallurgical processes.
Academy of Sciences, Wenhua Road 72, Shenyang 110016, China. In earlier studies, such potential interactions between
Tel.: [phone]; fax: [phone] (C. Zheng), tel.: +49 211 recrystallization and phase transformation have been
6792340;fax:[phone](D.Raabe). reported to occur for various intercritically annealed steels
E-mail addresses: [e-mail] (C. Zheng), d.raabe@
onmaterialsthathadbeeninitiallycoldrolled[9–11].Yang
mpie.de(D.Raabe).
1359-6454/$36.00(cid:2)2013ActaMaterialiaInc.PublishedbyElsevierLtd.Allrightsreserved.
http://dx.doi.org/10.1016/j.actamat.2013.05.040
C.Zheng,D.Raabe/ActaMaterialia61(2013)5504–5517 5505
et al. [9] observed austenite nucleation both on grain and transformation in several DP microstructures. How-
boundaries of unrecrystallized ferrite and at the interfaces ever, their model did not involve detailed thermodynamic
between recrystallized and unrecrystallized grains. This criteria of either recrystallization or phase transformation.
work revealed an influence of ferrite recrystallization on In this work, we present a modified two-dimensional
the formation and distribution of austenite. Huang et al. (2-D)CAmodeltoinvestigatethecompetitionbetweenfer-
[10]systematicallyinvestigatedtheeffectoftheinitialheat- rite recrystallization and austenitic transformation during
ingrateonausteniteformationandferriterecrystallization the intercritical annealing of cold-rolled DP steels. In this
in two steels with chemical compositions that are typically model, discrete microstructural constituents either in
used for DP and transformation-induced plasticity (TRIP) recrystallization or in phase transformation are depicted
steels. They suggested that there was a strong interaction through involving relevant thermodynamic criteria (stored
between ferrite recrystallization and austenite formation, deformation energy, chemical transformation driving
which could affect the kinetics of austenite formation as force, etc.) and kinetic effects (grain boundary mobility,
well as its spatial distribution. Their findings were recently carbon diffusion, etc.), so that a detailed microstructural
verifiedbyAzizi-Alizaminietal.[11]inaplainlow-carbon insight into the mutual interactions between these various
steel, including a similar morphology shift from randomly metallurgical processes can be obtained. This model also
distributedtoabandedstructureofaustenitewhenincreas- enables us to study the influence of initial heating rate
ingtheinitialheatingrate.Despitetheseimportantfindings and annealing temperature on subsequent isothermal
and their potential practical relevance, further investiga- transformation kinetics and the associated microstructure
tionsofsuchinteractionphenomenaaswellastheirpoten- evolution.
tial effect on the final microstructure and properties of the
steels annealed in the intercritical region are still required. 2. Model concept
Morespecifically,theinteractionbetweenthetwometallur-
gicalprocessesmaycausepropertyvariationsandmakesit 2.1. Austenite transformation
difficulttoidentifytherelationbetweendirectthermalpro-
cessing settings and the final product properties. However, During the intercritical annealing of DP steels, two dif-
theapproachofintegrated microstructural simulationthat ferentsituationsofaustenitenucleationareusuallyconsid-
includesallrelevantmetallurgicalprocessesisideallysuited ered[19,20].Oneisrelatedtotheausteniteformationatthe
toprovidethedesiredinsightforthisproblem,whichhence ferrite/cementite interfaces within the carbon containing
enables us to conduct quantitative microstructure design colonies,e.g.withinthepearlite.Theotheristhenucleation
for optimal properties. on the ferrite/ferrite grain boundaries. In general, nucle-
With the recent development of mesoscale microstruc- ation of austenite starts from the pearlite colonies. The
ture-based transformation models [12], e.g. the cellular newly formed austenite nuclei grow rapidly at the expense
automaton (CA), the Monte Carlo (MC) and the phase of the pearlite and subsequently of the ferrite. During this
field(PF),simulationscannowprovidedeeperinsightinto process,austenitegrowthismainlylimitedbycarbondiffu-
the mechanism and morphological complexity of both the sion inside the austenite, as schematically represented in
phase transformation and recrystallization in steels Fig. 1. The transformation proceeds much faster for the
[13,14].Numericalmodelingisthusemergingasanalterna- pearlite-nucleated austenite than that in ferrite due to the
tivetooltoinvestigatetheinteractionmechanismofrecrys-
tallization and phase transformation in DP steels.
Recently, Rudnizki et al. [15] developed a PF model to
describe the austenite formation from a ferrite–pearlite
aggregate during the annealing of a cold-rolled DP steel.
However, their simulation started from an already recrys-
tallized microstructure. Hence, the approach did not con-
sider the interaction between recrystallization and phase
transformation. Bos et al. [16,17] presented an integrated
three-dimensional (3-D) CA model to describe the
through-processmicrostructureevolutionduringtheentire
processing of DP steels. In their model, simulation of con-
current ferrite recrystallization and austenite formation
was involved. However, their interest was placed on the
model development [16] and its usage on a study of
the influence of individual transformation processes on
the final DP microstructure [17], whereas the interaction
between recrystallization and phase transformation was
Fig. 1. Schematic drawing about the variation in the carbon content
notaddressed.Okudaetal.[18]performed anMCsimula- acrosstheaustenite–ferriteboundary[20]:c0=pearlite-nucleatedausten-
tion to examine the competition between recrystallization ite,a=ferriteandc=grain-boundary-nucleatedaustenite.
5506 C.Zheng,D.Raabe/ActaMaterialia61(2013)5504–5517
availablesurplusofcarbon.Asfortheaustenitenucleation @x/ (cid:2) (cid:3)
c ¼r(cid:3) D/rx/ ð5Þ
attheferrite/ferriteboundaries,anaustenitenucleusforms @t c c
withoutdirectcontactwiththecarbonsource.Inthiscase,
where / acts as a structure indicator and denotes either
the subsequent growth of the austenite nuclei requires car- phaseaorphasec,x/ isthecarbonconcentrationinphase
c
bondiffusionfromthecarbon-richareasthroughtheferrite / and D/ is the carbon diffusion coefficient in either the a
c
matrix in order to support the austenite formation at the or c phase. The diffusion coefficient D/ is assumed to be
moving c/a interface, as shown in Fig. 1. c
thermally activated according to
In our current simulation, both scenarios of austenite (cid:2) (cid:3)
nucleation, namely nucleation within pearlite and nucle- D/ ¼D/ exp (cid:2)Q/=RT ð6Þ
c c;0 c
ationonferrite/ferriteboundaries,areconsidered.Theaus-
with D/ the pre-exponential constant and Q/ the activa-
tenite nucleated within the carbon-rich regions is here c;0 c
tion energy for carbon diffusion.
referred to as “pearlite-nucleated austenite” and that
In thissimulation, austenitenucleationisdescribedasa
formed at the ferrite grain boundaries as “grain-bound-
continuousnucleationevent.Thedependenceofnucleation
ary-nucleated austenite”. rate N_A on the annealing temperature is described accord-
In order to describe the two situations of austenite for-
ing to the classic nucleation theory [27]:
mation, a mixed-mode growth kinetics model [21] is !
adopted in the present simulations. The interface velocity K
can be described by [22] N_A ¼K1DccðkTÞ(cid:2)12exp (cid:2)kTðDG2 Þ2 ð7Þ
N
v ¼MacDG ð1Þ
ac whereK isaconstantrelatedtothenucleationsitedensity,
1
where Macisthe interface mobility and DGisthe chemical K is a constant related to all the interface involved in
2
drivingforce. The mobility isassumedto follow an Arrhe- nucleation, Dcc is the carbon diffusion coefficient in austen-
nius relationship [23]: ite, k is the Boltzmann constant (1.38(cid:4)10(cid:2)23JK(cid:2)1) and
(cid:2) (cid:3) DG isthedriving force for austenite formation.The driv-
N
Mac ¼Ma0cexp (cid:2)Qac=RT ð2Þ ing force DGN depends on the annealing temperature and
the carbon concentration, i.e. the carbon concentration of
whereQ istheactivationenergyforboundarymigration,
ac
Mac is the pre-exponential factor of the interface mobility, the initial pearlite and the ferrite. Then the nucleation rate
an0d R and T are the universal gas constant (8.314Jmol(cid:2)1 of the two austenite nucleation scenarios can be distin-
K(cid:2)1) and absolute temperature, respectively. guished. DGN is here also considered to be proportional
The chemical driving force, DG, is here considered in a to the deviation from the equilibrium concentration as
indicate by Eqs. (3) and (4).
first approximation as proportional to the deviation from
the equilibrium concentration on the moving interface
2.2. Ferrite recrystallization
[24,25]. For the austenite formed within the pearlite colo-
nies, the driving force for growth outwards into ferrite
Nucleation of primary static recrystallization is treated
can be rewritten as [24,25]
(cid:2) (cid:3) asathermallyactivatedprocess.Weimplementedacontin-
DGI ¼vðTÞ xc0=a(cid:2)xc ð3Þ uous nucleation law to describe ferrite recrystallization.
where v is a proportionality factor, which can be calcu- The nucleation rate N_RX is described by a phenomenologi-
lated us(iTn)g Thermo-Calc [26]. xc0=a and xc are the carbon cal relatio(cid:2)n [28]: (cid:3) (cid:2) (cid:3)
concentrations atthemoving c/ainterface andtheequilib- N_RX ¼C0 ED(cid:2)ECD exp (cid:2)QNRX=RT ð8Þ
rium concentration of austenite, respectively, as shown in
with E the stored deformation energy, EC the critical
Fig.1.Inthecurrentsimulation,pearliteistreatedasasin- D D
stored deformation energy for triggering recrystallization
gle effective phase with an averaged carbon content of
whichcanbe determined by thecriticaldeformation strain
0.71wt.% (i.e. the eutectoid carbon concentration for this
andQN theapparentactivationenergyforferriterecrystal-
specific alloy). RX
lization.C isafittingparameter(1.7(cid:4)1014s(cid:2)1J(cid:2)1).Here,
Asfortheaustenitenucleatedattheferritegrainbound- 0
EC is set as the stored deformation energy at the strain of
aries, the driving force for the austenite growth can be D
0.1. Recrystallization nucleation is hence treated as being
described by
both temperature- and time-dependent.
(cid:2) (cid:3)
DGII ¼vðTÞ xa=c(cid:2)xa ð4Þ The velocity of the recrystallization front, vRX, moving
into the deformed ferrite can be expressed as follows [29]:
with xa/c the interfacial carbon concentration at the ferrite
side of the moving interface and xa the equilibrium ferrite vRX ¼MRXðED(cid:2)PZÞ ð9Þ
concentration at the given temperature. xc and xa can be where E is the driving pressure for the primary static
D
derived from the Fe–C phase diagram. recrystallization front movement, which is provided by
The solute diffusion in the two phases (a and c) is the difference in stored deformation energy between the
described by recrystallized grains and the deformed matrix, and P is
Z
C.Zheng,D.Raabe/ActaMaterialia61(2013)5504–5517 5507
thepotentialpinningforcestemmingfromtheprecipitation wheregisthegrainboundaryenergyandjisthecurvature
ofsmallausteniteparticles[30].Thestoreddeformationen- of the grain boundary. In the present model, the grain
ergy, E , is related to the dislocation density, q: boundarycurvatureiscalculatedusinganapproachknown
D
fromthecurvaturecalculationinlattice-basedmodels[37]:
1
ED ¼ lb2q ð10Þ A Kink(cid:2)N
2 j¼ i ð16Þ
where l is the shear modulus of the material and q is a Ccell N þ1
function of the prior strain level and the deformation tem- whereC isthegridspacingintheCAmodel,A=1.28is
cell
perature. During the continuous annealing of cold-rolled a topological coefficient, N=18 is the number of the first
DP steels, the stored deformation energy will be released and second nearest neighbor sites for a hexagonal lattice,
due to recovery. The evolution of the stored energy ED(t) Ni is the number of cells within the neighborhood belong-
as function of temperature T and annealing time t is given ingtograiniandKink=9isthenumberofcellswithinthe
as follows [31]: neighborhood belonging to grain i for a flat interface
(cid:6) (cid:4) (cid:5)(cid:7)
t 2 (j=0). The topological considerations behind this model
EDðtÞ¼ EDðt0Þ1=2(cid:2)C1l(cid:2)1=2kT ln 1þs ð11Þ can be found in Figs. A1–A3 in Ref. [37].
0
where E (t ) is the initial stored energy of deformation, t 3. CA model
D 0 0
is the time when recovery starts, C is a combined fitting
1
parameter (5.7(cid:4)1018m(cid:2)3), l is the shear modulus of the In this work, a 2-D CA approach is implemented as a
materialandkandT have their usual meanings.Recovery solver to simulate the competing phase transformation
isassumedtooccurfromthestartofthereheatingprocess, and the recrystallization phenomena in a DP steel accord-
i.e. t =0s. s is a time constant which is set as 1s in this ing to the equations outlined above. In this formulation,
0 0
simulation. Details of the calculation of the stored defor- the spatial system is discretized onto a 2-D regular equal
mation energy can be found in Refs. [32,33]. spaced hexagonal lattice. Each cell represents a volume of
The Zener-based particle back-driving force derived real material characterized by certain attributes with a dis-
from small-sized austenitic precipitations, P , can be tinctphase,solutecontentandanorientationindictor.The
Z
described by [34] neighbors of a cell are defined by von Neumann’s rule,
Pz ¼32cmfrp ð12Þ wthheicmhiccroonsstirduecrtsurteheevnoelaurteiostnsoixf cpehlalss.eItnraonrsdfeorrmtoatdioenscrainbde
recrystallization during the intercritical annealing, eight
herecmisthegrainboundaryenergy,fpisthevolumefrac- state variables are used on each CA node. These are: (1)
tion of the grain boundary nucleated austenite particles the phase state variable that denotes whether the cell is
and r is their mean radius. MRX is the boundary mobility pearlitic, ferritic, austenitic or contains c/a, P/c interfaces;
of high angle grain boundary which can be estimated by (2)theferriterecrystallizationstatusthatindicateswhether
[35] it belongs to deformed ferrite, recrystallized ferrite or the
(cid:4) (cid:5)
D b2 Q interface;(3)thecarbonconcentrationvariable;(4)theori-
MRX ¼ k0T exp (cid:2)RTb ð13Þ entationvariablewhichisassignedanintegeridentifierrep-
resenting its crystallographic orientation; (5) the austenite
where Qb is the activation energy for grain-boundary mo- transformation fraction variable, fc,quantifying the aus-
tion, D0 is the boundary self-diffusion coefficient and b is tenite fraction transformed from ferrite; (6) the austenite
the magnitude of the Burgers vector. transformation fraction variable, f0; representing the aus-
c
tenite fraction transformed from pearlite; (7) the ferrite
2.3. Grain coarsening recrystallization fraction variable, f ; and (8) the fraction
RX
variable, f,used for the motion of the boundary segment
Competitive growth of the grains caused by the bound- within an c/c or a/a boundary cell.
ary curvature effect would lead to grain coarsening after The values of each state variable on each of the CA
hard impingement among the neighboring grains. The nodes are functions of their respective previous states and
velocity of a grain boundary segment driven by the curva- thepreviousstatesoftheirneighbors.Theyaredetermined
ture can be expressed by [36] according to the sub-models described in Section 2. The
v ¼MccF ð14Þ kinetics of the automaton is realized by synchronously
cc
updatingthestatevariablesforalllatticecellsineachtime
where Mcc is the grain boundary mobility between grains
step.
andFisthedrivingforceoriginatingfrominterfacecurva-
Details regarding the mapping of the constitutive and
ture.Thedrivingforceforcapillary-drivengrainboundary
kineticlawsoutlinedaboveintothediscreteCAapproach,
motion F is expressed by [36]
i.e. nucleation, growth and competitive grain coarsening
F ¼gj ð15Þ for phase transformation and recrystallization, are given
5508 C.Zheng,D.Raabe/ActaMaterialia61(2013)5504–5517
inRefs.[38,39].Here,onlytheitemsrelevanttothecurrent ferrite–pearlite aggregate is firstly built using a separate
simulation are outlined in more detail: CA simulation, as shown in Fig. 2a. The white regions
indicate ferrite and the gray areas are pearlite colonies.
(1) ThegridsizeusedinthepresentCAmodelis0.4lm, The black lines represent the a/a grain boundaries or
whichistoocoarsetodescribetheindividualpearlitic a/P hetero-interfaces. The initial simulated domain is
lamellaestructure.Pearliteishenceconsideredasone defined by a 150(cid:4)700 CA lattice, representing a physical
effective phase with a carbon concentration of domain of 60lm(cid:4)280lm in real material. The initial
0.71wt.% in accordance with a Thermo-Calc structure consists of (cid:5)9vol.% pearlite and 91vol.% fer-
calculation. rite. The initial average ferrite grain size (diameter) is
(2) Thegrowthofausteniteintopearliteisassumedtobe (cid:5)15lm. In this simulation, pearlite is considered as one
controlled solely by interface migration, with the effective phase, as assumed in previous simulations [15–
driving force derived from the effective pearlite 17], with an effective carbon concentration of 0.71wt.%.
carbon concentration (0.71wt.%). The ferrite matrix is assigned an initial carbon concentra-
(3) Simulation of cementite spheroidization/dissolution tion of 0.01wt.% [40]. Then a uniaxial compression of
and the associated effects on the carbon concentra- 80% thickness reduction is applied to mimic a cold-rolled
tion field and subsequent austenite formation are grain structure (Fig. 2b). The simulated domain is corre-
not involved. spondingly mapped onto a 498(cid:4)210 CA lattice, equiva-
(4) A contribution of the stored deformation energy as lent to 199lm(cid:4)84lm in the real material. The
an additional portion to the driving force for phase microstructure is characterized by the alignment of ferrite
transformation is not considered. This means that and pearlite along the rolling direction. This specific cold-
the occurrence of primary recrystallization does not rolling microstructure is important for the subsequent
alter the (chemical) driving force for phase topology evolution during ferrite recrystallization. Firstly,
transformation. the distribution and shape of the pearlite colonies are geo-
(5) Curvature-driven grain coarsening is assumed to metrically modified by the simulated cold deformation.
occurbetweenaustenitegrainsaswellaswithrecrys- This type of distorted microstructure provides characteris-
tallized ferrite grains after impingement. tic boundary conditions for the grain growth during
ferrite recrystallization. Secondly, the prior cold deforma-
tion in the mixed-microstructure with hard pearlite and
4. Microstructure set-up and initial conditions soft ferrite introduces an inhomogeneous distribution of
the deformation energy. The stored deformation energy
The simulated material is a DP steel with chemical is concentrated in the vicinity of the pearlite/ferrite
composition (wt.%) 0.08 C, 0.01 Si and 1.75 Mn. The boundaries which, therefore, provide favorable sites for
transformation temperature A3 is calculated as 817(cid:3)C the nucleation of ferrite recrystallization. In the current
by Thermo-Calc. In order to create the starting micro- simulation, both the ferrite/ferrite grain boundaries and
structure for the simulation, a method indicated by Bos the pearlite/ferrite interfaces are hence defined as prefer-
et al. [16] has been implemented. A fine, unbanded ential nucleation sites for ferrite recrystallization.
Fig. 2. Formation of the starting microstructure for the intercritical annealing simulation: (a) the initial unbanded ferrite–pearlite aggregate before
deformation;(b)themicrostructureafter80%coldreductionasinputforthesimulation.Inthismodel,pearliteistreatedasasingleeffectivephase.
C.Zheng,D.Raabe/ActaMaterialia61(2013)5504–5517 5509
Fig.3. Schematicrepresentationofthethermalcyclesusedincurrentsimulations:(a)influenceofvariousintercriticaltemperatures;afastreheatingis
imposedhere;(b)influenceoftheinitialheatingrate.
Therelatedthermalprocessingscheduleimplementedin and austenite transformation takes place. For a better
the simulation is shown schematically in Fig. 3. To study understanding of the interactions between these two phe-
theinteractionbetweenferriterecrystallizationandausten- nomena,wehereconsiderinmoredetailisothermalanneal-
ite formation under isothermal conditions, fast heating is ing at an intercritial temperature of 760(cid:3)C where full
imposedtoyieldfull coupling between these twoprocesses coupling of these two processes occurs. Fig. 4 shows the
duringtheisothermalannealing.Thentheinfluenceofvar- simulated transformation kinetics of competitive ferrite
ious intercritical temperatures is discussed, as shown in recrystallization and austenite formation at 760(cid:3)C. The
Fig. 3a. As for the heating rate examination, two specific associated kinetics of microstructure formation (left-hand
rates of 50 and 5(cid:3)Cs(cid:2)1 are applied, where the samples side) and the carbon concentration fields in the ferrite
are heated into the intercritical region at the two heating (right-hand side) are shown in Fig. 5. In the simulated
rates (50 and 5(cid:3)Cs(cid:2)1) and then held for a predetermined microstructures, the yellow regions indicate the austenite
time at the given annealing temperature, as seen in formed within the original pearlite domains (c0). The small
Fig.3b.Thekeyparametersusedinthemodelingarelisted red patches are the austenite grains formed at ferrite grain
in Table 1. boundaries (c). The blue areas are the recrystallized ferrite
(a ), and the white zones are the non-recrystallized ferrite
R
5. Simulation results and discussion (a ).
NR
During intercritical annealing, austenite formation
5.1. Interaction between ferrite recrystallization and starts from the initial pearlite colonies by nucleation,
austenite transformation during intercritical annealing occurringinstantaneously[4].Subsequently,theseaustenite
nucleigrowrapidly,consumingthedissolvingpearliteuntil
During intercritical annealing of the cold-rolled DP theoriginalpearliteisreplacedentirely.However,themor-
steel, competition and overlap of ferrite recrystallization phology of the newly formed austenite grains is strongly
Table1
Theparametersusedinsimulations.
Symbol Definitionandunites Value Refs.
K Austenitenucleationfactor(J1/2m(cid:2)4) 2.07(cid:4)1011 [27]
1
K Austenitenucleationfactor(J3m(cid:2)2) 2.5(cid:4)10(cid:2)18 [41]
2
Dcc Carbondiffusioncoefficientinaustenite(m2s(cid:2)1) 1.5(cid:4)10(cid:2)5exp((cid:2)142,100/RT) [42]
Dac Carbondiffusioncoefficientinferrite(m2s(cid:2)1) 2.2(cid:4)10(cid:2)4exp((cid:2)122,500/RT) [42]
Mac Mobilityofthea/cinterface(molmJ(cid:2)1s(cid:2)1) 0.5exp((cid:2)140,000/RT) [21,32]
MRX Mobilityofhighanglea/agrainboundary(m4J(cid:2)1s(cid:2)1) 0:429exp((cid:2)120,000/RT) [32]
T
QNRX Activationenergyforferriterecrystallization(kJmol(cid:2)1) 170 [33]
b Burgersvector(m) 2.58(cid:4)10(cid:2)10 [32]
c Grainboundaryenergyofhigh-anglea/aboundary(Jm(cid:2)2) 0.56 [32]
m
u Shearmodulusofferrite(GPa) 32 [32]
5510 C.Zheng,D.Raabe/ActaMaterialia61(2013)5504–5517
0.7 a slow recrystallization rate [43]. Moreover, with the
d recrystallization front traversing across the region between
me 0.6 t t t the closely spaced austenite colonies, the strongly curved
or t 4 5 6 moving boundaries would experience pinning at the inter-
sf 0.5 3 ferrite recrystallization
n faces in conjunction with different constituents, which also
a
n tr 0.4 t2 slows down the recrystallization rate.
o The pearlite-nucleated austenite forms with relatively
cti 0.3 high carbon concentrations, which leads to high driving
e fra 0.2 t1 austenitization forcesactingonthea/c0interfacesmovingtosweepthesur-
m roundingferrite.Therefore,rapidthickeningandlengthen-
u
ol 0.1 ing of the austenite bands is expected at the beginning of
V thea-to-c0 dissolution. Advancing ofrapid austenitethick-
0.0
0 5 10 15 20 25 30 35 40 45 ening affects the concurrent ferrite recrystallization as fol-
Annealing time, s lows: (I) if the surrounding ferrite matrix remains
unrecrystallized, rapid thickening of the austenite bands
Fig.4. Kineticsofferriterecrystallizationandausteniteformationinthe will consume most of the potential nucleation sites of
cold-rolledDPsteelintercriticallyannealedat760(cid:3)C.Here,afastinitial
recrystallization located in the vicinity of prior a/P inter-
heatingrateisimposed.
faces. As a consequence, nucleation of ferrite recrystalliza-
determinedbytheshapeoftheinitialpearlitezones,which tion will be inhibited through the elimination of its most
henceproducesbandingstructuresofaustenite,asrevealed favorable interface nucleation sites by the advancing aus-
in Fig. 5. Such austenitebandslead to local growthcondi- tenite interfaces. This effect can be clearly observed in the
tions such as encountered in thin films for the concurrent simulatedmicrostructureinFig.5c.Wecanseethatacon-
ferrite recrystallization. Therefore, further growth of siderable amount of ferrite still remains un-recrystallized,
recrystallizing ferrite grains along the compression direc- even after a long period of annealing up to 40s. In these
tion will be topologically restricted. This effect results in regions, further nucleation of recrystallization is blocked
Fig.5. Simulatedmicrostructure(left)andthecarbonconcentrationfield(wt.%)inferritephase(right)atdifferentsoakingtimesasindicatedinFig.4:(a)
t =5s,(b)t =20s;(c)t =40sduringtheisothermalholdingof760(cid:3)C.Inthesimulatedmicrostructure(imageleft-handside),theyellowareasarethe
2 4 6
pearlite-nucleated austenite; the small-sized red patches (image left-hand side) are the grain-boundary-nucleated austenite. The blue regions indicate
therecrystallizedferriteandthewhiteindicateunrecrystallizedferrite(imageleft-handside).Theblacklinesinthefiguresindicatethegrainboundaries.
Theimagesontheright-handsideindicatethedistributionofcarbon.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderis
referredtothewebversionofthisarticle.)
C.Zheng,D.Raabe/ActaMaterialia61(2013)5504–5517 5511
completely.Therecrystallizationbecomesdominatedsolely as shown in Fig. 5c. In experimental observations,
by growing laterally into the deformed matrix. However, intragranularausteniticparticleswereusuallyconsid-
the well-recovered microstructure produces extremely low ered to be associated with the presence of carbides
driving forces for the migration of the recrystallization within the ferrite matrix prior to transformation that
fronts,which isresponsible forthe prevalence ofthe resid- can stimulate austenite nucleation and support the
ual deformed ferrite. (II) If the surrounding ferrite has growth by the surplus of carbon [9]. Obviously, cur-
already been recrystallized, the intensive austenite growth rent simulation reveals another reasonable explana-
will occupy the recrystallized regions and transform them tion about the mechanism of their formation from
into austenite. The recrystallization fraction hence is the perspective of interaction between recrystalliza-
decreased gradually due to the phase transformation. This tion and phase transformation.
willleadtoacompetitionofrecrystallizationsofteningand 3. At the a /a boundaries, the situation becomes
NR NR
phase transformation hardening in the material properties morecomplexsincerecrystallizationandphasetrans-
as discussed in Section 5.2. formation both are preferentially nucleated at these
Duringintercriticalannealing,austenitenucleimayalso sites. This indicates that the austenite nucleation
appear at various ferrite grain boundaries, i.e. the a /a , occurs in competition with the nucleation of ferrite
R R
a /a ora /a boundaries.Savranetal.[19]oncepro- recrystallization at the a /a boundaries. How-
R NR NR NR NR NR
vided a thermodynamic explanation on the austenite for- ever, the extensive nucleation of the fine austenite
mation within the intercritical temperature range. They precipitates will inversely stabilize the deformation
argued that beyond the preferable austenite formation in structure andthushindertheferriterecrystallization.
the carbon-rich areas, such as pearlite, nucleation is also It will influence the subsequent development of the
possible at lower than equilibrium carbon content in aus- microstructure in following annealing steps.
tenite,whichcanfavornucleationontheboundariesoffer-
ritegrainswithoutcontactwithcementite[19].Inthiscase, It should be pointed out that the discussions so far are
as indicated in Fig. 1, the austenite formation is promoted made in two dimensions based on the 2-D simulations.
bythecarbonrejectedfromtheferrite-solidsolution.How- This might give rise to potential limitations implied by
ever, subsequent growth of these austenite grains highly the2-Dnatureofthesimulation.Inthecurrentsimulation,
depends on the carbon removal from the carbon-rich area thesimulateddomainisselectedwithinthe2-Dcutparallel
towards the moving c/a interface to “feed” the austenite withtherollingdirection,whichhencecontainsmorealign-
formation as shown in Fig. 1. This leads to very slow ment-like deformation structures of ferrite grains and
migration of the c/a interface and hence small austenite pearlitecoloniesintheconsideredsectioncomparedtothat
particles are formed at the ferrite boundaries, as shown within other 2-D sections, e.g. the cross-section of the 3-D
inFig. 5.Thisresultisconsistent with themeasuredkinet- microstructure.Thisindeedimpliesanexaggeratedeffectof
ics related to the austenite nucleation and growth on fer- topological restrictions on ferrite recrystallization derived
rite–ferrite grain boundaries by 3-D X-ray diffraction from the initial banded microstructure, which thus leads
microscopyconductedatthelevelofindividualgrains[20]. to a much slower recrystallization rate compared to 3-D
Although the small-sized austenitic particles that form simulations.Inaddition,thepinningeffectontherecrystal-
at the ferrite grain boundaries contribute only little to the lizationexertedbytheformationofthesmall-sizedausten-
overall volume fraction of austenite, it profoundly affects iteparticlesin2-Dsimulationisactuallylargerthanthatin
the microstructure evolution of the recrystallizing ferrite: three dimensions [44]. Consequently, the intragranular
austeniticparticlesasshown inFig.5occurlessfrequently
1. Thepresenceoflargepopulationofa /a boundaries than those in the 3-D simulation such that they may be
R R
after recrystallization favors austenite nucleation at found located mainly at the grain boundaries in current
these sites. However, the appearance of the small- 2-D results. This might also render the 2-D recrystalliza-
sizedausteniticparticleswillimpedegraincoarsening tion kinetics slightly different from corresponding 3-D
within the recrystallized ferrite by pinning the grain results. Despite the limitations, however, current 2-D sim-
boundaries and hence stabilize the microstructures. ulationpresentsasuccessfulmicrostructuraldescriptionof
This effect promotes microstructure refinement of the interaction between recrystallization and phase trans-
the DP steel processed by intercritical annealing. formation.Wecanfindthattheinteractionbetweenferrite
2. At the moving a /a boundaries, however, the recrystallization and austenite formation does affect not
R NR
recrystallization front is suffering pinning due to only the transformation kinetics but also the morphology
appearance of the fine austenitic particles. This effect and spatial distribution of austenite.
might slow down the recrystallization rate slightly. Fig.6showstheresultantmicrostructureastheresultof
Yet the moving interface can easily escape across concurrent ferrite recrystallization and austenitic transfor-
these small particles owing to insufficient pinning, mationincarbonsteelsderivedfromboththemicrographs
particularlyattheearly stageoftherecrystallization. [11]andthesimulations.Adetailedcomparisonamongthe
These particles of grain-boundary-nucleated austen- various microstructural constituents is made in Fig. 6c. It
ite are then changed to be intragranularly located, can be seen that the simulated phase arrangement and
5512 C.Zheng,D.Raabe/ActaMaterialia61(2013)5504–5517
Fig.6. Comparisonoftheresultantmicrostructurebetweenthemicrographs(a)andthesimulations(b)asaresultofcompetitiveferriterecrystallization
andaustenitictransformationincarbonsteels.Detailsofthevariousmicrostructuralconstituentsareshownin(c)with(I)theausteniticislandsformed
from prior pearlitic regions; (II) the austenitic patches located at the ferrite grain boundaries; (III) intragranular austenite grains; and (IV) the
unrecrystallizedferritezone.Inthesimulatedmicrostructure,theyellowareasarethepearlite-nucleatedausteniteandthesmall-sizedredpatchesarethe
grain-boundary-nucleatedaustenite.Theblueregionsindicatetherecrystallizedferriteandthewhitezonesaretheunrecrystallizedferrite.Theblacklines
inthefiguresindicategrainboundaries.ThemicrographresultistakenfromRef.[11].(Forinterpretationofthereferencestocolorinthisfigurelegend,
thereaderisreferredtothewebversionofthisarticle.)
the grain structure resemble the micrographic results very As a diffusion-controlled process, austenite formation
well in both the grain morphology and their spatial distri- should be easier at higher temperature in the intercritical
bution.ThepresentCAmodelingcanreproducetherecrys- regime. Firstly, the carbon solubility in austenite reduces
tallization and the phase transformation satisfactorily and with the temperature increase. Therefore, less carbon is
also match the experimental results well. requiredtoformausteniteatthetransformingc/ainterface.
Thephasetransformationismore facilitatedandproduces
5.2. Effect of the annealing temperature largeramountsofaustenite,asshowninFig.7b.Secondly,
higher annealing temperature leads to higher diffusivity of
Further understanding on the interaction between carbon. Thus, transfer of carbon within the pearlite-
recrystallization and phase transformation can also be nucleated austenite or across the ferrite zones becomes
made by examining the microstructure changes for differ- easier to “feed” carbon for austenite formation at the c/a
entintercriticaltemperatures.Fig.7aandbshowsthesim- interfaces.Thiswillevidentlyacceleratethephasetransforma-
ulated transformation kinetics of ferrite recrystallization tion. Thirdly, both the mobility of the moving interface and
andausteniteformation,respectively,atdifferentannealing the chemical driving force for the phase transformation are
temperatures. We observe that recrystallization and phase increased,whichalsoleadstoahighertransformationrate.
transformation are both promoted significantly with the Asathermallyactivatedprocess,ferriterecrystallization
increase of the annealing temperature. is also enhanced upon temperature increase. Its kinetics is
C.Zheng,D.Raabe/ActaMaterialia61(2013)5504–5517 5513
(a) 0.8 500
ed 480 695 0C
ystalliz 00..67 5 444402460000 777247500 000CCC
errite recr 00..45 dness, HV 333330246800000 830 0C
of f 0.3 870800 00CC Har 226800
on 0.2 760 0C 240
cti 0.1 720 0C 220200
a 700 0C
r 180
F
0.0 160
1 10 100 10 100 1000
Annealing time, s Annealing Time, s
Fig. 8. Experimentally observed hardness values as a function of the
(b) 0.6
annealingtime,measuredincold-rolledDPsteelsheetsatvariousferritic
800 0C or,respectively,intercriticalannealingtemperatures[45].
0.5 780 0C
n 760 0C
o 720 0C
cti 0.4 hardness of the steel after quenching is a consequence of
ra the dynamic balance between ferrite recrystallization soft-
e f 0.3 ening and phase transformation hardening, as shown in
nit Fig. 8. However, the hardness measurement alone is an
e
st 0.2 integral measure and does not include any topological
u
A information on the development of the different micro-
0.1 structural constituents, be it the recrystallized ferrite dis-
Original pearlite fraction persion or the transformed austenite or, respectively,
0.0
martensite fraction. The current simulation can provide
1 10 100
Annealing time,s this information, and hence enables a closer inspection of
the kinetic and morphological interactions between the
Fig. 7. Simulated transformation kinetics of ferrite recrystallization (a) two metallurgical processes on a microscopic level as well
and austenite formation (b) during isothermal holding at various
as their mechanical consequences.
annealingtemperatures.
In Fig. 8, we observe that at the ferritic temperature of
695(cid:3)C the hardness decreases gradually with annealing
closely correlated with the progress in phase transforma- time and then remains constant during the subsequent
tion, as revealed by Fig. 7a. At the ferritic temperature of transformation. This course reveals the individual soften-
700(cid:3)C, without occurrence of phase transformation, the ing process associated with ferrite recrystallization, as
recrystallized fraction increases gradually, following a typ- shown by the simulation result for 700(cid:3)C in Fig. 7. The
ical sigmoidal curve [29]. Within the intercritical tempera- hardness minimum corresponds to the state where the fer-
ture range, recrystallization proceeds much faster with rite recrystallization is completed. When the temperature
increasing annealing temperature. The recrystallized frac- increases within the lower intercritical temperature range
tiondropssignificantlyatthelatestageofthephasetrans- (e.g. see hardness data and microstructures at T=725(cid:3)C
formation. This declining trend becomes more obvious at and 740(cid:3)C), the reduction in hardness is faster due to the
higherintercriticalannealingtemperatures.Attheintercrit- acceleratedferriterecrystallization.However,inthesecases
itical temperature of 800(cid:3)C, a distinct fraction peak the hardness increases continuously. This is attributed to
appears in the recrystallization kinetics. This microstruc- the ongoing phase transformation, which leads to an
turalresultcanbeappliedtorationalizetheobservedprop- increaseinthemartensitevolumefractionafterquenching.
erty variation of the studied steel in more detail. At the medium intercritical temperature regime (e.g.
Inapreviousstudy,Peranioetal.[45]analyzedthecom- T=770(cid:3)C), the hardness is observed to decrease slowly
petition between ferrite recrystallization and phase trans- at the early stage of the transformation. Surprisingly, the
formation in a cold-rolled DP steel by performing a hardnessdropsmuchmoreslowlycomparedtothedecline
series of hardness measurements on differently annealed observed at lower temperatures. This is attributed to the
samples.ForannealedDPsteels,thesofteningeffectcaused fact that in the experiments the ferrite recrystallization
by ferrite recrystallization is responsible for the hardness accelerateswithincreasingtemperature,asseeninthesim-
reduction, whereas hardness increase is correlated with ulationat780(cid:3)C,whereastherecrystallizationsofteningis
the ongoing austenite formation during annealing as it graduallycompensatedbythecompetinghardeningassoci-
turns into martensite after quenching. Therefore, the ated with the phase transformation. When the hardening