Materials Science & Engineering A 573 (2013) 84–91

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Carbide precipitation in austenite of a Ti–Mo-containing low-carbon steelduring stress relaxation

Zhenqiang Wang a,b,n, Xinjun Sun b, Zhigang Yang a, Qilong Yong b, Chi Zhang a, Zhaodong Li b,Yuqing Weng c

a Key Laboratory of Advanced Materials, Department of Materials Science and Engineering, Tsinghua University, Haidian District, Beijing 100084, Chinab Department for Structural Steels, Central Iron and Steel Research Institute, No. 76, Xueyuan Nanlu, Beijing 100081, Chinac The Chinese Society for Metals, No. 46, Dongsixi Street, Beijing 100711, China

a r t i c l e i n f o

Article history:

Received 29 January 2013

Received in revised form

25 February 2013

Accepted 27 February 2013Available online 6 March 2013

Keywords:

Precipitation

HSLA steel

TiC

Molybdenum

HRTEM

93/$ - see front matter & 2013 Elsevier B.V. A

x.doi.org/10.1016/j.msea.2013.02.056

espondence to: School of Materials Science a

a University, Beijing 100084, China. Tel.: þ8

6 10 627 71160.

ail address: wangzhe19840203@163.com (Z.

a b s t r a c t

The carbide precipitation behavior in austenite of a 0.04%C–0.10%Ti–0.21% Mo micro-alloyed steel was

investigated by the stress relaxation method and transmission electron microscopy. Results showed

that the precipitation-time-temperature diagram for carbide precipitation exhibited a typical ‘‘C’’ curve,

the nose of which was located at about 925 1C. The carbide was identified as a (Ti, Mo)C particle with a

NaCl-type crystal structure that contains a certain amount of Mo. As compared with TiC particle in Ti

steel, (Ti, Mo)C particle in Ti–Mo steel exhibits a superior coarsening resistance during the coarsening

stage. The fraction of Mo in (Ti, Mo)C particle decreases with isothermal holding time or particle

growing, indicating that the high level replacement of Ti by Mo in TiC lattice is in a ‘‘metastable’’ state

with respect to the equilibrium precipitation of (Ti, Mo)C in austenite.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

In order to reduce fuel consumption, weight and improveproduct quality in automobiles, advanced high-strength low alloysteels have been investigated and developed [1–5]. In a recentwork performed at JFE Steel Corporation [1], tensile strength of780 MPa with excellent stretch flange formability have beenobtained in Ti–Mo-bearing low carbon sheet steels by producinga microstructure that only consists of ferrite and nanometer-sizedcarbides. The contribution to the yield strength from precipitationstrengthening was estimated to be approximately 300 MPa,which was attributed to nanometer-sized (Ti, Mo)C precipitatesthat were formed at the austenite–ferrite interfaces duringtransformation. Later, many researchers, Yen et al. [6,7] and Janget al. [8], using high resolution transmission electron microscopy(HRTEM) and/or first-principles calculations, systematically stu-died this nanometer-sized (Ti, Mo)C carbide including its crystalstructure, orientation relationship with respect to the ferrite andthe role of Mo in relation to its the coarsening resistance. Theyfound that the (Ti, Mo)C carbide possessed a NaCl-type crystalstructure with a lattice parameter of �0.430 nm, and adopted aBaker–Nutting orientation relationship with respect to ferrite.

ll rights reserved.

nd Engineering,

6 10 627 95031;

Wang).

More importantly, this (Ti, Mo)C particle has an excellent thermalstability due to the decrease in the interfacial energy with ferritematrix by the partial replacement of Ti by Mo in the TiClattice [8].

Another significant contribution to the yield strength, up to�280 MPa, in Ti–Mo-bearing steels produced by the JFE SteelCorporation, came from grain refinement strengthening. Theaverage ferrite grain size of a Ti–Mo micro-alloyed steel in theirwork was measured as only 3.1 mm. It is well established that theprecipitation of micro-alloying elements in austenite play animportant role in controlling the final microstructure. In the caseof conventional controlled rolling, roughing deformation is suc-ceeded by a fast cooling and finishing passes are carried out attemperatures where the austenite remains un-recrystallized. Themicro-alloying elements such as Ti, which remain in solutionduring roughing deformation, start precipitating following thefinishing rolling at low temperatures. These fine precipitates suchas TiC play an effective role in retarding recovery and recrystalli-zation of deformed austenite, thus help to retain the accumulatedstrain and deformed structures of austenite grains. This in turn,leads to a high nucleation rate for ferrite during subsequent g-aphase transformation, thus favoring the refinement of the finialmicrostructure and the improvement of the properties of pro-ducts [9–11]. In our previous reports and some other works[12–14], the carbonitride precipitation behaviors after austenitedeformation in Ti micro-alloyed steels were systematicallystudied using various hot deformation methods, including high

Z. Wang et al. / Materials Science & Engineering A 573 (2013) 84–91 85

temperature flow curve, stress relaxation method and two stageinterrupted method. The precipitation kinetics curves i.e.precipitation-time-temperature (PTT) diagrams were determinedby different methods and all exhibit typical ‘‘C’’ shape curve. Inaddition, the precipitates were identified by TEM as TiC or Ti (CN)particle with a NaCl-type crystal structure, and they were con-sidered to be nucleated on dislocation and dislocation sub-structures in hot working austenite. The growth of the precipi-tates approximately followed a parabolic law during the growingstage, and then entered into a coarsening stage with a timeexponential of �0.1 [12,13]. However, as compared with carbo-nitride precipitation in Ti micro-alloyed steel and other complexcarbonitrides precipitation in Ti–V and Nb–V micro-alloyed steels[15], carbide precipitation in Ti–Mo micro-alloyed steel duringhot working has not been extensively investigated so far,although many studies on carbide precipitation in ferrite orduring g-a phase transformation of Ti–Mo micro-alloyed steelwere conducted by many researchers as mentioned above. There-fore, based on the importance of micro-alloying element precipi-tation in hot working austenite, the purpose of this work was toinvestigate, using systematic stress relaxation experiments, highresolution electron microscopy and thermodynamics calculation,the kinetics of carbide precipitation and the crystal structure,nucleation, growth, coarsening and compositional evolution ofprecipitate in Ti–Mo micro-alloyed steel. In addition, the coarsen-ing resistance of carbide in Ti–Mo micro-alloyed steel wasdiscussed by comparing with that in Ti micro-alloyed steel.

2. Experimental

The chemical compositions of the investigated steels weregiven in Table 1. The Ti–Mo micro-alloyed steel contains a basecomposition of 0.04C–0.10Ti–0.21Mo in wt%. A Ti micro-alloyedsteel with the composition of 0.05C–0.10Ti in wt% was used hereas a reference steel to study the role of Mo in terms of the sizeevolution of precipitate. The two experimental steels were pre-pared by vacuum melting, and then hot forged to 20 mmdiameter rods. After homogenization in the austenite phase fieldfor 300 min at 1200 1C followed by water quenching, the cylind-rical specimens with 8 mm in diameter and 12 mm in length forhot compression test were cut from the center of theas-homogenized rods using a wire cut electrical discharge machining.In order to study the precipitation kinetics of Ti–Mo micro-alloyed steel, stress relaxation tests [12] were performed usinga Gleeble1500D simulator. The specimen was first preheated at1150 1C for 3 min to dissolve all carbide except a small amount ofTiN particles, and then cooled to a deformation temperature inthe range of 875–975 1C, which was chosen in the austenitic zonedue to the phase transformation critical temperature (Ae3) of855 1C calculated by Thermo-calc with database TCFE6. At thistemperature, the specimen was compressively deformed by a 20%reduction along its main axis at a strain rate of 1.0 s-1.The reduction of 20% is very close to the value of one pass of rollingin industry application. Relaxation of the applied compressivestress was then monitored as a function of time up to 50 minbefore the specimen was cooled by water quenching. In order to

Table 1Chemical compositions of the investigated steels.

Steel C Mn Si Ti Mo N

Ti–Mo wt% 0.04 1.51 0.20 0.10 0.21 0.002

at% 0.19 1.54 0.40 0.12 0.12 0.008

Ti wt% 0.05 1.47 0.12 0.10 – 0.002

at% 0.23 1.50 0.24 0.12 – 0.008

study the size evolution of precipitate in Ti–Mo and Ti micro-alloyed steels, stress relaxation tests with shorter holding timeswere conducted. The extraction replicas method [12,13] was usedto study the precipitates in the investigated specimens. Eachspecimen was sectioned perpendicularly to the deformation axis,polished, and then etched in 4% nital for about 1 min. A carbonlayer about 20 nm in thickness was deposited on the treatedsurface using an evaporator. The carbon film coated surfaces ofthe specimens were then scribed using a knife to produce squaresabout 3�3 mm2 in size. The replicas were released in the sameetching solution, and then analyzed in a field emission gunscanning transmission electron microscopy (Tecnai F20). Thesizes of these precipitates were measured by a quantitative imageanalyzer, and the results were obtained by averaging at least 200measurements. Chemical analyses for the precipitates were con-ducted using nano-beam energy-dispersive spectroscopy (EDS).At least 10 precipitates formed during stress relaxation wereanalyzed for each specimen by TEM/EDS to examine the composi-tional evolution of precipitate in Ti–Mo micro-alloyed steel withisothermal holding time. Each EDS data was obtained from thewhole area of each individual precipitate projection as viewed inTEM mode. In addition, the equilibrium chemical composition ofthe precipitate in Ti–Mo micro-alloyed steel over the temperaturerange 500–1000 1C was calculated by the Thermo-calc with thedatabase TCFE6.

3. Results and discussion

3.1. Stress relaxation curve and precipitation-time-temperature

diagram of Ti–Mo micro-alloyed steel

The stress relaxation curves of the Ti–Mo micro-alloyed steelat different temperatures are shown in Fig. 1. As stated earlier allthe deformation temperatures were chosen in austenitic field. Liuand Jonas [12] suggested that strain induced precipitation indeformed austenite occurs mostly on the dislocations and sub-boundaries developed by deformation, which implies that auste-nite grain size will not be a dominant factor in influencing theprecipitation kinetics. In Fig. 1, the stress relaxation curves at950 1C and below exhibit an initial linear stress drop, whichcorresponds to a static recrystallization process [15]. After the

Fig. 1. Stress relaxation curves of the Ti–Mo micro-alloyed steel at different

temperatures. SRX denotes the fast static recrystallization. Ps and Pf represent the

start and finish times of plateau, respectively.

Z. Wang et al. / Materials Science & Engineering A 573 (2013) 84–9186

linear stress drop process, a relaxation stress plateau appears inthese curves, indicating the onset of strain induced precipitation,which halts the progress of recrystallization. The relative dom-inance of these two processes depends on the relative magnitudesof FR (driving force for recrystallization front migration) and FPin

(retarding force due to pinning of dislocations by precipitatedparticles). If FRoFPin, the interfaces will be completely arrested.Initially the driving force for recrystallization is more owing to alarge amount of stored energy in the form of heavily dislocatedmatrix. Recrystallization and precipitation are competing pro-cesses and progress of recrystallization can be halted by the dragexerted on the migrating grain boundaries by the presence ofsolute Ti and Mo or by Zener pinning exerted by the straininduced precipitates which preferentially nucleate on dislocation.The precipitates grow faster due to pipe diffusion throughdislocations and once the precipitates coarsen sufficiently, recrys-tallization again takes over resulting in the fall in stress asindicated in the relaxation curves. Liu and Jonas [12] alsosuggested that the stress vs log(time) relationship under thiscondition can be described as follows:

s¼ s0�alogð1þbtÞþDs ð1Þ

where s is the relaxation stress, s0 is the initial stress, t is theholding time after deformation in second, a and b are experi-mental constants and Ds is the stress increment due to precipita-tion. For sufficiently long times, btb1, and Eq. (1) becomes

s¼ A�alog tþDs ð2Þ

Here A¼ s0�alog b. According to Eq. (2), Ds equals �0 duringthe initial linear stress drop stage. As relaxation proceeds, Dsincreases gradually and finally reaches the maximum value at acertain time which is marked by arrow (Pf) in Fig. 1. Themaximum value of Ds is also a function of testing temperatureand it decreases with increasing temperature as shown in Fig. 2.That was because of the decrease of the volume fraction ofprecipitates and the increase of precipitate size with increasingisothermal temperature [9,10,13]. The stress relaxation curve at975 1C does not show a relaxation plateau. Instead, a fast drop instress value appears after a linear-drop stage, which indicates theoccurrence of a fast static recrystallization as marked by SRX inFig. 1. It is known that the fast recrystallization progress willresult in a rapid drop in the density of structural defects such asdislocations in the austenite matrix that are subjected to

Fig. 2. Maximum of Ds as a function of testing temperature.

deformation. Since these defects are the nucleation sites for straininduced precipitates [16], and thus their rapid disappearance atthis high temperature of 975 1C is expected to hinder theprecipitation process.

According to previous workers [12], the start and finish timesof the plateau in the stress relaxation curves, which are markedby arrows in Fig. 1, are defined as the onset (Ps) and end (Pf) timesof the precipitation induced by strain, respectively. Ps pointindicates the occurrence of the precipitation, and Pf point repre-sents the time at which the precipitation hardening reaches themaximum, i.e. Ds reaches the maximum. It should be noted thatPf point does not denote the volume fraction of precipitatesreaching an equilibrium value, but possibly represents the transi-tion of the mechanism of particle growth [16]. The precipitation-time-temperature (PTT) diagram for carbide precipitation inTi–Mo micro-alloyed steel was successfully obtained as shown inFig. 3. The PTT diagram exhibits a typical ‘‘C’’ shape; its nose,which corresponds to the minimum incubation time for precipi-tation, is located at about 925 1C. This temperature is very close tothat of TiC precipitation reported in our previous work on a Timicro-alloyed steel with a similar chemical composition, butwithout Mo addition [13]. In addition, the start time of the PTTdiagram is within 50 s in the temperature range of 875–925 1C,but exceeds 150 s at 950 1C.

3.2. Characterization of precipitates in Ti–Mo micro-alloyed steel

3.2.1. Undissolved precipitates

In the present work, a certain number of undissolved cube-shaped TiN particles, which could be formed during smelting and/or casting process [17], were occasionally observed in the Ti–Momicro-alloyed steel by TEM. As shown in Fig. 4, these particleshave a typical size of �1 mm, so that they had little effect on therecovery and recrystallization of deformed austenite during stressrelaxation [9,18]. Their number density was very small on carbonreplica film, which is due to the limited N content, 0.002 wt% inthe studied alloy.

3.2.2. Precipitates formed during stress relaxation in Ti–Mo

micro-alloyed steel

Fig. 5 is a TEM image showing a carbide particle formed in thespecimen deformed at 925 1C followed by a hold for 1800 s, and itwas identified as Ti-rich MC carbide with the NaCl-type crystal

Fig. 3. PTT diagram of the studied Ti–Mo microalloyed steel, where Ps and Pf are

the start and finish times of carbide precipitation, respectively.

Fig. 4. (a) TEM image showing an undissolved TiN particle in Ti–Mo micro-alloyed steel, and (b) the corresponding EDS analysis of this TiN particle. It should be noted that

the peaks of Cu on the EDS spectrum are from Cu grid used to support carbon replica film.

Fig. 5. (a) TEM image showing a (Ti, Mo)C precipitate, (b) selected area electron diffraction (SAD) and (c) energy dispersive spectroscopy (EDS). It should be noted that the

peaks of Cu and Si on the EDS spectrum are from Cu grid used to support carbon replica film and the inclusion in carbon replica film, respectively.

Fig. 6. HAADF-STEM image showing the cell-like distribution of (Ti, Mo)C carbide on

carbon replica film, formed in the specimen deformed at 900 1C and held for 1800 s.

Z. Wang et al. / Materials Science & Engineering A 573 (2013) 84–91 87

structure containing a certain amount of Mo by selected areaelectron diffraction (SAD) and EDS analysis shown in Fig. 5(b) and(c). The atomic ratio of Ti/Mo quantified by EDS, in the carbide isabout 8.0, which is larger than that of the (Ti, Mo)C particle inferrite reported by Jang et al. [8] and Funakawa et al. [1].

The nucleation site of the precipitates formed in the Ti–Mo micro-alloyed steel during stress relaxation can be confirmed indirectlyby analyzing the distribution of particles on the carbon replica film.A high-angle annular dark-field scanning transmission electronmicroscopy (HAADF-STEM) image shown in Fig. 6 clearly exhibiteda cell-like distribution of precipitates on the carbon replica, implyingthat the precipitates nucleated on dislocations or on dislocation sub-structures [13]. The sizes of these ‘‘sub-grains’’, which were producedby deformation and subsequent recovery process, were measured tobe in the range of 0.2–1.0 mm, which is much smaller than the prioraustenite grain size of �100 mm. In addition, the shape of the mostprecipitates as seen in Fig. 6 is polyhedron rather than a cube thatseems to be identified from TEM image in Fig. 5. A precipitate whichlooks like a cube observed from TEM image was selected as anexample to clarify the difference. Fig. 7 shows the TEM image, STEMimage of the precipitate and the corresponding selected area electrondiffraction (SAD) with a magnetic rotation angle of 901 relative tothe TEM and STEM images. It can be seen that precipitate seemsto have an almost perfect cube-like shape as shown in Fig. 7(a).However, the strong three-dimensional contrast in Fig. 7(b) togetherwith the annular equal thickness fringes in Fig. 7(a) indicate that the

Fig. 7. A carbide particle formed in the specimen deformed at 925 1C and held for 1800 1C: (a) TEM image, (b) HAADF-STEM image and (c) the corresponding selected area

electron diffraction (SAD). It should be noted that the shape of this precipitate is rectangular pyramid or an octahedron as observed in (b) rather than a cube as seen in (a).

In addition, the two diagonals of this pyramid-like or octahedron-shaped precipitate are on the plane {200}, which is identified by SAD in (c).

Fig. 8. (a) HRTEM image showing a carbide particle in the specimen deformed at

925 1C and held for 3000 s and (b) IFFT lattice image of the area marked by a

white-line frame on the carbide particle in (a).

Z. Wang et al. / Materials Science & Engineering A 573 (2013) 84–9188

precipitate has a pyramid-like shape or an octahedron shape if theprecipitate has a symmetry with respect to the observation plane,rather than a cube-like shape. Moreover, the two diagonals of thispyramid-like or octahedron-shaped precipitate were determined tobe parallel with plane {200} of the precipitate, indicating that themajority of the facets were not on the plane {200}. But the facet ofcube-like TiN particle precipitated in austenite is just the plane {200}[19]. The equilibrium shape of M(C, N) particle with the B1 structure,where M¼Ti, Nb, V, Mo or their combination, depends on theinterplay between interfacial and elastic strain energy minimizationduring precipitation in austenite [20]. According to Yang and Eno-moto [19], the interfacial energy includes structure energy arising outof the lattice misfit between M(C, N) and austenite matrix, andchemical energy from the difference in chemical composition at theM(C, N)/austenite interface. The elastic strain energy comes from thedifference in elastic property between M(C, N) and austenite. Yangand Enomoto stated [19] that the cube shape of TiN particle thatadopts a cube-on-cube orientation relationship with respect to theaustenite matrix, was mainly attributed to the anisotropy of thechemical interfacial energy, because the anisotropy of the structuralinterfacial energy of TiN/austenite interfaces (�15%) and the elasticstrain energy are not large at higher temperature. However, for otherB1-carbides (and nitrides) i.e. NbC having a larger misfit withaustenite (�22%) and considerable elastic strain energy due to itslower precipitation temperature, the cube-on-cube orientation rela-tionship with respect to austenite matrix may not be always main-tained. Thus, the morphology is expected to become more irregular(see reference [21,22]). In the present study, the misfit betweencarbide and austenite was determined as �18% (lattice parameterequals �0.43 nm by SAD and assuming that the austenite latticeparameter is 0.365 nm [9]). This value lies in between that of TiN andNbC. Moreover, the precipitation temperature of the carbide in thepresent work is close to that of NbC reported by [21,22], so that theelastic strain energy cannot be ignored under this condition. There-fore, the carbide in the present study is expected to exhibit a shapethat lies in between that of TiN and NbC. Of course, accuratelypredicting the morphology of this carbide needs more work includingcalculating interfacial energy, elastic strain energy, their particle sizedependences, etc. However, this is beyond the scope of thepresent work.

A high-resolution transmission electron microscopy (HRTEM)investigation of the carbides formed in the Ti–Mo micro-alloyedsteel was performed in this study, and an example of the latticeimage of a carbide is presented in Fig. 8(a). It is identified as a (Ti,Mo)C particle with a NaCl-type crystal structure using a two-dimensional fast Fourier transformation (FFT) analysis, which isconsistent with SAD result (see Fig. 5). The lattice image obtainedby an inverse fast Fourier transformation (IFFT) shown inFig. 8(b) has been identified to have a lattice parameter of0.43 nm, which is very close to that (0.423–0.430 nm) of the

inter-phase precipitated (Ti, Mo)C particles reported by Yen et al.[7] and Funakawa et al. [1].

3.3. Growth and coarsening of precipitates

In the present work, the particle size evolutions of (Ti, Mo)Cparticle in the Ti–Mo micro-alloyed steel and TiC in a reference Tisteel with isothermal holding time were investigated, and theresults at the testing temperature of 925 1C are presented in Fig. 9.It can be clearly seen that the particle sizes of carbide in both steelwere very close with each other for 200 s holding time (seeFig. 9(a) and (e)). However, with the increase of holding time to600–1800 s and to 3000 s, (Ti, Mo)C particle in Ti–Mo steelexhibited smaller size and higher density than TiC in Ti steel(see Fig. 9(b),–(d), (f)–(h)). In order to better understand thegrowth and coarsening behavior of carbide in the two steels, theaverage particle sizes for various holding times at 925 1C weremeasured and plotted in Fig. 10. At the initial stage of precipita-tion, the carbide in both steel grows very quickly, and showsalmost the same value in growth rate. The growth of carbide atthis stage approximately followed a parabolic law, i.e. d¼ a

ffiffiffiffiffiffi

Dtp

,where d is the size of the particle, a is the growth coefficient andD is the diffusion coefficient of the element which is controllingthe growth rate. With the increase of holding time, the growthrate of carbide slowed down for both steel, especially for (Ti, Mo)Cparticle in Ti–Mo steel being almost unchanged from 200 s to1800 s. During this stage, precipitate lies in the coarsening stagei.e. Ostwald ripening stage. The transition time from growth tocoarsening was �200 s for (Ti, Mo)C particle and �600 s for TiC.It should be noted that the transition time from growth tocoarsening for (Ti, Mo)C particle is roughly comparable with Pf

time (�400 s) given in stress relaxation curve (see Fig. 1). Moreimportantly, (Ti, Mo)C particle in Ti–Mo steel exhibit a superior

Fig. 9. (a)–(d) TEM images showing carbide particles formed at 925 1C for various holding time in Ti–Mo micro-alloyed steel: (a) 200 s, (b) 600 s, (c) 1800 s and (d) 3000 s.

(e)–(h) TEM images showing carbide particles formed at 925 1C for various holding time in Ti micro-alloyed steel: (e) 200 s, (f) 600 s, (g) 1800 s and (h) 3000 s.

Fig. 10. Average particle sizes of carbides at 925 1C as functions of isothermal

holding time. The relation between average particle size and holding time at the

initial stage of precipitation, before 200 s for Ti–Mo steel and before 600 s for Ti

steel, is roughly determined as d¼ kt1=2, where d is the average size of the particle,

k is a constant and t is isothermal holding time.

Fig. 11. Physical–chemical phase analysis showing the precipitated fraction of Ti

in carbide (TiC or (Ti, Mo)C) for 600 s and 1800 s isothermal holding after one pass

rolling with the reduction of 20% at �925 1C in Ti and Ti–Mo micro-alloyed steels.

It should be noted that the total Ti content is 0.1 wt% for both steels. The results

come from reference [23] which will be published.

Z. Wang et al. / Materials Science & Engineering A 573 (2013) 84–91 89

coarsening resistance to TiC particle in Ti steel during this stage asshown in Fig. 10. This phenomenon was often observed by manyresearchers [1,5–8] for (Ti, Mo)C particles precipitated in ferrite orduring g-a phase transformation.

According to Ostwald’s ripening theory

dnt�dn

0 ¼k

RTV2

mCDgt ð3Þ

where dt is average particle size at a given time, d0 is the initialaverage particle size, n is 3 for volume diffusion controlledcoarsening, k is a constant, Vm is the molar volume of theprecipitate, C is the concentration of solute in the matrix that isin equilibrium with the precipitate, D is the diffusivity of thesolute, g is the interfacial energy per unit area between theprecipitate and the matrix, R and T have their usual meanings,the coarsening rate of carbide at a given temperature T is mainlydependent on the interfacial energy g, the diffusivity D and theconcentration C of the controlling element in austenite [8,9].Since interstitial atoms diffuse much faster than substitutional

atoms in austenite, the coarsening process is considered to becontrolled by the diffusion of substitutional element Ti or Mo.According to Yong’s theory [9], the coarsening process of ternary(Ti, Mo)C particle depends on the product of D and C of substitu-tional solute atom in austenite. The element that has a smallerproduct of D and C, is considered as the controlling element.As discussed in Section 3.2, (Ti, Mo)C particle is rich in Ti rather thanMo, so that the concentration of Ti in solution is much lower thanthat of Mo during the coarsening stage. In addition, the diffusivityof Ti in austenite is a little larger (�1.1–1.2 times) than that of Moover the investigated temperature range [9]. Therefore, thecontrolling element of the coarsening process of (Ti, Mo)C carbidein Ti–Mo steel is determined as Ti, which is also the one of TiCcoarsening process in Ti steel. In another work that will bepublished [23], the effect of Mo on the kinetics of carbideprecipitation in Ti micro-alloyed steel was investigated by hotrolling experiments. Fig. 11 is the physical–chemical phaseanalysis result showing the precipitated fraction of Ti in carbide(TiC or (Ti, Mo)C) for 600 s and 1800 s isothermal holding at

Z. Wang et al. / Materials Science & Engineering A 573 (2013) 84–9190

�925 1C in Ti and Ti–Mo steels. Results showed that the additionof Mo into Ti steel can accelerate the precipitation of Ti elementas carbide out of austenite. Therefore, the remaining Ti solute inaustenite for Ti–Mo steel is lower than that for Ti steel duringcoarsening process. Consequently, the decrease of Ti concentra-tion by Mo addition is considered to result in the decrease ofcoarsening rate of (Ti, Mo)C particle according to Eq. (3). On theother hand, the lattice parameters of carbides were identified byTEM/SAD as �0.430 nm for both (Ti, Mo)C and TiC carbide.Therefore, the lattice misfit between carbide and austenite matrixis almost the same for the two steel, indicating that the structuralinterfacial energy of (Ti, Mo)C particle approximately equals thatof TiC particle if the cube-on-cube orientation relationship ismaintained between carbide and austenite [9]. However, thepartial replacement of Ti by Mo in TiC crystal lattice results in adecrease of the contributions of chemical binding to the inter-facial energy of carbide/austenite according to our calculationresult [23] and Yang’s DLP/NNBB theory [24,25]. Thus, thechemical interfacial energy is possibly reduced by the partialreplacement of Ti by Mo in TiC lattice, although the exactchemical interfacial energy depends on the spread over whichthe interface is defined. As a result, the total interfacial energy of

Fig. 12. Atomic ratio of Ti/Mo in carbide as a function of isothermal holding time.

The figures above Ti/Mo–log(time) curve represent the average particle sizes of

the measured precipitates.

Fig. 13. Variations of atomic fractions of (a) Ti, (b) Mo and (c) C in MC carbide parti

measured atomic fraction of Mo in the MC particle were given by assuming that no va

perfect NaCl-type structure. The data marked by symbols in the temperature range of 8

holding. The data marked by a quadrangle at 620 1C is from the work of Funakawa et

studied steel, and was isothermal held at 620 1C for 3600 s after finish rolling and furn

(Ti, Mo)C particle with austenite is possibly reduced as comparedwith that of TiC, and in turn decreasing the coarsening rate of (Ti,Mo)C carbide according to Eq. (3).

3.4. Thermodynamic and kinetic analysis for (Ti, Mo)C phase

In this paper, the compositional evolution of (Ti, Mo)C particlein Ti–Mo steel was studied at the testing temperature of 925 1C.As shown in Fig. 12, the atomic ratio of Ti/Mo in (Ti, Mo)C particleincreased with isothermal holding time or particle growing. Thisphenomenon seems to indicate that on the one hand, theincorporation of Mo into TiC favors the nucleation and growthduring the early stages of precipitation, on the other hand, thehigh level replacement of Ti by Mo in TiC lattice is not stableenough or can be called as ‘‘metastable’’ with respect to equili-brium precipitation of (Ti, Mo)C phase. Fig. 13 shows the varia-tions of the equilibrium atomic fractions of Ti, Mo and C in MCphase with temperature calculated by the Thermo-calc. FCC andBCC phases were selected as Thermo-calc calculation was carriedout. This means that MC phase is in equilibrium with austenite athigher temperature and with ferrite at lower temperature. Inaddition, the calculated MC phase contains a small amount of Feand Mn elements, thus leading to the sum of atom factions of Tiand Mo being not 0.5 as shown in Fig. 13(a) and (b), especially atlower temperatures. In Fig. 13, the equilibrium chemical compo-sition of MC phase with the fcc structure approaches the pure TiCat the temperature above 800 1C. As the temperature decreases,the equilibrium atomic fraction of Mo in MC phase increases.When the temperature decreases to below 700 1C, the increase ofthe atomic fraction of Mo with temperature becomes faster. Theatomic ratio of Mo/Ti is about 1.0 in the temperature range of500–600 1C. The measured atomic fractions of Mo by EDS in MCphase at different temperatures for 1800 s isothermal holdingwere also shown in Fig. 13(b). Here, it is assumed that novacancies are present at C atom positions in the MC lattice,namely a perfect NaCl-type MC phase. In this case, the atomicfraction of Mo in MC reaches the minimum because the partialreplacement of Ti by Mo in the TiC lattice possibly produces acertain amount of vacancies at C atom positions according toreference [8]. In addition, the experimental result from Funakawaet al. [1], of a Ti–Mo micro-alloyed steel with a similar chemicalcomposition to that of the present steel was given in Fig. 13(b) fora comparison. As the temperature decreases, the measuredatomic fraction of Mo in MC phase increases. However, they are

cle with temperature calculated by Thermo-calc with database TCFE6. In (b), the

cancies are present at C atom positions in the NaCl-type crystal structure, namely

75–950 1C are the present measured data under the condition of 1800 s isothermal

al. [1], whose steel has a similar chemical composition with that of the present

ace cooled to room temperature.

Z. Wang et al. / Materials Science & Engineering A 573 (2013) 84–91 91

much higher than those calculated by Thermo-calc. And thedifference becomes larger with decreasing temperature, forexample, �3% at 950 1C, but up to �8% at 875 1C. As for the steelfrom Funakawa et al., the difference is �11%. As discussed above,the site fraction of Mo in the (Ti, Mo)C lattice decreases withisothermal holding time or with particle growing. Such a findingtogether with the comparison between the experimental resultsand theoretical calculation indicates that the greater replacementof Ti by Mo in the TiC lattice is energetically unfavorable withrespect to the equilibrium precipitation, when the other energyconditions including interfacial energy and elastic strain energybetween precipitate and matrix are not considered.

As discussed in Section 3.3, the partial replacement of Ti by Moin the TiC lattice possibly decreases the chemical interfacialenergy between (Ti, Mo)C carbide and austenite [23]. Therefore,this effect, in fact, favors the decrease of the nucleation energybarrier, thus enhancing the nucleation of (Ti, Mo)C phase duringthe early stages of precipitation. Accordingly, smaller (Ti, Mo)Cparticle contains more Mo as shown in Fig. 12. However, withparticle growing, the surface area to volume ratio of particlebecomes not considerable, i.e. the interface effect becomes not sosignificant. At the moment, the incorporation of Ti into (Ti, Mo)Cphase is more beneficial to the decrease of the total free energy ofsystem, thus resulting in the decrease of the fraction of Mo in the(Ti, Mo)C phase, as shown in Fig. 12. However, the incorporationrate of Ti atom into the (Ti, Mo)C phase depends on the diffusivityof Ti in austenite, which is a function of isothermal temperature.The diffusion rate of Ti atom is slower at lower temperature, thusleading to the larger difference in terms of the faction of Mo in the(Ti, Mo)C phase, between the experimental measurements andthe equilibrium results calculated by Thermo-calc at lowertemperatures.

4. Conclusion

In summary, the precipitation-time-temperature diagram forthe kinetics of carbide precipitation in Ti–Mo micro-alloyed steeldetermined by a stress relaxation method exhibited a typical ‘‘C’’shape curve, and its nose was located at �925 1C. The precipitatesformed during stress relaxation in Ti–Mo micro-alloyed steelwere identified as polyhedral Ti-rich (Ti, Mo)C carbides posses-sing a NaCl-type crystal structure that contains a certain amountof Mo. The (Ti, Mo)C precipitates were heterogeneously distrib-uted in a cell like manner on carbon replica film, implying that theprecipitates nucleated on dislocations or on dislocationsub-structures, which were produced by deformation. The growth

of carbide particles in Ti–Mo micro-alloyed steel approximatelyfollowed a parabolic law during growing stage. During coarseningstage, (Ti, Mo)C particles in Ti–Mo micro-alloyed steel exhibited ahigher coarsening resistance as compared with TiC particles in Timicro-alloyed steel, which is attributed, on the one hand, to thedecrease of Ti concentration in austenite by the accelerating effectof Mo on Ti precipitation as carbide, on the other hand, possibly tothe decrease in the chemical interfacial energy of carbide/auste-nite by the Mo incorporation into the TiC lattice.

Acknowledgments

The authors appreciate the financial support by both NationalBasic Research Program of China (973 Program 2010CB630805) andNational Natural Science Foundation of China (No. 51171087).

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