Hot working and geometric dynamic recrystallisation behaviourof a near-α titanium alloy with acicular microstructure

I. Balasundar a,n, T. Raghu a, B.P. Kashyap b

a Near Net Shape Group, Aeronautical Materials Division, Defence Metallurgical Research Laboratory, Hyderabad 500058, Indiab Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India

a r t i c l e i n f o

Article history:Received 26 September 2013Received in revised form29 January 2014Accepted 29 January 2014Available online 8 February 2014

Keywords:Near-α titanium alloyIMI 834GlobularisationAvrami analysisAcicular microstructure

a b s t r a c t

The hot working behaviour of near-α titanium alloy – TITAN 29A (equivalent to IMI 834) with an acicularstarting microstructure was evaluated by carrying out hot compression tests over a range of temperatures(850–1060 1C) and strain rates (3�10�4–100/s). Using the flow curves, processing maps were generated toidentify the safe processing window for the material. The material exhibits a deterministic domain between920 and 1030 1C at low strain rates of 3�10�4–10�3/s where it undergoes geometric dynamic recrystallisa-tion (GDRX) or globularisation of α lamellae. The initiation and evolution of globularisation was investigatedusing the flow curve analysis method. The work hardening rate (θ)–flow stress (s) curve was used toestimate the critical strain (εc) required for initiation of globularisation and the saturation stress (ssat) fordynamic recovery (DRV). The recrystallised or globularised volume fraction (X) was estimated from thedifference between the calculated DRV and experimental DRX curves. The estimated globularised volumefraction modelled using Avrami equation was found to match with the microstructural observations.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Near-α titanium alloys are used extensively as aeroenginecomponent material because of their excellent creep and fatigueproperties. TITAN 29A (equivalent to IMI 834) is one such materialthat exhibits excellent creep and fatigue properties up to atemperature of 600 1C [1–3]. This material is expected to replaceIMI 685 as high pressure compressor rotor and stator because ofits higher thermal capability. As these aeroengine stators (ringsand blades) and rotors (discs, shafts and blades) are critical class-Icomponents, they are expected to have a combination of static anddynamic mechanical properties [4–10]. In order to achieve theseproperties it is essential to have an understanding on the hightemperature deformation behaviour of the material. This knowl-edge is required not only to control the microstructure andproperties but also to design a suitable thermo-mechanical pro-cess (TMP) schedule to produce these critical components onreliable and repeatable basis [11]. The processing map techniqueis widely used to understand the high temperature deformationbehaviour and microstructural evolution over a range of tempera-tures and strain rates [11]. This technique has also been used byearlier investigators to address the high temperature deformationcharacteristics of various other titanium alloys [12–16].

The processing map is developed on the basis of dynamicmaterials modelling (DMM) concept that considers the rate ofviscoplastic heat generation during deformation, and the rate ofenergy dissipation associated with concurrent microstructuralchanges as complementary. A non-dimensional efficiency indexη is used to represent the power dissipation through microstruc-tural mechanisms and is given as [11]

η¼ 2mmþ1

ð1Þ

where m is the strain rate sensitivity index of the material, whichmay be a function of deformation temperature and strain rate, andcould represent a specific deformation mechanism. The iso-effi-ciency contour plot on the temperature–strain rate field constitutesthe power dissipation map. Several domains can be identified in themap based on the η contours (i.e. power dissipation characteristics),each of which representing a dominant deformation mechanism. Thepeak efficiency condition of the domain is taken to be the optimumdeformation condition. In addition to the η contours, the instabilitycriterion [11] given by the following equation (Eq. (2)) is applied todelineate the temperature–strain rate regimes of flow instability onthe processing map.

ξð_εÞ ¼ ∂ lnðm=mþ1Þ∂ ln _ε

þmo0 ð2Þ

A detailed description of the development of the model as well as thesignificance of η value in the interpretation of the domain was givenby Prasad and Sasidhara [11].

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Materials Science & Engineering A

http://dx.doi.org/10.1016/j.msea.2014.01.0880921-5093 & 2014 Elsevier B.V. All rights reserved.

n Corresponding author.E-mail address: i_balasundar@dmrl.drdo.in (I. Balasundar).

Materials Science & Engineering A 600 (2014) 135–144

Though the high temperature deformation behaviour of IMI834 (equivalent to TITAN 29A) has been studied and reportedearlier by various researchers [17–22], these studies were limitedin terms of test conditions and microstructure aspects. Except forthe preliminary studies by the present group [7,23], no studies onthe processing maps for the material with an acicular startingmicrostructure have been reported.

It is well reported that the acicular structure provides bettercreep, fracture toughness represented by stress intensity factor K1C

and resistance to fatigue crack growth due to low cycle fatigue.Conversely, for high cycle fatigue, crack imitation is the importantfactor and it is necessary to have a fine equiaxed structure [1–3].However, from the thermo-mechanical processing point of view,for a given temperature and strain rate, the initial acicularstructure is reported to higher flow stress when compared to theequiaxed structure and also it undergoes notable dynamic soft-ening which is due, at least in part, to the fragmentation of the αlamellae [12–16]. This fragmentation of acicular α phase isdependent on strain and strain path [12–16]. When thermo-mechanical processing is carried out to produce critical class-Iaeroengine components with complex geometry, different regionsof the component would experience different amount of strainleading to difference in the volume fraction or globularisation αphase in different regions which is undesirable. Further, if theacicular structure can be converted into a fine equiaxed structure,aeroengine components can be produced under superplasticconditions. Therefore, it is essential to understand the deformationbehaviour of TITAN 29A with acicular starting microstructure.

The objective of the current work is therefore (i) to evaluate thehot working behaviour of the material by carrying out hotcompression test over a range of temperature and strain rate.Using the flow curves so generated, (ii) establish processing mapsto identify optimum processing conditions in terms of tempera-ture and strain rate. (iii) Identify the micro-mechanism operatingunder the optimal conditions and evaluate its characteristics. Theinformation generated in the current study would provide usefulguidelines to select the temperature and strain rate conditionsalong with the knowledge of concurrent microstructure evolutionfor better control during component manufacturing stages.

2. Experimental procedure

The as-cast TITAN 29A material was cogged to impart 30%deformation by M/s MIDHANI, Hyderabad, at 1100 1C. After defor-mation the material was air cooled. This material was procuredfrom M/s MIDHANI, Hyderabad, in the form of 150 mm diameterbars. The chemical composition of the alloy was analysed to beTi–5.8Al–4.0Sn–3.5Zr–0.7Nb–0.5Mo–0.35Si–0.06C (wt%) andtraces of Fe and Ni above 250 ppm. The as-received material wasfound to have deformed acicular microstructure as shown in Fig. 1.The transformed β grain size and the β transus of the materialwere found to be about 1–1.5 mm and 1070 1C respectively. As thematerial was received in as-forged or deformed condition, it isessential to evaluate whether the prior deformation received bythe material is sufficient to cause recrystallisation of the α lamellaeor the β grains. The as-received material was exposed to hightemperature (850–1060 1C) for 60 min and quenched in water. Forcompression testing, cylindrical samples with 10 mm diameterand 15 mm height were electro-discharge machined (EDM) fromthe as-received bar. The edges of the machined samples werechamfered to avoid fold-over during the initial stages of testing.A small hole of 0.8 mm in diameter, reaching the centre of thesample, was drilled at its mid-height through which a K-typethermocouple was inserted to monitor and record the temperature[11]. Deltaglaze 347 coated TITAN 29A samples were then heated

to the deformation temperature at a rate of 5 1C/min using a splittype furnace, held for 30 min and compressed under constant truestrain rates on a computer controlled servo-hydraulic testingmachine, custom built by M/s. DARTEC, UK. Isothermal hotcompression tests were conducted over a range of temperaturesand strain rates, as shown in Table 1, to generate the hightemperature flow curves. The adiabatic temperature rise duringdeformation was recorded and corrections were made in thestress–strain curve as discussed elsewhere [11]. Using the flowcurves, the efficiency and instability parameters were evaluatedand plotted on a temperature–strain rate scale to obtain theprocessing maps. Subsequently, the processing maps were usedto identify various micro-mechanisms and delineate the unsafe–safe regions based on microstructural observations. The sampleswere generally water quenched upon deformation to freeze thehigh temperature microstructure. The water quenched sampleswere then cut parallel to compression direction. The cut faceswere mechanically polished and etched with Kroll's reagentcomposed of 6 ml HNO3–3 ml HF–100 ml H2O. Microstructuralexamination was made using an optical microscope.

3. Results and discussions

3.1. Effect of heat treatment

Typical microstructures obtained after subjecting the materialto heat treatment at temperatures from 850 to 1060 1C for 60 minfollowed by water quenching are shown in Fig. 2. It can be readilyinferred from Fig. 2 that though a certain amount of staticrecrystallisation or globularisation of α lamellae is observed, theprior deformation of 30% provided by the material supplier is notsufficient enough to cause complete break-up of the lamellarstructure. The break-up or globularisation of lamellae observedhere is a result of α dissolving into the β phase and not fromdynamic globularisation. It can also be seen that most of the αphase retains its lamellar structure in spite of concomitant

Fig. 1. As-received TITAN 29A with acicular microstructure.

Table 1Test conditions used for compression tests.

Parameter Condition

Temperature (1C) 850, 900, 950, 1000, 1030, 1060Strain rate (1/s) 3�10�4, 10�3, 10�2, 10�1, 100

% Reduction in height 50%� True strain (ε): 0.694

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changes in the thickness and volume fraction over this heattreatment temperature range.

3.2. Flow curves

The true stress–true strain curves obtained from the hotcompression tests are shown in Fig. 3. It can be seen that thematerial exhibits flow softening behaviour at high strain rates. Therate of softening is higher at lower strain and decreases consider-ably at higher strains. Typically, the flow stress increases initiallyand reaches a peak at a critical strain and thereafter decreaseswith further straining but eventually reaches a steady state formost cases around a strain of 0.6. As the deformation is carried outat high temperature, dynamic restoration processes such asrecovery and recrystallisation play an important role in theevolution of dislocation density. As these restoration processesgain significance, the flow stress decreases sharply and reaches asteady state where the dynamic softening effect is able to counterthe work-hardening effect and establish a dynamic equilibrium.The peak stress is found to decrease with increasing temperatureand decreasing strain rate. Further, the strain (εp) at which a peakin the flow stress (sp) is observed was found to increase withincreasing strain rate. However, no such noticeable trend wasobserved with varying temperature. The degree of flow softeningwas found to decrease with increasing temperature and decreas-ing strain rate. Yield drop in true stress–true strain curve isobserved when the material is deformed between 1030 and1060 1C. The occurrence of the yield drop is attributed to the highsolute content (E15%) and the large atomic size difference ofcarbon and silicon with respect to titanium as explained byWanjara et al. [18] and Philippart et al. [24].

3.2.1. Effect of temperatureThe variation of flow stress at strain of 0.5 with respect to

temperature is shown in Fig. 4a. It can be seen that above 1000 1C,the flow stress is less sensitive to temperature where as below1000 1C it is highly temperature sensitive. At temperatures below1000 1C, the α phase controls the deformation behaviour whereas

above 1000 1C, the β phase controls the deformation behaviour.During deformation, the material dissipates the instantaneouspower by metallurgical processes commensurate with the levelof power applied. The applied power induces an entropy produc-tion rate which is controlled by the second law of thermodynamicsand is directly related to the grain size [25]. The rate of entropyproduction by the material reaches a maximumwhen the materialhas the potential to develop very fine grain size or new interfaces[25]. The rate of entropy production decreases when grain growthor coarsening takes place. Temperature sensitivity or the entropyrate ratio ‘S’ evaluated ðS¼ ð1=TÞ½∂ log s=∂ð1=TÞ�Þ is shown inFig. 4b. It can be seen that, irrespective of the strain rate, theentropy rate ratio reaches to a peak value at intermediatetemperature (950 1C). The material is expected to exhibit a finegrain structure in this temperature range. It can also be seen at850 1C for high strain rates such as 10�1, 100/s that the value oftemperature sensitivity parameter (S) is less than 1 which impliesthat the material experiences unstable flow under these condi-tions. Microstructural observations with respect to temperaturesensitivity S are discussed later.

3.2.2. Effect of strain rateThe variation of flow stress and strain rate sensitivity

ðm¼ ∂ ln s=∂ ln _εÞ with strain rate is shown in Fig. 5a and brespectively. The flow stress of the material increases withincreasing strain rate. The material exhibits a high strain ratesensitivity at lower strain rates for all temperatures except at1060 1C. At 1060 1C, the material exhibits higher strain ratesensitivity at intermediate strain rate. At higher strain ratesensitivity regions the material is expected to have better work-ability. The maximum strain rate sensitivity of 0.34 is noted at950 1C for a strain rate of 3�10�4/s.

3.3. Processing map

The processing map generated for the material at a true plasticstrain of 0.5 is shown in Fig. 6. The instability map super-imposed

Fig. 2. Effect of thermal exposure on the as-received microstructure at (a) 850, (b) 950, (c) 1030, and (d) 1060 1C.

I. Balasundar et al. / Materials Science & Engineering A 600 (2014) 135–144 137

Fig. 3. True stress–true strain curves for TITAN 29A at various temperatures and strain rates.

Fig. 4. Variation of (a) flow stress and (b) temperature sensitivity parameter ‘S’ with temperature.

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(shaded region) with the efficiency map divides the map intostable and unstable flow or instability region.

3.3.1. Unstable regionThe unstable flow region lies between 850 and 900 1C and 10�1

and 100/s. Microstructural observation on the samples testedunder the unstable flow regime (region marked A in Fig. 6)exhibits intense flow localisation in the form of bands andcavitation at the prior β grain boundaries. This is illustrated inFig. 7. The intense deformation localisation observed here can befound to lie at about 451 to the compression axis. At high strainrates, adiabatic heat generated during deformation is not con-ducted away due to insufficient time and low thermal conductivityof titanium alloys. This localised adiabatic heating increases thetemperature of the sample. As the temperature increases, the flowstress required for further deformation decreases. This localiseddecrease in flow stress at certain region due to adiabatic heatingcauses further deformation to be concentrated in that regionleading to the formation of such bands. Two types of bandsnamely shear bands and deformation bands are observed in theinstability region. Shear bands are non-crystallographic in natureand may pass through several grains, and even extend through the

specimen [26]. They are a result of plastic instability, and can bethought of as equivalent to necking which occurs in a tensile test.The shear bands should be distinguished clearly from deformationbands that are found within individual grains [26]. It is often foundin coarse grained materials that the individual grains subdivide ona large scale during deformation into regions of different orienta-tion, as a consequence of either inhomogeneous stresses trans-mitted by neighbouring grains or the intrinsic instability of thegrain during plastic deformation. The resulting deformation bandsdeform on different slip systems and may develop widely diver-gent orientations [26]. The narrow regions between the deforma-tion bands may be either diffuse or sharp and are called astransition bands. Two reasons have been put forth for the forma-tion of deformation bands: one originates in the ambiguityassociated with the selection of the operative slip systems. Inmany cases the imposed strain can be accommodated by morethan one set of slip systems and the different sets lead to rotationsin different senses. In the second type, different regions of a grainmay experience different strains if the work done within the bandsis less than that required for homogeneous deformation and if thebands can be arranged so that the net strain matches the overalldeformation [26]. The banding shown in Fig. 7a is a shear bandwhile the one shown in (b) is a deformation band as it is observedwithin a prior beta grain and does not extend over other grains.

The microstructure consists of three micro-constituents: lamel-lar α colonies inside the grains, grain boundary α at the prior βgrain boundaries and a thin layer of β in-between the colonyboundary and grain boundary α layer. It is well known that the hcpα lamellae generally exhibits a Burgers orientation relationship(OR) with the matrix bcc β phase in titanium alloys. The same ORis also observed between the grain boundary (GB) α lamellae andthe β matrix. It is not possible for the GB α to form whilemaintaining the Burgers OR with both the adjacent β grains[27–29]. Thus, the GB α maintains the Burgers OR with the βphase in one of the adjacent grains, and it generally chooses aspecific orientation that allows it to have as small a deviation fromthe Burgers OR as possible with the other grain. As a result, it isalso able to maintain partial coherency with the β grain on the“non-Burgers” side, because of this the partial coherent interfacewill have ledges and misfit-compensating dislocations [27–29].Out of these three, the colonies have the highest strength due tothe specific crystallographic orientation relationship while the βlayer is inherently a softest phase at the deformation temperaturein view of its bcc structure. During deformation by uniaxialcompression, sliding of the prior β boundary with a near 451orientation occurs across the soft β layer and produces stressconcentration at the GB α–thin β interface. If the stress

Fig. 5. Variation of (a) flow stress and (b) strain rate sensitivity with strain rate at various temperatures.

Fig. 6. Processing map for TITAN 29A with acicular starting microstructure.

I. Balasundar et al. / Materials Science & Engineering A 600 (2014) 135–144 139

concentration is not relieved by the deformation of adjacent GB αphase, cracks like the ones shown in Fig. 7c and d are expected toform along the interface.

3.3.2. Stable regionThe map exhibits one domain between 920 and 1030 1C and

3�10�4 and 10�3/s with a maximum efficiency value of 50%.As per dynamic materials modelling (DMM), the domains arethe regions in which deterministic deformation mechanisms areoperating [11]. It can be observed that, the temperature–strain rateregime, where the deterministic domain is observed, correspondsto the regime of high entropy rate ratio (Fig. 4b) and high strainrate sensitivity (Fig. 5b) exhibited by the material. The micro-structure (Fig. 8) observed within this temperature–strain rateregime (regions D–F in Fig. 6) indicates that the acicular lamellarstructure that was present in the material is destroyed to variousdegrees and converted into globular structure. The degree oflamellae break-up is seen to increase with increase in temperatureand decrease in strain rate as shownin Figs. 8 and 9.

Globularisation of α lamellae consists of two events: (1) break-ing up of lamellae due to subgrain formation as proposed byMargolin and Cohen [30,31] or by shear banding as proposed byWeiss et al. [32], and (2) formation of globules by penetration of βphase along the α/α interface [33]. Therefore, it can be seen thatbreak-up of lamellae is strain dependent while the completion ofglobularisation is diffusion dependent. As the temperatureincreases and strain rate decreases, diffusional processes requiredfor interface movement to achieve complete globularisationincrease and hence the globularised volume fraction increaseswith increasing temperature and decreasing strain rate.

From these observations on the microstructure, high entropy rateratio and high strain rate sensitivity, it can be concluded that thedomain corresponds to continuous or geometric dynamic recrystalli-sation (DRX) in which the lamellar structure is converted into aglobular or equiaxed structurewithout any clear demarcation between

the nucleation and growth stage [34,35]. The efficiency value (50%)obtained here also concurs well with that reported for globularisationof other titanium alloys [12–16]. The microstructure obtained in thebifurcation regions such as B, C, H, J, G and I in Fig. 6 is shown in Fig. 9.It can be seen that in regions B and C that correspond to a deformationtemperature of 900 1C, the material exhibits extensive kinking of αlamellae. As the deformation temperature increases to 1000 1C(regions H and J), kinking and partial recrystallisation of lamellaecan be observed. In the regions G and I that have efficiency valuesclose to 45%, the material exhibits continuous dynamic recrystallisa-tion of α lamellae.

3.4. Flow curve analysis for globularisation kinetics

The globularisation fraction estimated experimentally as afunction of strain in various titanium alloys [36–40] is plottedusing the Johnson–Mehl–Arvami–Kolmogorov (JMAK) or morepopularly the Avrami equation:

X ¼ 1�expð�ktnÞ ð3Þhere, X represents the globularised volume fraction, t is the time,k is the Avrami constant, and n is the Avrami time exponent.However, for the current study, the globularisation kinetics isdetermined using a flow curve analysis method that was originallyproposed by Medina and Hernandez [41] and recently modified byJonas et al. [42]. The concept of flow curve analysis for the study ofglobularisation kinetics is described below.

During hot deformation, the dynamic restoration processestend to cancel out the work hardening effects. In dynamicrecovery, the generation and accumulation of dislocations due towork hardening are continuously offset by dislocation rearrange-ment and annihilation, resulting in a steady state (ssat) value asshown in Fig. 10 (marked DRV). When DRX is the restorationprocess, the flow curve (marked DRX) rises initially as a result ofwork hardening and recovery processes to a peak value (sp),beyond which the flow stress drops with increasing strain to a

Fig. 7. Flow instabilities: (a) shear band in the material deformed at 850 1C and 100/s, (b) deformation band in the material deformed at 900 1C and 100/s, and (c) cavitationat prior beta boundaries in the material deformed at 850 1C and (d) a strain rate of 10�1/s.

I. Balasundar et al. / Materials Science & Engineering A 600 (2014) 135–144140

Fig. 8. Microstructures of the material deformed with a strain rate of 3�10�4/s at (a) 950, (b) 1000, and (c) 1030 1C.

Fig. 9. Microstructures obtained in the bifurcation regions within Fig. 6. (a) B – 900 1C; 10�3/s, (b) C – 900 1C; 10�2/s, (c) H – 1000 1C; 10�2/s, (d) J – 1000 1C; 10�1/s,(e) G – 1030 1C; 10�3/s, and (f) I – 1030 1C; 10�2/s – of the processing maps.

I. Balasundar et al. / Materials Science & Engineering A 600 (2014) 135–144 141

steady state value (sss) at large strain. This flow behaviour istypical of DRX and has been reported for a wide variety of metalsand alloys including titanium [39–42]. It has been shown that acritical value of strain (εc) is required for initiating the DRXprocess. In general, the strain required for arriving at the steadystate (sss) in DRV is much higher than εc for DRX.

Intuitively then, the effect of time on structural changes in SRXis similar to that of strain in DRX [42]. Eq. (3) can be modified to beconsistent with the DRX mechanism by replacing time (t) from thestart of DRX with strain (εx) at a given rate. The modified form ofthe equation is

X ¼ 1�expð�kðε�εcÞnÞ ð4ÞNote that the strain under consideration is beyond the criticalstrain associated with the DRX process and is represented accord-ingly as (ε�εc). Since fraction globularised or recrystallised (X) isrelated to the loss of dislocations, in principle, it can be estimatedfrom the difference between the DRX flow curve (obtained byexperiment) and the corresponding DRV flow curve (expectedstress–strain behaviour if recovery was the only operative restora-tion process) predicted under similar conditions of deformation.

In this modelling technique, an important consideration is theconstruction of the DRV flowcurve. The necessary inputs for thisare stress parameters like sc (corresponding to εc), sp, ssat,associated strain parameters, and work hardening. A key assump-tion in this modelling technique is that the DRV work hardeningbehaviour represents the behaviour of the un-recrystallisedvolume and it is similar to that before the initiation of DRX. Inthis sense, the work hardening behaviour of DRV is expected to besimilar to that of the experimental DRX curve prior to sc.

In this work, the DRX or globularisation kinetics of the materialis evaluated using the method developed by Jonas et al. [42]. Thefirst step toward DRX analysis is the identification of εc and thecorresponding sc. Conventionally, εc is determined from a plot ofwork hardening rate, i.e., θ¼ds/dε (calculated from the experi-mental s–ε data) versus s. A typical plot of θ versus s for TITAN29A sample deformed at 1030 1C and 3�10�4/s is presented inFig. 11a, which shows that θ decreases with increasing s. The onsetof DRX corresponds to the point of deviation from linearity in thiswork hardening curve. Since it is difficult to discern the exactlocation of this deviation in such plots, the suggestion of Poliakand Jonas [43] is adopted here to determine sc from a plot ofthe derivative of the work hardening rate (�dθ/ds) against s.A minimum in the plot of (�dθ/ds) versus s, shown in the inset inFig. 11a delineates the point of inflection of the work hardeningplot. The stress value corresponding to this minimum is sc (the

associated εc is noted from the s–ε curve). The initial rapiddecrease of θ with increase in s is considered to be associatedwith dynamic recovery [41,42], and a linear extrapolation of thepart just before the critical point to θ¼0 establishes ssat. Locatingsp and εp is straight forward from s–ε plot as it is related toθ¼ds/dε¼0. The next step is to generate the DRV curve. Jonaset al. [42] described work hardening using the Estrin–Mecking[44] equation that was established to evaluate the change indislocation density (ρ) with respect to strain:

dρdε

¼ h�rρ ð5Þ

where h is the athermal work hardening rate and r is the rate ofdynamic recovery. Using this equation, Jonas et al. [41] derived theequation for flow stress for dynamic recovery as

s¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½s2

sat�ðs2sat�s2

0Þexpð�rεÞ�q

ð6Þ

where s0 is the yield stress and can be determined from theexperimental flow curve. Using some simple algebraic substitu-tions, the following relationship was established:

sdsdε

¼ sθ¼ 0:5rs2sat�0:5rs2 ð7Þ

It is seen from Eq. (7) that, r and ssat can be obtained from theslope and intercept of the sθ versus s2 curve, respectively. Fig. 11bshows the corresponding work hardening or recovery curveobtained using the r and ssat along with the experimental DRXcurve. Similar such curves were established for 1000 1C, 3�10�4/sand 1030 1C, 10�3/s deformation conditions.

The recrystallised or globularised volume fraction is consideredto be responsible for the difference between the DRV and DRXflow curves. The difference between these two curves (Δss) is thenet softening and is directly attributed to DRX. The maximumvalue of Δss is (ssat–sss) where sss is the steady state stress underDRX conditions. The evolution of fractional softening with strain isexpressed as X¼Δss/(ssat–sss). Thus, once the recovery curve isderived for a particular deformation condition, the evolution of Xwith (ε–εc) can be obtained in a straight forward manner. Fig. 12aand b shows the variation of globularised fraction (X) with (ε–εc)for various temperatures and strain rates respectively. The Avramiexponents n and k are determined by nonlinear regression fit ofthe calculated X versus (ε–εc) data according to Eq. (4). The nvalues obtained for different deformation conditions are found tobe between 1.40 and 1.95. The n values obtained here fall withinthe range that has been reported for various titanium alloys [35–39]. It can be seen from Fig. 12 that the globularised volumefraction (X) varies sigmoidally with strain and increases withincreasing temperature and decreasing strain rate. The resultshere conform well to microstructural observations describedearlier.

4. Conclusions

The hot working behaviour of near-α titanium alloy TITAN 29Awith an acicular starting microstructure was evaluated using hotcompression tests. The flow curves were used to generate theprocessing maps and dynamic recovery (DRV) curves to character-ise the recrystallisation behaviour. The conclusions drawn arepresented below.

� The flow curves exhibit typical DRX behaviour with a singlepeak stress which then decreases gradually to achieve a steady-state for most of the deformation conditions.

� TITAN 29A material, exhibits instabilities in the form of shearbands, deformation bands and cavitation at prior β boundaries

Fig. 10. Schematic representation of flow curve during dynamic recovery anddynamic recrystallisation defining various stresses and strain parameters involvedin the Avrami or flow curve analysis.

I. Balasundar et al. / Materials Science & Engineering A 600 (2014) 135–144142

when deformed between 850 and 900 1C and at 10�1–100/s.The safe deterministic domain lies between 920 and 1030 1Cand at 3�10�4–10�3/s where geometric dynamic recrystalli-sation (GDRX) or globularisation of α lamellae takes place.

� The initiation and progress of globularisation of α lamellae canbe well predicted on the basis of the Avrami relation inconjunction with the features of flow curve and workhardening rate.

� As diffusion of β phase to separate the globularised particles isthe rate controlling step, the fraction globularised increasedwith increasing temperature and decreasing strain rate. Byincreasing deformation temperature and decreasing strain rate,the globularisation curve shifts to lower strains which concurswell with the microstructural observations.

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Fig. 12. Globularised fraction (X) with strain and (a) deformation temperature, (b) strain rate.

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