plastic deformation and fracture behaviour of ti–6al–4v alloy loaded with high strain rate under...

$: Plastic deformation and fracture behaviour of Ti–6Al–4V alloy loaded with high strain rate under various temperatures.pdf$
Materials Science and Engineering A241 (1998) 48–59

Plastic deformation and fracture behaviour of Ti–6Al–4V alloyloaded with high strain rate under various temperatures

Woei-Shyan Lee *, Chi-Feng LinDepartment of Mechanical Engineering, National Cheng Kung Uni6ersity, Tainan 70101, Taiwan, ROC

Received 8 November 1996; received in revised form 10 March 1997

Abstract

This study investigates the plastic deformation and fracture behaviour of titanium alloy (Ti–6Al–4V) under high strain ratesand various temperature conditions. Mechanical tests are performed at constant strain rates ranging from 5×102 to 3×103 s−1

at temperatures ranging from room temperature to 1100°C by means of the compressive split-Hopkinson bar technique. Thematerial’s dynamic stress–strain response, strain rate, temperature effects and possible deformation mechanisms are discussed.Furthermore, the plastic flow response of this material is described by a deformation constitutive equation incorporating theeffects of temperature, strain rate, strain and work hardening rate. The simulated results based on this constitutive equation areverified. The fracture behaviour and variations of adiabatic shear band produced by deformation at each test condition areinvestigated with optical microscopy and scanning electron microscopy. The results show that the flow stress of Ti–6Al–4V alloyis sensitive to both temperature and strain rate. Nevertheless, the effect on flow stress of temperature is greater than that of strainrate. Fracture observations reveal that adiabatic shear banding turns out to be the major fracture mode when the material isdeformed to large plastic strain at high temperature and high strain rate. © 1998 Elsevier Science S.A.

Keywords: Plastic deformation; Adiabatic shear fracture; Titanium alloys; High strain rates; Temperature sensitivity

1. Introduction

Ti–6Al–4V, an a+b type titanium alloy, is of greatimportance in many industrial applications due to itshighly attractive properties, such as good deformability,low density, high specific strength, excellent corrosionresistance and high temperature strength retention [1–3]. Since the mechanical characterization of Ti–6Al–4Vis of great complexity and is strongly sensitive to theprocessing parameters, i.e. strain rate and temperature,it is important to clarify its deformation modes and therelationship between the processing variables, mi-crostructure and properties under different loading con-ditions.

A number of quasi-static loading rate studies on thismaterial have been carried out by means of variousnumerical, analytical and experimental methods, andtheir results have been published [4–7]. However, thedata obtained for this material at high temperature and

with high strain rates is scanty. In fact, the high strainrate and high temperature properties of Ti–6Al–4V aremost crucial in the design of structures and componentssubjected to impact or shock loading, which can lead toa drastic change in deformation modes and failuremechanisms. The conditions for which Ti–6Al–4Vseems best suited are specifically the those which havenot been adequately studied. Therefore, in order toobtain better insight into these problems, a systematicstudy of the effects of strain rate and temperature onthe dynamic plastic deformation behaviour of Ti–6Al–4V alloy is required.

It is well recognized that strain rate, as well astemperature, affect many materials’ properties includ-ing fracture initiation. A split-Hopkinson bar techniquehas been successfully developed to investigate the strainrate and temperature effects on the mechanical re-sponse of materials in the high strain rate regime [8].Results obtained by Yadav and Ramesh [9] by thistechnique for two tungsten-based composites demon-strate that both composites display substantial increasesin flow stress with increases in the applied strain rate

* Corresponding author. Tel.: +886 6 2757575 ext. 62174; fax:+886 6 2352973.

0921-5093/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved.

PII S0921 -5093 (97 )00 47 1 -1

W.-S. Lee, C.-F. Lin / Materials Science and Engineering A241 (1998) 48–59 49

Fig. 1. Schematic presentation of the compression split-Hopkinson bar apparatus.

under a strain rate ranging from 103 to 105 s−1. Chiemand Duffy [10] employed a torsional Hopkinson bar tostudy the dynamic flow behaviour and strain rate his-tory effect on aluminum single crystal; they found astrong increase in strain rate sensitivity observed atstrain rates exceeding 500 s−1. More recently, Lee et al.[11,12] performed detailed investigations into the be-haviour of AISI 4340 steel and tungsten compositesundergoing deformation at dynamic rates and con-cluded that the higher the imposed strain rate, thegreater the flow stress.

On the other hand, it is generally accepted that a riseof temperature tends to reduce the resistance of flowstress by lowering activation barriers associated withthe atomic mechanisms of deformation. When a struc-tural material is subjected to dynamic and high temper-ature loadings, a competing process between workhardening (resulting from the production, motion andinterference of dislocations and other defects) and ther-mal softening occurs and affects the material’s funda-mental stress–strain behaviour. Extensive research intothe temperature dependence of stress–strain curveparameters for many bcc and fcc metals have beencarried out [13–15]. These experimental results showthat at high temperature regimes, after work hardeningto a peak stress, flow stress drops abruptly and then isfollowed by steady state behavior. These results also

show that temperature has proportionately a muchgreater effect on material strength than strain rate if thedeformation is performed at both high strain rate andhigh temperature conditions.

The purpose of this paper is to present the influenceof temperature and strain rate on the dynamic plasticdeformation behaviour of Ti–6Al–4V alloy at strainrates ranging from 5×102 to 5×103 s−1 in the temper-ature range between room temperature and 1100°Cusing a compressive split-Hopkinson bar system. Theformation of adiabatic shear bands and fracture fea-tures associated with different loading conditions arealso described.

2. Experimental procedure

2.1. Material and specimens preparation

Hot-rolled commercial Ti–6Al–4V alloy bars, 15mm in diameter and purchased from B and S AircraftAlloys Inc., New York, were used in this investigation.Metallographic examination showed that the startingmaterial had a structure characterized by final process-ing in the a+b field. The chemical composition of theas-received bars is 6.1% Al, 4.0% V, 0.2% Fe, 0.014%C, 0.008% N, 0.0057% H, and 0.15% O. The cylindrical

Fig. 2. Temperature distribution and strain gage stations of bars.

Table 1Some mechanical characteristics of DC53 die steel bars

Density (r) 7.87 g cm−3

Young’s modulus (E) 212.8 GPa83.16 GPaShear modulus (G)

Poisson’s ratio (n) 0.285200 m s−1Wave velocity (C0)2880 MPaYield stress (sy)

W.-S. Lee, C.-F. Lin / Materials Science and Engineering A241 (1998) 48–5950

Table 2Strain rate values obtained from different driving pressure, impact velocity and temperature conditions

50 60 70Pressure (kg cm−2) 20 30 8040

54 60 65Impact velocity (m s−1) 35 7242 49

Temperature (°C)1400 170025 — 400 450 2000800

270025002000300 1700— 800 14002500 —500 750 1400 1700 2000 —3300 —700 800 1700 2000 2500 —

—— —900 —1700 2000 2500— — —1100 2000 2500 ——

specimens are all machined from the hot-rolled bar andturned to 10 mm in diameter and 10 mm in height insuch a way that the compression axis is along therolling direction. The actual dimensions reach an accu-racy of 0.01 mm, as used in all our calculations.

2.2. Test procedures

Compression tests are carried out at constant strainrates ranging from 5×102 to 5×103 s−1 at tempera-tures ranging from room temperature to 1100°C bymeans of a split-Hopkinson pressure bar. A schematicdrawing of the apparatus is shown in Fig. 1, which isessentially the same as that described by Lindholm [16].This system consists of incident and transmitter pres-sure bars on which SR-4 gages are installed to monitorthe incident and transmitted pulses. The specimen ismounted between the incident and transmitter bars,with impact provided by a projectile propelled by ahorizontal gas gun. The projectile, incident bar andtransmitter bar are made from DC53 die steel with adiameter of 20 mm. The length of the incident andtransmitted pressure bars is 1 m, while the striker bar(projectile) is 317 mm. Some mechanical characteristics

of DC53 die steel bars are presented in Table 1. Toensure the occurrence of fracture in the material by thefirst pulse during compression testing, an interruptingcollar is placed around the specimen. For test tempera-tures below 300°C, the specimens are lubricated with acommercial molybdenum disulfide (Molykote). Fortemperatures ranging from 500 to 1100°C, a glass paste(80% PbO and 20% B2O3 melted together and pow-dered with mortar and pestle, then mixed with alcohol)is used.

After the specimen assembly has been loaded into theinduction furnace and aligned with the gun barrel, thefurnace is put into operation and the specimen is heatedup to the specified test temperature. The specimentemperature is regulated by a Eurotherm 211 pro-grammer/controller connected to a Inconel sheathedchromel–alumel thermocouple, 1.5 mm diameter, at-tached to the specimen. The maximum temperature of atest sample is reached in about 10 min. The pressurebar ends extend into the furnace and thus are alsoheated. This heat is gradually distributed along thelength of the bars, attaining an essentially steady-statetemperature distribution along the pressure bars within20 min. In order to measure the temperature distribu-tion on the bars, additional thermocouples at intervalsof 50 mm are cemented along the bars. The tempera-ture distribution shows that the temperature, at 40 cmfrom the center, is only slightly above room tempera-ture and therefore has a negligible effect on the neareststrain gage at 50 cm from the center. Because thethermal gradient not only affects the pulse reflections,but also changes the elastic modulus of the bars, calcu-lations of specimen stress and strain must take thethermal gradient along the pressure bars into accountwhen the specimen and adjacent portions of the pres-sure bars are heated.

Now, let a denote the specimen interface with theincident bar and b the interface with the transmitterbar, while l and h denote the temperature distributionsin the incident and transmitter bars, respectively, asshown in Fig. 2. Under these circumstances, the dis-placement at the ends of the specimen is given by

Fig. 3. Typical true stress–strain curves of Ti–6Al–4V alloy de-formed at different strain rates and temperature conditions.


Table 3Yielding strength (A), material constant (B), and work hardening coefficient (n) of Ti–6Al–4V alloy deformed at different conditions

A sy (MPa)Strain rate (s−1) n (work hardening coefficient)B (material constant)Temperature (°C)

0.3951125.925 400 9700.381040982450

998 850800 0.321010 8111400 0.303

8011017 0.29817000.286775.922000 1030

591 0.312300 800 861876 557.81400 0.291884 540 0.281700

530 0.2652000 8910.265109092500

499 0.252700 923551 0.29500 800 717.9

729 506.31400 0.265736.9 0.255484.871700

476.2 0.2312000 746468.5 0.2232500 754

580 459.4700 800 0.26595 417.4 0.241700

379 0.232000 6150.21355.66302500

341 0.193300 644313.5 0.23900 1700 470

480 298.52000 0.215495 278.5 0.192500

2000 330 255.7 0.211002500 0.19343 245.7

ua=Ca

& t

0

(2eIa−eTb−2ea%−eb¦) dt (1)

ub=Cb

& t

0

(eTb−eb¦) dt (2)

where Ca=Cb, since the temperature is the same onboth sides of the specimen.

If the length of the specimen is taken as L0, then thenominal strain in the specimen is

es=(ua−ub)

L0

(3)

or in terms of the strain pulses

es=2Ca

L0

& t

0

(eIa−eTb−ea% ) dt (4)

where eIa and eTb are obtained from the strain pulsesand, which are recorded at the incident and transmitterbar gage stations but corrected in amplitude accordingto the following relations. These relations compensatefor pulse changes caused by transmission through thethermal gradient.

eT

eI

=2E1

[E2+ (E1E2)1/2](5)

where E1 and E2 are the moduli of elasticity on the twosides of the thermal gradient of the bars and are

dependent on temperature. ea% is a reflection pulse whichcan be determined from eIa and eTb. Eq. (4) is used tocalculated specimen strain in high temperature ranges.The time in Eq. (4) is measured the instant that theincident strain pulse reaches the specimen. It can beseen that to determine the specimen strain, one doesnot need to obtain a record of the reflected pulse at theincident gage station.

The stress in the specimen is obtained from the strainat the face of the transmitter bar in contact with thespecimen, that is eTb+eb¦. Since this bar remains elas-tic, we have

ss=Eb(eTb+eb¦) (6)

where eb¦ is a pulse which can be determined from eIa

and eTb.In the case of room temperature tests, the following

formulations are used to calculate the strain, strain rateand stress of the specimen.

e=�2C0

L0

� & t

0

er dt (7)

e; =2C0er

L0

(8)

s=E�A

A0

�et (9)


Table 4Comparison of calculated and measured flow stress values at true strain of 0.1

smeas (MPa) scal (MPa)Temperature (°C) Strain rate (s−1) scal−smeas/smeas (%)

1404.81386.8800 1.3251419.4 1413.7 −0.41400

1.91421.31394.817001406.2 1431.52000 1.81155.0 1149.2300 800 −0.5

1162.11140.4 1.914001151.3 1167.4 1.41700

1178.9 −1.42000 1195.61171.7 1189.32500 1.51170.3 1197.2 2.32700

1004.1 2.7500 1400 977.7−2.11006.41028.01700

1025.7 2.32000 1002.61033.8 2.32500 1010.6

814.6 832.5700 800 2.2813.2 2.7835.21700849.2 838.162000 −1.3

849.3 −1.52500 862.2887.3 864.23300 −2.6645.6 654.6 1.41700900

661.9 2.52000 645.80.9674.8668.82500

491.3 −2.71100 2000 504.9501.6 2.92500 487.5

Average=0.81S.D.=1.84True strain=0.1

where C0 is the longitudinal wave velocity in the split-Hopkinson bar; L0 is the effective gage length of thespecimen; E is the Young’s modulus of the split bar; Aand A0 are the cross-sectional areas of the split bar andthe specimen, respectively.

2.3. Microstructural obser6ations

After mechanical deformation, the microstructure isexamined using optical and transmission electron mi-croscopy (TEM) techniques. For optical microscopy,the specimens are sectioned on a Metaserve cut-offmachine and then mounted in Metaserve DAP moldingpowder. After grinding with 400, 800 and 1200 gritpaper, the specimens are polished with microcloth usinga slurry of 0.3 mm alumina and then etched in asolution of 2% HF, 10% HNO3 and 88% H2O for 10min. Finally, they are observed with MeF3 opticalmicroscopy. For fractured specimens, features are stud-ied using a JEOL JXA-840 scanning electron micro-scope operating at an acceleration potential of 20 Kv.

3. Results and discussion3.1. Flow stress cur6e beha6ior and mechanicalproperties

The intensity of the dynamic load and the strain rate

in specimens is controlled by varying the impact veloc-ity of the projectile. The strain rates listed in Table 2are used for mechanical testing in order to compare theeffects of both strain rate and temperature on thespecimen’s mechanical response. Under these strain rateand temperature conditions, the typical true stress–strain curves of Ti–6Al–4V are presented in Fig. 3.These curves are of the same kind and have a parabolicmonotonic character with a pronounced loading maxi-mum achieved before fracture. It is also clear that boththe strain rate and temperature have obvious effects onthe plastic deformation behaviour. Generally, flowstress increases with strain rate for a given temperaturebut decreases markedly with temperature if the speci-men is deformed at a fixed strain rate. It should benoted here that although the flow stress shows a strongdependence on strain rate and temperature, the effect ofthe latter is more pronounced than that of the former.In addition, flow stress drops rapidly with temperature,indicating that dislocation annihilation is occurring farmore rapidly than generation, and that the rate ofthermal softening is much greater than that of workhardening during deformation, especially for the speci-mens deformed at temperatures higher than 500°C.

Actually, these stress–strain relations can be de-scribed suitably by a very simple model proposed byLudwik [17] with the form of

s=A+B ·en (10)


Table 5Comparison of calculated and measured flow stress values at true strain of 0.2

scal (MPa) scal−smeas/smeas (%)Temperature (°C) Strain rate (s−1) smeas (MPa)

1513.8 −1.325 1700 1533.71501.6 1519.62000 1.2

1228.11229.3 −0.117003002.31237.02000 1209.2

1258.4 1244.62500 −1.11251.41273.0 −1.727001058.5 0.2500 1700 1056.4

−2.51074.21101.720001103.8 1080.62500 −2.1

869.1 878.7700 1700 1.11.5876.7863.72000

883.6 0.22500 881.8907.9 895.23300 −1.4

686.5702.7 −2.31700900691.2 −2.42000 708.2

2.5700.1683.02500507.7 515.31100 2000 1.5526.6 524.02500 −0.5

Average=−0.27S.D.=1.67True strain=0.2

where A represents a constant, and is often yieldstrength. B is the material constant and n is the workhardening coefficient. Computed in accordance withthis model, the variations of A, B and n with strain rateand temperature are shown in Table 3. It is found thatthe yield strength increases with strain rate at tempera-tures ranging from 25 to 1100°C but decreases withtemperature for a given strain rate. For material con-stant B, it is seen that a decrease of temperature or anincrease of strain rate leads to a decrease in the materialconstant B. With regard to the work hardening coeffi-

cient, n, for all the strain rates and temperatures stud-ied, the rate of work hardening decreases considerablyas the testing temperature and strain rate increase. Thisresult indicates that thermal softening always occurs athigh temperature and at high strain rates and thatdeformation and interface friction cause the specimentemperature to increase. However, this rise of tempera-ture leads to a dramatic reduction of the flow strengthand the rate of work hardening.

In order to compare the accuracy of flow stress, ascalculated by Ludwik’s equation with that obtained

Fig. 5. Variations of strain rate sensitivity as a function of plasticstrain for specimen deformed at 700°C under different strain rateranges.

Fig. 4. Influence of strain rate on flow stress at a constant plasticstrain of 10%, as a function of temperature.


Fig. 6. Variations of strain rate sensitivity as a function of tempera-ture for deformation at a true strain of 0.05 under different strain rateranges.

Fig. 8. Variations of temperature sensitivity as a function of tempera-ture under different strain rates.

3.2. Effects of strain rate on flow stress

The influence of strain rate on flow stress at 10%fixed plastic strain is shown in Fig. 4, which presentsthe variations of flow stress at different temperatureswith the logarithm of the mean strain rate. For eachtested temperature, the strain rate sensitivity, as definedby the slope of the flow stress versus the log strain raterelationship, is almost constant. However, as seen in thecomparison of temperature ranges, flow stress is quitesensitive to temperature but relatively less sensitive tostrain rate. Typically, the macroscopic flow stress s

(compared at constant strain e) varies linearly withstrain rate, meaning that a thermally activated mecha-nism controls the deformation process. The same be-havior has been observed for many materials [18–20],and their strength appears to increase dramaticallywhen the strain rate is raised above 103 s−1 (or even 104

s−1). The work of Follansbee et al. [21] on pure poly-crystalline copper showed that at a strain rate ofaround 104 s−1, the mechanism controlling the rate ofdislocation motion changed from thermal activation atthe lower strain rate to viscous drag at the higher strainrate.

The plot of flow stress against the logarithm of strainrate, as mentioned above, can be utilized to obtain thestrain rate sensitivity parameter b, defined as:

b=(s2−s1)ln(e; 2/e; 1)

(12)

where the compressive stresses s2 and s1 are obtainedin tests conducted at the constant strain rates e; 2 and e; 1respectively and are calculated at the same value ofcompressive plastic strain. Fig. 5 represents strain ratesensitivity as a function of true strain at different strainrate ranges for specimens tested at 700°C. When aspecimen is deformed to a large strain value, the rate of

from the experiments, a mean error of flow stress isdefined as:

percent error=100(calculated stress−measured stress)

/measured stress. (11)

Flow stress is calculated at a true strain of 0.1 and0.2 using the Ludwik equation. An estimate of theconsistency of this technique is obtained from the stan-dard deviation. Table 4 and Table 5 list the results ofthis evaluation and show that the average error in theflow stress estimate is 0.81 and 0.27%, and the S.D. is1.84 and 1.67% for true strains of 0.1 and 0.2, respec-tively. Although the calculated values agree quite wellwith the experimental ones, it should be noted that thelatter are used for our subsequent mechanical charac-teristics analysis and data treatment.

Fig. 7. Variations of temperature sensitivity as a function of plasticstrain for a strain rate of 2×103 s−1 under different temperatureranges.


Table 6Increase values of temperature for specimen deformed at strain rate of 2×103 s−1 and strains ranging from 0.05 to 0.25 under six initial testedtemperatures

Initial tested temperature (°C) DT (°C)

e=0.15 e=0.2e=0.05 e=0.25e=0.1

117.085.9 148.955.725 26.671.2 96.6300 22.4 122.546.461.9 84.0500 19.5 40.4 106.5

68.750.7 87.033.0700 15.926.1 40.0 54.2 68.7900 12.6

29.6 40.21100 9.3 19.3 50.0

thermal softening caused by temperature increase isgreater than that of strain hardening induced by plasticdeformation, and thus it can be seen that strain ratesensitivity decreases rapidly with true strain for all thestrain rate ranges. In addition, at a fixed strain value,strain rate sensitivity increases with increasing strainrate range. A similar relationship between strain ratesensitivity and true strain are also found for our othertested temperatures. The dependence of strain rate sen-sitivity on temperature is also shown in Fig. 6, whichindicates that strain rate sensitivity increases with tem-perature for four tested strain rate regions. Fig. 6 alsoindicates that the increase rate of strain rate sensitivityis more pronounced at high strain rates and hightemperature.

3.3. Temperature sensiti6ity of flow stress

From the dynamic stress–strain curves in Fig. 3, itcan be seen that temperature has considerable effect onthe flow stress, especially at high temperature ranges.Based on these results, temperature sensitivity is ex-pressed and calculated by a parameter na, defined as

na = {ln(s2/s1)}/{ln(T2/T1)} (13)

where T2\T1, and T1=25°C. Using the flow stress–strain data, na can be easily calculated by Eq. (13). Fig.7 shows the variation of na with true strain for speci-mens deformed at a strain rate of 2×103 s−1 underdifferent temperature ranges. As can be seen from Fig.7, na increases slightly with true strain for each incre-mental temperature range. However, at a fixed truestrain value, it increases rapidly with temperature incre-ment. On the basis of these results, it is clear that theeffect of temperature on the variations of temperaturesensitivity is more pronounced than that of true strain.This implies that during deformation, the rate of ther-mal softening dominates the flow stress behaviour andthat the rate of strain hardening does not play a leadingrole in temperature sensitivity characteristics.

As mentioned above, temperature sensitivity has noobvious dependence on plastic true strain. For compari-

son purposes, we can neglect the effect of plastic truestrain and take an average temperature sensitivity valuefor each temperature range under different strain rateconditions. Fig. 8 shows the average na as a function oftemperature under five different strain rate conditions.It can be seen that for a given temperature range, underdifferent strain rate conditions, the value of average na

is about the same and appears to be independent ofstrain rate, which indicates that the average na does notchange as strain rate increases. In addition, the higherthe temperature, the more the average na increases. Thisimplies that a considerable temperature sensitivity offlow stress exists, especially when the material is sub-jected to high temperature loading. It should also benoted that in Fig. 8, because flow stress–strain data fora strain rate of 2.5×103 s−1 at room temperature isabsent, a reference temperature of 300°C is chosen forcalculation, and a similar relation between average na

and temperature is obtained.

3.4. Deformation constituti6e equation

Macroscopic results obtained in our study haveshown that the plastic deformation behaviour of Ti–6Al–4V alloy depends strongly on strain rate and tem-perature. There are currently many differentconstitutive models available to describe the dynamicbehaviour of materials with specific material constants[22–27]. One of the most common rate-dependent mod-els, called the Johnson–Cook model [28], is used todescribe the above mentioned deformation behavior.This model presents a constitutive equation for metalssubjected to large strains, high strain rates and hightemperatures and is expressed as

s= (A+Ben)(1+c ln e; *)(1−T*m) (14)

where e is the equivalent plastic strain; e; *=e; /e; 0 is theratio of test strain rate to a reference strain rate, wherewe have chosen e; =10−5 s−1; T* is the homologoustemperature (T−Troom)/(Tmelt−Troom), and s and e arestress and strain, respectively. The five material con-stants are A, B, n, c, and m. The expression in the first


Table 7Material parameters of Ti–6Al–4V alloy, AISI 4340 alloy and tungsten composite based on Johnson–Cook equation

B (MPa) n c mMaterials A (MPa)

1.00.0350.47683.1Ti–6Al–4V 724.7510 0.26 0.0144340 Alloy 1.03792

0.019 0.78Tungsten composite 1093 1270 0.42

set of brackets gives stress as a function of strain withstrain hardening coefficient B and strain hardeningexponent n. The expression in the second and third setsof brackets represents the effects of strain rate andtemperature, respectively.

The stress–strain curve data in the plot of Fig. 3 canbe used to determine coefficients and exponents of theconstitutive equation by a regression analysis techniquewhich determines the best-fit parameters for all of thedata for a given alloy. It should be noted that duringplastic deformation, the work done in plastic flow isconverted to heat which produces a rise in temperaturein the specimen. Thus, the magnitude of temperaturerise must be reckoned and a current temperature shouldbe used to calculate the flow stress in our simulationmodel. At the presented test conditions, the tempera-ture increase caused by the plastic work done, DW, canbe estimated by DT=DW/(rCp), where DT is the in-crease in temperature, Cp is the specific heat (0.13 cal (g°C)−1), r the density (4.43 g cm−3) and DW is the areaunder the stress–strain curve, which is given by DW=e

0sx · dex. This calculation has been made for each ofthe tested temperature–strain-rate conditions. Table 6lists the increase values of the temperature for speci-mens deformed at a strain rate of 2×103 s−1 andstrains of 0.05, 0.1, 0.15, 0.2 and 0.25 under six initialtested temperatures. According to the Johnson–Cookconstitutive equation, and to replace the initial temper-ature with the current temperature for each interval of

strain in the regression process, the values of specificmaterial parameters A, B, n, c, and m for Ti–6Al–4Valloy are obtained and listed in Table 7, in which theones for AISI 4340 alloy [29], and tungsten composites[9] evaluated by other investigators are also shown forcomparison. By putting these five obtained materialparameters into the Johnson–Cook constitutive equa-tion, the deformation response of Ti–6Al–4V alloyunder mathematical conditions equivalent to our actualexperimental test conditions is predicted, and an exam-ple of the result corresponding to a strain rate of isshown in Fig. 9. Thus, we can conclude that thetheoretical predictions do agree with the experimentalresult.

3.5. Fracture beha6iour and microstructuralobser6ations on deformed specimens

After mechanical testing, scanning electron micro-scope studies were performed on the deformed speci-mens in an effort to identify fracture characteristics andmechanisms. We found that fracture occurred at anangle of 45° to the compression axis, was catastrophicand associated with adiabatic shear bands under strainrates higher than for all the tested temperatures. Aspecimen deformed at 500°C under a strain rate of2.5×103 s−1, in Fig. 10a, is given as an example. In thetop view of the sample as seen in Fig. 10b, an arc-shaped adiabatic shear band can be seen, while a flatshear band can be seen in the side view shown in Fig.10c. All these observations show that there is a mi-crostructural change in the shear bands. Traditionally,there are two types of adiabatic shear bands which canbe distinguished: (a) transformed bands, in which aphase change occurs, and (b) deformed bands, whichare characterized by a very high shear strain in a verythin zone of deformation. In our case, there is no doubtthat the transformed band plays an important role inthe fracture behaviour and is the predominant fracturefeature of Ti–6Al–4V alloy.

From the observed fracture features, it is found thatthe rupture of specimens always occurs due to a separa-tion along the adiabatic shear bands. Initially, voids areusually nucleated circularly or elliptically in the cross-section of the shear band. Then, generally, the voids arejoined by severing of the separating ligaments. In Fig.11, a typical array of coalesced voids in a well-devel-

Fig. 9. Comparison between predicted and measured stress–straincurves for a strain rate of 2×103 s−1.


Fig. 10. a. Scanning electron micrographs of the specimen afterfracture at 500°C and at 2.5×103 s−1, showing typical adiabaticshear failure. b. Top view by optical microscopy of the specimen afterfracture at 500°C and 2×103 s−1, showing arc type of adiabaticshear band. c. Side view by optical microscopy of the specimen afterfracture at 500°C and 2×103 s−1, showing planar type of adiabaticshear band.

Fig. 11. Voids and cracks in an adiabatic shear band for the specimendeformed at 700°C under 2×103 s−1.

ture features and the orientation of the adiabatic shearband is shown in Fig. 12. In the separated fracturesurface, two regions, called the shear zone and thetension zone, are indicated. It is known that in uniaxialcompression, bands of localized deformation occur onplanes of maximum shear stress oriented at 45° to theaxis of compression. However, when there is a bulge onthe specimen, a hoop stress appears at the equatorialplane of the cylindrical surface which induces a tensileloading state. Therefore, the shear zone and tensionzone coexist in the shear band and form an X in thefracture plane. Besides, it is generally recognized thatquickly loading most materials under high strain ratedeformation will cause a dramatic rise of temperature.This rise in temperature will then cause thermal soften-ing and transform the deformation from a homoge-neous state to a heterogeneous state characterized by adistribution of localized shear bands. Thus, we can saythat the formation and propagation of an adiabaticshear band is the favourite mode of failure for thismaterial.

It is interesting to note that adiabatic shear behaviorcan also be found in the specimen tested above theb-transus temperature, i.e. 997.5°C. This phenomenon

Fig. 12. Schematic description of fracture features and orientation ofadiabatic shear band.

oped shear band is shown. The diameters of the voidsand the widths of the cracks are always less than thoseof the shear band from which they formed. Our obser-vations also demonstrate that the fracture sites can bemicrovoids nucleated either at weak points in the adia-batic shear zone, or at sections of the shear surfaceswhere significant thermal softening is undergone.

In order to describe the fracture mechanisms operat-ing in this material, a schematic of the observed frac-


Fig. 13. Optical micrograph of adiabatic shear band obtained fromthe specimen tested at 1100°C under 2×103 s−1.

of left side. This can be explained by the fact that thedeformation between the shear band and equatorialplane of the cylindrical surface is larger than that of thecentral region of specimen.

It is also noticeable that the thickness of adiabaticshear band is dependent upon the transus temperature.For example, under a strain rate of 2.5×103 s−1, thethickness of the adiabatic shear band increases from14.7 mm at 500°C to 45 mm at 1100°C. This indicatesthat formation and growth of the adiabatic shear bandare more active in the b phase than in the a+b phaseand that all microstructural variants in the adiabaticshear band are very sensitive to transus temperature.Also, the thickness of the adiabatic shear band de-creases fairly rapidly with tested temperature, indicatingthat deformation becomes more difficult for specimenstested below the transus temperature.

4. Conclusions

The plastic deformation behaviour of Ti–6Al–4Valloy subjected to high strain rate under various tem-perature conditions has been reported. Results obtainedfrom mechanical testing show that flow stress, materialconstants and work hardening coefficient are sensitiveto strain rate and temperature. Evaluation of tempera-ture effects shows that temperature sensitivity increaseswith the increase of temperature, but is independent ofstrain rate. By using our experimentally determinedspecific material parameters in our proposed constitu-tive equation, a fairly good agreement with the experi-mental results is seen. Fracture observations reveal thatthe adiabatic shear bands are the precursor to crackformation and fracture. Hardness and thickness of theadiabatic shear bands are found to change directly withthe transus temperature. An increase of temperatureresults in a decrease of the microhardness of the shearbands, but the thickness of the shear bands is found toincrease with temperature.

References

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is clearly seen in Fig. 13, which corresponds to aspecimen deformed at 1100°C and 2.5×103 s−1. Whenthe tested temperature exceeds the b-transus tempera-ture, there is a dramatic change in matrix structure, i.e.from a+b phase to a single phase of b. Although theadiabatic shear band features both below and above thetransus temperature are similar to each other, there is alarge difference in the hardness and thickness of theshear bands (see Fig. 14). In other words, the hardnessof the adiabatic shear band obtained from the specimentested below transus temperature, 450 Hv, is muchgreater than that of above, i.e. 395 Hv. In addition, inboth cases, the hardness reaches its maximum at thecenter of the shear band, then dramatically decreases tomatrix hardness at the two sides. Moreover, the hard-ness in the right side of shear band is higher than that

Fig. 14. Change in microhardness of adiabatic shear band for speci-mens tested at strain rate of, at both 500°C and 1100°C.


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