Correlation between microstructural features and ...

Materials Science & Engineering A 609 (2014) 241–249

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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea

Correlation between microstructural features and creep strain in a near-α titanium alloy processed in the α þ β regime 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 10 March 2014 Received in revised form 15 April 2014 Accepted 17 April 2014 Available online 10 May 2014

High temperature creep is an important property of titanium alloys used in aeroengines. Creep resistance of titanium alloys generally varies with heat treatment, temperature and cooling rate. Both the parameters affect the morphology and topology of the α (HCP) and β (BCC) phase present in the material. Various theories have been proposed in the literature to explain (i) the increase in creep strain with decreasing solution treatment temperature and (ii) the U-shaped variation of creep strain with cooling rate. Some of these theories are quite contradictory. An attempt is made here to systematically (a) evaluate and establish a direct microstructure–mechanical property correlation and (b) to explain the observed variation in the creep behaviour of a near-α titanium alloy IMI 834. The results obtained indicate that the observed U-shaped variation of creep curve is due to the counter acting nature of various microstructural features present in the material. & 2014 Elsevier B.V. All rights reserved.

Keywords: IMI 834 Near-α Titanium alloys Creep Structure–property correlations

1. Introduction Near-α titanium alloy IMI 834, with a nominal composition Ti– 5.8Al–4.0Sn–3.5Zr–0.7Nb–0.5Mo–0.35Si–0.06C (wt%), has been developed to make various rotor and stator components for aeroengines [1–3]. It has been reported that a microstructure containing 10–15% primary α in a transformed β matrix provides the optimum combination of fatigue and creep properties up to a temperature of 600 1C [4,5]. As high temperature creep is an important mechanical property required for an aeroengine material, numerous studies [6–10] have been carried out to understand the effect of various parameters on the creep behaviour of the material. Andres et al. [6,7] studied the effect of temperature and cooling rate on the creep property of lamellar and bi-modal microstructures and pointed out that creep resistance is high at some intermediate cooling rates due to alloying element partitioning. Daeuber et al. [8] evaluated the effect of heat treatment parameters on the mechanical properties of the as-cast material and reported that with increasing cooling rate, the creep resistance increases due to decrease in the lamellae thickness which results in reduced slip length. Cope and Hill [9] evaluated the influence of ageing temperature and concluded that ageing at progressively higher temperature results in higher tensile strength

n

Corresponding author. Tel.: þ 91 40 24586741; fax: þ 91 40 24340640. E-mail address: [email protected] (I. Balasundar).

http://dx.doi.org/10.1016/j.msea.2014.04.079 0921-5093/& 2014 Elsevier B.V. All rights reserved.

and creep resistance, but at the expense of tensile ductility and crack propagation resistance. Borchert and Daeubler [10] studied the influence of different heat treatment conditions on the tensile, creep and fatigue properties. They reported that rapid quenching from the heat treatment temperature produces fine lamellar spacing, which results in high static strength, fatigue life and ductility but low creep resistance. Mishra et al. [11] studied the effect of trace elements such as Fe and Ni on the creep behaviour of the material and reported that these elements lead to the deterioration of creep resistance in both α þ β and β heat treated conditions due to high diffusivity of these elements in the α phase. Es-Souni et al. [12] evaluated the microstructure, temperature and stress dependencies of primary and secondary creep. Results of their study suggest that the creep mechanism is controlled by bow-out and climb of dislocation segments pinned at lamellar boundaries and second-phase particles. The strain hardening in primary creep is thought to be controlled by long range stresses due to bow-out of pinned dislocation segments. It can be readily inferred from the above literatures [6–12], that a variety of factors such as morphology, topology and dimensions of α and β phase present in the material affect the high temperature creep resistance. The other factors that have been reported to affect the creep resistance are the degree of ageing, and presence of silicon either in the form of solid solution or in the form of silicide [13]. It is a known fact in titanium alloys that a fully transformed β microstructure provides a better creep resistance when compared to a bimodal or duplex microstructure containing

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globular primary α particles in a transformed β matrix [4–7,13]. Further, it is also well established that with increasing cooling rate, for any heat treatment temperature, the creep resistance first increases, reaches a maximum at some intermediate cooling rate and thereafter decreases [6,7,13]. A variety of reasons [6–10] have been put forth to explain the observations. Though valid, some of these theories are quite contradictory. Although there were some attempts [6–10,14] to study the effects of various heat treatment parameters on the high temperature creep resistance of the material, no attempt seems to systematically establish a direct microstructure–mechanical property correlation. The correlation studies reported so far [6–10,14] are based on simplifying assumptions that (i) varying a heat treatment parameter affects only a particular microstructural feature of interest, (ii) even if other microstructural features vary, their variations are insignificant, (iii) microstructural features have independent effects but there appears no synergistic effect of these microstructural features on the resulting mechanical properties. These assumptions are valid in the case of single phase materials where the grain size or grain size distribution alone controls the resulting mechanical (static and dynamic) properties. Such an approach cannot be applied to titanium alloy such as IMI 834 which has dual phase (α and β) which differs in morphology and topology. The microstructural features present in titanium alloys not only vary over a wide range of length scale but are also highly interdependent. These microstructural features need to be quantified in order to establish a direct microstructure–mechanical property correlation. Even after quantifying the microstructural features, establishing a structure–property correlation is not an easy task as there is no model available for such a mapping. As there are a large number of highly interdependent and complex microstructural variables, simple regression analysis would not be able to establish these correlations. This limitation is circumvented using artificial neural networks (ANN) [15–18]. These ANN can be trained to establish any complex nonlinear relationship that exists between any input and output parameters [15–19]. An attempt is made here to (i) systematically evaluate the effect of heat treatment parameters (solution treatment temperature and cooling rate) on the microstructure and high temperature creep resistance of the material, (ii) establish a direct microstructure–mechanical property (creep strain) using artificial neural network and (iii) use ANN predictions to explain the observed variation in the creep behaviour of titanium alloy IMI 834.

providing sufficient soaking time (1 hr/in. of ruling section) to attain thermal equilibrium, heated billets were transferred to a 2000 MT forge press and isothermally forged to 70% of their height with an average strain rate of 0.003/s. The forging temperature and strain rate used here were decided based on the processing maps developed for the material which is discussed elsewhere [20]. The isothermally forged billets were removed from the forge press and air cooled. 2.2. Heat treatment Isothermally forged billets were then cut into two halves and a total of 20 such halves were generated. Out of the 20 samples, 5 samples were used for each solution treatment temperature (i.e., 5 piece 4 temperature¼20 samples) identified for the study. After solution treatment at each identified temperature, each sample was quenched in different cooling media (i.e., 5 different cooling media/temperature). The heat treatment parameters used for the current study are listed in Table 1. After solution treatment, all the samples (4 temperature 5 cooling rate¼20 samples) were aged or stress relieved at 700 72 1C for 120 min and air cooled. 2.3. Creep testing From the solution treated and aged material, blanks were extracted through electro-discharge machining (EDM) and standard creep samples of dimension 5 mm diameter and 25 mm gauge length were prepared. A minimum of three samples were prepared for each heat treatment condition (4 solution treatment temperature 5 cooling rate 3 samples ¼60 samples). The creep test was carried out at 600 1C and a stress of 150 MPa for 100 h. During testing, the temperature of the furnace was controlled to be within 72 1C of the test temperature. Creep strain till 100 h of testing was measured using a linear variable differential transducer (LVDT) connected to an extensometer which was mounted on the ridges of the creep sample. 2.4. Microstructural examination

2.1. Isothermal forging

From the heat treated (solution treated and aged) material, samples were also extracted for metallographic examination. For metallography, the samples were mechanically polished and etched. As the conventional Kroll's reagent (100 ml H2Oþ6 ml HNO3 þ3 ml HF) was not sufficient to reveal all the desired microstructural features, a variety of etchants were evaluated to identify a suitable etchant for revealing specific features. The following etchants were found to be useful for this purpose:

As forged and machined near-α titanium alloy IMI 834 (Ti–5.8Al–4.0Sn–3.5Zr–0.7Nb–0.5Mo–0.35Si–0.06C (wt%)) was procured from M/s. TIMET, U.K., in the form of 172 mm diameter bars. Ten billets with 172 mm diameter and 180 mm height were extracted from the as-received bar. The extracted billets were coated with Deltaglaze 347 and heated to 940 1C in a resistance heating furnace. IN 100 dies for isothermal forging were heated to 940 1C using a line frequency (50 Hz) induction heater. After

(i) 10 ml HNO3 þ8 ml HFþ82 ml H2O – the polished sample was swabbed with this etchant for few seconds and then cleaned immediately with water to reveal the transformed β (Tβ) grains (ii) 2 ml HNO3 þ1 ml HF þ97 ml H2O – the sample was first etched with this etchant to reveal α lamellae and primary α followed by immersion in 2 ml HF þ98 ml H2O to remove etching stains on the α phase.

2. Experimental procedure

Table 1 Details on the solution treatment conditions used for the current study on microstructure–creep strain correlation. Parameter

Condition

Temperature (1C) Soaking time (min) Cooling medium Cooling rate (1C/min)

1015 120 Water 7500

1030

1045

1060

Polymer (5% polyalkylene glycol) 4800

Oil 3000

Air 900

Furnace 420


Microstructures of the samples were then examined and recorded using an optical and scanning electron microscope (SEM). In SEM, both secondary and back scattered images were recorded using JEOL 840A operating at 20 kV. The micrographs were taken at various magnifications (12.5–5000 ). Proper care was taken while recording the images to ensure that the micrographs taken are true representative of the features present in the material. Seven important microstructures that include (1) volume fraction of globular primary α, (2) size of globular primary α, (3) volume fraction of grain boundary α, (4) size or thickness of grain boundary α, (5) thickness of α lamellae, (6) colony size factor and (7) prior β grain size were evaluated using automated and semi-automated stereological procedures that were established by Collins et al. [21] and Tiley et al. [22,23]. Image analysis software like Image tool 3.0 [24], Adobe Photoshop CS 7.0 [25] and Image analysis plus [26] were used to quantify the microstructural features. As stereological measurements are estimates of 3D features on a 2D plane, factors such as sample homogeneity, magnification, number of fields etc. affect the reliability and repeatability of the data [27]. Measures such as 95% confidence limit (95% CL) and percentage relative accuracy (% RA) were used in order to ensure that the database generated is reliable [27]. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi t ∑ðX i μÞ2 =ðN 1Þ t∑ðX i μÞ t SD pffiffiffiffiffiffiffiffiffiffiffi ¼ 95% Confidence Limit ðCLÞ ¼ pffiffiffiffiffiffiffiffiffiffiffi ¼ ðN 1Þ N 1 N 1

ð1Þ % Relative Accuracy ð% RAÞ ¼

95% Confidence Limit 100 Mean ðμÞ

ð2Þ

where SD is the standard deviation, m is the mean, N is the number of measurement, and t is constant that varies from 1.96 to 2 depending on the number of measurements. For the current study, the relative accuracy was maintained below 710%. If the relative accuracy or error was higher, then the measurements were repeated to reduce % RA. The number of measurements to be carried out in order to obtain a specific % RA was given by De Hoff [28] as 200 SD 2 No: of fields to be measured ¼ ð3Þ % RA μ

2.5. Artificial neural network A two hidden layer feed forward neural network with a 7–8–5– 3 architecture i.e., a neural network with 7 neurons in input layer, 8 neurons in the first hidden layer, 5 neurons in the second hidden layer and 3 neurons in the output layer, was identified as the optimum network architecture to establish the structure–property correlation based on the Taguchi design of experiments approach [29]. Seven neurons in the input layer correspond to the seven microstructural features considered in the study. Three output neurons correspond to yield strength, tensile strength and high temperature creep strain of the material. The network was trained using the Levenberg–Marquart (LM) algorithm with the Bayesian regularisation [30]. The LM algorithm has been proved to converge faster and finds better optima with better regularisation for a variety of problems [17,18,30,31]. The Bayesian regularisation does not require validation data set to be separated out of the training data set. This advantage is especially noticeable when the size of the data set is small like the current one [30–32]. Details on the optimisation of ANN architecture and training parameters using the Taguchi based design of experiments approach can be found elsewhere [29]. The neural network was trained to establish a direct microstructure–mechanical property correlation. Though

243

the network has been established to correlate microstructure with tensile and creep properties, only creep strain is referred to in the current study. For the current study, only the average values of the seven types of microstructural features were used for correlation. Though it is well known that the distribution of the microstructural features also affects the mechanical properties, they are not included in the current study because of the complexity involved. The trained neural network was then used to carry out virtual experiments i.e., vary one particular microstructural feature while maintaining other features at their some constant values (mean value) within the experimental range and study the effect of the former on the creep strain. In order to gain further insight, the virtual experiment trend plots were normalised between 0 and 1 using the following expression: xN ¼

x xmin xmax xmin

ð4Þ

where, xN is the normalised value of certain parameter, and x is the predicted value of this parameter. xmin and xmax are the minimum and the maximum values in the database for this parameter.

3. Results and discussions 3.1. Effect of heat treatment on microstructure Typical microstructures obtained by heat treating the near isothermally forged material under various conditions are shown in Figs. 1–3. Qualitative variations of microstructural features are presented here. 3.1.1. Globular primary α With increasing solution treatment temperature, the volume fraction and size of globular primary α phase decrease (Fig. 1) with complete disappearance at 1060 1C. At high temperature, the globular primary α phase is found essentially on the transformed β grain boundary triple points whereas they form a complete network along the transformed β boundaries at low temperatures as shown in Fig. 2. Occasionally, the globular α phase is seen within the transformed β grains. Cooling rate also influences the volume fraction of primary α phase as illustrated in Fig. 2. With decreasing cooling rate, the volume fraction and size of globular primary α increase, especially in the furnace cooled samples (Fig. 2e). 3.1.2. Transformed β grain size As expected, the transformed β grain size increases with the increase in solution treatment temperature (Fig. 1). With the decrease in cooling rate, the size of transformed β grain decreases (Fig. 2). In the sample solution treated at lower temperature and subsequently furnace cooled (Fig. 2e), the transformed β is reduced considerably and is seen only at the triple points of equiaxed primary α grains. It can therefore be said that, solutionising temperature and cooling rate from the α þ β field decides the volume fraction and size of primary α which in turn determine the transformed β grain size. The resulting transformed β grain size affects the colony size and length of α lamellae etc. 3.1.3. Lamellar α Slow cooling rate from the solution treatment temperature results in a lamellar structure (Fig. 3a) with large colonies comprising of aligned α lamellae that belongs to the same crystallographic orientation. These lamellae are formed by nucleation and growth process [33]. High cooling rate produces martensitic structure by the diffusion less transformation process which has strong

244


Fig. 1. Typical microstructures obtained by air cooling the material after solution treatment at (a) 1015 1C, (b) 1030 1C, (c) 104 1C and (d) 1060 1C for 120 min followed by ageing at 700 1C/120 min/air cooled.

Fig. 2. Typical microstructures obtained by solution treating the isothermally forged material at 1015 1C and quenching in (a) water, (b) polymer, (c) oil, (d) air and (e) furnace followed by ageing at 700 1C/120 min/air cooled.


245

Fig. 3. Typical microstructure obtained by heating the material at 1060 1C (β-transus) followed by quenching in (a) furnace, (b) oil, (c) polymer and (d) water.

Fig. 4. . (a) Low and (b) high magnification micrographs showing the presence of colony structure close to the grain boundary region and the basket weave structure at the grain interiors of air cooled sample solutionized at 1060 1C and aged at 700 1C/2 h/ air cooled.

orientation difference between neighbouring platelets [33]. Thickness of the α lamellae present in the transformed β grain of fully lamellar microstructure (Fig. 3) as well as in the bimodal microstructure (Fig. 2) increases with decreasing cooling rate as reported in various investigations of titanium alloys [6–10]. The length of the lamellae seems to decrease with the decreasing cooling rate in the material heat treated at lower temperatures. This can be attributed to the presence of dispersed globular α particles, which limits the transformed β grain size by the Zener pinning [4,5].

3.1.4. Colony size When the transformed β grain size is small (either due to lower heat treatment temperature e.g., Fig. 1a or due to slow cooling rate e.g., Fig. 2d and e), α lamellae of similar orientation (colonies) that originate from the transformed β grain boundaries, engulf the whole transformed β grain. However, with large transformed β grains, the colonies terminate after a certain length beyond whose basket weave structure is developed as shown in Fig. 4. Thus, there is an effect of transformed β grain size on the resulting colony size at a particular cooling rate as shown in Figs. 1–4. The size of the colony is found to increase with the decreasing cooling rate and the increasing solution treatment temperature.

3.1.5. Grain boundary α lamellae The formation of grain boundary α (GB α) phase is not observed in the water quenched specimen but the same is formed in the polymer quenched samples. However, the GB α phase formed is found to be discontinuous (Fig. 5), which implies that a critical cooling rate is required for the formation of continuous GB α lamellae network along the prior β grain boundaries. The observation here concurs well with that reported in literature [33]. Volume fraction and thickness of grain boundary α lamellae increase with the decreasing cooling rate as shown in Fig. 3. Details on the stereology procedure used for quantification of the abovementioned microstructural features are provided in Appendix A. The average values of the quantified microstructural features along with the 100 h creep strain obtained from testing are listed in Table 2. Typical distributions of few microstructural features are shown in Fig. 6. 3.2. Creep strain The variation in 100 h creep strain (%) with solution treatment temperature and cooling rate is summarised in Fig. 7. It can be seen that with decreasing heat treatment temperature, creep strain increases (or the creep resistance decreases) irrespective of cooling

246


Fig. 5. Discontinuous grain boundary α phase in the sample solution treated at 1060 1C for 2 h and quenched in polymer (5% polyalkylene glycol in water).

Table 2 Database of microstructural features and mechanical properties used to establish the microstructure–mechanical property correlation in near-α titanium alloy IMI 834. Input parameters: microstructural features

Output

Volume fraction of globular primary alpha (%)

Size of globular Volume fraction of grain boundary primary alpha alpha (%) (μm)

Size or thickness of grain boundary alpha (μm)

Trans-formed beta grain size (μm)

Colony size factor

Lamellae thickness (μm)

Yield strength (MPa)

Ultimate tensile strength (MPa)

% Creep strain after 100 h (600 1C/150 MPa)

24.9 25.5 28.4 33.5 59.2 15.9 16.5 20.5 22.4 53.7 6.425 7.05 7.49 10.35 12.14 0 0 0 0 0

19 20.1 22.6 25.7 28.6 16.2 18.4 20.7 23.4 26.8 14.4 17.1 17.9 19.7 22.5 0 0 0 0 0

0 0.83 0.97 2.37 7.56 0 0.91 1.11 2.74 8.43 0 1.19 1.54 3.3 9.13 0 1.54 1.75 3.63 10.72

93 87 64 59 48 137 132 129 115 88 595 520 495 479 439 834 795 725 690 658

3.32 4.04 4.52 15.73 82.01 3.55 5.76 6.59 20.07 106.75 4.71 6.63 11.5 30.15 133.36 5.88 7.75 18.3 38.65 248.36

0.83 0.87 0.92 1.17 3.03 0.9 0.98 1.04 1.18 4.1 1.23 1.43 1.52 1.66 5.15 1.25 1.87 2.01 2.45 6.45

986.0 965.0 948.0 919.5 880.5 1015.5 975.0 964.0 935.5 886.0 977.0 944.5 922.5 901.5 841.0 968.5 930.5 906.5 849.5 773.5

1087.0 1068.0 1041.5 1020.5 977.5 1133.5 1089.0 1069.5 1048.5 985.5 1078.0 1050.5 1030.0 990.0 931.5 1049.5 1027.5 996.0 921.0 851.0

1.3 0.8 0.55 0.54 0.58 1.1 0.65 0.42 0.44 0.45 0.89 0.39 0.25 0.21 0.35 0.72 0.28 0.11 0.12 0.25

0 3.2 4.7 8.8 13.5 0 2.5 3.5 6.6 11.6 0 1.4 2.6 4.8 9.2 0 0.08 1.8 3 7.5

rate. Further, with the increasing cooling rate, the creep strain initially decreases, reaches a minimum value at some intermediate cooling rate (between air and oil) and thereafter increases again with the increasing cooling rate for any condition of heat treatment temperature. The behaviour observed here is similar to that exhibited by various titanium alloys [6–10]. Various theories have been proposed to explain the observed trend in the variation of creep strain which shall be discussed later. Though a specific trend is observed in 100 h creep strain with respect to the solution treatment temperature and cooling rate, no trend can be deduced when the creep strain is plotted against the quantified microstructural features. For example, % creep strain plotted against the volume fraction of primary α phase is shown in Fig. 8. A large scatter in the properties can be readily inferred. A similar trend (scattered) is observed when the creep strain is plotted against other microstructural features as well. This scatter makes it difficult to establish a direct microstructure-property correlation using conventional regression analysis techniques. However, this issue can be overcome using a suitable neural network. 3.3. Effect of individual microstructural features The effect of individual microstructural features on the creep strain of the material predicted by the artificial neural network is

shown in the form of normalised trend as plotted in Fig. 9. It can be seen from the neural network prediction that, increasing certain microstructural features increases the creep strain while others decrease. For example, increasing primary α volume fraction increases creep strain whereas increasing the transformed β grain size decreases it. As neural networks are essentially numerical models, the results obtained from ANN should be explained and discussed using metallurgical observations. 3.4. Microstructure-creep strain correlation It can be clearly seen from Fig. 7 that with the decreasing solution treatment temperature, the 100 h creep strain (%) increases irrespective of cooling rate. It can also be seen that the creep resistance increases initially, reaches a peak at a certain intermediate cooling rate and thereafter decreases. A variety of theories such as (i) alloying element partitioning between primary α and transformed β [6], (ii) refined grain size of transformed β structure due to pinning of globular α phase which leads to grain boundary sliding [7,11,34], (iii) thin layer of β phase seen around equiaxed α providing a high diffusivity path [7], (iv) larger slip length of primary α as compared to that of α lamellae in transformed β structure [35], (v) banding and texture of primary α leading to accelerated creep [36], (vi) retention of silicon in solid


247

Fig. 6. Typical size distribution of various quantified microstructural features.

Fig. 7. Variation of 100 h creep strain with solution treatment temperature and cooling rate.

solution at high cooling rates, removal of silicon from the matrix due to silicide precipitation [7,13], (vii) decreasing α lamellae width making the alloy prone to recrystallisation and grain growth

Fig. 8. Variaiton of creep strain with volume fraction of primary α.

[37], (viii) dynamic equilibrium between strengthening and restoration processes [6,7,11], (ix) increasing slip length with decreasing cooling rate [8] etc., have been put forth to explain the observed U-shape pattern of the creep curve shown in Fig. 7.

248


Fig. 9. Variaiton of creep strain with individual microstructural features as predicted by artificial neural network.

These theories were justified by making use of experimental observations. However, a satisfactory explanation for this Ushape pattern of the creep curve still seems to be missing. Extensive studies carried out on Si containing near-α titanium alloys led to the conclusion that, beyond a critical temperature and cooling rate, silicon comes out of solid solution and precipitates as silicide [6,7,34,37]. It is this removal of silicon from solid solution which was used to explain the observed U-shaped nature of the creep curves. Silicon either in the solid solution or as a silicide interacts with the dislocations and provides necessary resistance or strengthening [11]. However, even non-silicon bearing alloys such as Ti–6Al–4V exhibit such variation in creep curve with respect to heat treatment temperature and cooling rate [6,7]. Hence, the effect of silicon to cause the minima in the creep curve is eliminated. The increase in creep strain with the decrease in solution treatment temperature can be attributed to preferential partitioning of α stabiliser to the primary α phase with the decrease in solution treatment temperature and decreased cooling rate as proposed by Andres et al. [6]. Further, the bimodal or duplex structure obtained by heat treating the material at lower temperatures has a more refined microstructure as compared to fully lamellar structure in terms of colony size and prior β grain size (Fig. 1). This refined grain size and colony size can provide a significant contribution to overall creep strain [7,34]. It should also be remembered that the boundary between the globular primary α phase formed by the deformation–recrystallisation mechanism and the parent β phase is incoherent. These incoherent boundaries are preferred sites for deformation initiation. Further diffusion processes are much faster through these incoherent boundaries [38] which result in faster recovery by dislocation annihilation and hence high creep strains can be achieved. Therefore, increasing the volume fraction of globular primary α, increases the fraction of incoherent boundaries and hence reduces the creep resistance. As deformation takes place predominantly in the α phase, increasing the size of primary α increases the slip length to cause decrease in creep resistance [8]. These reasons explain why the creep resistance of a bimodal or duplex material exhibits poor creep resistance when compared to a fully transformed microstructure. The effect of primary α, transformed β grain size and colony size on creep strain predicted by the artificial neural network (Fig. 9) concurs well with the above observations. With the increasing volume fraction and size of GB α, ANN predicts an increase in creep strain or decrease in creep resistance. The GB α–β interfaces are reported to be incoherent [33] and are preferred site for inhomogeneous deformation. As the dislocation annihilation can happen at a higher rate through these boundaries due to enhanced diffusivity, the creep strain increases or the creep resistance decreases with the increasing volume fraction of grain

boundary α phase as predicted by neural network. As the size or thickness of GB α increases, the slip length increases and hence there is an increase in the creep strain. Increasing the transformed β grain size reduces the creep strain as expected (Fig. 9). The creep strain is found to decrease initially to reach a minimum and thereafter increases again with the increasing α lamellae thickness and colony size. Creep can be considered as a balance between the deformation strengthening (strain hardening due to accumulation of dislocations) and recovery due to dislocation annihilation [6,7,11] at the interfaces. The nature of α–β interfaces present in Ti-alloys play an important role in the deformation process. The α lamellae that form from the parent β phase maintains the Burgers orientation relationship ðf110gβ jjf0001gα jj; 〈111〉β jj〈1120〉α Þ with the β phase and therefore the boundary between the lamellar α and the adjacent β phase present within a colony is semi-coherent whereas, there is no such orientation relationship between the primary α and adjacent β interface [11,31]. These interfaces not only act as barriers to dislocation motion but also provide sites for dislocation annihilation. The balance between these two opposing micro-mechanisms (strengthening and annihilation) decides the creep strain that can be achieved. This observation concurs well with the prediction of neural networks. At faster cooling rate, the thickness of α lamellae and colony size reduces. The increase in creep strain is a result of increased annihilation of dislocations at these colony boundaries. As the cooling rate is reduced, the creep resistance improves or the creep strain decreases till a critical point. This can be attributed to the decrease in the volume fraction of semi-coherent boundaries. Beyond the critical point, the decrease in creep resistance can be attributed to the increase in the thickness of lamellae which provides greater strain path in fully lamellar microstructures. Based on aforementioned discussion, it can be concluded that the reason for the formation of the U-shaped curve with increasing cooling rate can be attributed to the individual and synergistic effects of various counter acting microstructural features as shown in Fig. 9. The counter balance between dislocation annihilation (recovery) and accumulation (strain hardening) at the interface of these microstructural features results in the U-shaped creep curve showing high creep resistance at some intermediate cooling rates.

4. Conclusion Based on the microstructure–creep strain correlation study carried out on near-α titanium alloy IMI 834, the following can be concluded:

Increasing the solution treatment temperature provides better creep resistance for any given cooling rate.

The increased creep resistance with solutionising temperature

can be attributed to the decrease in volume of fraction of incoherent α-β interface, reduced portioning of alloying elements and increased transformed β grain size. The formation of the U-shaped curve with increasing cooling rate is due to individual and synergistic effects of various counter acting microstructural features. The counter balance between dislocation annihilation and accumulation at the interface of various microstructural features results in the U-shaped creep curve showing high creep resistance at some intermediate cooling rates.

Acknowledgements The authors express their gratitude to Dr. Amol A. Gokhale, Director, Defence Metallurgical Research Laboratory (DMRL) and


Dr. A. K. Gogia, Division Head, Aeronautical Materials Division (AMD) for encouraging us to publish this work. The authors acknowledge the support rendered by the mechanical behaviour group (MBG) and structure and failure analysis group (SFAG) in preparing the samples for metallographic investigation. Authors thank Ms. Susmitha, Timnath, Collarado, USA, for helping in extensive quantitative characterisation of microstructural features. The funding provided by the Defence Research and Development Organisation (DRDO) to carry out the work is acknowledged.

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Appendix A - Quantification of Microstructural Features

series of line segments as shown in Fig. A.3d. The length of these line segments are then measured to provide the mean intercept length. This procedure is repeated by rotating the line grid in a series of 10 degree steps

I. Volume Fraction of Primary  Volume fraction of a particular phase or constituent in a microstructure can be estimated using areal analysis (AA), lineal analysis (LL) or point counting (PP) [27]. Point count is the most common method (ASTM E562) in which the volume fraction (Vv) is measured by point fraction (PP). A regular grid of points is overlaid onto the image and points that fall onto the feature of interest are marked as shown in Fig. A.1. Volume fraction (V v) of that particular feature is then given by the ratio of number of points which lie on the specific feature of interest (Vi) to the total number of grid points used (V) as provided below. v

i

(A.1)

Fig. A.2 Microstructure of the material solution treated at 1030 oC /2 hr/ polymer quenched and aged at 700 oC/ 2 hr/ air cooled super imposed with three concentric circles to calculate size of globular primary  phase

III. Thickness of lamellar 

Fig. A.1 Scattered SEM image of IMI 834 heat treated at 1030 oC / 2 hr/ air cooled and aged at 700 oC/ 2 hr/ air cooled superimposed with regular grid points (yellow circle) using Fovea pro plugin for Adobe photoshop to estimate the volume fraction of primary  (red diamond) In most works, the volume fraction is expressed as percentage by multiplying AA, LL or PP by 100. It has frequently been shown that all the three methods yield equivalent results within the limits of statistical accuracy i.e. (A.2) where AA is the ratio between sum of the areas of the phase or constituent of interest to the total measurement area, LL is the ratio of total length of randomly placed lines within the phase of interest to the total length of line [27].

II. Size of Primary  The mean size of primary  is quantified following ASTM E 112. Manual and semi-automatic methods were used to measure the size of the globular  phase. In the manual method, the volume fraction of globular  phase (Vfα) is first measured using the procedure stated earlier in section A. Next, a three-circle test grid (circles with diameter ratio of 3:2:1) is placed on the image as shown in Fig. A.2. Number of primary  grains (Nα) that are intercepted by the test lines are counted [27]. The mean linear intercept of the globular  phase is then estimated according to (A.3) where, LT is total line length calculated at 1X. In the semi-automatic method [21-23], the globular  phase is first extracted or the transformed  phase is removed from the original image as shown Fig. A.3. If  particles are found to be clustered together they are delineated using the Fovea pro plugin for Adobe Photoshop [21-23]. This sets the stage for measuring the size of primary  phase. Using an automated procedure in the Fovea pro plugin, a grid of parallel lines are first drawn over the copy of the threshold image as shown in Fig. A.3c. A simple Boolean operation between the threshold image and its copy produces

The grey image (Fig. A.4a) of the microstructure is first converted into a binary image as shown in Fig. A.4b using a suitable threshold procedure [2526]. A copy of this binary image is made and superimposed with parallel line grids (red colour lines in Fig. A.4c, as explained in section. B). A simple Boolean operation between the binary image and its copy provides a series of broken line segments corresponding to the width of the -lamellae as shown in Fig. A.4d. The length of these broken lines are measured using Fovea pro plugin for Adobe Photoshop. By inverting the length and calculating the mean value, the mean thickness of the  lamellae is calculated using the Fullman [39] and Gunderson correction [40] factor shown in Eq. A.4 Thickness = 1/(1.5 (1/ λ)mean)

(A.4)

where λ represents the measured intercept length. When the cooling rate is high, the resulting  lamellae are finer. Hence, higher magnification SEM images as shown in Fig. A.5 are used to estimate the lamellae thickness. In case of bimodal microstructures, the primary  and grain boundary  phases if present are selectively removed from the image before measuring the lamellae thickness. The above mentioned procedure was repeated after rotating the angle of the super imposed parallel lines in order to obtain statistically reliable data.

IV. Colony Size Factor Colonies are clusters of α lamellae belonging to the same crystallographic variant. It is very difficult to determine the size of colonies without making assumptions about their shape and morphology [21]. Further, three-dimensional (3D) imaging of titanium alloys has shown a very complicated shape which is not easy to characterize or generalize [21]. Hence, the colony size is estimated as a factor using the conventional mean intercept length method as reported by Collins et al. [21]. A set of random lines are drawn on the image of appropriate magnification, All the intersections of such lines with the colony boundaries are marked as shown in Fig. A.6. Colony size factor is then obtained by dividing the total line-length by the total number of marks. Colony size factor has a dimension of length that represents the colony size. It is named as size factor because as it does not provide any information on the shape of the colonies [21, 22]. Different fields of view or images of the sample were used to ensure the accuracy and reliability of the measured values

V. Transformed  grain size Transformed β grain size is difficult to measure without assumptions on the actual 3- dimensional shape of the grains. This parameter is difficult to measure on fully lamellar or transformed microstructures unless the grains are delineated by grain boundary α.

A1

Fig. A.3 Semi-automated procedure to calculate globular alpha size (a) original image of material heat treated at 1030 oC / 2 hr / polymer quenched and aged at 700 oC/ 2 hr/ air cooled (b) globular alpha extracted from the original image (c) parallel random lines imposed on the image (d) image after Boolean operation showing the line segments.

Fig. A.4 Quantifying  lamellae thickness (a) microstructure of the material heat treated at 1060 oC/ 2 hr / furnace cooled and aged at 700 oC/ 2 hr / air cooled (b) binary image (c) copy of binary image superimposed with parallel

A2

It is important to use images showing more than few grains to get accurate estimates of the true value. For this study, low magnification optical images were used to provide adequate number of grains. The images are overlaid with set random lines of known length as shown in Fig. A.6. The number of grain boundary intercepts are counted [27]. The intercept length (PL) is calculated as PL = (number of intersection points) / total length of lines

(A.5)

In case of samples having duplex or bimodal microstructure, the procedure described to measure the primary  size (section B) is used. Instead of primary  size, the transformed  grain size is measured.

VI. Volume fraction of grain boundary  The volume fraction of grain boundary  phase is measured using the procedure described for measuring the primary  volume fraction (section I). Here the feature of interest is the grain boundary  phase.

VII. Thickness of grain boundary  phase The procedure followed to determine the lamellar  thickness (section III) is used to measure the width or thickness of grain boundary  as well. Random lines are first drawn on the micrograph; the intersections of lines with the grain boundary α layer are marked with a particular colour. Then the image is threshold with the colour used to mark the grain boundary  layers. After threshold, the image is reduced to line segments indicating only the grain boundary  layers. The thickness of grain boundary  layer is then determined by measuring the lengths of the line segments as described in section III.

References [39]. R.L. Fullman, Trans. AIME 197, 1953, 447–452. [40]. H.J.G. Gundersen, E.B. Jenson and R. Osterby, J. Microsc. 113, 1978, 27–43.

Fig. A.5 SEM images of isothermally forged material solution treated at 1045 o C for 2 hr and quenched in (a) oil and (b) air, followed by ageing at 700 oC/ 2 hr/ air cooled

Fig. A.6 Random lines superimposed on the SEM image of material heat treated at 1060 oC/ 2 hr/ air cooled and aged at 700 oC/ 2 hr/ air cooled. The intersections of the superimposed random lines with colony boundaries are marked by circular dots.

A3