dynamic recrystallization behavior of ta15 titanium alloyunder isothermal compression

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


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


=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


) (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


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


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


0005 sminus1

005 sminus105 sminus1

1 sminus1


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)


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

)


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


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


[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

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


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


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





0005 55926 40186 26713 22019005 91980 66536 44411 3664405 148101 108832 73411 607491 16971 125647 85212 70622



119877119879 (8)





119876 = 119877120597 ln 120576

120597 ln [sinh (120572120590)]

10038161003816100381610038161003816100381610038161003816119879

120597 ln [sinh (120572120590)]120597 (1119879)

10038161003816100381610038161003816100381610038161003816120576

= RNW (9)



32 36 40 44 48 52

0

1

ln(stressMPa)

minus6

minus5

minus4

minus3

minus2

minus1

ln(s

trai

n ra

tesminus1)

1273K1223K

1203K1173K


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



119878


=2258Kgmol


120576119878


) (10)

00

0

1

minus6

minus5

minus4

minus3

minus2

minus1

ln(s

trai

n ra

tesminus1)

1273K1223K

1203K1173K


ln[sin h(120572120590)]


078 079 080 081 082 083 084 085 086

00

minus25

minus20

minus15

minus10

minus05

0005 sminus1




ln[s

in h(

120572120590

)]



120576119863


) (11)





0010

20

30

40

50

60

70


ln Z

ln[sin h(120572120590)]

ln ZD = 459ln[sin h(0004120590)] + 6486

ln ZS = 459ln[sin h(0004120590)] + 2421


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



120576119888

= 119896120576119901

(12)

where 120576119888




119888



002 004 006 008 010 012002

004

006

008

010

Peak

stra

in

Critical strain


and 120576119888


119901


and 120576119901


119888

and 120576119901


119888

= 083120576119901


120576119901

= 1205721

11988911989910

1205761198981 exp ( 1198761119877119879

) (13)

where 1198761



1

1198991

1198981


120576119901

= 1205721

1205761198981 exp( 1198761119877119879

) (14)


ln 120576119901

= ln1205721

+ 1198981

ln 120576 +1198761

119877119879 (15)


and Q1


119901



0ln(strain rate)

minus18

minus20

minus22

minus24

minus26

minus28

minus30

minus32

minus34

ln 120576 p


1273K1223K

1203K1173K


and ln 120576

078 079 080 081 082 083 084 085 086

minus20

minus22

minus24

minus26

minus28

minus30

minus32

minus34

ln 120576 p


0005 sminus1


1 sminus1


and 119879minus1

ln 120576119901


=005281 Q

1

= 9875478 Jmol 1205721


1


alloy is as follows

120576119901

= 4429 times 10minus6 12057600528 exp(9875478119877119879

) (16)




(120576 minus 120576119888

12057605

)119896

119889

] (17)

12057605

= 1205722

11988911989920

1205761198982 exp(1198762RT

) (18)



2


119896119889

1205722

1198992

1198982



119883drx =120590 minus 120590119901

120590119904

minus 120590119901

(19)

where 120590119901



and 120590119904



+ 119896119889

ln(120576 minus 120576119888

12057605

) (20)


119888


05


119889

= 0693 and 119896119889



12057605

)1502

] (21)


ln 12057605

= ln1205722

+ 1198992

ln 1198890

+ 1198982

ln 120576 +1198762

119877119879 (22)


= 0045 1198762

= 390635 Jmol 1205722



12057605

= 6295 times 10minus3 1205760045 exp (390635119877119879

) (23)


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(

)



120576119901

= 4429 times 10minus6 12057600528 exp(9785478119877119879

)

120576119888

= 083120576119901

12057605

= 6295 times 10minus3 1205760045 exp(390635119877119879

)


12057605

)1502

]

(24)





20120583m

(a)

20120583m

(b)

20120583m

(c)

20120583m

(d)



4 Conclusions



119878


119863

= 2258Kgmol





Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




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





0005 55926 40186 26713 22019005 91980 66536 44411 3664405 148101 108832 73411 607491 16971 125647 85212 70622



119877119879 (8)





119876 = 119877120597 ln 120576

120597 ln [sinh (120572120590)]

10038161003816100381610038161003816100381610038161003816119879

120597 ln [sinh (120572120590)]120597 (1119879)

10038161003816100381610038161003816100381610038161003816120576

= RNW (9)



32 36 40 44 48 52

0

1

ln(stressMPa)

minus6

minus5

minus4

minus3

minus2

minus1

ln(s

trai

n ra

tesminus1)

1273K1223K

1203K1173K


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



119878


=2258Kgmol


120576119878


) (10)

00

0

1

minus6

minus5

minus4

minus3

minus2

minus1

ln(s

trai

n ra

tesminus1)

1273K1223K

1203K1173K


ln[sin h(120572120590)]


078 079 080 081 082 083 084 085 086

00

minus25

minus20

minus15

minus10

minus05

0005 sminus1




ln[s

in h(

120572120590

)]



120576119863


) (11)





0010

20

30

40

50

60

70


ln Z

ln[sin h(120572120590)]

ln ZD = 459ln[sin h(0004120590)] + 6486

ln ZS = 459ln[sin h(0004120590)] + 2421


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



120576119888

= 119896120576119901

(12)

where 120576119888




119888



002 004 006 008 010 012002

004

006

008

010

Peak

stra

in

Critical strain


and 120576119888


119901


and 120576119901


119888

and 120576119901


119888

= 083120576119901


120576119901

= 1205721

11988911989910

1205761198981 exp ( 1198761119877119879

) (13)

where 1198761



1

1198991

1198981


120576119901

= 1205721

1205761198981 exp( 1198761119877119879

) (14)


ln 120576119901

= ln1205721

+ 1198981

ln 120576 +1198761

119877119879 (15)


and Q1


119901



0ln(strain rate)

minus18

minus20

minus22

minus24

minus26

minus28

minus30

minus32

minus34

ln 120576 p


1273K1223K

1203K1173K


and ln 120576

078 079 080 081 082 083 084 085 086

minus20

minus22

minus24

minus26

minus28

minus30

minus32

minus34

ln 120576 p


0005 sminus1


1 sminus1


and 119879minus1

ln 120576119901


=005281 Q

1

= 9875478 Jmol 1205721


1


alloy is as follows

120576119901

= 4429 times 10minus6 12057600528 exp(9875478119877119879

) (16)




(120576 minus 120576119888

12057605

)119896

119889

] (17)

12057605

= 1205722

11988911989920

1205761198982 exp(1198762RT

) (18)



2


119896119889

1205722

1198992

1198982



119883drx =120590 minus 120590119901

120590119904

minus 120590119901

(19)

where 120590119901



and 120590119904



+ 119896119889

ln(120576 minus 120576119888

12057605

) (20)


119888


05


119889

= 0693 and 119896119889



12057605

)1502

] (21)


ln 12057605

= ln1205722

+ 1198992

ln 1198890

+ 1198982

ln 120576 +1198762

119877119879 (22)


= 0045 1198762

= 390635 Jmol 1205722



12057605

= 6295 times 10minus3 1205760045 exp (390635119877119879

) (23)


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(

)



120576119901

= 4429 times 10minus6 12057600528 exp(9785478119877119879

)

120576119888

= 083120576119901

12057605

= 6295 times 10minus3 1205760045 exp(390635119877119879

)


12057605

)1502

]

(24)





20120583m

(a)

20120583m

(b)

20120583m

(c)

20120583m

(d)



4 Conclusions



119878


119863

= 2258Kgmol





Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




32 36 40 44 48 52

0

1

ln(stressMPa)

minus6

minus5

minus4

minus3

minus2

minus1

ln(s

trai

n ra

tesminus1)

1273K1223K

1203K1173K


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



119878


=2258Kgmol


120576119878


) (10)

00

0

1

minus6

minus5

minus4

minus3

minus2

minus1

ln(s

trai

n ra

tesminus1)

1273K1223K

1203K1173K


ln[sin h(120572120590)]


078 079 080 081 082 083 084 085 086

00

minus25

minus20

minus15

minus10

minus05

0005 sminus1




ln[s

in h(

120572120590

)]



120576119863


) (11)





0010

20

30

40

50

60

70


ln Z

ln[sin h(120572120590)]

ln ZD = 459ln[sin h(0004120590)] + 6486

ln ZS = 459ln[sin h(0004120590)] + 2421


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



120576119888

= 119896120576119901

(12)

where 120576119888




119888



002 004 006 008 010 012002

004

006

008

010

Peak

stra

in

Critical strain


and 120576119888


119901


and 120576119901


119888

and 120576119901


119888

= 083120576119901


120576119901

= 1205721

11988911989910

1205761198981 exp ( 1198761119877119879

) (13)

where 1198761



1

1198991

1198981


120576119901

= 1205721

1205761198981 exp( 1198761119877119879

) (14)


ln 120576119901

= ln1205721

+ 1198981

ln 120576 +1198761

119877119879 (15)


and Q1


119901



0ln(strain rate)

minus18

minus20

minus22

minus24

minus26

minus28

minus30

minus32

minus34

ln 120576 p


1273K1223K

1203K1173K


and ln 120576

078 079 080 081 082 083 084 085 086

minus20

minus22

minus24

minus26

minus28

minus30

minus32

minus34

ln 120576 p


0005 sminus1


1 sminus1


and 119879minus1

ln 120576119901


=005281 Q

1

= 9875478 Jmol 1205721


1


alloy is as follows

120576119901

= 4429 times 10minus6 12057600528 exp(9875478119877119879

) (16)




(120576 minus 120576119888

12057605

)119896

119889

] (17)

12057605

= 1205722

11988911989920

1205761198982 exp(1198762RT

) (18)



2


119896119889

1205722

1198992

1198982



119883drx =120590 minus 120590119901

120590119904

minus 120590119901

(19)

where 120590119901



and 120590119904



+ 119896119889

ln(120576 minus 120576119888

12057605

) (20)


119888


05


119889

= 0693 and 119896119889



12057605

)1502

] (21)


ln 12057605

= ln1205722

+ 1198992

ln 1198890

+ 1198982

ln 120576 +1198762

119877119879 (22)


= 0045 1198762

= 390635 Jmol 1205722



12057605

= 6295 times 10minus3 1205760045 exp (390635119877119879

) (23)


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(

)



120576119901

= 4429 times 10minus6 12057600528 exp(9785478119877119879

)

120576119888

= 083120576119901

12057605

= 6295 times 10minus3 1205760045 exp(390635119877119879

)


12057605

)1502

]

(24)





20120583m

(a)

20120583m

(b)

20120583m

(c)

20120583m

(d)



4 Conclusions



119878


119863

= 2258Kgmol





Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0010

20

30

40

50

60

70


ln Z

ln[sin h(120572120590)]

ln ZD = 459ln[sin h(0004120590)] + 6486

ln ZS = 459ln[sin h(0004120590)] + 2421


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



120576119888

= 119896120576119901

(12)

where 120576119888




119888



002 004 006 008 010 012002

004

006

008

010

Peak

stra

in

Critical strain


and 120576119888


119901


and 120576119901


119888

and 120576119901


119888

= 083120576119901


120576119901

= 1205721

11988911989910

1205761198981 exp ( 1198761119877119879

) (13)

where 1198761



1

1198991

1198981


120576119901

= 1205721

1205761198981 exp( 1198761119877119879

) (14)


ln 120576119901

= ln1205721

+ 1198981

ln 120576 +1198761

119877119879 (15)


and Q1


119901



0ln(strain rate)

minus18

minus20

minus22

minus24

minus26

minus28

minus30

minus32

minus34

ln 120576 p


1273K1223K

1203K1173K


and ln 120576

078 079 080 081 082 083 084 085 086

minus20

minus22

minus24

minus26

minus28

minus30

minus32

minus34

ln 120576 p


0005 sminus1


1 sminus1


and 119879minus1

ln 120576119901


=005281 Q

1

= 9875478 Jmol 1205721


1


alloy is as follows

120576119901

= 4429 times 10minus6 12057600528 exp(9875478119877119879

) (16)




(120576 minus 120576119888

12057605

)119896

119889

] (17)

12057605

= 1205722

11988911989920

1205761198982 exp(1198762RT

) (18)



2


119896119889

1205722

1198992

1198982



119883drx =120590 minus 120590119901

120590119904

minus 120590119901

(19)

where 120590119901



and 120590119904



+ 119896119889

ln(120576 minus 120576119888

12057605

) (20)


119888


05


119889

= 0693 and 119896119889



12057605

)1502

] (21)


ln 12057605

= ln1205722

+ 1198992

ln 1198890

+ 1198982

ln 120576 +1198762

119877119879 (22)


= 0045 1198762

= 390635 Jmol 1205722



12057605

= 6295 times 10minus3 1205760045 exp (390635119877119879

) (23)


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(

)



120576119901

= 4429 times 10minus6 12057600528 exp(9785478119877119879

)

120576119888

= 083120576119901

12057605

= 6295 times 10minus3 1205760045 exp(390635119877119879

)


12057605

)1502

]

(24)





20120583m

(a)

20120583m

(b)

20120583m

(c)

20120583m

(d)



4 Conclusions



119878


119863

= 2258Kgmol





Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0ln(strain rate)

minus18

minus20

minus22

minus24

minus26

minus28

minus30

minus32

minus34

ln 120576 p


1273K1223K

1203K1173K


and ln 120576

078 079 080 081 082 083 084 085 086

minus20

minus22

minus24

minus26

minus28

minus30

minus32

minus34

ln 120576 p


0005 sminus1


1 sminus1


and 119879minus1

ln 120576119901


=005281 Q

1

= 9875478 Jmol 1205721


1


alloy is as follows

120576119901

= 4429 times 10minus6 12057600528 exp(9875478119877119879

) (16)




(120576 minus 120576119888

12057605

)119896

119889

] (17)

12057605

= 1205722

11988911989920

1205761198982 exp(1198762RT

) (18)



2


119896119889

1205722

1198992

1198982



119883drx =120590 minus 120590119901

120590119904

minus 120590119901

(19)

where 120590119901



and 120590119904



+ 119896119889

ln(120576 minus 120576119888

12057605

) (20)


119888


05


119889

= 0693 and 119896119889



12057605

)1502

] (21)


ln 12057605

= ln1205722

+ 1198992

ln 1198890

+ 1198982

ln 120576 +1198762

119877119879 (22)


= 0045 1198762

= 390635 Jmol 1205722



12057605

= 6295 times 10minus3 1205760045 exp (390635119877119879

) (23)


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(

)



120576119901

= 4429 times 10minus6 12057600528 exp(9785478119877119879

)

120576119888

= 083120576119901

12057605

= 6295 times 10minus3 1205760045 exp(390635119877119879

)


12057605

)1502

]

(24)





20120583m

(a)

20120583m

(b)

20120583m

(c)

20120583m

(d)



4 Conclusions



119878


119863

= 2258Kgmol





Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




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(

)



120576119901

= 4429 times 10minus6 12057600528 exp(9785478119877119879

)

120576119888

= 083120576119901

12057605

= 6295 times 10minus3 1205760045 exp(390635119877119879

)


12057605

)1502

]

(24)





20120583m

(a)

20120583m

(b)

20120583m

(c)

20120583m

(d)



4 Conclusions



119878


119863

= 2258Kgmol





Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




20120583m

(a)

20120583m

(b)

20120583m

(c)

20120583m

(d)



4 Conclusions



119878


119863

= 2258Kgmol





Acknowledgments


References






























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



dynamic recrystallization behavior of ta15 titanium alloyunder isothermal compression

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