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Hot working and geometric dynamic recrystallisation behaviour of a near-α titanium alloy with acicular microstructure
Materials Science & Engineering A 600 (2014) 135–144
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Hot working and geometric dynamic recrystallisation behaviour of a near-α titanium alloy with acicular microstructure I. Balasundar a,n, T. Raghu a, B.P. Kashyap b a b
Near Net Shape Group, Aeronautical Materials Division, Defence Metallurgical Research Laboratory, Hyderabad 500058, India Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
art ic l e i nf o
a b s t r a c t
Article history: Received 26 September 2013 Received in revised form 29 January 2014 Accepted 29 January 2014 Available online 8 February 2014
The hot working behaviour of near-α titanium alloy – TITAN 29A (equivalent to IMI 834) with an acicular starting 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 to identify the safe processing window for the material. The material exhibits a deterministic domain between 920 and 1030 1C at low strain rates of 3 10 4–10 3/s where it undergoes geometric dynamic recrystallisation (GDRX) or globularisation of α lamellae. The initiation and evolution of globularisation was investigated using the flow curve analysis method. The work hardening rate (θ)–flow stress (s) curve was used to estimate the critical strain (εc) required for initiation of globularisation and the saturation stress (ssat) for dynamic recovery (DRV). The recrystallised or globularised volume fraction (X) was estimated from the difference between the calculated DRV and experimental DRX curves. The estimated globularised volume fraction modelled using Avrami equation was found to match with the microstructural observations. & 2014 Elsevier B.V. All rights reserved.
Keywords: Near-α titanium alloy IMI 834 Globularisation Avrami analysis Acicular microstructure
1. Introduction Near-α titanium alloys are used extensively as aeroengine component material because of their excellent creep and fatigue properties. TITAN 29A (equivalent to IMI 834) is one such material that exhibits excellent creep and fatigue properties up to a temperature of 600 1C [1–3]. This material is expected to replace IMI 685 as high pressure compressor rotor and stator because of its higher thermal capability. As these aeroengine stators (rings and blades) and rotors (discs, shafts and blades) are critical class-I components, they are expected to have a combination of static and dynamic mechanical properties [4–10]. In order to achieve these properties it is essential to have an understanding on the high temperature deformation behaviour of the material. This knowledge is required not only to control the microstructure and properties but also to design a suitable thermo-mechanical process (TMP) schedule to produce these critical components on reliable and repeatable basis [11]. The processing map technique is widely used to understand the high temperature deformation behaviour and microstructural evolution over a range of temperatures and strain rates [11]. This technique has also been used by earlier investigators to address the high temperature deformation characteristics of various other titanium alloys [12–16].
n
Corresponding author. E-mail address: [email protected] (I. Balasundar).
http://dx.doi.org/10.1016/j.msea.2014.01.088 0921-5093 & 2014 Elsevier B.V. All rights reserved.
The processing map is developed on the basis of dynamic materials modelling (DMM) concept that considers the rate of viscoplastic heat generation during deformation, and the rate of energy dissipation associated with concurrent microstructural changes as complementary. A non-dimensional efficiency index η is used to represent the power dissipation through microstructural mechanisms and is given as [11]
η¼
2m mþ1
ð1Þ
where m is the strain rate sensitivity index of the material, which may be a function of deformation temperature and strain rate, and could represent a specific deformation mechanism. The iso-efficiency contour plot on the temperature–strain rate field constitutes the power dissipation map. Several domains can be identified in the map based on the η contours (i.e. power dissipation characteristics), each of which representing a dominant deformation mechanism. The peak efficiency condition of the domain is taken to be the optimum deformation condition. In addition to the η contours, the instability criterion [11] given by the following equation (Eq. (2)) is applied to delineate the temperature–strain rate regimes of flow instability on the processing map.
ξðε_ Þ ¼
∂ lnðm=m þ 1Þ þ m o0 ∂ ln ε_
ð2Þ
A detailed description of the development of the model as well as the significance of η value in the interpretation of the domain was given by Prasad and Sasidhara [11].
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Though the high temperature deformation behaviour of IMI 834 (equivalent to TITAN 29A) has been studied and reported earlier by various researchers [17–22], these studies were limited in terms of test conditions and microstructure aspects. Except for the preliminary studies by the present group [7,23], no studies on the processing maps for the material with an acicular starting microstructure have been reported. It is well reported that the acicular structure provides better creep, 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 important factor 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 acicular structure is reported to higher flow stress when compared to the equiaxed structure and also it undergoes notable dynamic softening which is due, at least in part, to the fragmentation of the α lamellae [12–16]. This fragmentation of acicular α phase is dependent on strain and strain path [12–16]. When thermomechanical processing is carried out to produce critical class-I aeroengine components with complex geometry, different regions of the component would experience different amount of strain leading to difference in the volume fraction or globularisation α phase in different regions which is undesirable. Further, if the acicular structure can be converted into a fine equiaxed structure, aeroengine components can be produced under superplastic conditions. Therefore, it is essential to understand the deformation behaviour of TITAN 29A with acicular starting microstructure. The objective of the current work is therefore (i) to evaluate the hot working behaviour of the material by carrying out hot compression test over a range of temperature and strain rate. Using the flow curves so generated, (ii) establish processing maps to identify optimum processing conditions in terms of temperature and strain rate. (iii) Identify the micro-mechanism operating under the optimal conditions and evaluate its characteristics. The information generated in the current study would provide useful guidelines to select the temperature and strain rate conditions along with the knowledge of concurrent microstructure evolution for 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 deformation the material was air cooled. This material was procured from M/s MIDHANI, Hyderabad, in the form of 150 mm diameter bars. The chemical composition of the alloy was analysed to be Ti–5.8Al–4.0Sn–3.5Zr–0.7Nb–0.5Mo–0.35Si–0.06C (wt%) and traces of Fe and Ni above 250 ppm. The as-received material was found to have deformed acicular microstructure as shown in Fig. 1. The transformed β grain size and the β transus of the material were found to be about 1–1.5 mm and 1070 1C respectively. As the material was received in as-forged or deformed condition, it is essential to evaluate whether the prior deformation received by the material is sufficient to cause recrystallisation of the α lamellae or the β grains. The as-received material was exposed to high temperature (850–1060 1C) for 60 min and quenched in water. For compression testing, cylindrical samples with 10 mm diameter and 15 mm height were electro-discharge machined (EDM) from the as-received bar. The edges of the machined samples were chamfered to avoid fold-over during the initial stages of testing. A small hole of 0.8 mm in diameter, reaching the centre of the sample, was drilled at its mid-height through which a K-type thermocouple was inserted to monitor and record the temperature [11]. Deltaglaze 347 coated TITAN 29A samples were then heated
Fig. 1. As-received TITAN 29A with acicular microstructure.
Table 1 Test conditions used for compression tests. Parameter
Condition
Temperature (1C) Strain rate (1/s) % Reduction in height
850, 900, 950, 1000, 1030, 1060 3 10 4, 10 3, 10 2, 10 1, 100 50% True strain (ε): 0.694
to the deformation temperature at a rate of 5 1C/min using a split type furnace, held for 30 min and compressed under constant true strain rates on a computer controlled servo-hydraulic testing machine, custom built by M/s. DARTEC, UK. Isothermal hot compression tests were conducted over a range of temperatures and strain rates, as shown in Table 1, to generate the high temperature flow curves. The adiabatic temperature rise during deformation was recorded and corrections were made in the stress–strain curve as discussed elsewhere [11]. Using the flow curves, the efficiency and instability parameters were evaluated and plotted on a temperature–strain rate scale to obtain the processing maps. Subsequently, the processing maps were used to identify various micro-mechanisms and delineate the unsafe– safe regions based on microstructural observations. The samples were generally water quenched upon deformation to freeze the high temperature microstructure. The water quenched samples were then cut parallel to compression direction. The cut faces were mechanically polished and etched with Kroll's reagent composed of 6 ml HNO3–3 ml HF–100 ml H2O. Microstructural examination was made using an optical microscope.
3. Results and discussions 3.1. Effect of heat treatment Typical microstructures obtained after subjecting the material to heat treatment at temperatures from 850 to 1060 1C for 60 min followed by water quenching are shown in Fig. 2. It can be readily inferred from Fig. 2 that though a certain amount of static recrystallisation or globularisation of α lamellae is observed, the prior deformation of 30% provided by the material supplier is not sufficient enough to cause complete break-up of the lamellar structure. The break-up or globularisation of lamellae observed here is a result of α dissolving into the β phase and not from dynamic globularisation. It can also be seen that most of the α phase retains its lamellar structure in spite of concomitant
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Fig. 2. Effect of thermal exposure on the as-received microstructure at (a) 850, (b) 950, (c) 1030, and (d) 1060 1C.
changes in the thickness and volume fraction over this heat treatment temperature range. 3.2. Flow curves The true stress–true strain curves obtained from the hot compression tests are shown in Fig. 3. It can be seen that the material exhibits flow softening behaviour at high strain rates. The rate of softening is higher at lower strain and decreases considerably at higher strains. Typically, the flow stress increases initially and reaches a peak at a critical strain and thereafter decreases with further straining but eventually reaches a steady state for most cases around a strain of 0.6. As the deformation is carried out at high temperature, dynamic restoration processes such as recovery and recrystallisation play an important role in the evolution of dislocation density. As these restoration processes gain significance, the flow stress decreases sharply and reaches a steady state where the dynamic softening effect is able to counter the work-hardening effect and establish a dynamic equilibrium. The peak stress is found to decrease with increasing temperature and decreasing strain rate. Further, the strain (εp) at which a peak in the flow stress (sp) is observed was found to increase with increasing strain rate. However, no such noticeable trend was observed with varying temperature. The degree of flow softening was found to decrease with increasing temperature and decreasing strain rate. Yield drop in true stress–true strain curve is observed when the material is deformed between 1030 and 1060 1C. The occurrence of the yield drop is attributed to the high solute content ( E15%) and the large atomic size difference of carbon and silicon with respect to titanium as explained by Wanjara et al. [18] and Philippart et al. [24]. 3.2.1. Effect of temperature The 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 below 1000 1C it is highly temperature sensitive. At temperatures below 1000 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 instantaneous power by metallurgical processes commensurate with the level of power applied. The applied power induces an entropy production rate which is controlled by the second law of thermodynamics and is directly related to the grain size [25]. The rate of entropy production by the material reaches a maximum when the material has the potential to develop very fine grain size or new interfaces [25]. The rate of entropy production decreases when grain growth or coarsening takes place. Temperature sensitivity or the entropy rate ratio ‘S’ evaluated ðS ¼ ð1=TÞ½∂ log s=∂ð1=TÞÞ is shown in Fig. 4b. It can be seen that, irrespective of the strain rate, the entropy rate ratio reaches to a peak value at intermediate temperature (950 1C). The material is expected to exhibit a fine grain structure in this temperature range. It can also be seen at 850 1C for high strain rates such as 10 1, 100/s that the value of temperature sensitivity parameter (S) is less than 1 which implies that the material experiences unstable flow under these conditions. Microstructural observations with respect to temperature sensitivity S are discussed later.
3.2.2. Effect of strain rate The variation of flow stress and strain rate sensitivity ðm ¼ ∂ ln s=∂ ln ε_ Þ with strain rate is shown in Fig. 5a and b respectively. The flow stress of the material increases with increasing strain rate. The material exhibits a high strain rate sensitivity at lower strain rates for all temperatures except at 1060 1C. At 1060 1C, the material exhibits higher strain rate sensitivity at intermediate strain rate. At higher strain rate sensitivity regions the material is expected to have better workability. The maximum strain rate sensitivity of 0.34 is noted at 950 1C for a strain rate of 3 10 4/s.
3.3. Processing map The processing map generated for the material at a true plastic strain of 0.5 is shown in Fig. 6. The instability map super-imposed
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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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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.
(shaded region) with the efficiency map divides the map into stable and unstable flow or instability region.
3.3.1. Unstable region The unstable flow region lies between 850 and 900 1C and 10 1 and 100/s. Microstructural observation on the samples tested under the unstable flow regime (region marked A in Fig. 6) exhibits intense flow localisation in the form of bands and cavitation at the prior β grain boundaries. This is illustrated in Fig. 7. The intense deformation localisation observed here can be found to lie at about 451 to the compression axis. At high strain rates, adiabatic heat generated during deformation is not conducted away due to insufficient time and low thermal conductivity of titanium alloys. This localised adiabatic heating increases the temperature of the sample. As the temperature increases, the flow stress required for further deformation decreases. This localised decrease in flow stress at certain region due to adiabatic heating causes further deformation to be concentrated in that region leading to the formation of such bands. Two types of bands namely shear bands and deformation bands are observed in the instability region. Shear bands are non-crystallographic in nature and may pass through several grains, and even extend through the
specimen [26]. They are a result of plastic instability, and can be thought of as equivalent to necking which occurs in a tensile test. The shear bands should be distinguished clearly from deformation bands that are found within individual grains [26]. It is often found in coarse grained materials that the individual grains subdivide on a large scale during deformation into regions of different orientation, as a consequence of either inhomogeneous stresses transmitted by neighbouring grains or the intrinsic instability of the grain during plastic deformation. The resulting deformation bands deform on different slip systems and may develop widely divergent orientations [26]. The narrow regions between the deformation bands may be either diffuse or sharp and are called as transition bands. Two reasons have been put forth for the formation of deformation bands: one originates in the ambiguity associated with the selection of the operative slip systems. In many cases the imposed strain can be accommodated by more than one set of slip systems and the different sets lead to rotations in different senses. In the second type, different regions of a grain may experience different strains if the work done within the bands is less than that required for homogeneous deformation and if the bands can be arranged so that the net strain matches the overall deformation [26]. The banding shown in Fig. 7a is a shear band while the one shown in (b) is a deformation band as it is observed within a prior beta grain and does not extend over other grains. The microstructure consists of three micro-constituents: lamellar α colonies inside the grains, grain boundary α at the prior β grain boundaries and a thin layer of β in-between the colony boundary and grain boundary α layer. It is well known that the hcp α lamellae generally exhibits a Burgers orientation relationship (OR) with the matrix bcc β phase in titanium alloys. The same OR is also observed between the grain boundary (GB) α lamellae and the β matrix. It is not possible for the GB α to form while maintaining the Burgers OR with both the adjacent β grains [27–29]. Thus, the GB α maintains the Burgers OR with the β phase in one of the adjacent grains, and it generally chooses a specific orientation that allows it to have as small a deviation from the Burgers OR as possible with the other grain. As a result, it is also able to maintain partial coherency with the β grain on the “non-Burgers” side, because of this the partial coherent interface will have ledges and misfit-compensating dislocations [27–29]. Out of these three, the colonies have the highest strength due to the specific crystallographic orientation relationship while the β layer is inherently a softest phase at the deformation temperature in view of its bcc structure. During deformation by uniaxial compression, sliding of the prior β boundary with a near 451 orientation occurs across the soft β layer and produces stress concentration at the GB α–thin β interface. If the stress
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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) cavitation at prior beta boundaries in the material deformed at 850 1C and (d) a strain rate of 10 1/s.
concentration is not relieved by the deformation of adjacent GB α phase, cracks like the ones shown in Fig. 7c and d are expected to form along the interface.
3.3.2. Stable region The 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 are the regions in which deterministic deformation mechanisms are operating [11]. It can be observed that, the temperature–strain rate regime, where the deterministic domain is observed, corresponds to the regime of high entropy rate ratio (Fig. 4b) and high strain rate sensitivity (Fig. 5b) exhibited by the material. The microstructure (Fig. 8) observed within this temperature–strain rate regime (regions D–F in Fig. 6) indicates that the acicular lamellar structure that was present in the material is destroyed to various degrees and converted into globular structure. The degree of lamellae break-up is seen to increase with increase in temperature and decrease in strain rate as shownin Figs. 8 and 9. Globularisation of α lamellae consists of two events: (1) breaking up of lamellae due to subgrain formation as proposed by Margolin and Cohen [30,31] or by shear banding as proposed by Weiss et al. [32], and (2) formation of globules by penetration of β phase along the α/α interface [33]. Therefore, it can be seen that break-up of lamellae is strain dependent while the completion of globularisation is diffusion dependent. As the temperature increases and strain rate decreases, diffusional processes required for interface movement to achieve complete globularisation increase and hence the globularised volume fraction increases with increasing temperature and decreasing strain rate. From these observations on the microstructure, high entropy rate ratio and high strain rate sensitivity, it can be concluded that the domain corresponds to continuous or geometric dynamic recrystallisation (DRX) in which the lamellar structure is converted into a globular or equiaxed structure without any clear demarcation between
the nucleation and growth stage [34,35]. The efficiency value (50%) obtained here also concurs well with that reported for globularisation of other titanium alloys [12–16]. The microstructure obtained in the bifurcation 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 deformation temperature of 900 1C, the material exhibits extensive kinking of α lamellae. As the deformation temperature increases to 1000 1C (regions H and J), kinking and partial recrystallisation of lamellae can be observed. In the regions G and I that have efficiency values close to 45%, the material exhibits continuous dynamic recrystallisation of α lamellae. 3.4. Flow curve analysis for globularisation kinetics The globularisation fraction estimated experimentally as a function of strain in various titanium alloys [36–40] is plotted using the Johnson–Mehl–Arvami–Kolmogorov (JMAK) or more popularly the Avrami equation: X ¼ 1 expð kt n Þ
ð3Þ
here, 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 is determined using a flow curve analysis method that was originally proposed by Medina and Hernandez [41] and recently modified by Jonas et al. [42]. The concept of flow curve analysis for the study of globularisation kinetics is described below. During hot deformation, the dynamic restoration processes tend to cancel out the work hardening effects. In dynamic recovery, the generation and accumulation of dislocations due to work hardening are continuously offset by dislocation rearrangement and annihilation, resulting in a steady state (ssat) value as shown in Fig. 10 (marked DRV). When DRX is the restoration process, the flow curve (marked DRX) rises initially as a result of work hardening and recovery processes to a peak value (sp), beyond which the flow stress drops with increasing strain to a
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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.
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associated εc is noted from the s–ε curve). The initial rapid decrease of θ with increase in s is considered to be associated with dynamic recovery [41,42], and a linear extrapolation of the part just before the critical point to θ ¼0 establishes ssat. Locating sp and εp is straight forward from s–ε plot as it is related to θ ¼ ds/dε ¼ 0. The next step is to generate the DRV curve. Jonas et al. [42] described work hardening using the Estrin–Mecking [44] equation that was established to evaluate the change in dislocation density (ρ) with respect to strain: dρ ¼ h r ρ dε
Fig. 10. Schematic representation of flow curve during dynamic recovery and dynamic recrystallisation defining various stresses and strain parameters involved in the Avrami or flow curve analysis.
steady state value (sss) at large strain. This flow behaviour is typical of DRX and has been reported for a wide variety of metals and alloys including titanium [39–42]. It has been shown that a critical value of strain (εc) is required for initiating the DRX process. In general, the strain required for arriving at the steady state (sss) in DRV is much higher than εc for DRX. Intuitively then, the effect of time on structural changes in SRX is similar to that of strain in DRX [42]. Eq. (3) can be modified to be consistent with the DRX mechanism by replacing time (t) from the start of DRX with strain (εx) at a given rate. The modified form of the equation is X ¼ 1 expð kðε εc Þn Þ
ð4Þ
Note that the strain under consideration is beyond the critical strain associated with the DRX process and is represented accordingly as (ε εc). Since fraction globularised or recrystallised (X) is related to the loss of dislocations, in principle, it can be estimated from the difference between the DRX flow curve (obtained by experiment) and the corresponding DRV flow curve (expected stress–strain behaviour if recovery was the only operative restoration process) predicted under similar conditions of deformation. In this modelling technique, an important consideration is the construction of the DRV flowcurve. The necessary inputs for this are stress parameters like sc (corresponding to εc), sp, ssat, associated strain parameters, and work hardening. A key assumption in this modelling technique is that the DRV work hardening behaviour represents the behaviour of the un-recrystallised volume and it is similar to that before the initiation of DRX. In this sense, the work hardening behaviour of DRV is expected to be similar to that of the experimental DRX curve prior to sc. In this work, the DRX or globularisation kinetics of the material is evaluated using the method developed by Jonas et al. [42]. The first step toward DRX analysis is the identification of εc and the corresponding sc. Conventionally, εc is determined from a plot of work hardening rate, i.e., θ ¼ ds/dε (calculated from the experimental s–ε data) versus s. A typical plot of θ versus s for TITAN 29A sample deformed at 1030 1C and 3 10 4/s is presented in Fig. 11a, which shows that θ decreases with increasing s. The onset of DRX corresponds to the point of deviation from linearity in this work hardening curve. Since it is difficult to discern the exact location of this deviation in such plots, the suggestion of Poliak and Jonas [43] is adopted here to determine sc from a plot of the derivative of the work hardening rate ( dθ/ds) against s. A minimum in the plot of ( dθ/ds) versus s, shown in the inset in Fig. 11a delineates the point of inflection of the work hardening plot. The stress value corresponding to this minimum is sc (the
ð5Þ
where h is the athermal work hardening rate and r is the rate of dynamic recovery. Using this equation, Jonas et al. [41] derived the equation for flow stress for dynamic recovery as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ¼ ½s2sat ðs2sat s20 Þexpð rεÞ ð6Þ where s0 is the yield stress and can be determined from the experimental flow curve. Using some simple algebraic substitutions, the following relationship was established: ds ¼ sθ ¼ 0:5r s2sat 0:5r s2 dε
s
ð7Þ
It is seen from Eq. (7) that, r and ssat can be obtained from the slope and intercept of the sθ versus s2 curve, respectively. Fig. 11b shows the corresponding work hardening or recovery curve obtained using the r and ssat along with the experimental DRX curve. Similar such curves were established for 1000 1C, 3 10 4/s and 1030 1C, 10 3/s deformation conditions. The recrystallised or globularised volume fraction is considered to be responsible for the difference between the DRV and DRX flow curves. The difference between these two curves (Δss) is the net softening and is directly attributed to DRX. The maximum value of Δss is (ssat–sss) where sss is the steady state stress under DRX conditions. The evolution of fractional softening with strain is expressed as X¼ Δss/(ssat–sss). Thus, once the recovery curve is derived for a particular deformation condition, the evolution of X with (ε–εc) can be obtained in a straight forward manner. Fig. 12a and b shows the variation of globularised fraction (X) with (ε–εc) for various temperatures and strain rates respectively. The Avrami exponents n and k are determined by nonlinear regression fit of the calculated X versus (ε–εc) data according to Eq. (4). The n values obtained for different deformation conditions are found to be between 1.40 and 1.95. The n values obtained here fall within the range that has been reported for various titanium alloys [35– 39]. It can be seen from Fig. 12 that the globularised volume fraction (X) varies sigmoidally with strain and increases with increasing temperature and decreasing strain rate. The results here conform well to microstructural observations described earlier.
4. Conclusions The hot working behaviour of near-α titanium alloy TITAN 29A with an acicular starting microstructure was evaluated using hot compression tests. The flow curves were used to generate the processing maps and dynamic recovery (DRV) curves to characterise the recrystallisation behaviour. The conclusions drawn are presented below.
The flow curves exhibit typical DRX behaviour with a single
peak stress which then decreases gradually to achieve a steadystate for most of the deformation conditions. TITAN 29A material, exhibits instabilities in the form of shear bands, deformation bands and cavitation at prior β boundaries
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Fig. 11. (a) θ versus s plot, (b) reconstructed dynamic recovery (DRV) curve with experimental DRX curve for TITAN 29A deformed at 1030 1C, 3 10 4/s.
Fig. 12. Globularised fraction (X) with strain and (a) deformation temperature, (b) strain rate.
when deformed between 850 and 900 1C and at 10 1–100/s. The safe deterministic domain lies between 920 and 1030 1C and at 3 10 4–10 3/s where geometric dynamic recrystallisation (GDRX) or globularisation of α lamellae takes place. The initiation and progress of globularisation of α lamellae can be well predicted on the basis of the Avrami relation in conjunction with the features of flow curve and work hardening rate. As diffusion of β phase to separate the globularised particles is the rate controlling step, the fraction globularised increased with increasing temperature and decreasing strain rate. By increasing deformation temperature and decreasing strain rate, the globularisation curve shifts to lower strains which concurs well with the microstructural observations.
References [1] D.F. Neal, Titanium 95-science and technology, in: Proceedings of VIII World Conference on Titanium, Birmingham, UK, 1995, pp. 2195–2204. [2] D.F. Neal, Proceedings of VI World Conference on Titanium, France, 1998, pp. 253–258. [3] T.W. Farthing, Proceedings of VI World Conference on Titanium, France, 1998, pp. 37–48. [4] T. Noda, M. Okabe, S. Isobe, S., Nishikiori, H. Hattori, Titanium 95-science and technology, in: Proceedings of VIII World Conference on Titanium, Birmingham, UK, 1995, pp. 2258–2264. [5] Y. Honnorat, Proceedings of VI World Conference on Titanium, France, 1998, pp. 365–379.
[6] I. Balasundar, M. Sudhakara Rao, T. Raghu, G.G. Saha, DMRL Technical Report, DMRL TR 2005 381, , 2005. [7] I. Balasundar, M. Sudhakara Rao, M. Rohatgi, T. Raghu, B.P. Kashyap, J. Mach. Form. Technol. 2 (2010) 141–156. [8] R.R. Boyer, Mater. Sci. Eng. A 213 (1996) 103–114. [9] B.P. Bewlay, M.F.X. Gigliotti, F.Z. Utyashev, O.A. Kaibyshev, Mater. Des. 21 (2000) 287–295. [10] B.P. Bewlay, M.F.X. Gigliotti, F.Z. Utyashev, O.A. Kaibyshev, J. Mater. Process. Technol. 135 (2003) 324–329. [11] Y.V.R.K. Prasad, S. Sasidhara, Hot Working Guide – A Compendium of Processing Maps, ASM International, Ohio, 1997. [12] Miaoquan Li, Hongsi Pan, Lin Yingying, Jia Luo, J. Mater. Process. Technol. 183 (2007) 71–76. [13] Young Niu, Hou Hongliang, Li Miaoquan, Zhiqiang Li, Mater. Sci. Eng. A 492 (2008) 24–28. [14] T. Seshacharyulu, S.C. Medeiros, W.G. Frazier, Y.V.R.K. Prasad, Mater. Sci. Eng. A 284 (2000) 184–194. [15] T. Seshacharyulu, S.C. Medeiros, J.T. Morgan, J.C. Malas, W.G. Frazier, Y.V.R. K. Prasad, Scr. Mater. 41 (1998) 283–288. [16] Weiju Jia, Weidong Zenga, Yigang Zhou, Jianrong Liu, Qingjiang Wang, Mater. Sci. Eng. A 528 (2011) 4068–4074. [17] P.S. Bate, P.L. Blackwell, J.W. Brooks, Proceedings of VI World Conference on Titanium, France, 1998, pp. 287–292. [18] P. Wanjara, M. Jahazi, H. Monajati, S. Yue, J.P. Immarigeon, Mater. Sci. Eng. A 396 (2005) 50–60. [19] P. Wanjara, M. Jahazi, H. Monajati, S. Yue, Mater. Sci. Eng. A 416 (2006) 300–311. [20] P. Vo, M. Jahazi, S. Yue, P. Bocher, Mater. Sci. Eng. A 447 (2007) 99–110. [21] M. Zhou, Mater. Sci. Eng. A 245 (1998) 29–38. [22] X. Wang, M. Jahazi, S. Yue, Mater. Sci. Eng. A 434 (2006) 188–193. [23] I. Balasundar, T. Raghu, B.P. Kashyap, Mater. Sci. Forum 710 (2012) 533–538. [24] I. Philippart, H.J. Rack, Mater. Sci. Eng. A 243 (1998) 196–200. [25] H.L. Gegel, J.C. Malas, S.M. Doraivelu, V.A. Shende, Forging and Forming, ASM Metals Handbook, Vol 14, 1998, ASM International; Ohio. [26] F.J. Humpreys, M. Hatherly, Recrystallization and Related Annealing Phenomenon, second edition, Elsevier, Oxford, 2004.
144
I. Balasundar et al. / Materials Science & Engineering A 600 (2014) 135–144
[27] T. Furuhara, J.M. Howe, H.I. Aaronson, Acta Metall. Mater. 39 (1991) 2873–2886. [28] T. Furuhara, T. Makai, Mater. Sci. Eng. A 312 (2001) 145–154. [29] R. Banerjee, Acta Mater. 52 (2004) 377–385. [30] H. Margolin, P. Cohen, Titanium 80-science and technology, in: Proceedings of IV International Conference on Titanium, Japan, 1980, pp. 1555–1561. [31] H. Margolin, P. Cohen, Titanium 80-science and technology, in: Proceedings of IV International Conference on Titanium, 1980, pp. 2991–2997. [32] I. Weiss, F.H. Froes, D. Eylon, G.E. Welsch, Metall. Trans. A 17 (1986) 1935–1947. [33] N.G Jones, M. Jackson, Mater. Sci. Technol. 27 (2011) 1025–1032. [34] H.J. McQueen, J.K. Solberg, N. Ryum, Philos. Mag. A 60 (1989) 473–485. [35] R.D. Doherty, D.A. Hughes, F.J. Humphreys, Mater. Sci. Eng. A 238 (1997) 219–274.
[36] Chan Hee Park, Kyung-Tae Park, Dong Hyuk Shin, Chong Soo Lee, Mater. Trans. 49 (2008) 2196–2200. [37] S.L. Semiatin, J.F. Thomas, P. Dadras, Metall. Trans. A 14 (1983) 2363–2374. [38] Hong-Wu Song, Shi-Hong Zhang, Ming Cheng, J. Alloys Compd. 480 (2009) 922–927. [39] Wu Cheng-bao, Yang He, Fan Xiao-guang, Sun Zhi-chao, Trans. Nonferr. Soc. China 21 (2011) 1963–1969. [40] Kaixuan Wanga, Weidong Zenga, Yongqing Zhao, Yunjin Lai, Yigang Zhoua, Mater. Sci. Eng. A 527 (2010) 2559–2566. [41] S.F. Medina, C.A. Hernandez, Acta Mater. 44 (1996) 165–171. [42] J.J. Jonas, X. Quelennee, L. Jiang, E. Martin, Acta Mater. 57 (2009) 2748–2756. [43] E.I. Poliak, J.J. Jonas, Acta Mater. 44 (1996) 127–136. [44] Y. Estrin, H. Mecking, Acta Mater. 32 (1984) 57–70.
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Hot working and geometric dynamic recrystallisation behaviour of a near-α titanium alloy with acicular microstructure I. Balasundar a,n, T. Raghu a, B.P. Kashyap b a b
Near Net Shape Group, Aeronautical Materials Division, Defence Metallurgical Research Laboratory, Hyderabad 500058, India Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
art ic l e i nf o
a b s t r a c t
Article history: Received 26 September 2013 Received in revised form 29 January 2014 Accepted 29 January 2014 Available online 8 February 2014
The hot working behaviour of near-α titanium alloy – TITAN 29A (equivalent to IMI 834) with an acicular starting 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 to identify the safe processing window for the material. The material exhibits a deterministic domain between 920 and 1030 1C at low strain rates of 3 10 4–10 3/s where it undergoes geometric dynamic recrystallisation (GDRX) or globularisation of α lamellae. The initiation and evolution of globularisation was investigated using the flow curve analysis method. The work hardening rate (θ)–flow stress (s) curve was used to estimate the critical strain (εc) required for initiation of globularisation and the saturation stress (ssat) for dynamic recovery (DRV). The recrystallised or globularised volume fraction (X) was estimated from the difference between the calculated DRV and experimental DRX curves. The estimated globularised volume fraction modelled using Avrami equation was found to match with the microstructural observations. & 2014 Elsevier B.V. All rights reserved.
Keywords: Near-α titanium alloy IMI 834 Globularisation Avrami analysis Acicular microstructure
1. Introduction Near-α titanium alloys are used extensively as aeroengine component material because of their excellent creep and fatigue properties. TITAN 29A (equivalent to IMI 834) is one such material that exhibits excellent creep and fatigue properties up to a temperature of 600 1C [1–3]. This material is expected to replace IMI 685 as high pressure compressor rotor and stator because of its higher thermal capability. As these aeroengine stators (rings and blades) and rotors (discs, shafts and blades) are critical class-I components, they are expected to have a combination of static and dynamic mechanical properties [4–10]. In order to achieve these properties it is essential to have an understanding on the high temperature deformation behaviour of the material. This knowledge is required not only to control the microstructure and properties but also to design a suitable thermo-mechanical process (TMP) schedule to produce these critical components on reliable and repeatable basis [11]. The processing map technique is widely used to understand the high temperature deformation behaviour and microstructural evolution over a range of temperatures and strain rates [11]. This technique has also been used by earlier investigators to address the high temperature deformation characteristics of various other titanium alloys [12–16].
n
Corresponding author. E-mail address: [email protected] (I. Balasundar).
http://dx.doi.org/10.1016/j.msea.2014.01.088 0921-5093 & 2014 Elsevier B.V. All rights reserved.
The processing map is developed on the basis of dynamic materials modelling (DMM) concept that considers the rate of viscoplastic heat generation during deformation, and the rate of energy dissipation associated with concurrent microstructural changes as complementary. A non-dimensional efficiency index η is used to represent the power dissipation through microstructural mechanisms and is given as [11]
η¼
2m mþ1
ð1Þ
where m is the strain rate sensitivity index of the material, which may be a function of deformation temperature and strain rate, and could represent a specific deformation mechanism. The iso-efficiency contour plot on the temperature–strain rate field constitutes the power dissipation map. Several domains can be identified in the map based on the η contours (i.e. power dissipation characteristics), each of which representing a dominant deformation mechanism. The peak efficiency condition of the domain is taken to be the optimum deformation condition. In addition to the η contours, the instability criterion [11] given by the following equation (Eq. (2)) is applied to delineate the temperature–strain rate regimes of flow instability on the processing map.
ξðε_ Þ ¼
∂ lnðm=m þ 1Þ þ m o0 ∂ ln ε_
ð2Þ
A detailed description of the development of the model as well as the significance of η value in the interpretation of the domain was given by Prasad and Sasidhara [11].
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Though the high temperature deformation behaviour of IMI 834 (equivalent to TITAN 29A) has been studied and reported earlier by various researchers [17–22], these studies were limited in terms of test conditions and microstructure aspects. Except for the preliminary studies by the present group [7,23], no studies on the processing maps for the material with an acicular starting microstructure have been reported. It is well reported that the acicular structure provides better creep, 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 important factor 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 acicular structure is reported to higher flow stress when compared to the equiaxed structure and also it undergoes notable dynamic softening which is due, at least in part, to the fragmentation of the α lamellae [12–16]. This fragmentation of acicular α phase is dependent on strain and strain path [12–16]. When thermomechanical processing is carried out to produce critical class-I aeroengine components with complex geometry, different regions of the component would experience different amount of strain leading to difference in the volume fraction or globularisation α phase in different regions which is undesirable. Further, if the acicular structure can be converted into a fine equiaxed structure, aeroengine components can be produced under superplastic conditions. Therefore, it is essential to understand the deformation behaviour of TITAN 29A with acicular starting microstructure. The objective of the current work is therefore (i) to evaluate the hot working behaviour of the material by carrying out hot compression test over a range of temperature and strain rate. Using the flow curves so generated, (ii) establish processing maps to identify optimum processing conditions in terms of temperature and strain rate. (iii) Identify the micro-mechanism operating under the optimal conditions and evaluate its characteristics. The information generated in the current study would provide useful guidelines to select the temperature and strain rate conditions along with the knowledge of concurrent microstructure evolution for 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 deformation the material was air cooled. This material was procured from M/s MIDHANI, Hyderabad, in the form of 150 mm diameter bars. The chemical composition of the alloy was analysed to be Ti–5.8Al–4.0Sn–3.5Zr–0.7Nb–0.5Mo–0.35Si–0.06C (wt%) and traces of Fe and Ni above 250 ppm. The as-received material was found to have deformed acicular microstructure as shown in Fig. 1. The transformed β grain size and the β transus of the material were found to be about 1–1.5 mm and 1070 1C respectively. As the material was received in as-forged or deformed condition, it is essential to evaluate whether the prior deformation received by the material is sufficient to cause recrystallisation of the α lamellae or the β grains. The as-received material was exposed to high temperature (850–1060 1C) for 60 min and quenched in water. For compression testing, cylindrical samples with 10 mm diameter and 15 mm height were electro-discharge machined (EDM) from the as-received bar. The edges of the machined samples were chamfered to avoid fold-over during the initial stages of testing. A small hole of 0.8 mm in diameter, reaching the centre of the sample, was drilled at its mid-height through which a K-type thermocouple was inserted to monitor and record the temperature [11]. Deltaglaze 347 coated TITAN 29A samples were then heated
Fig. 1. As-received TITAN 29A with acicular microstructure.
Table 1 Test conditions used for compression tests. Parameter
Condition
Temperature (1C) Strain rate (1/s) % Reduction in height
850, 900, 950, 1000, 1030, 1060 3 10 4, 10 3, 10 2, 10 1, 100 50% True strain (ε): 0.694
to the deformation temperature at a rate of 5 1C/min using a split type furnace, held for 30 min and compressed under constant true strain rates on a computer controlled servo-hydraulic testing machine, custom built by M/s. DARTEC, UK. Isothermal hot compression tests were conducted over a range of temperatures and strain rates, as shown in Table 1, to generate the high temperature flow curves. The adiabatic temperature rise during deformation was recorded and corrections were made in the stress–strain curve as discussed elsewhere [11]. Using the flow curves, the efficiency and instability parameters were evaluated and plotted on a temperature–strain rate scale to obtain the processing maps. Subsequently, the processing maps were used to identify various micro-mechanisms and delineate the unsafe– safe regions based on microstructural observations. The samples were generally water quenched upon deformation to freeze the high temperature microstructure. The water quenched samples were then cut parallel to compression direction. The cut faces were mechanically polished and etched with Kroll's reagent composed of 6 ml HNO3–3 ml HF–100 ml H2O. Microstructural examination was made using an optical microscope.
3. Results and discussions 3.1. Effect of heat treatment Typical microstructures obtained after subjecting the material to heat treatment at temperatures from 850 to 1060 1C for 60 min followed by water quenching are shown in Fig. 2. It can be readily inferred from Fig. 2 that though a certain amount of static recrystallisation or globularisation of α lamellae is observed, the prior deformation of 30% provided by the material supplier is not sufficient enough to cause complete break-up of the lamellar structure. The break-up or globularisation of lamellae observed here is a result of α dissolving into the β phase and not from dynamic globularisation. It can also be seen that most of the α phase retains its lamellar structure in spite of concomitant
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Fig. 2. Effect of thermal exposure on the as-received microstructure at (a) 850, (b) 950, (c) 1030, and (d) 1060 1C.
changes in the thickness and volume fraction over this heat treatment temperature range. 3.2. Flow curves The true stress–true strain curves obtained from the hot compression tests are shown in Fig. 3. It can be seen that the material exhibits flow softening behaviour at high strain rates. The rate of softening is higher at lower strain and decreases considerably at higher strains. Typically, the flow stress increases initially and reaches a peak at a critical strain and thereafter decreases with further straining but eventually reaches a steady state for most cases around a strain of 0.6. As the deformation is carried out at high temperature, dynamic restoration processes such as recovery and recrystallisation play an important role in the evolution of dislocation density. As these restoration processes gain significance, the flow stress decreases sharply and reaches a steady state where the dynamic softening effect is able to counter the work-hardening effect and establish a dynamic equilibrium. The peak stress is found to decrease with increasing temperature and decreasing strain rate. Further, the strain (εp) at which a peak in the flow stress (sp) is observed was found to increase with increasing strain rate. However, no such noticeable trend was observed with varying temperature. The degree of flow softening was found to decrease with increasing temperature and decreasing strain rate. Yield drop in true stress–true strain curve is observed when the material is deformed between 1030 and 1060 1C. The occurrence of the yield drop is attributed to the high solute content ( E15%) and the large atomic size difference of carbon and silicon with respect to titanium as explained by Wanjara et al. [18] and Philippart et al. [24]. 3.2.1. Effect of temperature The 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 below 1000 1C it is highly temperature sensitive. At temperatures below 1000 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 instantaneous power by metallurgical processes commensurate with the level of power applied. The applied power induces an entropy production rate which is controlled by the second law of thermodynamics and is directly related to the grain size [25]. The rate of entropy production by the material reaches a maximum when the material has the potential to develop very fine grain size or new interfaces [25]. The rate of entropy production decreases when grain growth or coarsening takes place. Temperature sensitivity or the entropy rate ratio ‘S’ evaluated ðS ¼ ð1=TÞ½∂ log s=∂ð1=TÞÞ is shown in Fig. 4b. It can be seen that, irrespective of the strain rate, the entropy rate ratio reaches to a peak value at intermediate temperature (950 1C). The material is expected to exhibit a fine grain structure in this temperature range. It can also be seen at 850 1C for high strain rates such as 10 1, 100/s that the value of temperature sensitivity parameter (S) is less than 1 which implies that the material experiences unstable flow under these conditions. Microstructural observations with respect to temperature sensitivity S are discussed later.
3.2.2. Effect of strain rate The variation of flow stress and strain rate sensitivity ðm ¼ ∂ ln s=∂ ln ε_ Þ with strain rate is shown in Fig. 5a and b respectively. The flow stress of the material increases with increasing strain rate. The material exhibits a high strain rate sensitivity at lower strain rates for all temperatures except at 1060 1C. At 1060 1C, the material exhibits higher strain rate sensitivity at intermediate strain rate. At higher strain rate sensitivity regions the material is expected to have better workability. The maximum strain rate sensitivity of 0.34 is noted at 950 1C for a strain rate of 3 10 4/s.
3.3. Processing map The processing map generated for the material at a true plastic strain of 0.5 is shown in Fig. 6. The instability map super-imposed
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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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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.
(shaded region) with the efficiency map divides the map into stable and unstable flow or instability region.
3.3.1. Unstable region The unstable flow region lies between 850 and 900 1C and 10 1 and 100/s. Microstructural observation on the samples tested under the unstable flow regime (region marked A in Fig. 6) exhibits intense flow localisation in the form of bands and cavitation at the prior β grain boundaries. This is illustrated in Fig. 7. The intense deformation localisation observed here can be found to lie at about 451 to the compression axis. At high strain rates, adiabatic heat generated during deformation is not conducted away due to insufficient time and low thermal conductivity of titanium alloys. This localised adiabatic heating increases the temperature of the sample. As the temperature increases, the flow stress required for further deformation decreases. This localised decrease in flow stress at certain region due to adiabatic heating causes further deformation to be concentrated in that region leading to the formation of such bands. Two types of bands namely shear bands and deformation bands are observed in the instability region. Shear bands are non-crystallographic in nature and may pass through several grains, and even extend through the
specimen [26]. They are a result of plastic instability, and can be thought of as equivalent to necking which occurs in a tensile test. The shear bands should be distinguished clearly from deformation bands that are found within individual grains [26]. It is often found in coarse grained materials that the individual grains subdivide on a large scale during deformation into regions of different orientation, as a consequence of either inhomogeneous stresses transmitted by neighbouring grains or the intrinsic instability of the grain during plastic deformation. The resulting deformation bands deform on different slip systems and may develop widely divergent orientations [26]. The narrow regions between the deformation bands may be either diffuse or sharp and are called as transition bands. Two reasons have been put forth for the formation of deformation bands: one originates in the ambiguity associated with the selection of the operative slip systems. In many cases the imposed strain can be accommodated by more than one set of slip systems and the different sets lead to rotations in different senses. In the second type, different regions of a grain may experience different strains if the work done within the bands is less than that required for homogeneous deformation and if the bands can be arranged so that the net strain matches the overall deformation [26]. The banding shown in Fig. 7a is a shear band while the one shown in (b) is a deformation band as it is observed within a prior beta grain and does not extend over other grains. The microstructure consists of three micro-constituents: lamellar α colonies inside the grains, grain boundary α at the prior β grain boundaries and a thin layer of β in-between the colony boundary and grain boundary α layer. It is well known that the hcp α lamellae generally exhibits a Burgers orientation relationship (OR) with the matrix bcc β phase in titanium alloys. The same OR is also observed between the grain boundary (GB) α lamellae and the β matrix. It is not possible for the GB α to form while maintaining the Burgers OR with both the adjacent β grains [27–29]. Thus, the GB α maintains the Burgers OR with the β phase in one of the adjacent grains, and it generally chooses a specific orientation that allows it to have as small a deviation from the Burgers OR as possible with the other grain. As a result, it is also able to maintain partial coherency with the β grain on the “non-Burgers” side, because of this the partial coherent interface will have ledges and misfit-compensating dislocations [27–29]. Out of these three, the colonies have the highest strength due to the specific crystallographic orientation relationship while the β layer is inherently a softest phase at the deformation temperature in view of its bcc structure. During deformation by uniaxial compression, sliding of the prior β boundary with a near 451 orientation occurs across the soft β layer and produces stress concentration at the GB α–thin β interface. If the stress
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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) cavitation at prior beta boundaries in the material deformed at 850 1C and (d) a strain rate of 10 1/s.
concentration is not relieved by the deformation of adjacent GB α phase, cracks like the ones shown in Fig. 7c and d are expected to form along the interface.
3.3.2. Stable region The 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 are the regions in which deterministic deformation mechanisms are operating [11]. It can be observed that, the temperature–strain rate regime, where the deterministic domain is observed, corresponds to the regime of high entropy rate ratio (Fig. 4b) and high strain rate sensitivity (Fig. 5b) exhibited by the material. The microstructure (Fig. 8) observed within this temperature–strain rate regime (regions D–F in Fig. 6) indicates that the acicular lamellar structure that was present in the material is destroyed to various degrees and converted into globular structure. The degree of lamellae break-up is seen to increase with increase in temperature and decrease in strain rate as shownin Figs. 8 and 9. Globularisation of α lamellae consists of two events: (1) breaking up of lamellae due to subgrain formation as proposed by Margolin and Cohen [30,31] or by shear banding as proposed by Weiss et al. [32], and (2) formation of globules by penetration of β phase along the α/α interface [33]. Therefore, it can be seen that break-up of lamellae is strain dependent while the completion of globularisation is diffusion dependent. As the temperature increases and strain rate decreases, diffusional processes required for interface movement to achieve complete globularisation increase and hence the globularised volume fraction increases with increasing temperature and decreasing strain rate. From these observations on the microstructure, high entropy rate ratio and high strain rate sensitivity, it can be concluded that the domain corresponds to continuous or geometric dynamic recrystallisation (DRX) in which the lamellar structure is converted into a globular or equiaxed structure without any clear demarcation between
the nucleation and growth stage [34,35]. The efficiency value (50%) obtained here also concurs well with that reported for globularisation of other titanium alloys [12–16]. The microstructure obtained in the bifurcation 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 deformation temperature of 900 1C, the material exhibits extensive kinking of α lamellae. As the deformation temperature increases to 1000 1C (regions H and J), kinking and partial recrystallisation of lamellae can be observed. In the regions G and I that have efficiency values close to 45%, the material exhibits continuous dynamic recrystallisation of α lamellae. 3.4. Flow curve analysis for globularisation kinetics The globularisation fraction estimated experimentally as a function of strain in various titanium alloys [36–40] is plotted using the Johnson–Mehl–Arvami–Kolmogorov (JMAK) or more popularly the Avrami equation: X ¼ 1 expð kt n Þ
ð3Þ
here, 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 is determined using a flow curve analysis method that was originally proposed by Medina and Hernandez [41] and recently modified by Jonas et al. [42]. The concept of flow curve analysis for the study of globularisation kinetics is described below. During hot deformation, the dynamic restoration processes tend to cancel out the work hardening effects. In dynamic recovery, the generation and accumulation of dislocations due to work hardening are continuously offset by dislocation rearrangement and annihilation, resulting in a steady state (ssat) value as shown in Fig. 10 (marked DRV). When DRX is the restoration process, the flow curve (marked DRX) rises initially as a result of work hardening and recovery processes to a peak value (sp), beyond which the flow stress drops with increasing strain to a
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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.
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associated εc is noted from the s–ε curve). The initial rapid decrease of θ with increase in s is considered to be associated with dynamic recovery [41,42], and a linear extrapolation of the part just before the critical point to θ ¼0 establishes ssat. Locating sp and εp is straight forward from s–ε plot as it is related to θ ¼ ds/dε ¼ 0. The next step is to generate the DRV curve. Jonas et al. [42] described work hardening using the Estrin–Mecking [44] equation that was established to evaluate the change in dislocation density (ρ) with respect to strain: dρ ¼ h r ρ dε
Fig. 10. Schematic representation of flow curve during dynamic recovery and dynamic recrystallisation defining various stresses and strain parameters involved in the Avrami or flow curve analysis.
steady state value (sss) at large strain. This flow behaviour is typical of DRX and has been reported for a wide variety of metals and alloys including titanium [39–42]. It has been shown that a critical value of strain (εc) is required for initiating the DRX process. In general, the strain required for arriving at the steady state (sss) in DRV is much higher than εc for DRX. Intuitively then, the effect of time on structural changes in SRX is similar to that of strain in DRX [42]. Eq. (3) can be modified to be consistent with the DRX mechanism by replacing time (t) from the start of DRX with strain (εx) at a given rate. The modified form of the equation is X ¼ 1 expð kðε εc Þn Þ
ð4Þ
Note that the strain under consideration is beyond the critical strain associated with the DRX process and is represented accordingly as (ε εc). Since fraction globularised or recrystallised (X) is related to the loss of dislocations, in principle, it can be estimated from the difference between the DRX flow curve (obtained by experiment) and the corresponding DRV flow curve (expected stress–strain behaviour if recovery was the only operative restoration process) predicted under similar conditions of deformation. In this modelling technique, an important consideration is the construction of the DRV flowcurve. The necessary inputs for this are stress parameters like sc (corresponding to εc), sp, ssat, associated strain parameters, and work hardening. A key assumption in this modelling technique is that the DRV work hardening behaviour represents the behaviour of the un-recrystallised volume and it is similar to that before the initiation of DRX. In this sense, the work hardening behaviour of DRV is expected to be similar to that of the experimental DRX curve prior to sc. In this work, the DRX or globularisation kinetics of the material is evaluated using the method developed by Jonas et al. [42]. The first step toward DRX analysis is the identification of εc and the corresponding sc. Conventionally, εc is determined from a plot of work hardening rate, i.e., θ ¼ ds/dε (calculated from the experimental s–ε data) versus s. A typical plot of θ versus s for TITAN 29A sample deformed at 1030 1C and 3 10 4/s is presented in Fig. 11a, which shows that θ decreases with increasing s. The onset of DRX corresponds to the point of deviation from linearity in this work hardening curve. Since it is difficult to discern the exact location of this deviation in such plots, the suggestion of Poliak and Jonas [43] is adopted here to determine sc from a plot of the derivative of the work hardening rate ( dθ/ds) against s. A minimum in the plot of ( dθ/ds) versus s, shown in the inset in Fig. 11a delineates the point of inflection of the work hardening plot. The stress value corresponding to this minimum is sc (the
ð5Þ
where h is the athermal work hardening rate and r is the rate of dynamic recovery. Using this equation, Jonas et al. [41] derived the equation for flow stress for dynamic recovery as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ¼ ½s2sat ðs2sat s20 Þexpð rεÞ ð6Þ where s0 is the yield stress and can be determined from the experimental flow curve. Using some simple algebraic substitutions, the following relationship was established: ds ¼ sθ ¼ 0:5r s2sat 0:5r s2 dε
s
ð7Þ
It is seen from Eq. (7) that, r and ssat can be obtained from the slope and intercept of the sθ versus s2 curve, respectively. Fig. 11b shows the corresponding work hardening or recovery curve obtained using the r and ssat along with the experimental DRX curve. Similar such curves were established for 1000 1C, 3 10 4/s and 1030 1C, 10 3/s deformation conditions. The recrystallised or globularised volume fraction is considered to be responsible for the difference between the DRV and DRX flow curves. The difference between these two curves (Δss) is the net softening and is directly attributed to DRX. The maximum value of Δss is (ssat–sss) where sss is the steady state stress under DRX conditions. The evolution of fractional softening with strain is expressed as X¼ Δss/(ssat–sss). Thus, once the recovery curve is derived for a particular deformation condition, the evolution of X with (ε–εc) can be obtained in a straight forward manner. Fig. 12a and b shows the variation of globularised fraction (X) with (ε–εc) for various temperatures and strain rates respectively. The Avrami exponents n and k are determined by nonlinear regression fit of the calculated X versus (ε–εc) data according to Eq. (4). The n values obtained for different deformation conditions are found to be between 1.40 and 1.95. The n values obtained here fall within the range that has been reported for various titanium alloys [35– 39]. It can be seen from Fig. 12 that the globularised volume fraction (X) varies sigmoidally with strain and increases with increasing temperature and decreasing strain rate. The results here conform well to microstructural observations described earlier.
4. Conclusions The hot working behaviour of near-α titanium alloy TITAN 29A with an acicular starting microstructure was evaluated using hot compression tests. The flow curves were used to generate the processing maps and dynamic recovery (DRV) curves to characterise the recrystallisation behaviour. The conclusions drawn are presented below.
The flow curves exhibit typical DRX behaviour with a single
peak stress which then decreases gradually to achieve a steadystate for most of the deformation conditions. TITAN 29A material, exhibits instabilities in the form of shear bands, deformation bands and cavitation at prior β boundaries
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Fig. 11. (a) θ versus s plot, (b) reconstructed dynamic recovery (DRV) curve with experimental DRX curve for TITAN 29A deformed at 1030 1C, 3 10 4/s.
Fig. 12. Globularised fraction (X) with strain and (a) deformation temperature, (b) strain rate.
when deformed between 850 and 900 1C and at 10 1–100/s. The safe deterministic domain lies between 920 and 1030 1C and at 3 10 4–10 3/s where geometric dynamic recrystallisation (GDRX) or globularisation of α lamellae takes place. The initiation and progress of globularisation of α lamellae can be well predicted on the basis of the Avrami relation in conjunction with the features of flow curve and work hardening rate. As diffusion of β phase to separate the globularised particles is the rate controlling step, the fraction globularised increased with increasing temperature and decreasing strain rate. By increasing deformation temperature and decreasing strain rate, the globularisation curve shifts to lower strains which concurs well with the microstructural observations.
References [1] D.F. Neal, Titanium 95-science and technology, in: Proceedings of VIII World Conference on Titanium, Birmingham, UK, 1995, pp. 2195–2204. [2] D.F. Neal, Proceedings of VI World Conference on Titanium, France, 1998, pp. 253–258. [3] T.W. Farthing, Proceedings of VI World Conference on Titanium, France, 1998, pp. 37–48. [4] T. Noda, M. Okabe, S. Isobe, S., Nishikiori, H. Hattori, Titanium 95-science and technology, in: Proceedings of VIII World Conference on Titanium, Birmingham, UK, 1995, pp. 2258–2264. [5] Y. Honnorat, Proceedings of VI World Conference on Titanium, France, 1998, pp. 365–379.
[6] I. Balasundar, M. Sudhakara Rao, T. Raghu, G.G. Saha, DMRL Technical Report, DMRL TR 2005 381, , 2005. [7] I. Balasundar, M. Sudhakara Rao, M. Rohatgi, T. Raghu, B.P. Kashyap, J. Mach. Form. Technol. 2 (2010) 141–156. [8] R.R. Boyer, Mater. Sci. Eng. A 213 (1996) 103–114. [9] B.P. Bewlay, M.F.X. Gigliotti, F.Z. Utyashev, O.A. Kaibyshev, Mater. Des. 21 (2000) 287–295. [10] B.P. Bewlay, M.F.X. Gigliotti, F.Z. Utyashev, O.A. Kaibyshev, J. Mater. Process. Technol. 135 (2003) 324–329. [11] Y.V.R.K. Prasad, S. Sasidhara, Hot Working Guide – A Compendium of Processing Maps, ASM International, Ohio, 1997. [12] Miaoquan Li, Hongsi Pan, Lin Yingying, Jia Luo, J. Mater. Process. Technol. 183 (2007) 71–76. [13] Young Niu, Hou Hongliang, Li Miaoquan, Zhiqiang Li, Mater. Sci. Eng. A 492 (2008) 24–28. [14] T. Seshacharyulu, S.C. Medeiros, W.G. Frazier, Y.V.R.K. Prasad, Mater. Sci. Eng. A 284 (2000) 184–194. [15] T. Seshacharyulu, S.C. Medeiros, J.T. Morgan, J.C. Malas, W.G. Frazier, Y.V.R. K. Prasad, Scr. Mater. 41 (1998) 283–288. [16] Weiju Jia, Weidong Zenga, Yigang Zhou, Jianrong Liu, Qingjiang Wang, Mater. Sci. Eng. A 528 (2011) 4068–4074. [17] P.S. Bate, P.L. Blackwell, J.W. Brooks, Proceedings of VI World Conference on Titanium, France, 1998, pp. 287–292. [18] P. Wanjara, M. Jahazi, H. Monajati, S. Yue, J.P. Immarigeon, Mater. Sci. Eng. A 396 (2005) 50–60. [19] P. Wanjara, M. Jahazi, H. Monajati, S. Yue, Mater. Sci. Eng. A 416 (2006) 300–311. [20] P. Vo, M. Jahazi, S. Yue, P. Bocher, Mater. Sci. Eng. A 447 (2007) 99–110. [21] M. Zhou, Mater. Sci. Eng. A 245 (1998) 29–38. [22] X. Wang, M. Jahazi, S. Yue, Mater. Sci. Eng. A 434 (2006) 188–193. [23] I. Balasundar, T. Raghu, B.P. Kashyap, Mater. Sci. Forum 710 (2012) 533–538. [24] I. Philippart, H.J. Rack, Mater. Sci. Eng. A 243 (1998) 196–200. [25] H.L. Gegel, J.C. Malas, S.M. Doraivelu, V.A. Shende, Forging and Forming, ASM Metals Handbook, Vol 14, 1998, ASM International; Ohio. [26] F.J. Humpreys, M. Hatherly, Recrystallization and Related Annealing Phenomenon, second edition, Elsevier, Oxford, 2004.
144
I. Balasundar et al. / Materials Science & Engineering A 600 (2014) 135–144
[27] T. Furuhara, J.M. Howe, H.I. Aaronson, Acta Metall. Mater. 39 (1991) 2873–2886. [28] T. Furuhara, T. Makai, Mater. Sci. Eng. A 312 (2001) 145–154. [29] R. Banerjee, Acta Mater. 52 (2004) 377–385. [30] H. Margolin, P. Cohen, Titanium 80-science and technology, in: Proceedings of IV International Conference on Titanium, Japan, 1980, pp. 1555–1561. [31] H. Margolin, P. Cohen, Titanium 80-science and technology, in: Proceedings of IV International Conference on Titanium, 1980, pp. 2991–2997. [32] I. Weiss, F.H. Froes, D. Eylon, G.E. Welsch, Metall. Trans. A 17 (1986) 1935–1947. [33] N.G Jones, M. Jackson, Mater. Sci. Technol. 27 (2011) 1025–1032. [34] H.J. McQueen, J.K. Solberg, N. Ryum, Philos. Mag. A 60 (1989) 473–485. [35] R.D. Doherty, D.A. Hughes, F.J. Humphreys, Mater. Sci. Eng. A 238 (1997) 219–274.
[36] Chan Hee Park, Kyung-Tae Park, Dong Hyuk Shin, Chong Soo Lee, Mater. Trans. 49 (2008) 2196–2200. [37] S.L. Semiatin, J.F. Thomas, P. Dadras, Metall. Trans. A 14 (1983) 2363–2374. [38] Hong-Wu Song, Shi-Hong Zhang, Ming Cheng, J. Alloys Compd. 480 (2009) 922–927. [39] Wu Cheng-bao, Yang He, Fan Xiao-guang, Sun Zhi-chao, Trans. Nonferr. Soc. China 21 (2011) 1963–1969. [40] Kaixuan Wanga, Weidong Zenga, Yongqing Zhao, Yunjin Lai, Yigang Zhoua, Mater. Sci. Eng. A 527 (2010) 2559–2566. [41] S.F. Medina, C.A. Hernandez, Acta Mater. 44 (1996) 165–171. [42] J.J. Jonas, X. Quelennee, L. Jiang, E. Martin, Acta Mater. 57 (2009) 2748–2756. [43] E.I. Poliak, J.J. Jonas, Acta Mater. 44 (1996) 127–136. [44] Y. Estrin, H. Mecking, Acta Mater. 32 (1984) 57–70.