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Research ArticleDynamic Recrystallization Behavior of TA15 Titanium Alloyunder Isothermal Compression during Hot Deformation
Yuanxin Luo Yuqing Heng Yongqin Wang and Xingchun Yan
State Key Lab of Mechanical Transmission Chongqing University Chongqing 400044 China
Correspondence should be addressed to Yuanxin Luo yxluocqueducn
Received 13 June 2014 Revised 28 August 2014 Accepted 31 August 2014 Published 19 October 2014
Academic Editor Rui Vilar
Copyright copy 2014 Yuanxin Luo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
In order to improve the understanding of the dynamic recrystallization (DRX) behaviors of TA15 titanium alloy (Ti-6Al-2Zr-1Mo-1V) a series of experiments were conducted on a TMTS thermal simulator at temperatures of 1173 K 1203K 1223K and 1273Kwith the strain rates of 0005 sminus1 005 sminus1 05 sminus1 and 1 sminus1 By the regression analysis for conventional hyperbolic sine equationthe activation energy of DRX in (120572 + 120573) two-phase region is 119876
119878
= 5887Kgmol and in 120573 region is 119876119863
= 2258Kgmol and adimensionless parameter controlling the stored energy was determined as 119885119860 = 120576exp [(5887 times 103)119877119879] 669 times 1026 in (120572 + 120573)two-phase region and as 119885119860 = 120576exp [(2258 times 103)119877119879] 513 times 1011 in 120573 region The DRX behaviors of TA15 titanium alloy wereproposed on the strength of the experiment results Finally the theoretical prediction results of DRX volume fraction were shownto be in agreement with experimental observations
1 Introduction
The near 120572-type titanium alloy Ti-6Al-2Zr-1Mo-1V (TA15titanium alloy) with high specific strength good creepresistance and corrosion resistance good thermal stabilityand excellent welding performance has been widely used inaerospace industry [1ndash3] However it is difficult to form thecomponents with complexity in shape and high quality dueto its large deformation resistance and low ductility it is wellknown that suitable flow stress and dynamic recrystalliza-tion (DRX) model is necessary to describe the property ofbillet [4] There are several models that have been reportedto express the flow stress and the evolution of dynamicrecrystallization of alloy The constitutive model proposedby Sellars and Tegart has been widely used for describingflow behaviors of the metal alloys [5 6] The DRX modelmainly contains recrystallization kinetics and grain growthkinetics dynamic The recrystallization kinetics includes thepeak strain equation and dynamic recrystallization fractionequation while the grain growth kinetics dynamic can bedescribed by recrystallization grain size equation [7] TheJohnson-Mehl-Avrami-Kolmogorov (JMAK) microhardnessmodel was proposed by Kalu et al to quantify the kinetics of
restoration mechanisms in inhomogeneous microstructure[8] The DRX kinetics model was proposed based on Avramifunction to study the dynamic recrystallization formetal alloy[9 10] For titanium alloy the Sellars-Tegartmodel [11 12] andthe JMAK equation are widely used to express peak stress andthe dynamic recrystallization evolution [8]
In this paper the hot deformation behavior of TA15 tita-nium was studied for investigating the effects of temperatureand strain rate on the flow behaviors Then the constitutiveequation andDRX kineticmodel are obtained to characterizethe deformation behavior in the isothermal compressionFinally the theoretical prediction results of DRX volumefraction were shown to be in agreement with experimentalobservations
2 Experimental Procedure
Hot compression TA15 titanium alloy bar used in the exper-iments was with the chemical composition given in Table 1Titanium and titanium alloys have the characteristics ofallotrope change and TA15 titanium alloy includes body-centered cubic structure120573-phase and close-packed hexagonalstructure 120572-phase and 1205721015840-phase The 120572-phase trends to
Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2014 Article ID 413143 9 pageshttpdxdoiorg1011552014413143
2 Advances in Materials Science and Engineering
Table 1 The chemical composition of as-received TA15 titanium alloy (wt)
Al Mo V Zr Fe C N Ti63 132 168 19 004 001 001 Bal
Tem
pera
ture
(K) Time holding
Deformation
WQ
Time (s)
10Ks
Figure 1 The general isothermal loading route
transform into 120573-phase with the increasing of temperature[3] Its phase transition point is between 1243K and 1253K[13]
Prior to executing the experiments the specimens wereresistance heated to deformation temperatures with heatingratio of 10 Ks and homogenized for 180 s Cylindrical speci-mens with a height of 12mm and a diameter of 8mm wereprepared for hot compression tests which were conductedon a TMTS thermal simulation machine at temperaturesof 1173 K 1203K 1223K and 1273K and at strain rates of0005 sminus1 005 sminus1 05 sminus1 and 1 sminus1 The specimens werecompressed to 60 reduction and then quenched in waterimmediately The general isothermal loading schedule withdifferent temperature route is shown in Figure 1
3 Results and Discussion
31 Flow Stress Behavior A series of typical true stress-truestrain curves obtained during hot compression of homog-enized TA15 titanium alloy at different strain rates anddeformation temperatures are presented in Figure 2
It can be easily observed from the true stress-strain curvesthat the flow stresses increase rapidly to their own peakpoints Then the stress decreases slowly and tends to be aconstant with the increases of strain It indicates that theDRX is the dominant softening mechanism under the testconditions The true stress-strain curves displayed that thework-hardening and softening mechanism vary with strainrate and deformation temperature which showed that theflow behavior is the conclusion of the dynamic recrystal-lization and dynamic recovery against work-hardening inisothermal hot compression tests of TA15 titanium alloy Thestress decreases with the increase of deformation temperatureat the same strain rate and with the decrease of strain rateunder the same deformation temperature It indicates that
the flow stress of TA15 titanium alloy is extremely sensitiveto strain rates and deformation temperature
32 Constitutive Equations for Flow Behavior with DRX Inorder to further investigate the combined effect of tempera-ture and deformation rate on the deformation behavior it isnecessary to study the constitutive characteristics of titaniumalloy represented by theZener-Hollomonparameter119885 in theexponent-type equation [14ndash16]
Z = 120576 exp ( 119876
119877119879) (1)
120576 = 1198601
120590119899 (minus119876
119877119879) (2)
120576 = 1198602
exp (120572119899120590) exp (minus 119876
119877119879) (3)
120576 = 119860[sin ℎ (120572120590)]119899 exp (minus 119876
119877119879) (4)
where 120576 is the strain rate (sminus1) 119877 is the universal gas constant(8314 Jmol timesK) 119879 is the absolute temperature (K) 119876 is theactivation energy for hot deformation (Jmol) 119860
1
1198602
119860 120572and 119899 are material constants and 120590 is the flow stress (MPa)
321 Calculation of Material Constants 119899 and 120572 The powerlaw equation (2) represents low stress the exponential law (3)is preferred for high stress and the hyperbolic sine law (4) canbe suitable for a wide range of stresses [15] Taking the naturallogarithms on both sides of (2) and (3) we can obtain
ln 120576 = ln1198601
+ 119899 ln120590 minus 119876
119877119879
ln 120576 = ln1198602
+ 120572119899120590 minus119876
119877119879
(5)
It can be easily derived that 119899 and 120572 can be obtained fromthe slope of the lines ln120590minus ln 120576 and 120590minus ln 120576 plots respectivelySubstituting measured flow stress of TA15 thermal deforma-tion at different temperatures given in Table 2 into (6) and (7)the experimental data and regression results of ln120590minus ln 120576 and120590 minus ln 120576 plots are shown in Figures 3 and 4
119899 =120597 ln 120576
120597 ln120590 (6)
120572119899 =120597 ln 120576
120597120590 (7)
Under different temperatures (1173ndash1273) K the meanvalue of all the slope rates is accepted as the inverse ofmaterial constants 119899 and 120572 The value of 119899 obtained by lineardependent coefficients is 459 Figures 5 and 6 show 120572119899obtained through the linear regression data is 001855 and thevalue of 120572 is 0004
Advances in Materials Science and Engineering 3
00 02 04 06 080
10
20
30
40
50
60Fl
ow st
ress
(MPa
)
True strain
1273K1223K
1203K1173K
0005 sminus1
00 02 04 06 080
10
20
30
40
50
60
70
80
90
100
Flow
stre
ss (M
Pa)
True strain
1273K1223K
1203K1173K
005 sminus1
00 02 04 06 080
50
100
150
Flow
stre
ss (M
Pa)
True strain
1273K1223K
1203K1173K
05 sminus1
00 02 04 06 080
50
100
150
200
Flow
stre
ss (M
Pa)
True strain
1273K1223K
1203K1173K
1 sminus1
Figure 2 The true stress-strain curves of TA15 titanium alloy at different strain rates
Table 2 Peak stress of TA15 stress-strain curves for differenttemperatures and strain rates
Strain rate(sminus1)
Deformation temperature (K)1173 1203 1223 1273
0005 55926 40186 26713 22019005 91980 66536 44411 3664405 148101 108832 73411 607491 16971 125647 85212 70622
322 Calculation of DRX Activation Energy 119876 Taking thenatural logarithms on both sides of (4) it can be rewrittenas follows
ln 120576 = ln119860 + 119899 ln [sinh (120572120590)] minus 119876
119877119879 (8)
Table 3 The value of ln[sinh(120572120590)] at different deformation condi-tions of TA15
Strain ratesminus1 TemperatureK1173 1203 1223 1273
0005 minus2428 minus2234 minus1824 minus1489005 minus1917 minus1723 minus1312 minus097705 minus1405 minus1211 minus08 minus04661 minus1251 minus1057 minus0646 minus0312
For a given strain rate the apparent activation energy 119876can be calculated as
119876 = 119877120597 ln 120576
120597 ln [sinh (120572120590)]
10038161003816100381610038161003816100381610038161003816119879
120597 ln [sinh (120572120590)]120597 (1119879)
10038161003816100381610038161003816100381610038161003816120576
= RNW (9)
The curves of ln[sinh(120572120590)] versus 1119879 are obtained fordifferent strain rates by using the data in Table 3 as shown
4 Advances in Materials Science and Engineering
32 36 40 44 48 52
0
1
ln(stressMPa)
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
Figure 3 The relationships between ln 120576 and ln120590
20 40 60 80 100 120 140
0
1
Stress (MPa)
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
Figure 4 The relationships between ln 120576 and 120590
in Figures 5 and 6119873 and119882 can be approximated by takingthe average slope of different strain rate It is found that theconstant of deformation activation energy in (120572 + 120573) two-phase region is 119876
119878
= 5887Kgmol and in 120573 region is 119876119863
=2258Kgmol
323 Construction of Constitutive Equation The equation offlow stress is given in (4) in which the undefined factors 119898120572 119860 119899 119876 can be obtained by using (6) (7) (8) and (9)respectively Also it is found that the peak flow stress modelin (120572 + 120573) two-phase region is
120576119878
= 669 times 1025[sinh (0004120590)]459 exp(minus588700119877119879
) (10)
00
0
1
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
minus25 minus20 minus15 minus10 minus05
ln[sin h(120572120590)]
Figure 5 The relationships between ln 120576 and ln[sinh(120572120590)]
078 079 080 081 082 083 084 085 086
00
minus25
minus20
minus15
minus10
minus05
0005 sminus1
005 sminus105 sminus11 sminus1
Tminus110minus4 (Kminus1)
120573-phase region 120572 + 120573 two-phase region
ln[s
in h(
120572120590
)]
Figure 6 The relationships between ln[sinh(120572120590)] and 1119879
and in 120573 region is
120576119863
= 513 times 1011[sinh (0004120590)]459 exp(minus225800119877119879
) (11)
Figure 7 displays the result of the relationships betweenln119885 and ln[sinh(120572120590)] It follows that the data were dividedinto two regions which express single-phase region and two-phase region And the coefficients obtained are presented inthis figure
33 DRX Kinetic Model
331 Critical Strain for Initiation of DRX Based on theprevious analysis the critical strain is necessary to activatetheDRXThe critical strains will change for differentmaterial
Advances in Materials Science and Engineering 5
0010
20
30
40
50
60
70
minus25minus20minus15minus10minus05
ln Z
ln[sin h(120572120590)]
ln ZD = 459ln[sin h(0004120590)] + 6486
ln ZS = 459ln[sin h(0004120590)] + 2421
Figure 7 The relationships between ln119885 and ln[sinh(120572120590)]
30 35 40 45 50
0
500
1000
1500
2000
2500
3000
3500
minus500
120579(M
Pa)
120590 (MPa)
120590c
120590p 120590s120590ss
1223K-005 sminus1
Figure 8 The relationship between hardening and flow stress ofTA15
and deformation conditionsThe relationship of critical strainand peak strain can be expressed as [17 18]
120576119888
= 119896120576119901
(12)
where 120576119888
is the critical strain 120576119901
is the peak strain and 119896 ismaterial constant It has been reported that 119896 ranges from065to 085 [19] for metal alloy
The critical conditions for the onset of DRX are attainedwhen the value of strain hardening rate 120579 = 119889120590119889120576 reachesthe minimum corresponding to an inflection of 120579 minus 120590 curve[20] Figure 8 shows the 120579 minus 120590 curve of TA15 titanium alloyat the temperature of 1223K and with the strain rate of005 sminus1 It can be generally divided into three segments Inthe first segment the hardening rate decreases rapidly dueto DRV with the increases of 120590 at the beginning of plasticdeformation The reason of this phenomenon is that DRVreduces the effect of dislocation density The second segmentbegins from the critical stress 120576
119888
to the peak stress 120576119901
Thesubgrain boundary formed with the continuous increase of
002 004 006 008 010 012002
004
006
008
010
Peak
stra
in
Critical strain
Figure 9 The relationships between 120576119901
and 120576119888
dislocation density in this segment which makes the work-hardening rate be still positive but decrease gradually In thethird segment the 120579 minus 120590 curve depicts the tendency of fallingsuddenly due to the occurrence of DRX effect and the valueof 120579 minus 120590 gradually reduces to less than zero and fluctuatesup and down and finally keeps a zero value which expressthat the continuous DRX occurred In this stage the value of120579 decreases to zero when the flow stress increases to 120576
119901
Thismethod can be used to determine the relationship between120576119888
and 120576119901
The critical stress can be read from the true stress-true strain curve after calculating the critical strain Figure 9shows the relation of 120576
119888
and 120576119901
with 119896 = 083 Consequentlythe critical strain model of TA15 titanium alloy is 120576
119888
= 083120576119901
332The PeakModel Strain of DRX It is of great importanceto determine DRX kinetics model due to realization of thesoftening mechanism in the hot working of alloys The peakstrain value is related to deformation temperature strain ratethe original grain size and deformation activation energyTherefore the peak strainmodel is represented as follows [17]
120576119901
= 1205721
11988911989910
1205761198981 exp ( 1198761119877119879
) (13)
where 1198761
is deformation activation energy 1198890
is the initialgrain size and 120572
1
1198991
1198981
are material constants Assume thatall of specimens are well heat treated and are with the samegrain size Hence the influence of the initial grain size on thecritical strain is neglectable [21] and (13) can be simplified as
120576119901
= 1205721
1205761198981 exp( 1198761119877119879
) (14)
Taking the logarithm on both sides of (14) it can berewritten as
ln 120576119901
= ln1205721
+ 1198981
ln 120576 +1198761
119877119879 (15)
From (14) the factor of 1198981
and Q1
can take the averageof the slopes of ln 120576 minus ln 120576
119901
(as shown in Figure 10) and 119879minus1 minus
6 Advances in Materials Science and Engineering
0ln(strain rate)
minus18
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
minus6 minus5 minus4 minus3 minus2 minus1 1
1273K1223K
1203K1173K
Figure 10 The relationships between ln 120576119901
and ln 120576
078 079 080 081 082 083 084 085 086
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
Tminus110minus4 (Kminus1)
0005 sminus1
005 sminus105 sminus1
1 sminus1
Figure 11 The relationships between ln 120576119901
and 119879minus1
ln 120576119901
(as shown in Figure 11) respectively We can get 1198981
=005281 Q
1
= 9875478 Jmol 1205721
is then obtained by using(13) 120572
1
= 4429 times 10minus6Consequently the peak strain model of TA15 titanium
alloy is as follows
120576119901
= 4429 times 10minus6 12057600528 exp(9875478119877119879
) (16)
333 Models for the Strain for 50 DRX and DRX VolumeFraction DRX is a process accompanied by nucleation andgrowth of grain and a time-dependent process determinedon the basis of the DRX kinetics equation The veracity ofDRX kinetics model is connected with the determinationof recrystallization fraction deformation parameters the
dynamic relationship of the process and the determinationof series of parameters of kinematic equation The relationsof DRX kinetics can be described by the JMAK equation asfollows [17]
119883drx = 1 minus exp[minus120573119889
(120576 minus 120576119888
12057605
)119896
119889
] (17)
12057605
= 1205722
11988911989920
1205761198982 exp(1198762RT
) (18)
where 119883drx is the DRX fraction 12057605
is the strain for 50DRX 119876
2
is DRX activation energy and 120573119889
119896119889
1205722
1198992
1198982
arematerial constants
It is difficult to determine the recrystallized frac-tion under different deformation conditions based on themicrostructures However it can be indirectly calculatedfrom the stress-strain curves by using the following equation[6 12]
119883drx =120590 minus 120590119901
120590119904
minus 120590119901
(19)
where 120590119901
is the peak stress 120590119904
is the steady-state stress and 120590119901
and 120590119904
can be calculated from true stress-true strain curvesThe DRX fractions of different conditions are calculated byusing (19) By substituting (19) into (17) it can be rewritten inlogarithm form
ln [minus ln (1 minus 119883drx)] = ln120573119889
+ 119896119889
ln(120576 minus 120576119888
12057605
) (20)
The stress of 50 DRX can be calculated by using (19)and then the 120576
119888
can be easily found in the true stress-straincurve By substituting 120576
05
Xdrx and 120576119888 into (20) it is obtainedthat 120573
119889
= 0693 and 119896119889
= 1502 The DRX fraction of TA15titanium alloy can be obtained as follows
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
] (21)
Taking natural logarithm of (18) we can get
ln 12057605
= ln1205722
+ 1198992
ln 1198890
+ 1198982
ln 120576 +1198762
119877119879 (22)
The materials constants can be calculated by using (22)1198982
= 0045 1198762
= 390635 Jmol 1205722
= 6295 times 10minus3 and1198992
= 0 for ignoring the effect of initial grain size Finally wecan get the strain of 50 DRX
12057605
= 6295 times 10minus3 1205760045 exp (390635119877119879
) (23)
Advances in Materials Science and Engineering 7
00 01 02 03 04 05 060
20
40
60
80
100
Strain
0005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
100
005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
10005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
1001 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
Figure 12 Predicted DRX volume fractions of TA15 at different conditions
Summarily the DRX kinetics equations of TA15 can berepresented as
120576119901
= 4429 times 10minus6 12057600528 exp(9785478119877119879
)
120576119888
= 083120576119901
12057605
= 6295 times 10minus3 1205760045 exp(390635119877119879
)
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
]
(24)
Based on the calculated results of this model the effectsof strain strain rate and deformation temperature on volumefraction of DRX are shown in Figure 12 It can be seen thatthe curves of volume fraction of DRX appeared as ldquoSrdquo shapeand this phenomenon indicates that the volume fraction ofDRX grows rapidly between the strain ranges of 01ndash045The volume fraction of DRX is also slightly affected by thetemperature This is because of the decreased mobility ofgrain boundaries in a low temperature and high strain rate
34Microstructure Observations Typical opticalmicrostruc-tures of TA15 alloy were examined and analyzed on thesection plane of specimen deformed to a strain of 06 Themicrostructures at different temperatures and strain rates areshown in Figure 13 The effects of deformation temperatureand strain rate on the microstructures can be seen clearlyfrom these opticalmicrographs FromFigures 13(a) and 13(b)it can be easily found that the small size grain will be obtainedat high strain rate for a given temperature It means thatthere is not enough time for the DRX to grow at high strainrate Conversely the grain size of DRX is large for the highertemperature as shown in Figures 13(a) and 13(c)
It can be found clearly that the percentage of 120573-phase ishigher in Figure 13(d) than that in Figure 13(d) It expressesthat there is a tendency of 120572 rarr 120573 phase transformationoccurring with the increase of temperatureThe close-packedhexagonal 120572-phase trends to transform into body-centeredcubic 120573-phase with the increase of temperature Becausebody-centered cubic120573-phase has the features of high stackingfault energy and a large number of slip systems the flow stressdecreases and becomes gently In the temperature range of1223Kndash1273K it can be found that the flow stresses are not so
8 Advances in Materials Science and Engineering
20120583m
(a)
20120583m
(b)
20120583m
(c)
20120583m
(d)
Figure 13 Optical microstructures of TA15 alloy deformed under different conditions (a)119879 = 1203K 120576 = 0005 s (b)119879 = 1203K 120576 = 005 sminus1(c) 119879 = 1223K 120576 = 005 sminus1 (d) 119879 = 1273K 120576 = 005 sminus1
sensitive to the temperature So the flow stress drops slightlyfor the increase of the temperature
4 Conclusions
Hot deformation behavior of TA15 titanium alloy is studiedat high temperatures under isothermal compression in thispaper Based on this research the following conclusions canbe drawn
(1) Through the regression analysis for conventionalhyperbolic sine equation the coefficient of plasticdeformation constitutive equation of TA15 titaniumalloy during high temperature is calculated in whichthe value of deformation activation energy in (120572 + 120573)two-phase region is 119876
119878
= 5887Kgmol and in 120573region is 119876
119863
= 2258Kgmol
(2) The constitutive equations and DRX kinetic modelare obtained by this investigation that can be used todescribe the flow behavior of TA15 titanium alloy inhot forming
(3) The optical microstructure observation of the TA15specimens deformed to a strain of 06 under differ-ent conditions verified the influence of deformationconditions on the evolution of DRX volume fraction
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research is supported by the National Natural ScienceFoundation of China (Grant no 51345013) and the Funda-mental Research Funds for the Central Universities (Grantno CDJZR12110002)
References
[1] Y Chen W-C Xu D-B Shan and B Guo ldquoMicrostructureevolution of TA15 titanium alloy during hot power spinningrdquoTransactions of Nonferrous Metals Society of China vol 21 no2 pp s323ndashs327 2011
[2] L Huang R Zeng X Zhang and J Li ldquoStudy on plasticdeformation behavior of hot splitting spinning of TA15 titaniumalloyrdquoMaterials amp Design vol 58 pp 465ndash474 2014
[3] S Zhu H Yang L G Guo and X G Fan ldquoEffect of cooling rateon microstructure evolution during 120572120573 heat treatment of TA15titanium alloyrdquo Materials Characterization vol 70 pp 101ndash1102012
[4] Q J Sun and G C Wang ldquoMicrostructure and superplasticityof TA15 alloyrdquoMaterials Science and Engineering A vol 606 pp401ndash408 2014
Advances in Materials Science and Engineering 9
[5] Y C Lin M-S Chen and J Zhong ldquoConstitutive modeling forelevated temperature flow behavior of 42CrMo steelrdquo Compu-tational Materials Science vol 42 no 3 pp 470ndash477 2008
[6] Y Xu LHua andY Sun ldquoDeformation behaviour and dynamicrecrystallization of AZ61 magnesium alloyrdquo Journal of Alloysand Compounds vol 580 pp 262ndash269 2013
[7] X N Peng H Z Guo Z F Shi C Qin Z L Zhao and ZYao ldquoStudy on the hot deformation behavior of TC4-DT alloywith equiaxed 120572+120573 starting structure based on processingmaprdquoMaterials Science and Engineering A vol 605 pp 80ndash88 2014
[8] P N Kalu and D R Waryoba ldquoA JMAK-microhardness modelfor quantifying the kinetics of restoration mechanisms in inho-mogeneous microstructurerdquoMaterials Science and EngineeringA vol 464 no 1-2 pp 68ndash75 2007
[9] J Liu Z Cui and L Ruan ldquoA new kinetics model of dynamicrecrystallization for magnesium alloy AZ31BrdquoMaterials Scienceand Engineering A vol 529 no 1 pp 300ndash310 2011
[10] J J Jonas X Quelennec L Jiang and E Martin ldquoThe Avramikinetics of dynamic recrystallizationrdquo Acta Materialia vol 57no 9 pp 2748ndash2756 2009
[11] J Xiao D S Li X Q Li and T S Deng ldquoConstitutive modelingand microstructure change of Ti-6Al-4V during the hot tensiledeformationrdquo Journal of Alloys and Compounds vol 541 pp346ndash352 2012
[12] W Peng W Zeng Q Wang and H Yu ldquoComparative study onconstitutive relationship of as-cast Ti60 titanium alloy duringhot deformation based on Arrhenius-type and artificial neuralnetwork modelsrdquoMaterials amp Design vol 51 pp 95ndash104 2013
[13] Z Sun S Guo and H Yang ldquoNucleation and growth mecha-nism of 120572-lamellae of Ti alloy TA15 cooling from an 120572 + 120573 phasefieldrdquo Acta Materialia vol 61 no 6 pp 2057ndash2064 2013
[14] S F Medina and C A Hernandez ldquoGeneral expression of theZener-Hollomon parameter as a function of the chemical com-position of low alloy and microalloyed steelsrdquo Acta Materialiavol 44 no 1 pp 137ndash148 1996
[15] YWang Y Liu G Y Yang et al ldquoHot deformation behaviors of120573 phase containing Ti-43Al-4Nb-14W-based alloyrdquo MaterialsScience and Engineering A vol 577 pp 210ndash217 2013
[16] C M Sellars and W J McTegart ldquoOn the mechanism of hotdeformationrdquo Acta Metallurgica vol 14 no 9 pp 1136ndash11381966
[17] C Zener and J H Hollomon ldquoEffect of strain rate upon plasticflow of steelrdquo Journal of Applied Physics vol 15 no 1 pp 22ndash321944
[18] M-S Chen Y C Lin and X-S Ma ldquoThe kinetics of dynamicrecrystallization of 42CrMo steelrdquo Materials Science and Engi-neering A vol 556 pp 260ndash266 2012
[19] Z Yang Y C Guo J P Li F He F Xia andM X Liang ldquoPlasticdeformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-05Zn-05Zr alloyrdquo Materials Science and EngineeringA vol 485 no 1-2 pp 487ndash491 2008
[20] A I Fernandez P Uranga B Lopez and JM Rodriguez-IbabeldquoDynamic recrystallization behavior covering a wide austenitegrain size range in Nb andNb-Timicroalloyed steelsrdquoMaterialsScience and Engineering A vol 361 no 1-2 pp 367ndash376 2003
[21] C M Sellars ldquoFrom trial and error to computer modellingof thermomechanical processingrdquo Ironmaking and Steelmakingvol 38 no 4 pp 250ndash257 2011
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
2 Advances in Materials Science and Engineering
Table 1 The chemical composition of as-received TA15 titanium alloy (wt)
Al Mo V Zr Fe C N Ti63 132 168 19 004 001 001 Bal
Tem
pera
ture
(K) Time holding
Deformation
WQ
Time (s)
10Ks
Figure 1 The general isothermal loading route
transform into 120573-phase with the increasing of temperature[3] Its phase transition point is between 1243K and 1253K[13]
Prior to executing the experiments the specimens wereresistance heated to deformation temperatures with heatingratio of 10 Ks and homogenized for 180 s Cylindrical speci-mens with a height of 12mm and a diameter of 8mm wereprepared for hot compression tests which were conductedon a TMTS thermal simulation machine at temperaturesof 1173 K 1203K 1223K and 1273K and at strain rates of0005 sminus1 005 sminus1 05 sminus1 and 1 sminus1 The specimens werecompressed to 60 reduction and then quenched in waterimmediately The general isothermal loading schedule withdifferent temperature route is shown in Figure 1
3 Results and Discussion
31 Flow Stress Behavior A series of typical true stress-truestrain curves obtained during hot compression of homog-enized TA15 titanium alloy at different strain rates anddeformation temperatures are presented in Figure 2
It can be easily observed from the true stress-strain curvesthat the flow stresses increase rapidly to their own peakpoints Then the stress decreases slowly and tends to be aconstant with the increases of strain It indicates that theDRX is the dominant softening mechanism under the testconditions The true stress-strain curves displayed that thework-hardening and softening mechanism vary with strainrate and deformation temperature which showed that theflow behavior is the conclusion of the dynamic recrystal-lization and dynamic recovery against work-hardening inisothermal hot compression tests of TA15 titanium alloy Thestress decreases with the increase of deformation temperatureat the same strain rate and with the decrease of strain rateunder the same deformation temperature It indicates that
the flow stress of TA15 titanium alloy is extremely sensitiveto strain rates and deformation temperature
32 Constitutive Equations for Flow Behavior with DRX Inorder to further investigate the combined effect of tempera-ture and deformation rate on the deformation behavior it isnecessary to study the constitutive characteristics of titaniumalloy represented by theZener-Hollomonparameter119885 in theexponent-type equation [14ndash16]
Z = 120576 exp ( 119876
119877119879) (1)
120576 = 1198601
120590119899 (minus119876
119877119879) (2)
120576 = 1198602
exp (120572119899120590) exp (minus 119876
119877119879) (3)
120576 = 119860[sin ℎ (120572120590)]119899 exp (minus 119876
119877119879) (4)
where 120576 is the strain rate (sminus1) 119877 is the universal gas constant(8314 Jmol timesK) 119879 is the absolute temperature (K) 119876 is theactivation energy for hot deformation (Jmol) 119860
1
1198602
119860 120572and 119899 are material constants and 120590 is the flow stress (MPa)
321 Calculation of Material Constants 119899 and 120572 The powerlaw equation (2) represents low stress the exponential law (3)is preferred for high stress and the hyperbolic sine law (4) canbe suitable for a wide range of stresses [15] Taking the naturallogarithms on both sides of (2) and (3) we can obtain
ln 120576 = ln1198601
+ 119899 ln120590 minus 119876
119877119879
ln 120576 = ln1198602
+ 120572119899120590 minus119876
119877119879
(5)
It can be easily derived that 119899 and 120572 can be obtained fromthe slope of the lines ln120590minus ln 120576 and 120590minus ln 120576 plots respectivelySubstituting measured flow stress of TA15 thermal deforma-tion at different temperatures given in Table 2 into (6) and (7)the experimental data and regression results of ln120590minus ln 120576 and120590 minus ln 120576 plots are shown in Figures 3 and 4
119899 =120597 ln 120576
120597 ln120590 (6)
120572119899 =120597 ln 120576
120597120590 (7)
Under different temperatures (1173ndash1273) K the meanvalue of all the slope rates is accepted as the inverse ofmaterial constants 119899 and 120572 The value of 119899 obtained by lineardependent coefficients is 459 Figures 5 and 6 show 120572119899obtained through the linear regression data is 001855 and thevalue of 120572 is 0004
Advances in Materials Science and Engineering 3
00 02 04 06 080
10
20
30
40
50
60Fl
ow st
ress
(MPa
)
True strain
1273K1223K
1203K1173K
0005 sminus1
00 02 04 06 080
10
20
30
40
50
60
70
80
90
100
Flow
stre
ss (M
Pa)
True strain
1273K1223K
1203K1173K
005 sminus1
00 02 04 06 080
50
100
150
Flow
stre
ss (M
Pa)
True strain
1273K1223K
1203K1173K
05 sminus1
00 02 04 06 080
50
100
150
200
Flow
stre
ss (M
Pa)
True strain
1273K1223K
1203K1173K
1 sminus1
Figure 2 The true stress-strain curves of TA15 titanium alloy at different strain rates
Table 2 Peak stress of TA15 stress-strain curves for differenttemperatures and strain rates
Strain rate(sminus1)
Deformation temperature (K)1173 1203 1223 1273
0005 55926 40186 26713 22019005 91980 66536 44411 3664405 148101 108832 73411 607491 16971 125647 85212 70622
322 Calculation of DRX Activation Energy 119876 Taking thenatural logarithms on both sides of (4) it can be rewrittenas follows
ln 120576 = ln119860 + 119899 ln [sinh (120572120590)] minus 119876
119877119879 (8)
Table 3 The value of ln[sinh(120572120590)] at different deformation condi-tions of TA15
Strain ratesminus1 TemperatureK1173 1203 1223 1273
0005 minus2428 minus2234 minus1824 minus1489005 minus1917 minus1723 minus1312 minus097705 minus1405 minus1211 minus08 minus04661 minus1251 minus1057 minus0646 minus0312
For a given strain rate the apparent activation energy 119876can be calculated as
119876 = 119877120597 ln 120576
120597 ln [sinh (120572120590)]
10038161003816100381610038161003816100381610038161003816119879
120597 ln [sinh (120572120590)]120597 (1119879)
10038161003816100381610038161003816100381610038161003816120576
= RNW (9)
The curves of ln[sinh(120572120590)] versus 1119879 are obtained fordifferent strain rates by using the data in Table 3 as shown
4 Advances in Materials Science and Engineering
32 36 40 44 48 52
0
1
ln(stressMPa)
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
Figure 3 The relationships between ln 120576 and ln120590
20 40 60 80 100 120 140
0
1
Stress (MPa)
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
Figure 4 The relationships between ln 120576 and 120590
in Figures 5 and 6119873 and119882 can be approximated by takingthe average slope of different strain rate It is found that theconstant of deformation activation energy in (120572 + 120573) two-phase region is 119876
119878
= 5887Kgmol and in 120573 region is 119876119863
=2258Kgmol
323 Construction of Constitutive Equation The equation offlow stress is given in (4) in which the undefined factors 119898120572 119860 119899 119876 can be obtained by using (6) (7) (8) and (9)respectively Also it is found that the peak flow stress modelin (120572 + 120573) two-phase region is
120576119878
= 669 times 1025[sinh (0004120590)]459 exp(minus588700119877119879
) (10)
00
0
1
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
minus25 minus20 minus15 minus10 minus05
ln[sin h(120572120590)]
Figure 5 The relationships between ln 120576 and ln[sinh(120572120590)]
078 079 080 081 082 083 084 085 086
00
minus25
minus20
minus15
minus10
minus05
0005 sminus1
005 sminus105 sminus11 sminus1
Tminus110minus4 (Kminus1)
120573-phase region 120572 + 120573 two-phase region
ln[s
in h(
120572120590
)]
Figure 6 The relationships between ln[sinh(120572120590)] and 1119879
and in 120573 region is
120576119863
= 513 times 1011[sinh (0004120590)]459 exp(minus225800119877119879
) (11)
Figure 7 displays the result of the relationships betweenln119885 and ln[sinh(120572120590)] It follows that the data were dividedinto two regions which express single-phase region and two-phase region And the coefficients obtained are presented inthis figure
33 DRX Kinetic Model
331 Critical Strain for Initiation of DRX Based on theprevious analysis the critical strain is necessary to activatetheDRXThe critical strains will change for differentmaterial
Advances in Materials Science and Engineering 5
0010
20
30
40
50
60
70
minus25minus20minus15minus10minus05
ln Z
ln[sin h(120572120590)]
ln ZD = 459ln[sin h(0004120590)] + 6486
ln ZS = 459ln[sin h(0004120590)] + 2421
Figure 7 The relationships between ln119885 and ln[sinh(120572120590)]
30 35 40 45 50
0
500
1000
1500
2000
2500
3000
3500
minus500
120579(M
Pa)
120590 (MPa)
120590c
120590p 120590s120590ss
1223K-005 sminus1
Figure 8 The relationship between hardening and flow stress ofTA15
and deformation conditionsThe relationship of critical strainand peak strain can be expressed as [17 18]
120576119888
= 119896120576119901
(12)
where 120576119888
is the critical strain 120576119901
is the peak strain and 119896 ismaterial constant It has been reported that 119896 ranges from065to 085 [19] for metal alloy
The critical conditions for the onset of DRX are attainedwhen the value of strain hardening rate 120579 = 119889120590119889120576 reachesthe minimum corresponding to an inflection of 120579 minus 120590 curve[20] Figure 8 shows the 120579 minus 120590 curve of TA15 titanium alloyat the temperature of 1223K and with the strain rate of005 sminus1 It can be generally divided into three segments Inthe first segment the hardening rate decreases rapidly dueto DRV with the increases of 120590 at the beginning of plasticdeformation The reason of this phenomenon is that DRVreduces the effect of dislocation density The second segmentbegins from the critical stress 120576
119888
to the peak stress 120576119901
Thesubgrain boundary formed with the continuous increase of
002 004 006 008 010 012002
004
006
008
010
Peak
stra
in
Critical strain
Figure 9 The relationships between 120576119901
and 120576119888
dislocation density in this segment which makes the work-hardening rate be still positive but decrease gradually In thethird segment the 120579 minus 120590 curve depicts the tendency of fallingsuddenly due to the occurrence of DRX effect and the valueof 120579 minus 120590 gradually reduces to less than zero and fluctuatesup and down and finally keeps a zero value which expressthat the continuous DRX occurred In this stage the value of120579 decreases to zero when the flow stress increases to 120576
119901
Thismethod can be used to determine the relationship between120576119888
and 120576119901
The critical stress can be read from the true stress-true strain curve after calculating the critical strain Figure 9shows the relation of 120576
119888
and 120576119901
with 119896 = 083 Consequentlythe critical strain model of TA15 titanium alloy is 120576
119888
= 083120576119901
332The PeakModel Strain of DRX It is of great importanceto determine DRX kinetics model due to realization of thesoftening mechanism in the hot working of alloys The peakstrain value is related to deformation temperature strain ratethe original grain size and deformation activation energyTherefore the peak strainmodel is represented as follows [17]
120576119901
= 1205721
11988911989910
1205761198981 exp ( 1198761119877119879
) (13)
where 1198761
is deformation activation energy 1198890
is the initialgrain size and 120572
1
1198991
1198981
are material constants Assume thatall of specimens are well heat treated and are with the samegrain size Hence the influence of the initial grain size on thecritical strain is neglectable [21] and (13) can be simplified as
120576119901
= 1205721
1205761198981 exp( 1198761119877119879
) (14)
Taking the logarithm on both sides of (14) it can berewritten as
ln 120576119901
= ln1205721
+ 1198981
ln 120576 +1198761
119877119879 (15)
From (14) the factor of 1198981
and Q1
can take the averageof the slopes of ln 120576 minus ln 120576
119901
(as shown in Figure 10) and 119879minus1 minus
6 Advances in Materials Science and Engineering
0ln(strain rate)
minus18
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
minus6 minus5 minus4 minus3 minus2 minus1 1
1273K1223K
1203K1173K
Figure 10 The relationships between ln 120576119901
and ln 120576
078 079 080 081 082 083 084 085 086
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
Tminus110minus4 (Kminus1)
0005 sminus1
005 sminus105 sminus1
1 sminus1
Figure 11 The relationships between ln 120576119901
and 119879minus1
ln 120576119901
(as shown in Figure 11) respectively We can get 1198981
=005281 Q
1
= 9875478 Jmol 1205721
is then obtained by using(13) 120572
1
= 4429 times 10minus6Consequently the peak strain model of TA15 titanium
alloy is as follows
120576119901
= 4429 times 10minus6 12057600528 exp(9875478119877119879
) (16)
333 Models for the Strain for 50 DRX and DRX VolumeFraction DRX is a process accompanied by nucleation andgrowth of grain and a time-dependent process determinedon the basis of the DRX kinetics equation The veracity ofDRX kinetics model is connected with the determinationof recrystallization fraction deformation parameters the
dynamic relationship of the process and the determinationof series of parameters of kinematic equation The relationsof DRX kinetics can be described by the JMAK equation asfollows [17]
119883drx = 1 minus exp[minus120573119889
(120576 minus 120576119888
12057605
)119896
119889
] (17)
12057605
= 1205722
11988911989920
1205761198982 exp(1198762RT
) (18)
where 119883drx is the DRX fraction 12057605
is the strain for 50DRX 119876
2
is DRX activation energy and 120573119889
119896119889
1205722
1198992
1198982
arematerial constants
It is difficult to determine the recrystallized frac-tion under different deformation conditions based on themicrostructures However it can be indirectly calculatedfrom the stress-strain curves by using the following equation[6 12]
119883drx =120590 minus 120590119901
120590119904
minus 120590119901
(19)
where 120590119901
is the peak stress 120590119904
is the steady-state stress and 120590119901
and 120590119904
can be calculated from true stress-true strain curvesThe DRX fractions of different conditions are calculated byusing (19) By substituting (19) into (17) it can be rewritten inlogarithm form
ln [minus ln (1 minus 119883drx)] = ln120573119889
+ 119896119889
ln(120576 minus 120576119888
12057605
) (20)
The stress of 50 DRX can be calculated by using (19)and then the 120576
119888
can be easily found in the true stress-straincurve By substituting 120576
05
Xdrx and 120576119888 into (20) it is obtainedthat 120573
119889
= 0693 and 119896119889
= 1502 The DRX fraction of TA15titanium alloy can be obtained as follows
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
] (21)
Taking natural logarithm of (18) we can get
ln 12057605
= ln1205722
+ 1198992
ln 1198890
+ 1198982
ln 120576 +1198762
119877119879 (22)
The materials constants can be calculated by using (22)1198982
= 0045 1198762
= 390635 Jmol 1205722
= 6295 times 10minus3 and1198992
= 0 for ignoring the effect of initial grain size Finally wecan get the strain of 50 DRX
12057605
= 6295 times 10minus3 1205760045 exp (390635119877119879
) (23)
Advances in Materials Science and Engineering 7
00 01 02 03 04 05 060
20
40
60
80
100
Strain
0005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
100
005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
10005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
1001 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
Figure 12 Predicted DRX volume fractions of TA15 at different conditions
Summarily the DRX kinetics equations of TA15 can berepresented as
120576119901
= 4429 times 10minus6 12057600528 exp(9785478119877119879
)
120576119888
= 083120576119901
12057605
= 6295 times 10minus3 1205760045 exp(390635119877119879
)
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
]
(24)
Based on the calculated results of this model the effectsof strain strain rate and deformation temperature on volumefraction of DRX are shown in Figure 12 It can be seen thatthe curves of volume fraction of DRX appeared as ldquoSrdquo shapeand this phenomenon indicates that the volume fraction ofDRX grows rapidly between the strain ranges of 01ndash045The volume fraction of DRX is also slightly affected by thetemperature This is because of the decreased mobility ofgrain boundaries in a low temperature and high strain rate
34Microstructure Observations Typical opticalmicrostruc-tures of TA15 alloy were examined and analyzed on thesection plane of specimen deformed to a strain of 06 Themicrostructures at different temperatures and strain rates areshown in Figure 13 The effects of deformation temperatureand strain rate on the microstructures can be seen clearlyfrom these opticalmicrographs FromFigures 13(a) and 13(b)it can be easily found that the small size grain will be obtainedat high strain rate for a given temperature It means thatthere is not enough time for the DRX to grow at high strainrate Conversely the grain size of DRX is large for the highertemperature as shown in Figures 13(a) and 13(c)
It can be found clearly that the percentage of 120573-phase ishigher in Figure 13(d) than that in Figure 13(d) It expressesthat there is a tendency of 120572 rarr 120573 phase transformationoccurring with the increase of temperatureThe close-packedhexagonal 120572-phase trends to transform into body-centeredcubic 120573-phase with the increase of temperature Becausebody-centered cubic120573-phase has the features of high stackingfault energy and a large number of slip systems the flow stressdecreases and becomes gently In the temperature range of1223Kndash1273K it can be found that the flow stresses are not so
8 Advances in Materials Science and Engineering
20120583m
(a)
20120583m
(b)
20120583m
(c)
20120583m
(d)
Figure 13 Optical microstructures of TA15 alloy deformed under different conditions (a)119879 = 1203K 120576 = 0005 s (b)119879 = 1203K 120576 = 005 sminus1(c) 119879 = 1223K 120576 = 005 sminus1 (d) 119879 = 1273K 120576 = 005 sminus1
sensitive to the temperature So the flow stress drops slightlyfor the increase of the temperature
4 Conclusions
Hot deformation behavior of TA15 titanium alloy is studiedat high temperatures under isothermal compression in thispaper Based on this research the following conclusions canbe drawn
(1) Through the regression analysis for conventionalhyperbolic sine equation the coefficient of plasticdeformation constitutive equation of TA15 titaniumalloy during high temperature is calculated in whichthe value of deformation activation energy in (120572 + 120573)two-phase region is 119876
119878
= 5887Kgmol and in 120573region is 119876
119863
= 2258Kgmol
(2) The constitutive equations and DRX kinetic modelare obtained by this investigation that can be used todescribe the flow behavior of TA15 titanium alloy inhot forming
(3) The optical microstructure observation of the TA15specimens deformed to a strain of 06 under differ-ent conditions verified the influence of deformationconditions on the evolution of DRX volume fraction
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research is supported by the National Natural ScienceFoundation of China (Grant no 51345013) and the Funda-mental Research Funds for the Central Universities (Grantno CDJZR12110002)
References
[1] Y Chen W-C Xu D-B Shan and B Guo ldquoMicrostructureevolution of TA15 titanium alloy during hot power spinningrdquoTransactions of Nonferrous Metals Society of China vol 21 no2 pp s323ndashs327 2011
[2] L Huang R Zeng X Zhang and J Li ldquoStudy on plasticdeformation behavior of hot splitting spinning of TA15 titaniumalloyrdquoMaterials amp Design vol 58 pp 465ndash474 2014
[3] S Zhu H Yang L G Guo and X G Fan ldquoEffect of cooling rateon microstructure evolution during 120572120573 heat treatment of TA15titanium alloyrdquo Materials Characterization vol 70 pp 101ndash1102012
[4] Q J Sun and G C Wang ldquoMicrostructure and superplasticityof TA15 alloyrdquoMaterials Science and Engineering A vol 606 pp401ndash408 2014
Advances in Materials Science and Engineering 9
[5] Y C Lin M-S Chen and J Zhong ldquoConstitutive modeling forelevated temperature flow behavior of 42CrMo steelrdquo Compu-tational Materials Science vol 42 no 3 pp 470ndash477 2008
[6] Y Xu LHua andY Sun ldquoDeformation behaviour and dynamicrecrystallization of AZ61 magnesium alloyrdquo Journal of Alloysand Compounds vol 580 pp 262ndash269 2013
[7] X N Peng H Z Guo Z F Shi C Qin Z L Zhao and ZYao ldquoStudy on the hot deformation behavior of TC4-DT alloywith equiaxed 120572+120573 starting structure based on processingmaprdquoMaterials Science and Engineering A vol 605 pp 80ndash88 2014
[8] P N Kalu and D R Waryoba ldquoA JMAK-microhardness modelfor quantifying the kinetics of restoration mechanisms in inho-mogeneous microstructurerdquoMaterials Science and EngineeringA vol 464 no 1-2 pp 68ndash75 2007
[9] J Liu Z Cui and L Ruan ldquoA new kinetics model of dynamicrecrystallization for magnesium alloy AZ31BrdquoMaterials Scienceand Engineering A vol 529 no 1 pp 300ndash310 2011
[10] J J Jonas X Quelennec L Jiang and E Martin ldquoThe Avramikinetics of dynamic recrystallizationrdquo Acta Materialia vol 57no 9 pp 2748ndash2756 2009
[11] J Xiao D S Li X Q Li and T S Deng ldquoConstitutive modelingand microstructure change of Ti-6Al-4V during the hot tensiledeformationrdquo Journal of Alloys and Compounds vol 541 pp346ndash352 2012
[12] W Peng W Zeng Q Wang and H Yu ldquoComparative study onconstitutive relationship of as-cast Ti60 titanium alloy duringhot deformation based on Arrhenius-type and artificial neuralnetwork modelsrdquoMaterials amp Design vol 51 pp 95ndash104 2013
[13] Z Sun S Guo and H Yang ldquoNucleation and growth mecha-nism of 120572-lamellae of Ti alloy TA15 cooling from an 120572 + 120573 phasefieldrdquo Acta Materialia vol 61 no 6 pp 2057ndash2064 2013
[14] S F Medina and C A Hernandez ldquoGeneral expression of theZener-Hollomon parameter as a function of the chemical com-position of low alloy and microalloyed steelsrdquo Acta Materialiavol 44 no 1 pp 137ndash148 1996
[15] YWang Y Liu G Y Yang et al ldquoHot deformation behaviors of120573 phase containing Ti-43Al-4Nb-14W-based alloyrdquo MaterialsScience and Engineering A vol 577 pp 210ndash217 2013
[16] C M Sellars and W J McTegart ldquoOn the mechanism of hotdeformationrdquo Acta Metallurgica vol 14 no 9 pp 1136ndash11381966
[17] C Zener and J H Hollomon ldquoEffect of strain rate upon plasticflow of steelrdquo Journal of Applied Physics vol 15 no 1 pp 22ndash321944
[18] M-S Chen Y C Lin and X-S Ma ldquoThe kinetics of dynamicrecrystallization of 42CrMo steelrdquo Materials Science and Engi-neering A vol 556 pp 260ndash266 2012
[19] Z Yang Y C Guo J P Li F He F Xia andM X Liang ldquoPlasticdeformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-05Zn-05Zr alloyrdquo Materials Science and EngineeringA vol 485 no 1-2 pp 487ndash491 2008
[20] A I Fernandez P Uranga B Lopez and JM Rodriguez-IbabeldquoDynamic recrystallization behavior covering a wide austenitegrain size range in Nb andNb-Timicroalloyed steelsrdquoMaterialsScience and Engineering A vol 361 no 1-2 pp 367ndash376 2003
[21] C M Sellars ldquoFrom trial and error to computer modellingof thermomechanical processingrdquo Ironmaking and Steelmakingvol 38 no 4 pp 250ndash257 2011
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Advances in Materials Science and Engineering 3
00 02 04 06 080
10
20
30
40
50
60Fl
ow st
ress
(MPa
)
True strain
1273K1223K
1203K1173K
0005 sminus1
00 02 04 06 080
10
20
30
40
50
60
70
80
90
100
Flow
stre
ss (M
Pa)
True strain
1273K1223K
1203K1173K
005 sminus1
00 02 04 06 080
50
100
150
Flow
stre
ss (M
Pa)
True strain
1273K1223K
1203K1173K
05 sminus1
00 02 04 06 080
50
100
150
200
Flow
stre
ss (M
Pa)
True strain
1273K1223K
1203K1173K
1 sminus1
Figure 2 The true stress-strain curves of TA15 titanium alloy at different strain rates
Table 2 Peak stress of TA15 stress-strain curves for differenttemperatures and strain rates
Strain rate(sminus1)
Deformation temperature (K)1173 1203 1223 1273
0005 55926 40186 26713 22019005 91980 66536 44411 3664405 148101 108832 73411 607491 16971 125647 85212 70622
322 Calculation of DRX Activation Energy 119876 Taking thenatural logarithms on both sides of (4) it can be rewrittenas follows
ln 120576 = ln119860 + 119899 ln [sinh (120572120590)] minus 119876
119877119879 (8)
Table 3 The value of ln[sinh(120572120590)] at different deformation condi-tions of TA15
Strain ratesminus1 TemperatureK1173 1203 1223 1273
0005 minus2428 minus2234 minus1824 minus1489005 minus1917 minus1723 minus1312 minus097705 minus1405 minus1211 minus08 minus04661 minus1251 minus1057 minus0646 minus0312
For a given strain rate the apparent activation energy 119876can be calculated as
119876 = 119877120597 ln 120576
120597 ln [sinh (120572120590)]
10038161003816100381610038161003816100381610038161003816119879
120597 ln [sinh (120572120590)]120597 (1119879)
10038161003816100381610038161003816100381610038161003816120576
= RNW (9)
The curves of ln[sinh(120572120590)] versus 1119879 are obtained fordifferent strain rates by using the data in Table 3 as shown
4 Advances in Materials Science and Engineering
32 36 40 44 48 52
0
1
ln(stressMPa)
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
Figure 3 The relationships between ln 120576 and ln120590
20 40 60 80 100 120 140
0
1
Stress (MPa)
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
Figure 4 The relationships between ln 120576 and 120590
in Figures 5 and 6119873 and119882 can be approximated by takingthe average slope of different strain rate It is found that theconstant of deformation activation energy in (120572 + 120573) two-phase region is 119876
119878
= 5887Kgmol and in 120573 region is 119876119863
=2258Kgmol
323 Construction of Constitutive Equation The equation offlow stress is given in (4) in which the undefined factors 119898120572 119860 119899 119876 can be obtained by using (6) (7) (8) and (9)respectively Also it is found that the peak flow stress modelin (120572 + 120573) two-phase region is
120576119878
= 669 times 1025[sinh (0004120590)]459 exp(minus588700119877119879
) (10)
00
0
1
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
minus25 minus20 minus15 minus10 minus05
ln[sin h(120572120590)]
Figure 5 The relationships between ln 120576 and ln[sinh(120572120590)]
078 079 080 081 082 083 084 085 086
00
minus25
minus20
minus15
minus10
minus05
0005 sminus1
005 sminus105 sminus11 sminus1
Tminus110minus4 (Kminus1)
120573-phase region 120572 + 120573 two-phase region
ln[s
in h(
120572120590
)]
Figure 6 The relationships between ln[sinh(120572120590)] and 1119879
and in 120573 region is
120576119863
= 513 times 1011[sinh (0004120590)]459 exp(minus225800119877119879
) (11)
Figure 7 displays the result of the relationships betweenln119885 and ln[sinh(120572120590)] It follows that the data were dividedinto two regions which express single-phase region and two-phase region And the coefficients obtained are presented inthis figure
33 DRX Kinetic Model
331 Critical Strain for Initiation of DRX Based on theprevious analysis the critical strain is necessary to activatetheDRXThe critical strains will change for differentmaterial
Advances in Materials Science and Engineering 5
0010
20
30
40
50
60
70
minus25minus20minus15minus10minus05
ln Z
ln[sin h(120572120590)]
ln ZD = 459ln[sin h(0004120590)] + 6486
ln ZS = 459ln[sin h(0004120590)] + 2421
Figure 7 The relationships between ln119885 and ln[sinh(120572120590)]
30 35 40 45 50
0
500
1000
1500
2000
2500
3000
3500
minus500
120579(M
Pa)
120590 (MPa)
120590c
120590p 120590s120590ss
1223K-005 sminus1
Figure 8 The relationship between hardening and flow stress ofTA15
and deformation conditionsThe relationship of critical strainand peak strain can be expressed as [17 18]
120576119888
= 119896120576119901
(12)
where 120576119888
is the critical strain 120576119901
is the peak strain and 119896 ismaterial constant It has been reported that 119896 ranges from065to 085 [19] for metal alloy
The critical conditions for the onset of DRX are attainedwhen the value of strain hardening rate 120579 = 119889120590119889120576 reachesthe minimum corresponding to an inflection of 120579 minus 120590 curve[20] Figure 8 shows the 120579 minus 120590 curve of TA15 titanium alloyat the temperature of 1223K and with the strain rate of005 sminus1 It can be generally divided into three segments Inthe first segment the hardening rate decreases rapidly dueto DRV with the increases of 120590 at the beginning of plasticdeformation The reason of this phenomenon is that DRVreduces the effect of dislocation density The second segmentbegins from the critical stress 120576
119888
to the peak stress 120576119901
Thesubgrain boundary formed with the continuous increase of
002 004 006 008 010 012002
004
006
008
010
Peak
stra
in
Critical strain
Figure 9 The relationships between 120576119901
and 120576119888
dislocation density in this segment which makes the work-hardening rate be still positive but decrease gradually In thethird segment the 120579 minus 120590 curve depicts the tendency of fallingsuddenly due to the occurrence of DRX effect and the valueof 120579 minus 120590 gradually reduces to less than zero and fluctuatesup and down and finally keeps a zero value which expressthat the continuous DRX occurred In this stage the value of120579 decreases to zero when the flow stress increases to 120576
119901
Thismethod can be used to determine the relationship between120576119888
and 120576119901
The critical stress can be read from the true stress-true strain curve after calculating the critical strain Figure 9shows the relation of 120576
119888
and 120576119901
with 119896 = 083 Consequentlythe critical strain model of TA15 titanium alloy is 120576
119888
= 083120576119901
332The PeakModel Strain of DRX It is of great importanceto determine DRX kinetics model due to realization of thesoftening mechanism in the hot working of alloys The peakstrain value is related to deformation temperature strain ratethe original grain size and deformation activation energyTherefore the peak strainmodel is represented as follows [17]
120576119901
= 1205721
11988911989910
1205761198981 exp ( 1198761119877119879
) (13)
where 1198761
is deformation activation energy 1198890
is the initialgrain size and 120572
1
1198991
1198981
are material constants Assume thatall of specimens are well heat treated and are with the samegrain size Hence the influence of the initial grain size on thecritical strain is neglectable [21] and (13) can be simplified as
120576119901
= 1205721
1205761198981 exp( 1198761119877119879
) (14)
Taking the logarithm on both sides of (14) it can berewritten as
ln 120576119901
= ln1205721
+ 1198981
ln 120576 +1198761
119877119879 (15)
From (14) the factor of 1198981
and Q1
can take the averageof the slopes of ln 120576 minus ln 120576
119901
(as shown in Figure 10) and 119879minus1 minus
6 Advances in Materials Science and Engineering
0ln(strain rate)
minus18
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
minus6 minus5 minus4 minus3 minus2 minus1 1
1273K1223K
1203K1173K
Figure 10 The relationships between ln 120576119901
and ln 120576
078 079 080 081 082 083 084 085 086
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
Tminus110minus4 (Kminus1)
0005 sminus1
005 sminus105 sminus1
1 sminus1
Figure 11 The relationships between ln 120576119901
and 119879minus1
ln 120576119901
(as shown in Figure 11) respectively We can get 1198981
=005281 Q
1
= 9875478 Jmol 1205721
is then obtained by using(13) 120572
1
= 4429 times 10minus6Consequently the peak strain model of TA15 titanium
alloy is as follows
120576119901
= 4429 times 10minus6 12057600528 exp(9875478119877119879
) (16)
333 Models for the Strain for 50 DRX and DRX VolumeFraction DRX is a process accompanied by nucleation andgrowth of grain and a time-dependent process determinedon the basis of the DRX kinetics equation The veracity ofDRX kinetics model is connected with the determinationof recrystallization fraction deformation parameters the
dynamic relationship of the process and the determinationof series of parameters of kinematic equation The relationsof DRX kinetics can be described by the JMAK equation asfollows [17]
119883drx = 1 minus exp[minus120573119889
(120576 minus 120576119888
12057605
)119896
119889
] (17)
12057605
= 1205722
11988911989920
1205761198982 exp(1198762RT
) (18)
where 119883drx is the DRX fraction 12057605
is the strain for 50DRX 119876
2
is DRX activation energy and 120573119889
119896119889
1205722
1198992
1198982
arematerial constants
It is difficult to determine the recrystallized frac-tion under different deformation conditions based on themicrostructures However it can be indirectly calculatedfrom the stress-strain curves by using the following equation[6 12]
119883drx =120590 minus 120590119901
120590119904
minus 120590119901
(19)
where 120590119901
is the peak stress 120590119904
is the steady-state stress and 120590119901
and 120590119904
can be calculated from true stress-true strain curvesThe DRX fractions of different conditions are calculated byusing (19) By substituting (19) into (17) it can be rewritten inlogarithm form
ln [minus ln (1 minus 119883drx)] = ln120573119889
+ 119896119889
ln(120576 minus 120576119888
12057605
) (20)
The stress of 50 DRX can be calculated by using (19)and then the 120576
119888
can be easily found in the true stress-straincurve By substituting 120576
05
Xdrx and 120576119888 into (20) it is obtainedthat 120573
119889
= 0693 and 119896119889
= 1502 The DRX fraction of TA15titanium alloy can be obtained as follows
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
] (21)
Taking natural logarithm of (18) we can get
ln 12057605
= ln1205722
+ 1198992
ln 1198890
+ 1198982
ln 120576 +1198762
119877119879 (22)
The materials constants can be calculated by using (22)1198982
= 0045 1198762
= 390635 Jmol 1205722
= 6295 times 10minus3 and1198992
= 0 for ignoring the effect of initial grain size Finally wecan get the strain of 50 DRX
12057605
= 6295 times 10minus3 1205760045 exp (390635119877119879
) (23)
Advances in Materials Science and Engineering 7
00 01 02 03 04 05 060
20
40
60
80
100
Strain
0005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
100
005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
10005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
1001 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
Figure 12 Predicted DRX volume fractions of TA15 at different conditions
Summarily the DRX kinetics equations of TA15 can berepresented as
120576119901
= 4429 times 10minus6 12057600528 exp(9785478119877119879
)
120576119888
= 083120576119901
12057605
= 6295 times 10minus3 1205760045 exp(390635119877119879
)
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
]
(24)
Based on the calculated results of this model the effectsof strain strain rate and deformation temperature on volumefraction of DRX are shown in Figure 12 It can be seen thatthe curves of volume fraction of DRX appeared as ldquoSrdquo shapeand this phenomenon indicates that the volume fraction ofDRX grows rapidly between the strain ranges of 01ndash045The volume fraction of DRX is also slightly affected by thetemperature This is because of the decreased mobility ofgrain boundaries in a low temperature and high strain rate
34Microstructure Observations Typical opticalmicrostruc-tures of TA15 alloy were examined and analyzed on thesection plane of specimen deformed to a strain of 06 Themicrostructures at different temperatures and strain rates areshown in Figure 13 The effects of deformation temperatureand strain rate on the microstructures can be seen clearlyfrom these opticalmicrographs FromFigures 13(a) and 13(b)it can be easily found that the small size grain will be obtainedat high strain rate for a given temperature It means thatthere is not enough time for the DRX to grow at high strainrate Conversely the grain size of DRX is large for the highertemperature as shown in Figures 13(a) and 13(c)
It can be found clearly that the percentage of 120573-phase ishigher in Figure 13(d) than that in Figure 13(d) It expressesthat there is a tendency of 120572 rarr 120573 phase transformationoccurring with the increase of temperatureThe close-packedhexagonal 120572-phase trends to transform into body-centeredcubic 120573-phase with the increase of temperature Becausebody-centered cubic120573-phase has the features of high stackingfault energy and a large number of slip systems the flow stressdecreases and becomes gently In the temperature range of1223Kndash1273K it can be found that the flow stresses are not so
8 Advances in Materials Science and Engineering
20120583m
(a)
20120583m
(b)
20120583m
(c)
20120583m
(d)
Figure 13 Optical microstructures of TA15 alloy deformed under different conditions (a)119879 = 1203K 120576 = 0005 s (b)119879 = 1203K 120576 = 005 sminus1(c) 119879 = 1223K 120576 = 005 sminus1 (d) 119879 = 1273K 120576 = 005 sminus1
sensitive to the temperature So the flow stress drops slightlyfor the increase of the temperature
4 Conclusions
Hot deformation behavior of TA15 titanium alloy is studiedat high temperatures under isothermal compression in thispaper Based on this research the following conclusions canbe drawn
(1) Through the regression analysis for conventionalhyperbolic sine equation the coefficient of plasticdeformation constitutive equation of TA15 titaniumalloy during high temperature is calculated in whichthe value of deformation activation energy in (120572 + 120573)two-phase region is 119876
119878
= 5887Kgmol and in 120573region is 119876
119863
= 2258Kgmol
(2) The constitutive equations and DRX kinetic modelare obtained by this investigation that can be used todescribe the flow behavior of TA15 titanium alloy inhot forming
(3) The optical microstructure observation of the TA15specimens deformed to a strain of 06 under differ-ent conditions verified the influence of deformationconditions on the evolution of DRX volume fraction
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research is supported by the National Natural ScienceFoundation of China (Grant no 51345013) and the Funda-mental Research Funds for the Central Universities (Grantno CDJZR12110002)
References
[1] Y Chen W-C Xu D-B Shan and B Guo ldquoMicrostructureevolution of TA15 titanium alloy during hot power spinningrdquoTransactions of Nonferrous Metals Society of China vol 21 no2 pp s323ndashs327 2011
[2] L Huang R Zeng X Zhang and J Li ldquoStudy on plasticdeformation behavior of hot splitting spinning of TA15 titaniumalloyrdquoMaterials amp Design vol 58 pp 465ndash474 2014
[3] S Zhu H Yang L G Guo and X G Fan ldquoEffect of cooling rateon microstructure evolution during 120572120573 heat treatment of TA15titanium alloyrdquo Materials Characterization vol 70 pp 101ndash1102012
[4] Q J Sun and G C Wang ldquoMicrostructure and superplasticityof TA15 alloyrdquoMaterials Science and Engineering A vol 606 pp401ndash408 2014
Advances in Materials Science and Engineering 9
[5] Y C Lin M-S Chen and J Zhong ldquoConstitutive modeling forelevated temperature flow behavior of 42CrMo steelrdquo Compu-tational Materials Science vol 42 no 3 pp 470ndash477 2008
[6] Y Xu LHua andY Sun ldquoDeformation behaviour and dynamicrecrystallization of AZ61 magnesium alloyrdquo Journal of Alloysand Compounds vol 580 pp 262ndash269 2013
[7] X N Peng H Z Guo Z F Shi C Qin Z L Zhao and ZYao ldquoStudy on the hot deformation behavior of TC4-DT alloywith equiaxed 120572+120573 starting structure based on processingmaprdquoMaterials Science and Engineering A vol 605 pp 80ndash88 2014
[8] P N Kalu and D R Waryoba ldquoA JMAK-microhardness modelfor quantifying the kinetics of restoration mechanisms in inho-mogeneous microstructurerdquoMaterials Science and EngineeringA vol 464 no 1-2 pp 68ndash75 2007
[9] J Liu Z Cui and L Ruan ldquoA new kinetics model of dynamicrecrystallization for magnesium alloy AZ31BrdquoMaterials Scienceand Engineering A vol 529 no 1 pp 300ndash310 2011
[10] J J Jonas X Quelennec L Jiang and E Martin ldquoThe Avramikinetics of dynamic recrystallizationrdquo Acta Materialia vol 57no 9 pp 2748ndash2756 2009
[11] J Xiao D S Li X Q Li and T S Deng ldquoConstitutive modelingand microstructure change of Ti-6Al-4V during the hot tensiledeformationrdquo Journal of Alloys and Compounds vol 541 pp346ndash352 2012
[12] W Peng W Zeng Q Wang and H Yu ldquoComparative study onconstitutive relationship of as-cast Ti60 titanium alloy duringhot deformation based on Arrhenius-type and artificial neuralnetwork modelsrdquoMaterials amp Design vol 51 pp 95ndash104 2013
[13] Z Sun S Guo and H Yang ldquoNucleation and growth mecha-nism of 120572-lamellae of Ti alloy TA15 cooling from an 120572 + 120573 phasefieldrdquo Acta Materialia vol 61 no 6 pp 2057ndash2064 2013
[14] S F Medina and C A Hernandez ldquoGeneral expression of theZener-Hollomon parameter as a function of the chemical com-position of low alloy and microalloyed steelsrdquo Acta Materialiavol 44 no 1 pp 137ndash148 1996
[15] YWang Y Liu G Y Yang et al ldquoHot deformation behaviors of120573 phase containing Ti-43Al-4Nb-14W-based alloyrdquo MaterialsScience and Engineering A vol 577 pp 210ndash217 2013
[16] C M Sellars and W J McTegart ldquoOn the mechanism of hotdeformationrdquo Acta Metallurgica vol 14 no 9 pp 1136ndash11381966
[17] C Zener and J H Hollomon ldquoEffect of strain rate upon plasticflow of steelrdquo Journal of Applied Physics vol 15 no 1 pp 22ndash321944
[18] M-S Chen Y C Lin and X-S Ma ldquoThe kinetics of dynamicrecrystallization of 42CrMo steelrdquo Materials Science and Engi-neering A vol 556 pp 260ndash266 2012
[19] Z Yang Y C Guo J P Li F He F Xia andM X Liang ldquoPlasticdeformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-05Zn-05Zr alloyrdquo Materials Science and EngineeringA vol 485 no 1-2 pp 487ndash491 2008
[20] A I Fernandez P Uranga B Lopez and JM Rodriguez-IbabeldquoDynamic recrystallization behavior covering a wide austenitegrain size range in Nb andNb-Timicroalloyed steelsrdquoMaterialsScience and Engineering A vol 361 no 1-2 pp 367ndash376 2003
[21] C M Sellars ldquoFrom trial and error to computer modellingof thermomechanical processingrdquo Ironmaking and Steelmakingvol 38 no 4 pp 250ndash257 2011
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
4 Advances in Materials Science and Engineering
32 36 40 44 48 52
0
1
ln(stressMPa)
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
Figure 3 The relationships between ln 120576 and ln120590
20 40 60 80 100 120 140
0
1
Stress (MPa)
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
Figure 4 The relationships between ln 120576 and 120590
in Figures 5 and 6119873 and119882 can be approximated by takingthe average slope of different strain rate It is found that theconstant of deformation activation energy in (120572 + 120573) two-phase region is 119876
119878
= 5887Kgmol and in 120573 region is 119876119863
=2258Kgmol
323 Construction of Constitutive Equation The equation offlow stress is given in (4) in which the undefined factors 119898120572 119860 119899 119876 can be obtained by using (6) (7) (8) and (9)respectively Also it is found that the peak flow stress modelin (120572 + 120573) two-phase region is
120576119878
= 669 times 1025[sinh (0004120590)]459 exp(minus588700119877119879
) (10)
00
0
1
minus6
minus5
minus4
minus3
minus2
minus1
ln(s
trai
n ra
tesminus1)
1273K1223K
1203K1173K
minus25 minus20 minus15 minus10 minus05
ln[sin h(120572120590)]
Figure 5 The relationships between ln 120576 and ln[sinh(120572120590)]
078 079 080 081 082 083 084 085 086
00
minus25
minus20
minus15
minus10
minus05
0005 sminus1
005 sminus105 sminus11 sminus1
Tminus110minus4 (Kminus1)
120573-phase region 120572 + 120573 two-phase region
ln[s
in h(
120572120590
)]
Figure 6 The relationships between ln[sinh(120572120590)] and 1119879
and in 120573 region is
120576119863
= 513 times 1011[sinh (0004120590)]459 exp(minus225800119877119879
) (11)
Figure 7 displays the result of the relationships betweenln119885 and ln[sinh(120572120590)] It follows that the data were dividedinto two regions which express single-phase region and two-phase region And the coefficients obtained are presented inthis figure
33 DRX Kinetic Model
331 Critical Strain for Initiation of DRX Based on theprevious analysis the critical strain is necessary to activatetheDRXThe critical strains will change for differentmaterial
Advances in Materials Science and Engineering 5
0010
20
30
40
50
60
70
minus25minus20minus15minus10minus05
ln Z
ln[sin h(120572120590)]
ln ZD = 459ln[sin h(0004120590)] + 6486
ln ZS = 459ln[sin h(0004120590)] + 2421
Figure 7 The relationships between ln119885 and ln[sinh(120572120590)]
30 35 40 45 50
0
500
1000
1500
2000
2500
3000
3500
minus500
120579(M
Pa)
120590 (MPa)
120590c
120590p 120590s120590ss
1223K-005 sminus1
Figure 8 The relationship between hardening and flow stress ofTA15
and deformation conditionsThe relationship of critical strainand peak strain can be expressed as [17 18]
120576119888
= 119896120576119901
(12)
where 120576119888
is the critical strain 120576119901
is the peak strain and 119896 ismaterial constant It has been reported that 119896 ranges from065to 085 [19] for metal alloy
The critical conditions for the onset of DRX are attainedwhen the value of strain hardening rate 120579 = 119889120590119889120576 reachesthe minimum corresponding to an inflection of 120579 minus 120590 curve[20] Figure 8 shows the 120579 minus 120590 curve of TA15 titanium alloyat the temperature of 1223K and with the strain rate of005 sminus1 It can be generally divided into three segments Inthe first segment the hardening rate decreases rapidly dueto DRV with the increases of 120590 at the beginning of plasticdeformation The reason of this phenomenon is that DRVreduces the effect of dislocation density The second segmentbegins from the critical stress 120576
119888
to the peak stress 120576119901
Thesubgrain boundary formed with the continuous increase of
002 004 006 008 010 012002
004
006
008
010
Peak
stra
in
Critical strain
Figure 9 The relationships between 120576119901
and 120576119888
dislocation density in this segment which makes the work-hardening rate be still positive but decrease gradually In thethird segment the 120579 minus 120590 curve depicts the tendency of fallingsuddenly due to the occurrence of DRX effect and the valueof 120579 minus 120590 gradually reduces to less than zero and fluctuatesup and down and finally keeps a zero value which expressthat the continuous DRX occurred In this stage the value of120579 decreases to zero when the flow stress increases to 120576
119901
Thismethod can be used to determine the relationship between120576119888
and 120576119901
The critical stress can be read from the true stress-true strain curve after calculating the critical strain Figure 9shows the relation of 120576
119888
and 120576119901
with 119896 = 083 Consequentlythe critical strain model of TA15 titanium alloy is 120576
119888
= 083120576119901
332The PeakModel Strain of DRX It is of great importanceto determine DRX kinetics model due to realization of thesoftening mechanism in the hot working of alloys The peakstrain value is related to deformation temperature strain ratethe original grain size and deformation activation energyTherefore the peak strainmodel is represented as follows [17]
120576119901
= 1205721
11988911989910
1205761198981 exp ( 1198761119877119879
) (13)
where 1198761
is deformation activation energy 1198890
is the initialgrain size and 120572
1
1198991
1198981
are material constants Assume thatall of specimens are well heat treated and are with the samegrain size Hence the influence of the initial grain size on thecritical strain is neglectable [21] and (13) can be simplified as
120576119901
= 1205721
1205761198981 exp( 1198761119877119879
) (14)
Taking the logarithm on both sides of (14) it can berewritten as
ln 120576119901
= ln1205721
+ 1198981
ln 120576 +1198761
119877119879 (15)
From (14) the factor of 1198981
and Q1
can take the averageof the slopes of ln 120576 minus ln 120576
119901
(as shown in Figure 10) and 119879minus1 minus
6 Advances in Materials Science and Engineering
0ln(strain rate)
minus18
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
minus6 minus5 minus4 minus3 minus2 minus1 1
1273K1223K
1203K1173K
Figure 10 The relationships between ln 120576119901
and ln 120576
078 079 080 081 082 083 084 085 086
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
Tminus110minus4 (Kminus1)
0005 sminus1
005 sminus105 sminus1
1 sminus1
Figure 11 The relationships between ln 120576119901
and 119879minus1
ln 120576119901
(as shown in Figure 11) respectively We can get 1198981
=005281 Q
1
= 9875478 Jmol 1205721
is then obtained by using(13) 120572
1
= 4429 times 10minus6Consequently the peak strain model of TA15 titanium
alloy is as follows
120576119901
= 4429 times 10minus6 12057600528 exp(9875478119877119879
) (16)
333 Models for the Strain for 50 DRX and DRX VolumeFraction DRX is a process accompanied by nucleation andgrowth of grain and a time-dependent process determinedon the basis of the DRX kinetics equation The veracity ofDRX kinetics model is connected with the determinationof recrystallization fraction deformation parameters the
dynamic relationship of the process and the determinationof series of parameters of kinematic equation The relationsof DRX kinetics can be described by the JMAK equation asfollows [17]
119883drx = 1 minus exp[minus120573119889
(120576 minus 120576119888
12057605
)119896
119889
] (17)
12057605
= 1205722
11988911989920
1205761198982 exp(1198762RT
) (18)
where 119883drx is the DRX fraction 12057605
is the strain for 50DRX 119876
2
is DRX activation energy and 120573119889
119896119889
1205722
1198992
1198982
arematerial constants
It is difficult to determine the recrystallized frac-tion under different deformation conditions based on themicrostructures However it can be indirectly calculatedfrom the stress-strain curves by using the following equation[6 12]
119883drx =120590 minus 120590119901
120590119904
minus 120590119901
(19)
where 120590119901
is the peak stress 120590119904
is the steady-state stress and 120590119901
and 120590119904
can be calculated from true stress-true strain curvesThe DRX fractions of different conditions are calculated byusing (19) By substituting (19) into (17) it can be rewritten inlogarithm form
ln [minus ln (1 minus 119883drx)] = ln120573119889
+ 119896119889
ln(120576 minus 120576119888
12057605
) (20)
The stress of 50 DRX can be calculated by using (19)and then the 120576
119888
can be easily found in the true stress-straincurve By substituting 120576
05
Xdrx and 120576119888 into (20) it is obtainedthat 120573
119889
= 0693 and 119896119889
= 1502 The DRX fraction of TA15titanium alloy can be obtained as follows
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
] (21)
Taking natural logarithm of (18) we can get
ln 12057605
= ln1205722
+ 1198992
ln 1198890
+ 1198982
ln 120576 +1198762
119877119879 (22)
The materials constants can be calculated by using (22)1198982
= 0045 1198762
= 390635 Jmol 1205722
= 6295 times 10minus3 and1198992
= 0 for ignoring the effect of initial grain size Finally wecan get the strain of 50 DRX
12057605
= 6295 times 10minus3 1205760045 exp (390635119877119879
) (23)
Advances in Materials Science and Engineering 7
00 01 02 03 04 05 060
20
40
60
80
100
Strain
0005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
100
005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
10005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
1001 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
Figure 12 Predicted DRX volume fractions of TA15 at different conditions
Summarily the DRX kinetics equations of TA15 can berepresented as
120576119901
= 4429 times 10minus6 12057600528 exp(9785478119877119879
)
120576119888
= 083120576119901
12057605
= 6295 times 10minus3 1205760045 exp(390635119877119879
)
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
]
(24)
Based on the calculated results of this model the effectsof strain strain rate and deformation temperature on volumefraction of DRX are shown in Figure 12 It can be seen thatthe curves of volume fraction of DRX appeared as ldquoSrdquo shapeand this phenomenon indicates that the volume fraction ofDRX grows rapidly between the strain ranges of 01ndash045The volume fraction of DRX is also slightly affected by thetemperature This is because of the decreased mobility ofgrain boundaries in a low temperature and high strain rate
34Microstructure Observations Typical opticalmicrostruc-tures of TA15 alloy were examined and analyzed on thesection plane of specimen deformed to a strain of 06 Themicrostructures at different temperatures and strain rates areshown in Figure 13 The effects of deformation temperatureand strain rate on the microstructures can be seen clearlyfrom these opticalmicrographs FromFigures 13(a) and 13(b)it can be easily found that the small size grain will be obtainedat high strain rate for a given temperature It means thatthere is not enough time for the DRX to grow at high strainrate Conversely the grain size of DRX is large for the highertemperature as shown in Figures 13(a) and 13(c)
It can be found clearly that the percentage of 120573-phase ishigher in Figure 13(d) than that in Figure 13(d) It expressesthat there is a tendency of 120572 rarr 120573 phase transformationoccurring with the increase of temperatureThe close-packedhexagonal 120572-phase trends to transform into body-centeredcubic 120573-phase with the increase of temperature Becausebody-centered cubic120573-phase has the features of high stackingfault energy and a large number of slip systems the flow stressdecreases and becomes gently In the temperature range of1223Kndash1273K it can be found that the flow stresses are not so
8 Advances in Materials Science and Engineering
20120583m
(a)
20120583m
(b)
20120583m
(c)
20120583m
(d)
Figure 13 Optical microstructures of TA15 alloy deformed under different conditions (a)119879 = 1203K 120576 = 0005 s (b)119879 = 1203K 120576 = 005 sminus1(c) 119879 = 1223K 120576 = 005 sminus1 (d) 119879 = 1273K 120576 = 005 sminus1
sensitive to the temperature So the flow stress drops slightlyfor the increase of the temperature
4 Conclusions
Hot deformation behavior of TA15 titanium alloy is studiedat high temperatures under isothermal compression in thispaper Based on this research the following conclusions canbe drawn
(1) Through the regression analysis for conventionalhyperbolic sine equation the coefficient of plasticdeformation constitutive equation of TA15 titaniumalloy during high temperature is calculated in whichthe value of deformation activation energy in (120572 + 120573)two-phase region is 119876
119878
= 5887Kgmol and in 120573region is 119876
119863
= 2258Kgmol
(2) The constitutive equations and DRX kinetic modelare obtained by this investigation that can be used todescribe the flow behavior of TA15 titanium alloy inhot forming
(3) The optical microstructure observation of the TA15specimens deformed to a strain of 06 under differ-ent conditions verified the influence of deformationconditions on the evolution of DRX volume fraction
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research is supported by the National Natural ScienceFoundation of China (Grant no 51345013) and the Funda-mental Research Funds for the Central Universities (Grantno CDJZR12110002)
References
[1] Y Chen W-C Xu D-B Shan and B Guo ldquoMicrostructureevolution of TA15 titanium alloy during hot power spinningrdquoTransactions of Nonferrous Metals Society of China vol 21 no2 pp s323ndashs327 2011
[2] L Huang R Zeng X Zhang and J Li ldquoStudy on plasticdeformation behavior of hot splitting spinning of TA15 titaniumalloyrdquoMaterials amp Design vol 58 pp 465ndash474 2014
[3] S Zhu H Yang L G Guo and X G Fan ldquoEffect of cooling rateon microstructure evolution during 120572120573 heat treatment of TA15titanium alloyrdquo Materials Characterization vol 70 pp 101ndash1102012
[4] Q J Sun and G C Wang ldquoMicrostructure and superplasticityof TA15 alloyrdquoMaterials Science and Engineering A vol 606 pp401ndash408 2014
Advances in Materials Science and Engineering 9
[5] Y C Lin M-S Chen and J Zhong ldquoConstitutive modeling forelevated temperature flow behavior of 42CrMo steelrdquo Compu-tational Materials Science vol 42 no 3 pp 470ndash477 2008
[6] Y Xu LHua andY Sun ldquoDeformation behaviour and dynamicrecrystallization of AZ61 magnesium alloyrdquo Journal of Alloysand Compounds vol 580 pp 262ndash269 2013
[7] X N Peng H Z Guo Z F Shi C Qin Z L Zhao and ZYao ldquoStudy on the hot deformation behavior of TC4-DT alloywith equiaxed 120572+120573 starting structure based on processingmaprdquoMaterials Science and Engineering A vol 605 pp 80ndash88 2014
[8] P N Kalu and D R Waryoba ldquoA JMAK-microhardness modelfor quantifying the kinetics of restoration mechanisms in inho-mogeneous microstructurerdquoMaterials Science and EngineeringA vol 464 no 1-2 pp 68ndash75 2007
[9] J Liu Z Cui and L Ruan ldquoA new kinetics model of dynamicrecrystallization for magnesium alloy AZ31BrdquoMaterials Scienceand Engineering A vol 529 no 1 pp 300ndash310 2011
[10] J J Jonas X Quelennec L Jiang and E Martin ldquoThe Avramikinetics of dynamic recrystallizationrdquo Acta Materialia vol 57no 9 pp 2748ndash2756 2009
[11] J Xiao D S Li X Q Li and T S Deng ldquoConstitutive modelingand microstructure change of Ti-6Al-4V during the hot tensiledeformationrdquo Journal of Alloys and Compounds vol 541 pp346ndash352 2012
[12] W Peng W Zeng Q Wang and H Yu ldquoComparative study onconstitutive relationship of as-cast Ti60 titanium alloy duringhot deformation based on Arrhenius-type and artificial neuralnetwork modelsrdquoMaterials amp Design vol 51 pp 95ndash104 2013
[13] Z Sun S Guo and H Yang ldquoNucleation and growth mecha-nism of 120572-lamellae of Ti alloy TA15 cooling from an 120572 + 120573 phasefieldrdquo Acta Materialia vol 61 no 6 pp 2057ndash2064 2013
[14] S F Medina and C A Hernandez ldquoGeneral expression of theZener-Hollomon parameter as a function of the chemical com-position of low alloy and microalloyed steelsrdquo Acta Materialiavol 44 no 1 pp 137ndash148 1996
[15] YWang Y Liu G Y Yang et al ldquoHot deformation behaviors of120573 phase containing Ti-43Al-4Nb-14W-based alloyrdquo MaterialsScience and Engineering A vol 577 pp 210ndash217 2013
[16] C M Sellars and W J McTegart ldquoOn the mechanism of hotdeformationrdquo Acta Metallurgica vol 14 no 9 pp 1136ndash11381966
[17] C Zener and J H Hollomon ldquoEffect of strain rate upon plasticflow of steelrdquo Journal of Applied Physics vol 15 no 1 pp 22ndash321944
[18] M-S Chen Y C Lin and X-S Ma ldquoThe kinetics of dynamicrecrystallization of 42CrMo steelrdquo Materials Science and Engi-neering A vol 556 pp 260ndash266 2012
[19] Z Yang Y C Guo J P Li F He F Xia andM X Liang ldquoPlasticdeformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-05Zn-05Zr alloyrdquo Materials Science and EngineeringA vol 485 no 1-2 pp 487ndash491 2008
[20] A I Fernandez P Uranga B Lopez and JM Rodriguez-IbabeldquoDynamic recrystallization behavior covering a wide austenitegrain size range in Nb andNb-Timicroalloyed steelsrdquoMaterialsScience and Engineering A vol 361 no 1-2 pp 367ndash376 2003
[21] C M Sellars ldquoFrom trial and error to computer modellingof thermomechanical processingrdquo Ironmaking and Steelmakingvol 38 no 4 pp 250ndash257 2011
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Advances in Materials Science and Engineering 5
0010
20
30
40
50
60
70
minus25minus20minus15minus10minus05
ln Z
ln[sin h(120572120590)]
ln ZD = 459ln[sin h(0004120590)] + 6486
ln ZS = 459ln[sin h(0004120590)] + 2421
Figure 7 The relationships between ln119885 and ln[sinh(120572120590)]
30 35 40 45 50
0
500
1000
1500
2000
2500
3000
3500
minus500
120579(M
Pa)
120590 (MPa)
120590c
120590p 120590s120590ss
1223K-005 sminus1
Figure 8 The relationship between hardening and flow stress ofTA15
and deformation conditionsThe relationship of critical strainand peak strain can be expressed as [17 18]
120576119888
= 119896120576119901
(12)
where 120576119888
is the critical strain 120576119901
is the peak strain and 119896 ismaterial constant It has been reported that 119896 ranges from065to 085 [19] for metal alloy
The critical conditions for the onset of DRX are attainedwhen the value of strain hardening rate 120579 = 119889120590119889120576 reachesthe minimum corresponding to an inflection of 120579 minus 120590 curve[20] Figure 8 shows the 120579 minus 120590 curve of TA15 titanium alloyat the temperature of 1223K and with the strain rate of005 sminus1 It can be generally divided into three segments Inthe first segment the hardening rate decreases rapidly dueto DRV with the increases of 120590 at the beginning of plasticdeformation The reason of this phenomenon is that DRVreduces the effect of dislocation density The second segmentbegins from the critical stress 120576
119888
to the peak stress 120576119901
Thesubgrain boundary formed with the continuous increase of
002 004 006 008 010 012002
004
006
008
010
Peak
stra
in
Critical strain
Figure 9 The relationships between 120576119901
and 120576119888
dislocation density in this segment which makes the work-hardening rate be still positive but decrease gradually In thethird segment the 120579 minus 120590 curve depicts the tendency of fallingsuddenly due to the occurrence of DRX effect and the valueof 120579 minus 120590 gradually reduces to less than zero and fluctuatesup and down and finally keeps a zero value which expressthat the continuous DRX occurred In this stage the value of120579 decreases to zero when the flow stress increases to 120576
119901
Thismethod can be used to determine the relationship between120576119888
and 120576119901
The critical stress can be read from the true stress-true strain curve after calculating the critical strain Figure 9shows the relation of 120576
119888
and 120576119901
with 119896 = 083 Consequentlythe critical strain model of TA15 titanium alloy is 120576
119888
= 083120576119901
332The PeakModel Strain of DRX It is of great importanceto determine DRX kinetics model due to realization of thesoftening mechanism in the hot working of alloys The peakstrain value is related to deformation temperature strain ratethe original grain size and deformation activation energyTherefore the peak strainmodel is represented as follows [17]
120576119901
= 1205721
11988911989910
1205761198981 exp ( 1198761119877119879
) (13)
where 1198761
is deformation activation energy 1198890
is the initialgrain size and 120572
1
1198991
1198981
are material constants Assume thatall of specimens are well heat treated and are with the samegrain size Hence the influence of the initial grain size on thecritical strain is neglectable [21] and (13) can be simplified as
120576119901
= 1205721
1205761198981 exp( 1198761119877119879
) (14)
Taking the logarithm on both sides of (14) it can berewritten as
ln 120576119901
= ln1205721
+ 1198981
ln 120576 +1198761
119877119879 (15)
From (14) the factor of 1198981
and Q1
can take the averageof the slopes of ln 120576 minus ln 120576
119901
(as shown in Figure 10) and 119879minus1 minus
6 Advances in Materials Science and Engineering
0ln(strain rate)
minus18
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
minus6 minus5 minus4 minus3 minus2 minus1 1
1273K1223K
1203K1173K
Figure 10 The relationships between ln 120576119901
and ln 120576
078 079 080 081 082 083 084 085 086
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
Tminus110minus4 (Kminus1)
0005 sminus1
005 sminus105 sminus1
1 sminus1
Figure 11 The relationships between ln 120576119901
and 119879minus1
ln 120576119901
(as shown in Figure 11) respectively We can get 1198981
=005281 Q
1
= 9875478 Jmol 1205721
is then obtained by using(13) 120572
1
= 4429 times 10minus6Consequently the peak strain model of TA15 titanium
alloy is as follows
120576119901
= 4429 times 10minus6 12057600528 exp(9875478119877119879
) (16)
333 Models for the Strain for 50 DRX and DRX VolumeFraction DRX is a process accompanied by nucleation andgrowth of grain and a time-dependent process determinedon the basis of the DRX kinetics equation The veracity ofDRX kinetics model is connected with the determinationof recrystallization fraction deformation parameters the
dynamic relationship of the process and the determinationof series of parameters of kinematic equation The relationsof DRX kinetics can be described by the JMAK equation asfollows [17]
119883drx = 1 minus exp[minus120573119889
(120576 minus 120576119888
12057605
)119896
119889
] (17)
12057605
= 1205722
11988911989920
1205761198982 exp(1198762RT
) (18)
where 119883drx is the DRX fraction 12057605
is the strain for 50DRX 119876
2
is DRX activation energy and 120573119889
119896119889
1205722
1198992
1198982
arematerial constants
It is difficult to determine the recrystallized frac-tion under different deformation conditions based on themicrostructures However it can be indirectly calculatedfrom the stress-strain curves by using the following equation[6 12]
119883drx =120590 minus 120590119901
120590119904
minus 120590119901
(19)
where 120590119901
is the peak stress 120590119904
is the steady-state stress and 120590119901
and 120590119904
can be calculated from true stress-true strain curvesThe DRX fractions of different conditions are calculated byusing (19) By substituting (19) into (17) it can be rewritten inlogarithm form
ln [minus ln (1 minus 119883drx)] = ln120573119889
+ 119896119889
ln(120576 minus 120576119888
12057605
) (20)
The stress of 50 DRX can be calculated by using (19)and then the 120576
119888
can be easily found in the true stress-straincurve By substituting 120576
05
Xdrx and 120576119888 into (20) it is obtainedthat 120573
119889
= 0693 and 119896119889
= 1502 The DRX fraction of TA15titanium alloy can be obtained as follows
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
] (21)
Taking natural logarithm of (18) we can get
ln 12057605
= ln1205722
+ 1198992
ln 1198890
+ 1198982
ln 120576 +1198762
119877119879 (22)
The materials constants can be calculated by using (22)1198982
= 0045 1198762
= 390635 Jmol 1205722
= 6295 times 10minus3 and1198992
= 0 for ignoring the effect of initial grain size Finally wecan get the strain of 50 DRX
12057605
= 6295 times 10minus3 1205760045 exp (390635119877119879
) (23)
Advances in Materials Science and Engineering 7
00 01 02 03 04 05 060
20
40
60
80
100
Strain
0005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
100
005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
10005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
1001 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
Figure 12 Predicted DRX volume fractions of TA15 at different conditions
Summarily the DRX kinetics equations of TA15 can berepresented as
120576119901
= 4429 times 10minus6 12057600528 exp(9785478119877119879
)
120576119888
= 083120576119901
12057605
= 6295 times 10minus3 1205760045 exp(390635119877119879
)
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
]
(24)
Based on the calculated results of this model the effectsof strain strain rate and deformation temperature on volumefraction of DRX are shown in Figure 12 It can be seen thatthe curves of volume fraction of DRX appeared as ldquoSrdquo shapeand this phenomenon indicates that the volume fraction ofDRX grows rapidly between the strain ranges of 01ndash045The volume fraction of DRX is also slightly affected by thetemperature This is because of the decreased mobility ofgrain boundaries in a low temperature and high strain rate
34Microstructure Observations Typical opticalmicrostruc-tures of TA15 alloy were examined and analyzed on thesection plane of specimen deformed to a strain of 06 Themicrostructures at different temperatures and strain rates areshown in Figure 13 The effects of deformation temperatureand strain rate on the microstructures can be seen clearlyfrom these opticalmicrographs FromFigures 13(a) and 13(b)it can be easily found that the small size grain will be obtainedat high strain rate for a given temperature It means thatthere is not enough time for the DRX to grow at high strainrate Conversely the grain size of DRX is large for the highertemperature as shown in Figures 13(a) and 13(c)
It can be found clearly that the percentage of 120573-phase ishigher in Figure 13(d) than that in Figure 13(d) It expressesthat there is a tendency of 120572 rarr 120573 phase transformationoccurring with the increase of temperatureThe close-packedhexagonal 120572-phase trends to transform into body-centeredcubic 120573-phase with the increase of temperature Becausebody-centered cubic120573-phase has the features of high stackingfault energy and a large number of slip systems the flow stressdecreases and becomes gently In the temperature range of1223Kndash1273K it can be found that the flow stresses are not so
8 Advances in Materials Science and Engineering
20120583m
(a)
20120583m
(b)
20120583m
(c)
20120583m
(d)
Figure 13 Optical microstructures of TA15 alloy deformed under different conditions (a)119879 = 1203K 120576 = 0005 s (b)119879 = 1203K 120576 = 005 sminus1(c) 119879 = 1223K 120576 = 005 sminus1 (d) 119879 = 1273K 120576 = 005 sminus1
sensitive to the temperature So the flow stress drops slightlyfor the increase of the temperature
4 Conclusions
Hot deformation behavior of TA15 titanium alloy is studiedat high temperatures under isothermal compression in thispaper Based on this research the following conclusions canbe drawn
(1) Through the regression analysis for conventionalhyperbolic sine equation the coefficient of plasticdeformation constitutive equation of TA15 titaniumalloy during high temperature is calculated in whichthe value of deformation activation energy in (120572 + 120573)two-phase region is 119876
119878
= 5887Kgmol and in 120573region is 119876
119863
= 2258Kgmol
(2) The constitutive equations and DRX kinetic modelare obtained by this investigation that can be used todescribe the flow behavior of TA15 titanium alloy inhot forming
(3) The optical microstructure observation of the TA15specimens deformed to a strain of 06 under differ-ent conditions verified the influence of deformationconditions on the evolution of DRX volume fraction
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research is supported by the National Natural ScienceFoundation of China (Grant no 51345013) and the Funda-mental Research Funds for the Central Universities (Grantno CDJZR12110002)
References
[1] Y Chen W-C Xu D-B Shan and B Guo ldquoMicrostructureevolution of TA15 titanium alloy during hot power spinningrdquoTransactions of Nonferrous Metals Society of China vol 21 no2 pp s323ndashs327 2011
[2] L Huang R Zeng X Zhang and J Li ldquoStudy on plasticdeformation behavior of hot splitting spinning of TA15 titaniumalloyrdquoMaterials amp Design vol 58 pp 465ndash474 2014
[3] S Zhu H Yang L G Guo and X G Fan ldquoEffect of cooling rateon microstructure evolution during 120572120573 heat treatment of TA15titanium alloyrdquo Materials Characterization vol 70 pp 101ndash1102012
[4] Q J Sun and G C Wang ldquoMicrostructure and superplasticityof TA15 alloyrdquoMaterials Science and Engineering A vol 606 pp401ndash408 2014
Advances in Materials Science and Engineering 9
[5] Y C Lin M-S Chen and J Zhong ldquoConstitutive modeling forelevated temperature flow behavior of 42CrMo steelrdquo Compu-tational Materials Science vol 42 no 3 pp 470ndash477 2008
[6] Y Xu LHua andY Sun ldquoDeformation behaviour and dynamicrecrystallization of AZ61 magnesium alloyrdquo Journal of Alloysand Compounds vol 580 pp 262ndash269 2013
[7] X N Peng H Z Guo Z F Shi C Qin Z L Zhao and ZYao ldquoStudy on the hot deformation behavior of TC4-DT alloywith equiaxed 120572+120573 starting structure based on processingmaprdquoMaterials Science and Engineering A vol 605 pp 80ndash88 2014
[8] P N Kalu and D R Waryoba ldquoA JMAK-microhardness modelfor quantifying the kinetics of restoration mechanisms in inho-mogeneous microstructurerdquoMaterials Science and EngineeringA vol 464 no 1-2 pp 68ndash75 2007
[9] J Liu Z Cui and L Ruan ldquoA new kinetics model of dynamicrecrystallization for magnesium alloy AZ31BrdquoMaterials Scienceand Engineering A vol 529 no 1 pp 300ndash310 2011
[10] J J Jonas X Quelennec L Jiang and E Martin ldquoThe Avramikinetics of dynamic recrystallizationrdquo Acta Materialia vol 57no 9 pp 2748ndash2756 2009
[11] J Xiao D S Li X Q Li and T S Deng ldquoConstitutive modelingand microstructure change of Ti-6Al-4V during the hot tensiledeformationrdquo Journal of Alloys and Compounds vol 541 pp346ndash352 2012
[12] W Peng W Zeng Q Wang and H Yu ldquoComparative study onconstitutive relationship of as-cast Ti60 titanium alloy duringhot deformation based on Arrhenius-type and artificial neuralnetwork modelsrdquoMaterials amp Design vol 51 pp 95ndash104 2013
[13] Z Sun S Guo and H Yang ldquoNucleation and growth mecha-nism of 120572-lamellae of Ti alloy TA15 cooling from an 120572 + 120573 phasefieldrdquo Acta Materialia vol 61 no 6 pp 2057ndash2064 2013
[14] S F Medina and C A Hernandez ldquoGeneral expression of theZener-Hollomon parameter as a function of the chemical com-position of low alloy and microalloyed steelsrdquo Acta Materialiavol 44 no 1 pp 137ndash148 1996
[15] YWang Y Liu G Y Yang et al ldquoHot deformation behaviors of120573 phase containing Ti-43Al-4Nb-14W-based alloyrdquo MaterialsScience and Engineering A vol 577 pp 210ndash217 2013
[16] C M Sellars and W J McTegart ldquoOn the mechanism of hotdeformationrdquo Acta Metallurgica vol 14 no 9 pp 1136ndash11381966
[17] C Zener and J H Hollomon ldquoEffect of strain rate upon plasticflow of steelrdquo Journal of Applied Physics vol 15 no 1 pp 22ndash321944
[18] M-S Chen Y C Lin and X-S Ma ldquoThe kinetics of dynamicrecrystallization of 42CrMo steelrdquo Materials Science and Engi-neering A vol 556 pp 260ndash266 2012
[19] Z Yang Y C Guo J P Li F He F Xia andM X Liang ldquoPlasticdeformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-05Zn-05Zr alloyrdquo Materials Science and EngineeringA vol 485 no 1-2 pp 487ndash491 2008
[20] A I Fernandez P Uranga B Lopez and JM Rodriguez-IbabeldquoDynamic recrystallization behavior covering a wide austenitegrain size range in Nb andNb-Timicroalloyed steelsrdquoMaterialsScience and Engineering A vol 361 no 1-2 pp 367ndash376 2003
[21] C M Sellars ldquoFrom trial and error to computer modellingof thermomechanical processingrdquo Ironmaking and Steelmakingvol 38 no 4 pp 250ndash257 2011
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
6 Advances in Materials Science and Engineering
0ln(strain rate)
minus18
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
minus6 minus5 minus4 minus3 minus2 minus1 1
1273K1223K
1203K1173K
Figure 10 The relationships between ln 120576119901
and ln 120576
078 079 080 081 082 083 084 085 086
minus20
minus22
minus24
minus26
minus28
minus30
minus32
minus34
ln 120576 p
Tminus110minus4 (Kminus1)
0005 sminus1
005 sminus105 sminus1
1 sminus1
Figure 11 The relationships between ln 120576119901
and 119879minus1
ln 120576119901
(as shown in Figure 11) respectively We can get 1198981
=005281 Q
1
= 9875478 Jmol 1205721
is then obtained by using(13) 120572
1
= 4429 times 10minus6Consequently the peak strain model of TA15 titanium
alloy is as follows
120576119901
= 4429 times 10minus6 12057600528 exp(9875478119877119879
) (16)
333 Models for the Strain for 50 DRX and DRX VolumeFraction DRX is a process accompanied by nucleation andgrowth of grain and a time-dependent process determinedon the basis of the DRX kinetics equation The veracity ofDRX kinetics model is connected with the determinationof recrystallization fraction deformation parameters the
dynamic relationship of the process and the determinationof series of parameters of kinematic equation The relationsof DRX kinetics can be described by the JMAK equation asfollows [17]
119883drx = 1 minus exp[minus120573119889
(120576 minus 120576119888
12057605
)119896
119889
] (17)
12057605
= 1205722
11988911989920
1205761198982 exp(1198762RT
) (18)
where 119883drx is the DRX fraction 12057605
is the strain for 50DRX 119876
2
is DRX activation energy and 120573119889
119896119889
1205722
1198992
1198982
arematerial constants
It is difficult to determine the recrystallized frac-tion under different deformation conditions based on themicrostructures However it can be indirectly calculatedfrom the stress-strain curves by using the following equation[6 12]
119883drx =120590 minus 120590119901
120590119904
minus 120590119901
(19)
where 120590119901
is the peak stress 120590119904
is the steady-state stress and 120590119901
and 120590119904
can be calculated from true stress-true strain curvesThe DRX fractions of different conditions are calculated byusing (19) By substituting (19) into (17) it can be rewritten inlogarithm form
ln [minus ln (1 minus 119883drx)] = ln120573119889
+ 119896119889
ln(120576 minus 120576119888
12057605
) (20)
The stress of 50 DRX can be calculated by using (19)and then the 120576
119888
can be easily found in the true stress-straincurve By substituting 120576
05
Xdrx and 120576119888 into (20) it is obtainedthat 120573
119889
= 0693 and 119896119889
= 1502 The DRX fraction of TA15titanium alloy can be obtained as follows
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
] (21)
Taking natural logarithm of (18) we can get
ln 12057605
= ln1205722
+ 1198992
ln 1198890
+ 1198982
ln 120576 +1198762
119877119879 (22)
The materials constants can be calculated by using (22)1198982
= 0045 1198762
= 390635 Jmol 1205722
= 6295 times 10minus3 and1198992
= 0 for ignoring the effect of initial grain size Finally wecan get the strain of 50 DRX
12057605
= 6295 times 10minus3 1205760045 exp (390635119877119879
) (23)
Advances in Materials Science and Engineering 7
00 01 02 03 04 05 060
20
40
60
80
100
Strain
0005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
100
005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
10005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
1001 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
Figure 12 Predicted DRX volume fractions of TA15 at different conditions
Summarily the DRX kinetics equations of TA15 can berepresented as
120576119901
= 4429 times 10minus6 12057600528 exp(9785478119877119879
)
120576119888
= 083120576119901
12057605
= 6295 times 10minus3 1205760045 exp(390635119877119879
)
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
]
(24)
Based on the calculated results of this model the effectsof strain strain rate and deformation temperature on volumefraction of DRX are shown in Figure 12 It can be seen thatthe curves of volume fraction of DRX appeared as ldquoSrdquo shapeand this phenomenon indicates that the volume fraction ofDRX grows rapidly between the strain ranges of 01ndash045The volume fraction of DRX is also slightly affected by thetemperature This is because of the decreased mobility ofgrain boundaries in a low temperature and high strain rate
34Microstructure Observations Typical opticalmicrostruc-tures of TA15 alloy were examined and analyzed on thesection plane of specimen deformed to a strain of 06 Themicrostructures at different temperatures and strain rates areshown in Figure 13 The effects of deformation temperatureand strain rate on the microstructures can be seen clearlyfrom these opticalmicrographs FromFigures 13(a) and 13(b)it can be easily found that the small size grain will be obtainedat high strain rate for a given temperature It means thatthere is not enough time for the DRX to grow at high strainrate Conversely the grain size of DRX is large for the highertemperature as shown in Figures 13(a) and 13(c)
It can be found clearly that the percentage of 120573-phase ishigher in Figure 13(d) than that in Figure 13(d) It expressesthat there is a tendency of 120572 rarr 120573 phase transformationoccurring with the increase of temperatureThe close-packedhexagonal 120572-phase trends to transform into body-centeredcubic 120573-phase with the increase of temperature Becausebody-centered cubic120573-phase has the features of high stackingfault energy and a large number of slip systems the flow stressdecreases and becomes gently In the temperature range of1223Kndash1273K it can be found that the flow stresses are not so
8 Advances in Materials Science and Engineering
20120583m
(a)
20120583m
(b)
20120583m
(c)
20120583m
(d)
Figure 13 Optical microstructures of TA15 alloy deformed under different conditions (a)119879 = 1203K 120576 = 0005 s (b)119879 = 1203K 120576 = 005 sminus1(c) 119879 = 1223K 120576 = 005 sminus1 (d) 119879 = 1273K 120576 = 005 sminus1
sensitive to the temperature So the flow stress drops slightlyfor the increase of the temperature
4 Conclusions
Hot deformation behavior of TA15 titanium alloy is studiedat high temperatures under isothermal compression in thispaper Based on this research the following conclusions canbe drawn
(1) Through the regression analysis for conventionalhyperbolic sine equation the coefficient of plasticdeformation constitutive equation of TA15 titaniumalloy during high temperature is calculated in whichthe value of deformation activation energy in (120572 + 120573)two-phase region is 119876
119878
= 5887Kgmol and in 120573region is 119876
119863
= 2258Kgmol
(2) The constitutive equations and DRX kinetic modelare obtained by this investigation that can be used todescribe the flow behavior of TA15 titanium alloy inhot forming
(3) The optical microstructure observation of the TA15specimens deformed to a strain of 06 under differ-ent conditions verified the influence of deformationconditions on the evolution of DRX volume fraction
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research is supported by the National Natural ScienceFoundation of China (Grant no 51345013) and the Funda-mental Research Funds for the Central Universities (Grantno CDJZR12110002)
References
[1] Y Chen W-C Xu D-B Shan and B Guo ldquoMicrostructureevolution of TA15 titanium alloy during hot power spinningrdquoTransactions of Nonferrous Metals Society of China vol 21 no2 pp s323ndashs327 2011
[2] L Huang R Zeng X Zhang and J Li ldquoStudy on plasticdeformation behavior of hot splitting spinning of TA15 titaniumalloyrdquoMaterials amp Design vol 58 pp 465ndash474 2014
[3] S Zhu H Yang L G Guo and X G Fan ldquoEffect of cooling rateon microstructure evolution during 120572120573 heat treatment of TA15titanium alloyrdquo Materials Characterization vol 70 pp 101ndash1102012
[4] Q J Sun and G C Wang ldquoMicrostructure and superplasticityof TA15 alloyrdquoMaterials Science and Engineering A vol 606 pp401ndash408 2014
Advances in Materials Science and Engineering 9
[5] Y C Lin M-S Chen and J Zhong ldquoConstitutive modeling forelevated temperature flow behavior of 42CrMo steelrdquo Compu-tational Materials Science vol 42 no 3 pp 470ndash477 2008
[6] Y Xu LHua andY Sun ldquoDeformation behaviour and dynamicrecrystallization of AZ61 magnesium alloyrdquo Journal of Alloysand Compounds vol 580 pp 262ndash269 2013
[7] X N Peng H Z Guo Z F Shi C Qin Z L Zhao and ZYao ldquoStudy on the hot deformation behavior of TC4-DT alloywith equiaxed 120572+120573 starting structure based on processingmaprdquoMaterials Science and Engineering A vol 605 pp 80ndash88 2014
[8] P N Kalu and D R Waryoba ldquoA JMAK-microhardness modelfor quantifying the kinetics of restoration mechanisms in inho-mogeneous microstructurerdquoMaterials Science and EngineeringA vol 464 no 1-2 pp 68ndash75 2007
[9] J Liu Z Cui and L Ruan ldquoA new kinetics model of dynamicrecrystallization for magnesium alloy AZ31BrdquoMaterials Scienceand Engineering A vol 529 no 1 pp 300ndash310 2011
[10] J J Jonas X Quelennec L Jiang and E Martin ldquoThe Avramikinetics of dynamic recrystallizationrdquo Acta Materialia vol 57no 9 pp 2748ndash2756 2009
[11] J Xiao D S Li X Q Li and T S Deng ldquoConstitutive modelingand microstructure change of Ti-6Al-4V during the hot tensiledeformationrdquo Journal of Alloys and Compounds vol 541 pp346ndash352 2012
[12] W Peng W Zeng Q Wang and H Yu ldquoComparative study onconstitutive relationship of as-cast Ti60 titanium alloy duringhot deformation based on Arrhenius-type and artificial neuralnetwork modelsrdquoMaterials amp Design vol 51 pp 95ndash104 2013
[13] Z Sun S Guo and H Yang ldquoNucleation and growth mecha-nism of 120572-lamellae of Ti alloy TA15 cooling from an 120572 + 120573 phasefieldrdquo Acta Materialia vol 61 no 6 pp 2057ndash2064 2013
[14] S F Medina and C A Hernandez ldquoGeneral expression of theZener-Hollomon parameter as a function of the chemical com-position of low alloy and microalloyed steelsrdquo Acta Materialiavol 44 no 1 pp 137ndash148 1996
[15] YWang Y Liu G Y Yang et al ldquoHot deformation behaviors of120573 phase containing Ti-43Al-4Nb-14W-based alloyrdquo MaterialsScience and Engineering A vol 577 pp 210ndash217 2013
[16] C M Sellars and W J McTegart ldquoOn the mechanism of hotdeformationrdquo Acta Metallurgica vol 14 no 9 pp 1136ndash11381966
[17] C Zener and J H Hollomon ldquoEffect of strain rate upon plasticflow of steelrdquo Journal of Applied Physics vol 15 no 1 pp 22ndash321944
[18] M-S Chen Y C Lin and X-S Ma ldquoThe kinetics of dynamicrecrystallization of 42CrMo steelrdquo Materials Science and Engi-neering A vol 556 pp 260ndash266 2012
[19] Z Yang Y C Guo J P Li F He F Xia andM X Liang ldquoPlasticdeformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-05Zn-05Zr alloyrdquo Materials Science and EngineeringA vol 485 no 1-2 pp 487ndash491 2008
[20] A I Fernandez P Uranga B Lopez and JM Rodriguez-IbabeldquoDynamic recrystallization behavior covering a wide austenitegrain size range in Nb andNb-Timicroalloyed steelsrdquoMaterialsScience and Engineering A vol 361 no 1-2 pp 367ndash376 2003
[21] C M Sellars ldquoFrom trial and error to computer modellingof thermomechanical processingrdquo Ironmaking and Steelmakingvol 38 no 4 pp 250ndash257 2011
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Advances in Materials Science and Engineering 7
00 01 02 03 04 05 060
20
40
60
80
100
Strain
0005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
100
005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
10005 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
00 01 02 03 04 05 06Strain
0
20
40
60
80
1001 sminus1
1273K
1223K
1203K
1173K
Xdr
x(
)
Figure 12 Predicted DRX volume fractions of TA15 at different conditions
Summarily the DRX kinetics equations of TA15 can berepresented as
120576119901
= 4429 times 10minus6 12057600528 exp(9785478119877119879
)
120576119888
= 083120576119901
12057605
= 6295 times 10minus3 1205760045 exp(390635119877119879
)
119883drx = 1 minus exp[minus0693(120576 minus 120576119888
12057605
)1502
]
(24)
Based on the calculated results of this model the effectsof strain strain rate and deformation temperature on volumefraction of DRX are shown in Figure 12 It can be seen thatthe curves of volume fraction of DRX appeared as ldquoSrdquo shapeand this phenomenon indicates that the volume fraction ofDRX grows rapidly between the strain ranges of 01ndash045The volume fraction of DRX is also slightly affected by thetemperature This is because of the decreased mobility ofgrain boundaries in a low temperature and high strain rate
34Microstructure Observations Typical opticalmicrostruc-tures of TA15 alloy were examined and analyzed on thesection plane of specimen deformed to a strain of 06 Themicrostructures at different temperatures and strain rates areshown in Figure 13 The effects of deformation temperatureand strain rate on the microstructures can be seen clearlyfrom these opticalmicrographs FromFigures 13(a) and 13(b)it can be easily found that the small size grain will be obtainedat high strain rate for a given temperature It means thatthere is not enough time for the DRX to grow at high strainrate Conversely the grain size of DRX is large for the highertemperature as shown in Figures 13(a) and 13(c)
It can be found clearly that the percentage of 120573-phase ishigher in Figure 13(d) than that in Figure 13(d) It expressesthat there is a tendency of 120572 rarr 120573 phase transformationoccurring with the increase of temperatureThe close-packedhexagonal 120572-phase trends to transform into body-centeredcubic 120573-phase with the increase of temperature Becausebody-centered cubic120573-phase has the features of high stackingfault energy and a large number of slip systems the flow stressdecreases and becomes gently In the temperature range of1223Kndash1273K it can be found that the flow stresses are not so
8 Advances in Materials Science and Engineering
20120583m
(a)
20120583m
(b)
20120583m
(c)
20120583m
(d)
Figure 13 Optical microstructures of TA15 alloy deformed under different conditions (a)119879 = 1203K 120576 = 0005 s (b)119879 = 1203K 120576 = 005 sminus1(c) 119879 = 1223K 120576 = 005 sminus1 (d) 119879 = 1273K 120576 = 005 sminus1
sensitive to the temperature So the flow stress drops slightlyfor the increase of the temperature
4 Conclusions
Hot deformation behavior of TA15 titanium alloy is studiedat high temperatures under isothermal compression in thispaper Based on this research the following conclusions canbe drawn
(1) Through the regression analysis for conventionalhyperbolic sine equation the coefficient of plasticdeformation constitutive equation of TA15 titaniumalloy during high temperature is calculated in whichthe value of deformation activation energy in (120572 + 120573)two-phase region is 119876
119878
= 5887Kgmol and in 120573region is 119876
119863
= 2258Kgmol
(2) The constitutive equations and DRX kinetic modelare obtained by this investigation that can be used todescribe the flow behavior of TA15 titanium alloy inhot forming
(3) The optical microstructure observation of the TA15specimens deformed to a strain of 06 under differ-ent conditions verified the influence of deformationconditions on the evolution of DRX volume fraction
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research is supported by the National Natural ScienceFoundation of China (Grant no 51345013) and the Funda-mental Research Funds for the Central Universities (Grantno CDJZR12110002)
References
[1] Y Chen W-C Xu D-B Shan and B Guo ldquoMicrostructureevolution of TA15 titanium alloy during hot power spinningrdquoTransactions of Nonferrous Metals Society of China vol 21 no2 pp s323ndashs327 2011
[2] L Huang R Zeng X Zhang and J Li ldquoStudy on plasticdeformation behavior of hot splitting spinning of TA15 titaniumalloyrdquoMaterials amp Design vol 58 pp 465ndash474 2014
[3] S Zhu H Yang L G Guo and X G Fan ldquoEffect of cooling rateon microstructure evolution during 120572120573 heat treatment of TA15titanium alloyrdquo Materials Characterization vol 70 pp 101ndash1102012
[4] Q J Sun and G C Wang ldquoMicrostructure and superplasticityof TA15 alloyrdquoMaterials Science and Engineering A vol 606 pp401ndash408 2014
Advances in Materials Science and Engineering 9
[5] Y C Lin M-S Chen and J Zhong ldquoConstitutive modeling forelevated temperature flow behavior of 42CrMo steelrdquo Compu-tational Materials Science vol 42 no 3 pp 470ndash477 2008
[6] Y Xu LHua andY Sun ldquoDeformation behaviour and dynamicrecrystallization of AZ61 magnesium alloyrdquo Journal of Alloysand Compounds vol 580 pp 262ndash269 2013
[7] X N Peng H Z Guo Z F Shi C Qin Z L Zhao and ZYao ldquoStudy on the hot deformation behavior of TC4-DT alloywith equiaxed 120572+120573 starting structure based on processingmaprdquoMaterials Science and Engineering A vol 605 pp 80ndash88 2014
[8] P N Kalu and D R Waryoba ldquoA JMAK-microhardness modelfor quantifying the kinetics of restoration mechanisms in inho-mogeneous microstructurerdquoMaterials Science and EngineeringA vol 464 no 1-2 pp 68ndash75 2007
[9] J Liu Z Cui and L Ruan ldquoA new kinetics model of dynamicrecrystallization for magnesium alloy AZ31BrdquoMaterials Scienceand Engineering A vol 529 no 1 pp 300ndash310 2011
[10] J J Jonas X Quelennec L Jiang and E Martin ldquoThe Avramikinetics of dynamic recrystallizationrdquo Acta Materialia vol 57no 9 pp 2748ndash2756 2009
[11] J Xiao D S Li X Q Li and T S Deng ldquoConstitutive modelingand microstructure change of Ti-6Al-4V during the hot tensiledeformationrdquo Journal of Alloys and Compounds vol 541 pp346ndash352 2012
[12] W Peng W Zeng Q Wang and H Yu ldquoComparative study onconstitutive relationship of as-cast Ti60 titanium alloy duringhot deformation based on Arrhenius-type and artificial neuralnetwork modelsrdquoMaterials amp Design vol 51 pp 95ndash104 2013
[13] Z Sun S Guo and H Yang ldquoNucleation and growth mecha-nism of 120572-lamellae of Ti alloy TA15 cooling from an 120572 + 120573 phasefieldrdquo Acta Materialia vol 61 no 6 pp 2057ndash2064 2013
[14] S F Medina and C A Hernandez ldquoGeneral expression of theZener-Hollomon parameter as a function of the chemical com-position of low alloy and microalloyed steelsrdquo Acta Materialiavol 44 no 1 pp 137ndash148 1996
[15] YWang Y Liu G Y Yang et al ldquoHot deformation behaviors of120573 phase containing Ti-43Al-4Nb-14W-based alloyrdquo MaterialsScience and Engineering A vol 577 pp 210ndash217 2013
[16] C M Sellars and W J McTegart ldquoOn the mechanism of hotdeformationrdquo Acta Metallurgica vol 14 no 9 pp 1136ndash11381966
[17] C Zener and J H Hollomon ldquoEffect of strain rate upon plasticflow of steelrdquo Journal of Applied Physics vol 15 no 1 pp 22ndash321944
[18] M-S Chen Y C Lin and X-S Ma ldquoThe kinetics of dynamicrecrystallization of 42CrMo steelrdquo Materials Science and Engi-neering A vol 556 pp 260ndash266 2012
[19] Z Yang Y C Guo J P Li F He F Xia andM X Liang ldquoPlasticdeformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-05Zn-05Zr alloyrdquo Materials Science and EngineeringA vol 485 no 1-2 pp 487ndash491 2008
[20] A I Fernandez P Uranga B Lopez and JM Rodriguez-IbabeldquoDynamic recrystallization behavior covering a wide austenitegrain size range in Nb andNb-Timicroalloyed steelsrdquoMaterialsScience and Engineering A vol 361 no 1-2 pp 367ndash376 2003
[21] C M Sellars ldquoFrom trial and error to computer modellingof thermomechanical processingrdquo Ironmaking and Steelmakingvol 38 no 4 pp 250ndash257 2011
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
8 Advances in Materials Science and Engineering
20120583m
(a)
20120583m
(b)
20120583m
(c)
20120583m
(d)
Figure 13 Optical microstructures of TA15 alloy deformed under different conditions (a)119879 = 1203K 120576 = 0005 s (b)119879 = 1203K 120576 = 005 sminus1(c) 119879 = 1223K 120576 = 005 sminus1 (d) 119879 = 1273K 120576 = 005 sminus1
sensitive to the temperature So the flow stress drops slightlyfor the increase of the temperature
4 Conclusions
Hot deformation behavior of TA15 titanium alloy is studiedat high temperatures under isothermal compression in thispaper Based on this research the following conclusions canbe drawn
(1) Through the regression analysis for conventionalhyperbolic sine equation the coefficient of plasticdeformation constitutive equation of TA15 titaniumalloy during high temperature is calculated in whichthe value of deformation activation energy in (120572 + 120573)two-phase region is 119876
119878
= 5887Kgmol and in 120573region is 119876
119863
= 2258Kgmol
(2) The constitutive equations and DRX kinetic modelare obtained by this investigation that can be used todescribe the flow behavior of TA15 titanium alloy inhot forming
(3) The optical microstructure observation of the TA15specimens deformed to a strain of 06 under differ-ent conditions verified the influence of deformationconditions on the evolution of DRX volume fraction
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research is supported by the National Natural ScienceFoundation of China (Grant no 51345013) and the Funda-mental Research Funds for the Central Universities (Grantno CDJZR12110002)
References
[1] Y Chen W-C Xu D-B Shan and B Guo ldquoMicrostructureevolution of TA15 titanium alloy during hot power spinningrdquoTransactions of Nonferrous Metals Society of China vol 21 no2 pp s323ndashs327 2011
[2] L Huang R Zeng X Zhang and J Li ldquoStudy on plasticdeformation behavior of hot splitting spinning of TA15 titaniumalloyrdquoMaterials amp Design vol 58 pp 465ndash474 2014
[3] S Zhu H Yang L G Guo and X G Fan ldquoEffect of cooling rateon microstructure evolution during 120572120573 heat treatment of TA15titanium alloyrdquo Materials Characterization vol 70 pp 101ndash1102012
[4] Q J Sun and G C Wang ldquoMicrostructure and superplasticityof TA15 alloyrdquoMaterials Science and Engineering A vol 606 pp401ndash408 2014
Advances in Materials Science and Engineering 9
[5] Y C Lin M-S Chen and J Zhong ldquoConstitutive modeling forelevated temperature flow behavior of 42CrMo steelrdquo Compu-tational Materials Science vol 42 no 3 pp 470ndash477 2008
[6] Y Xu LHua andY Sun ldquoDeformation behaviour and dynamicrecrystallization of AZ61 magnesium alloyrdquo Journal of Alloysand Compounds vol 580 pp 262ndash269 2013
[7] X N Peng H Z Guo Z F Shi C Qin Z L Zhao and ZYao ldquoStudy on the hot deformation behavior of TC4-DT alloywith equiaxed 120572+120573 starting structure based on processingmaprdquoMaterials Science and Engineering A vol 605 pp 80ndash88 2014
[8] P N Kalu and D R Waryoba ldquoA JMAK-microhardness modelfor quantifying the kinetics of restoration mechanisms in inho-mogeneous microstructurerdquoMaterials Science and EngineeringA vol 464 no 1-2 pp 68ndash75 2007
[9] J Liu Z Cui and L Ruan ldquoA new kinetics model of dynamicrecrystallization for magnesium alloy AZ31BrdquoMaterials Scienceand Engineering A vol 529 no 1 pp 300ndash310 2011
[10] J J Jonas X Quelennec L Jiang and E Martin ldquoThe Avramikinetics of dynamic recrystallizationrdquo Acta Materialia vol 57no 9 pp 2748ndash2756 2009
[11] J Xiao D S Li X Q Li and T S Deng ldquoConstitutive modelingand microstructure change of Ti-6Al-4V during the hot tensiledeformationrdquo Journal of Alloys and Compounds vol 541 pp346ndash352 2012
[12] W Peng W Zeng Q Wang and H Yu ldquoComparative study onconstitutive relationship of as-cast Ti60 titanium alloy duringhot deformation based on Arrhenius-type and artificial neuralnetwork modelsrdquoMaterials amp Design vol 51 pp 95ndash104 2013
[13] Z Sun S Guo and H Yang ldquoNucleation and growth mecha-nism of 120572-lamellae of Ti alloy TA15 cooling from an 120572 + 120573 phasefieldrdquo Acta Materialia vol 61 no 6 pp 2057ndash2064 2013
[14] S F Medina and C A Hernandez ldquoGeneral expression of theZener-Hollomon parameter as a function of the chemical com-position of low alloy and microalloyed steelsrdquo Acta Materialiavol 44 no 1 pp 137ndash148 1996
[15] YWang Y Liu G Y Yang et al ldquoHot deformation behaviors of120573 phase containing Ti-43Al-4Nb-14W-based alloyrdquo MaterialsScience and Engineering A vol 577 pp 210ndash217 2013
[16] C M Sellars and W J McTegart ldquoOn the mechanism of hotdeformationrdquo Acta Metallurgica vol 14 no 9 pp 1136ndash11381966
[17] C Zener and J H Hollomon ldquoEffect of strain rate upon plasticflow of steelrdquo Journal of Applied Physics vol 15 no 1 pp 22ndash321944
[18] M-S Chen Y C Lin and X-S Ma ldquoThe kinetics of dynamicrecrystallization of 42CrMo steelrdquo Materials Science and Engi-neering A vol 556 pp 260ndash266 2012
[19] Z Yang Y C Guo J P Li F He F Xia andM X Liang ldquoPlasticdeformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-05Zn-05Zr alloyrdquo Materials Science and EngineeringA vol 485 no 1-2 pp 487ndash491 2008
[20] A I Fernandez P Uranga B Lopez and JM Rodriguez-IbabeldquoDynamic recrystallization behavior covering a wide austenitegrain size range in Nb andNb-Timicroalloyed steelsrdquoMaterialsScience and Engineering A vol 361 no 1-2 pp 367ndash376 2003
[21] C M Sellars ldquoFrom trial and error to computer modellingof thermomechanical processingrdquo Ironmaking and Steelmakingvol 38 no 4 pp 250ndash257 2011
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Advances in Materials Science and Engineering 9
[5] Y C Lin M-S Chen and J Zhong ldquoConstitutive modeling forelevated temperature flow behavior of 42CrMo steelrdquo Compu-tational Materials Science vol 42 no 3 pp 470ndash477 2008
[6] Y Xu LHua andY Sun ldquoDeformation behaviour and dynamicrecrystallization of AZ61 magnesium alloyrdquo Journal of Alloysand Compounds vol 580 pp 262ndash269 2013
[7] X N Peng H Z Guo Z F Shi C Qin Z L Zhao and ZYao ldquoStudy on the hot deformation behavior of TC4-DT alloywith equiaxed 120572+120573 starting structure based on processingmaprdquoMaterials Science and Engineering A vol 605 pp 80ndash88 2014
[8] P N Kalu and D R Waryoba ldquoA JMAK-microhardness modelfor quantifying the kinetics of restoration mechanisms in inho-mogeneous microstructurerdquoMaterials Science and EngineeringA vol 464 no 1-2 pp 68ndash75 2007
[9] J Liu Z Cui and L Ruan ldquoA new kinetics model of dynamicrecrystallization for magnesium alloy AZ31BrdquoMaterials Scienceand Engineering A vol 529 no 1 pp 300ndash310 2011
[10] J J Jonas X Quelennec L Jiang and E Martin ldquoThe Avramikinetics of dynamic recrystallizationrdquo Acta Materialia vol 57no 9 pp 2748ndash2756 2009
[11] J Xiao D S Li X Q Li and T S Deng ldquoConstitutive modelingand microstructure change of Ti-6Al-4V during the hot tensiledeformationrdquo Journal of Alloys and Compounds vol 541 pp346ndash352 2012
[12] W Peng W Zeng Q Wang and H Yu ldquoComparative study onconstitutive relationship of as-cast Ti60 titanium alloy duringhot deformation based on Arrhenius-type and artificial neuralnetwork modelsrdquoMaterials amp Design vol 51 pp 95ndash104 2013
[13] Z Sun S Guo and H Yang ldquoNucleation and growth mecha-nism of 120572-lamellae of Ti alloy TA15 cooling from an 120572 + 120573 phasefieldrdquo Acta Materialia vol 61 no 6 pp 2057ndash2064 2013
[14] S F Medina and C A Hernandez ldquoGeneral expression of theZener-Hollomon parameter as a function of the chemical com-position of low alloy and microalloyed steelsrdquo Acta Materialiavol 44 no 1 pp 137ndash148 1996
[15] YWang Y Liu G Y Yang et al ldquoHot deformation behaviors of120573 phase containing Ti-43Al-4Nb-14W-based alloyrdquo MaterialsScience and Engineering A vol 577 pp 210ndash217 2013
[16] C M Sellars and W J McTegart ldquoOn the mechanism of hotdeformationrdquo Acta Metallurgica vol 14 no 9 pp 1136ndash11381966
[17] C Zener and J H Hollomon ldquoEffect of strain rate upon plasticflow of steelrdquo Journal of Applied Physics vol 15 no 1 pp 22ndash321944
[18] M-S Chen Y C Lin and X-S Ma ldquoThe kinetics of dynamicrecrystallization of 42CrMo steelrdquo Materials Science and Engi-neering A vol 556 pp 260ndash266 2012
[19] Z Yang Y C Guo J P Li F He F Xia andM X Liang ldquoPlasticdeformation and dynamic recrystallization behaviors of Mg-5Gd-4Y-05Zn-05Zr alloyrdquo Materials Science and EngineeringA vol 485 no 1-2 pp 487ndash491 2008
[20] A I Fernandez P Uranga B Lopez and JM Rodriguez-IbabeldquoDynamic recrystallization behavior covering a wide austenitegrain size range in Nb andNb-Timicroalloyed steelsrdquoMaterialsScience and Engineering A vol 361 no 1-2 pp 367ndash376 2003
[21] C M Sellars ldquoFrom trial and error to computer modellingof thermomechanical processingrdquo Ironmaking and Steelmakingvol 38 no 4 pp 250ndash257 2011
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials