This is a final submitted paper. The full text of the ...

This is a final submitted paper. The full text of the current paper is available at 10.1016/j.jallcom.2016.03.186

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Hot Workability and Microstructure Control in Co20Cr15W10Ni Cobalt-based Superalloy V. Anil kumar1, R.K. Gupta1,*, S.V.S. Narayana Murty1, Akula Durga Prasad2 1

Materials and Mechanical Entity, Vikram Sarabhai Space Centre, ISRO, Trivandrum-695022, India 2 Indian Institute of Technology Bombay, Mumbai-400076, India *Corresponding Author: Ph.-+91-471-2563810, Fax: +91-471-2705427, e-mail: [email protected]

Abstract: Hot isothermal compression tests were conducted on Cobalt-based superalloy Co-20Cr15W-10Ni using a thermo-mechanical simulator to study the hot workability and microstructure evolution over a wide range of temperatures and strain rates. Strain hardening was observed at lower strain rates and flow softening at higher strain rates. Microscopy revealed presence of deformation bands at a temperature of 1323 K and a strain rate of 10 s-1; whereas at temperatures above 1423 K, fine recrystallized grains were observed at all strain rates. Dynamic recrystallization (DRX) initiates at 1373 K. At 1473 K, sudden increase in the recrystallized grain size (DDRX) is noticed, indicating grain growth. Processing maps have been developed to delineate the regions of stable and unstable metal flow during high temperature deformation. Using Ziegler’s continuum principles and processing maps, regions of stable metal flow was observed in the temperature range of 1323 - 1500 K and strain rate range of 0.1 - 1 s-1. Activation energy (Qavg) for the alloy was found to be 421 kJ.mol-1. As Zener Holloman parameter (Z) increases, DDRX decreases indicating higher nucleation, restricted grain growth, when deformation resistance is high. Constitutive equation and relation between ‘Z’ and DDRX for the alloy has been established. Key words: Cobalt-based Superalloy; Hot-workability; Microstructure; EBSD; Processing map; Constitutive equation 1.0.

Introduction: Cobalt-based superalloys are used for structural applications at moderate to high temperatures. The first cobalt based superalloy developed by Haynes International Inc. was used in aircraft engines. Its good resistance to thermal shock and corrosion in hot gases made it superior to nickel-based alloys [1]. These alloys find applications in stationary gas turbines and aircraft turbines due to their excellent high temperature mechanical properties, resistance to hot gas corrosion, good weldability and workability. Applications of these alloys include both single crystals for rotating parts of turbines and polycrystalline sheet materials for the walls of combustion chambers [2]. These components are exposed to high thermal and complex mechanical loadings. Like all superalloys, the microstructures of cobalt-based superalloys consist of face centered cubic (FCC) γ matrix with a number of strengthening phases. However, the precipitation hardening in cobalt-base superalloys is not as effective as γ ′ or γ ″ strengthened nickel or nickel-iron based superalloys respectively. This has made the cobalt-base superalloys heavily dependent on strengthening by carbide formation and solid-solution strengthening [1-3]. Co-20Cr-15W-10Ni alloy is a non-magnetic superalloy combining excellent strength at both ambient and elevated temperatures with good resistance to corrosion and high temperature oxidation. Therefore, it is commonly used in the aerospace industry for gas turbine engines. This alloy forms ∑ 3 annealing twins in single phase γ microstructure. The annealed microstructure does not form hexagonal close packed (HCP) martensite. However, a small fraction of the material can undergo martensitic transformation during the room-temperature plastic deformation, which is called stress induced martensitic transformation (SIMT) [2].

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Some intermetallic phases and carbides can precipitate during annealing treatment in the temperature range of 873 K - 1373 K after prolonged exposure. Precipitation is not expected during annealing at any temperature for time periods of less than 1 hr. Laves phases form during ageing treatment below 973 K, and carbides form between 973 K and 1373 K [3,4]. For temperature above 1373 K, the precipitates are dissolved, and the material becomes a single phase FCC. Two main carbides are present in the alloy i.e. M6C and M23C6 [3, 4], where M is one or several of the metallic elements of the alloy. M7C3 is a transition phase appearing during earlier stage of ageing along the grain boundaries and thereafter disappears during prolonged ageing treatments. M23C6 appears as spheroidal particles, first on grain boundaries and then within matrix grains. It is coplanar with the matrix, the {111} planes of this carbide are parallel to those of the matrix [2]. For long aging time, plate-like M6C succeeds M23C6 formation within matrix grains. For temperatures higher than 1273 K, M6C can precipitate directly within the matrix, without involving the formation of transitional M23C6. The most common intermetallic compound is the Co2W phase [4], with a hexagonal C14 Laves structure (a = 0.473 nm, c = 0.770 nm, c/a = 1.63) [5]. Co2W succeeds M6C precipitation, and forms some platelets at grain boundaries. For longer aging time, they coagulate to large intergranular precipitates. This is identified as the main embrittling process in Co-Cr-W-Ni alloy. A typical TTT diagram for this alloy is given in literature [3]. Hot deformation of this alloy is usually carried out in the temperature range of 1373 K to 1523 K, which sometimes results in a coarse grained microstructure. However, with controlled deformation temperature and sufficient percentage of reduction, grain sizes between 50 and 100 µm can be obtained. The microstructure usually consists of FCC phase only, without precipitate phases. It is obtained by plastic deformation at high temperature, followed by a solution treatment above 1473 K to dissolve precipitates and undesired phases. Grain size plays an important role in fabrication as well as in service conditions, which is mainly governed by processing parameters (ε&, T ) . Hence, optimization of hot workability and control of microstructure, are essential to study the deformation characteristics of Co-20Cr-15W-10Ni alloy, especially for specialized applications. Accordingly, the purpose of the present study was threefold: a) to systematically conduct hot deformation studies in the temperature range of 1323 - 1523 K and strain rate range of 0.01 to 10 s-1 to understand the stress – strain behavior; b) to develop processing maps to arrive at the optimum processing conditions and correlate the microstructural evolution and c) to establish the constitutive equation for the alloy. 2.0.

Experimental Details: The alloy was prepared by vacuum induction melting (VIM) followed by electro slag refining (ESR). The ingot was forged to 50 x 50 x 100 mm3 block and was subjected to solution annealing heat treatment. Chemical composition and mechanical properties at room temperature are given in Table-1 and Table-2 respectively. Cylindrical specimens of ϕ10 mm x 15 mm height were machined by wire electro discharge machining (WEDM) from this forged block for conducting hot isothermal compression tests at different temperatures in the range of 1323 - 1523 K at 50 K intervals and at constant strain rates of 10-2, 10-1, 100 and 101 s-1 as per ASTM E-209 [6]. The deformation studies were carried out in a Gleeble-3500 thermomechanical simulator using hydrawedge module. In order to minimize the friction between the specimen and platens, the contact surfaces of the platens and the end faces of the specimen were coated with MoS2 lubricant. To accurately measure the temperature of the specimen during deformation, a thermocouple was welded to the surface of the specimen and temperature was recorded. The samples were heated to the test temperature at the rate of 5 K.s-1 and soaked for 60 s before deformation to 50% of their initial height as shown in schematic in Fig. 1. The deformed specimens were then water quenched so as to retain the high temperature microstructure. These deformed specimens were sectioned

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vertically parallel to the compression axis using WEDM technique to prepare metallography specimens to observe the microstructures. The sectioned samples were mounted in Bakelite and were polished using conventional metallography technique for both optical and scanning electron microscopy. Polished specimens were electrolytically etched with 4% H2SO4 at 10 V for 15 s to reveal the microstructure. Microstructures were observed using Olympus-make GX71 optical metallurgical microscope. Scanning electron microscopy was carried out on representative samples of all temperatures and strain rates using Environmental Scanning Electron Microscope (ESEM) of Carl ZEISS EVO 50 fitted with INCA EDS system. Table 1: Specified and actual chemical composition (wt. %) of Cobalt based superalloy Co-20Cr-15W-10Ni used in the present study Elements Specification, wt. % Actual , wt. %

C 0.15 (max.) 0.080

Cr

W

Ni

19-21

14-16

9-11

19.95

14.16

10.82

Fe 3 (max.) 0.10

Mn 1-2 1.35

Si 0.40 (max) 0.09

S 0.03 (max.) 0.002

P 0.04 (max.) 0.005

Co Bal.

Table 2: Room temperature mechanical properties of Co-20Cr-15W-10Ni forging in solution annealed condition used in the present study Specified Achieved

Hardness BHN 275 (max.) 253 - 263

YS MPa 310 (min.) 502 - 522

UTS MPa 862 (min.) 1008 - 1026

% El. (4d) 30 (min.) 38 - 40

Samples for electron back scattered diffraction (EBSD) were prepared by conventional metallographic polishing followed by fine colloidal silica polishing. The samples were then electropolished using a mixture of 80 % methanol + 20 % perchloric acid at a temperature of 273 K at a voltage of 16 V for 30 s in Struers-make Lectropol-5 model electropolishing unit. EBSD was carried out in FEI make Quanta 3D FEG-SEM 30 kV. Orientation imaging microscopy (OIM) maps were recorded with a scan area of 500 x 1000 µm2 with a step size of 1 µm. The EBSD data thus obtained was analyzed using TSL OIM software. Vertical section of samples representing two different deformation conditions for transmission electron microscopy were prepared by mechanical thinning of ϕ3 mm x 0.20 mm thick discs to a thickness of 80 - 100 µm. This was followed by dimple grinding to 60 µm thickness and polishing using twin-jet Tenupol with 10% HClO4 + n-Butanol as electrolyte at 263 K and 12 V to form a perforation suitable for observation using a JEOL- make JEM 200 CX model transmission electron microscope (TEM).

3.0. 3.1.

Theoretical considerations: Processing map and instability criteria Processing map is an explicit representation of the response of a material, in terms of microstructural evolution, to the applied process parameters such as strain, strain rate and temperature. It consists of superimposition of power dissipation map and an instability map. The map exhibits several efficiency ‘hills’, which appear as ‘domains’ with successively increasing isoefficiency contours. The efficiency of power dissipation represents the relative rate of entropy production, the highest being that for a linear dissipater. If the material system does not produce entropy constitutively at a rate that at least matches the rate of entropy input through imposed process parameters, the flow becomes localized and causes instability in metal flow. The

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deformation behavior at high temperature has been dealt with by many forming theories. Prasad et al. [7] developed the dynamic material model (DMM) under which the work piece is considered as a dissipater of power. They assumed power law type stress - strain behavior for the material. This model is very effective in describing the deformation behavior at high strain levels, where dynamic processes such as dynamic recovery (DRV) and dynamic recrystallization (DRX) can occur. It is used to construct processing map to identify the regimes of stable and unstable metal flow during high temperature deformation. Deformation processing should be conducted in the regions of maximum efficiency of power dissipation, unless structural instabilities like flow localization, wedge cracking and intercrystalline cracking occur. The location of regions of microstructural instability is based on principles of maximum rate of entropy production [8,9] and is found by mapping the instability parameter, ξ ( ε& ).In the present study, a modified DMM approach [10-12] is adopted which can be used for any type of flow stress - strain rate relationship. This model has been successfully applied to delineate the regions of stable and unstable metal flow regions in processing maps of various materials [13-19]. The detailed explanation of DMM is presented in Appendix-A.

3.2. Modelling of flow stress-strain curve: development and validation of constitutive equations For a given material, the relations between stress components and strain components are presented by an equation known as constitutive equation representing the behavior of that material. The simplest example of a constitutive equation is the well-known Hooke’s law. During plastic deformation of most of the metallic materials, the stress-strain curve becomes non-linear because of hardening or softening of the material. The strain rate can also influence the hardening or softening of material. Therefore general form of constitutive equation for deformation processing is given in Eq.1 below. σ ≡ f (ε , ε&, T ) (1) & where σ is the equivalent (effective) flow stress, ε is equivalent (effective) true strain, ε is strain rate and T is processing temperature. For, the deformation conditions over a specific temperature range the constitutive equation for a given alloy can be expressed as: ε& = A [sinh(ασ )]n exp[−Q / RT ] (2) Where ‘n’ is the strain hardening exponent, ‘Q’ is the activation energy, ‘R’ is universal gas constant, ‘T’ is the absolute temperature, ‘σ’ is the flow stress and ‘α’ is the slope of the plot between peak flow stress and temperature at a constant strain rate. The constitutive equation (Eq.2.) for hot deformation gives an estimate of the flow stress for the alloy and can be used to analyze the hot working process. This equation is an input to the finite element models to predict the strain, strain rate and temperature of a work piece during deformation. 4.0. Results and Discussion: 4.1. Hot Isothermal Compression Test Photograph of a few test specimens subjected to hot isothermal compression at different temperatures and strain rates is presented as inset in Fig. 1. A detailed visual/ low magnification observation of individual specimens subjected to hot compression testing at different temperatures and strain rates did not reveal any surface defects/ cracks except thin scales over the surface of

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specimens tested at higher temperatures. It indicates that the material can be deformed in the range of 1323 - 1523 K and at strain rates of 0.01 - 10 s-1, without gross surface defects.

Fig. 1: Schematic of hot isothermal compression test sequence used in the present study, inset image shows the samples compressed at different conditions At lower strain rates of deformation, most of the heat escapes through the anvils and to the environment, but at higher strain rates, there is insufficient time for heat to dissipate and hence specimen temperature rises. However, in the present study the adiabatic temperature rise in the specimen due to deformation heating in the temperature and strain rate regime studied is not very significant. Hence, temperature correction has not been incorporated in the present study.

4.2 Analysis of Flow Curves The true stress- true strain curves of the isothermal hot compression tested specimens of the alloy at various temperatures and strain rates are shown in Fig. 2 (a - e). The flow curve is found to be smooth in almost all the cases. The specimens were subjected to deformation up to minimum 0.65 strain for all conditions. The flow curves exhibited peak stresses at around 0.1 - 0.2 strain followed by flow softening. It can be observed that strain hardening has significant role till the initial phase of plastic deformation, i.e. up to 0.2 strain. Flow softening starts at around 0.2 strain and counterbalances the strain hardening, avoiding sudden failure of the specimen due to excessive softening. Undulations in stress - strain curves of specimens deformed at low strain rates were seen in some cases. This may be due to dynamic recrystallization which is examined and presented in subsequent sections. Similar observations have been reported in the literature [20, 23, 24]. During the initial stage of deformation, strain hardening is predominant and hence results in an increase in flow stress. Work hardening and thermally activated softening mechanisms occur simultaneously and whichever is dominant governs the flow behavior. The stress-strain curve can be divided into four regimes depending on the micro-mechanisms occurring during loading. They can be classified as: - Stage I (Work hardening), Stage II (Transition stage), Stage III (Flow Softening) and Stage IV (Steady state). During stage I, the strain hardening occurs due to pile-up of dislocations. Softening rate is lower than the strain hardening rate and hence dynamic recovery (DRV) operates during this regime. The flow stress rises steeply in this stage. Stage II occurs when the work hardening and softening phenomenon induced by both dynamic recovery and recrystallization (DRX) compete with each other. During the stage III, the flow stress drops steeply. This is due to the dominance of DRV and DRX over strain hardening. The flow stress stabilizes due to balance between softening and hardening mechanisms during the final stage and hence achieves

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a steady state also known as Stage IV [25] Based on the stress-strain curves presented in Fig.2 (a e), dynamic recrystallisation occurs in the temperature range of 1373 - 1523K and strain rate range of 0.01-1 s-1. At a temperature of 1323 K, DRX occurs at 0.01 s-1. At other temperatures and strain rates studied, the flow curves exhibit DRV. The occurrence of dynamic recrystallization in pure cobalt during hot working was investigated in detail by Kapoor and Paul [26, 27]. The oscillations in the stress-strain curves of pure cobalt correspond to the transient regime of the discontinuous dynamic recrystallization (DDRX), and were observed for lower strain rate (< 0.1 s-1) and higher temperature (T > 1023 K). In pure cobalt, for higher strain rate and lower temperature, flow curves with a single peak stress were observed [27]. In the present study, it is observed that, the peak flow stress decreases with increase in temperature and decrease in strain rates as shown in Fig.3. Effect of strain rate is found to be significant especially for the temperatures higher than 1373 K, where it shows a very strong dependence of flow stress with temperature. From the flow curves, it can be clearly seen that deformation resistance of the alloy is low at higher temperature and at lower strain rates (< 0.01 s-1) and is in agreement with reported literature [28]. Rate of decrease in peak stress with increasing temperature and decreasing strain rate are similar except for a strain rate of 10 s-1, where rate of decrease in peak stress with increasing temperature is relatively high as shown in Fig. 3. It indicates that at high strain rate of 10 s-1, adiabatic heating also may set in, which may be contributing towards flow softening to further bring down the peak stress.

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Fig. 2: Stress - Strain curves at various strain rates ( ε& ) and temperatures (T) – (a) 1323 K, (b) 1373 K, (c) 1423 K, (d) 1473 K and (e) 1523 K

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Fig. 3: Variation of peak flow stress (σp) with temperature (T) and strain rate ( ε& )

4.3. Microstructure Evolution Optical microstructure of the starting material is presented in Fig. 4(a). The microstructure shows completely recrystallized microstructure with presence of annealing twins. The initial grain size of the material is of the order of ~100µm. The microstructure of the sample deformed at a temperature of 1323 K and strain rate of 10 s-1 reveals deformation bands and fine necklace type recrystallized nuclei as shown in Fig. 4(b). The microstructural observations made from the deformed samples are summarized in Table-3.

Fig. 4: Optical Photomicrograph of alloy in (a) As-received condition and (b) Sample subjected to hot compression at a temperature of 1323 K, ε& = 10 s-1 revealing deformation bands A palette of SEM microstructures taken from the cross-section of the specimens subjected to hot isothermal compression testing at all conditions of deformation is presented in Fig. 5. The alloy essentially contains cobalt rich FCC matrix having austenitic grains and inter-dendritic M23C6 and M6C as primary carbides along with twins formed during annealing [29, 30]. Wide variation in microstructural features and grain size were observed among the specimens. Small necklace type recrystallized grains were observed in the vicinity of deformation bands in low temperature and high strain rate regimes. With increasing temperature and decreasing strain rate, the necklace type grains manifest and grow throughout the specimens. At 1323 K, microstructure clearly shows grain flow perpendicular to the axis of applied stress and presence of fine recrystallized grains at the

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intergranular sites. This indicates initiation of nucleation for recrystallization, showing fine grains at higher strain rates (10 s-1, Fig. 5 top left corner) and increase in size of the grains with decrease in strain rates (Fig. 5 bottom left corner). This phenomenon can be seen in almost all the specimens albeit to a different degree. As the temperature increases, deformed grains disappear and only recrystallized grains can be seen at a given strain rate. Progress of recrystallization of grains can be seen in Fig. 5 (from top left to right). Similarly, as the strain rate decreases, progress of recrystallization can be seen (from top to bottom). With further temperature rise, recrystallization totally eliminates the signature of deformed structure. The recrystallized structure at 1423 K is observed even at high strain rates. Marginally higher sizes of recrystallized grains are observed when the strain rates are lower. Further, at 1473 K and 1523 K, the microstructures are fully recrystallized at all the strain rates, where increase in size of recrystallized grains from 20 - 40 µm can be clearly seen from top to bottom. Growth of recrystallized grains with decreasing strain rate is due to availability of sufficient time for grain growth to occur. SEM observations also confirm dynamic recrystallization to be the primary mechanism of deformation for the temperature and strain rate regime of the present work.

Fig. 5: Palette of SEM micrographs of alloy samples subjected to hot isothermal compression at different temperatures (T) and strain rates ( ε& )

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Table 3: Summary of observations made from optical / SEM microstructures of deformed superalloy samples Temperature, K

1323

Strain Rate, s-1

Grain coarsening

10

1

0.1

0.01

1373

1423

1473

1523

Recrystallization + Grain Coarsening Necklace of fine recrystallized nuclei around unrecrystallized grains + deformation bands Necklace of coarse recrystallized nuclei around unrecrystallized grains + deformations bands Necklace of coarse recrystallized nuclei around unrecrystallized grains + deformation bands Few coarse recrystallized nuclei around unrecrystallized grains

Fine recrystallized nuclei and unrecrystallized grains

Fine recrystallized nuclei and Fine partially recrystallized grains

Fully recrystallized equiaxed microstructure


Necklace of fine recrystallized nuclei around unrecrystallized grains + deformation bands

Fine recrystallized nuclei and Fine partially recrystallized grains



Fine recrystallized nuclei and few unrecrystallized grains

Fine recrystallized grains + deformation twins

Grain growth onset

Grain growth onset

Fine recrystallized nuclei and unrecrystallized grains

Fine recrystallized grains + deformation twins

Grain growth + deformation twins

Abnormal grain coarsening

Further, selected specimens were also analyzed using EBSD and the results are presented in Fig. 6 (a - d) and 6 (a’ – d’). Fig. 6 (a - d) represent the inverse pole figures (IPF) of the alloy in asforged as well as in hot isothermal compressed conditions at various temperatures and strain rates. OIM- IPF maps indicate presence of random textures in all samples. Fig. 6 (a’ - d’) shows the image quality maps of the alloy in as-forged as well as in hot isothermal compressed conditions at various temperatures and strain rates. Deformation twins and annealing twins can be seen clearly in the as forged sample in Fig. 6 (a’). Deformation bands extending across the grain interiors are evident in Fig. 6 (b’) pertaining to the sample subjected to compression at 1323 K and strain rate of 0.1 s-1. Deformation twins are evident in Fig. 6 (b’- d’) as well. However, deformation bands are not present in samples subjected to compression at temperatures higher than 1373 K even at a strain rate of 1 s-1. Hence, flow softening balances or predominates the work hardening. Comparison of Fig. 6 (c’ and d’) shows that with increase in temperature and strain rate, the recrystallization process is almost similar except that, at a strain rate of 1 s-1, coarse grains coexist with necklace of fine grains evolving at the grain boundaries. This indicates insufficient time for uniform growth of recrystallized grains at higher strain rates. The samples subjected to two different combinations of deformation i.e. high temperature and high strain rate and low temperature and low strain rate were chosen for transmission electron microscopy so as to study the mechanisms of deformation. It was found that the samples subjected to low temperature and low strain rate showed dislocation tangles and evolution of sub-grain boundaries as indicated by arrows shown in Fig. 7 (a). On the other hand, the samples subjected to high temperature and strain rate revealed presence of arrays of stacking faults of HCP (‘ABAB’ type stacking) between the dislocations in FCC matrix (‘ABCABC’ type stacking sequence) as shown in Fig. 7 (b). These observations are similar to those reported in the literature [31].

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Fig. 6: OIM - IPF maps and Image Quality maps in (a, a’) as-received condition, compressed at (b, b’) 1323 K, ε& = 0.1 s-1, (c, c’) 1373 K, ε& = 0.1 s-1, (d, d’) 1473 K, ε& = 1 s-1

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Fig. 7: Transmission electron micrographs of the alloy deformed at (a) 1323 K, ε& = 0.01 s-1 and (b) 1523 K, ε& = 10 s-1 From an atomistic point of view, stacking faults are regarded as local HCP-structures with ‘ABAB’ type stacking embedded in FCC-matrix with ‘ABCABC’ type stacking. The phase-stability at stacking faults can be significantly affected by segregation of solute atoms, i.e. Suzuki segregation. To date, Suzuki segregation in Co-alloys has never been verified experimentally despite many attempts by researchers all over the world. Atomistic simulations are commonly applied to studies of interfacial segregation, but it is quite difficult to apply atomistic calculation to multinary systems such as cobalt-alloys [32]. Since in this study, the stacking faults were observed at higher strain rates of deformation where diffusion is sluggish, the phenomena of interfacial segregation may occur, but this needs further investigation. Sorensen et al. [33] reported that Mo segregated at the stacking faults and twins in Co-35Ni-20Cr-10Mo alloy acts as a dislocation barrier, resulting in an increase in strength at high strain rates.

Fig. 8: Variation of recrystallized grain size (DDRX) with temperature (T) and strain rate ( ε& )

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Recrystallized grain size of compression tested specimens was measured through optical microscopy/ SEM and it is presented in Fig. 8. It is observed that recrystallized grain size increases with increase in deformation temperature and decrease in strain rate. Increase in recrystallized grain size from ~20 - 40 µm is observed in compression tested specimens from 1373 - 1523 K at strain rates ranging from 0.1 - 10 s-1. However large increase in recrystallized grain size as high as 80 – 140 µm was observed when specimens were deformed at a temperature of 1473 - 1523 K at lower strain rate of 0.01 s-1 indicating abnormal grain growth in this regime. This could be due to dissolution of grain boundary carbides at higher temperature and slow strain rates where sufficient temperature and time are available for grain growth to occur due to higher grain boundary mobility.

4.4. Processing Maps Contour maps of strain rate sensitivity (m) and efficiency of power dissipation for two strains (0.3 and 0.5) are presented in Fig. 9 (a, b, a’, b’) and instability maps are presented in Fig.9 (a’’, b’’). Ziegler’s continuum principles were applied for identifying regions of unstable metal flow during high temperature deformation and the same was validated with the microstructures. For this purpose, Eqs. A1 - A8 have been used as presented in Appendix-A. The input to generate a processing map is the experimental data of flow stress as a function of temperature, strain rate and strain. As shown in Fig. 9 (a, b), strain rate sensitivity (m) is found to be in the range of 0.35 for the alloy at a strain of 0.5. The material shows highest ‘m’ in the strain rate range of 0.1 - 1 s-1 and in the temperature range of 1350 -1400 K and also at a strain rate of 0.01 s-1 at temperature regime of 1480 K to 1500 K. This indicates that the material exhibits good ductility in these regimes. This may be through grain refinement and accelerated DRX resulting in fine grains [24]. DRX domain for the alloy is found to be in the temperature, strain rate regime of 1350 1500 K and 0.01 - 1 s-1. For pure cobalt, DRX occurs in the temperature range of 923 - 1123 K and strain rate of 0.001 - 0.1 s-1 and for Co-33Ni-20Cr-1Mo alloy it occurs in the temperature range of 1373 - 1473 K and strain rate of 1 - 30 s-1 [34].The maximum efficiency of power dissipation in the DRX domain for the alloy under study is found to be 0.5. Higher efficiency of power dissipation indicates stable material flow during hot deformation. Based on the ‘m’ maps and power efficiency maps ( η ), stable regions can be identified. From Fig. 9 (a’, b’), it is clear that stable region lies in the strain rate regime of 0.1 - 1 s-1 and temperature range of 1323 - 1523 K. Hence, the alloy can be hot worked in the temperature range of 1350 - 1500 K at strain rates of 0.1 - 1 s-1. Processing maps for the alloy as shown in Fig.9 (a’’, b’’) reveal flow instabilities in the temperature range of 1323 - 1423 K in both lower (0.01 - 0.03 s-1) and higher strain rate (2 - 10 s-1) regimes. Further, there is a flow instability domain in the temperature range of 1473 - 1523 K in the strain rate range of 0.1 - 10 s-1. Also it may be noted that, the microstructures of the specimens deformed at 1323 K and 10 s-1 revealed presence of deformation bands and are well within the instability region of the processing map. At high strain rates and low temperatures, necklace type grains along with coarse grains were observed and are within the instability region of the processing map. Further, in the high strain rate, high temperature instability domain, the microstructures reveal a mixture of fine and coarse grains along with a high volume fraction of twins which may result in flow localization type of instability. It was also observed that these twin boundaries also act as regions of nucleation of necklace type grains.

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Fig. 9 : (a, b) Contour maps of strain rate sensitivity (m), (a’, b). Efficiency of power dissipation (ƞ) maps and (a’’, b’’) Instability maps for the alloy showing stable (safe) and unstable (unsafe) working zones at strains (a, a’, a’’). ε = 0.3 and (b, b’, b’’) ε = 0.5

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4.5.

Development of Constitutive Equations The values of ln ε&, ln σ , α , Q, ln[sinh(ασ )], n, A have been calculated using equations B1 B8 in Appendix-B, and the plots are depicted in Figs. 10(a - f). The slope of the plot shown in Fig 10 (a) between ln ε& vs. σp gives the value of ‘ α ’ at each temperature. The values as shown in Table- 4 are found to be in line with the earlier works reported for other high temperature materials [26, 27]. Apparent activation energy (Q) is determined from the plot shown in Fig.10 (b). Maximum activation energy (Qmax) of 501 kJ.mol-1 is obtained at 1473 K and at strain rate of 1 s-1. The minimum value of Q indicates the initial feasibility of deformation and highest value of Q ensures the continuation of deformation of the material. Mean value of activation energy ‘Qavg’ has been taken, since it leads to practical estimation for all deformation conditions. Qavg for alloy is found to be 421 kJ.mol-1. Work hardening exponent (n) for alloy is 0.952 indicating high degree of resistance to necking. The alloy possesses relatively low stacking fault energy (SFE) and therefore would be resistant to cross slip. The peak stress is found to be increasing with increase in strain rate indicating work hardening as shown in Fig.10 (c). Rate of such increase is noted to be marginally higher at lower temperatures, indicating that flow softening is playing a key role at higher temperatures. The variation in activation energy with strain rate and temperature due to the onset of non-steady state of deformation is shown in Fig.10 (d). It is noted to be increasing with temperature up to 1473 K and with strain rate up to 1 s-1. Zener Holloman parameter (Z) i.e. deformation resistance is found to be increasing with increase in peak stress and shown in Fig.10 (e, f). Table 4: ‘α’ value calculated using Eq. B1 and Fig. 3 at constant temperature Temperatures, K

‘α α’ value

1323 1373 1423 1473 1523

0.02173 0.02314 0.0337 0.03426 0.03338

The recrystallized grain size (DDRX ) in the alloy is found to be dependent on the deformation temperature and strain rate. As the ‘Z’ increases, dynamically recrystallized grain size is found to decrease. Therefore, D DRX exhibits an inverse co-relationship as seen from the plot shown in Fig.11 and is in agreement with literature [35-41]. For the present alloy, the DRX grain size varies with Z as given below:‘ ln D DRX = 5.459 − 0.05214 ln Z ’. Using the above calculated parameters, constitutive equation has been established as given below:ε& = 2.504 × 1010 [sinh(ασ )]0.952 exp[−421000 / R * T ] The flow stress values for different strain rates and temperatures have been calculated with the above constitutive equation and are compared with the experimental values as shown in Fig.12. It is observed that flow stress values calculated using constitutive equation are comparable to experimental values in the high temperature regime and at moderately high strain rates (1 and 10 s-1). At lower temperatures, error is found to be more but within the range of variation (15 - 25 %) except for isolated cases such as slow strain rates of 0.01 s-1. This can be due to higher strain hardening at lower temperatures.

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Fig. 10: (a) Plot of ln ε& vs. σp at various temperatures (slope of individual plot gives ‘ α ’ for the alloy at that temperature), (b) Relationship between peak stress (σp) and temperature (T) in two different forms used in determination of activation energy (Q), (c) Relationship between peak stress (σp) and strain rate ( ε& ), (d) Activation energy (Q) vs strain rate and temperature (T) and (e, f) Relationship between peak stress (σp) and Zener Holloman parameter (Z) in different forms

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Fig. 11: Variation of recrystallized grain size (DDRX) of alloy with Zener Holloman parameter (Z)

Fig. 12: Comparison of flow stress (σ) calculated using constitutive equation ε& = 2.504 × 1010 [sinh(ασ )]0.952 exp[− 421000 / R * T ] (with error bars) and experimental values at (a) ε& = 10 s-1, (b) ε& = 1 s-1, (c) ε& = 0.1 s-1 and (d) ε& = 0.01 s-1

18

4.6.

Deformation Mechanisms From the flow curves in the present study, it can be clearly seen that flow stress increases initially with strain and reaches a maximum, which is in line with the characteristic curve for DRX [42]. It can also be observed that, microstructures obtained in hot deformation of the alloy under different conditions consisted of fine recrystallized grains. Further, the flow stress variation is found to be changing significantly with temperature, which is also an indication of DRX process. Therefore, it can be summarized that DRX is the predominant mechanism occurring during hot deformation in this alloy and DRV may also be operative along with DRX below a certain temperature. Mechanisms resulting in unstable flow can cause either or both microstructural damage and inhomogeneity and hence are to be avoided. The processing maps containing such information are useful guides in designing hot working processes such that the process parameters are selected and controlled to be within the ‘safe’ processing domains. The DRX domain is mostly the chosen domain for bulk metal working in industrial process. In processing map approach, strain rate sensitivity (m) and power efficiency (ƞ) maps are very important to select the processing parameters. Deformation processing is conducted in the regions of maximum ‘m’ and ‘η’. Strain rate sensitivity (m) for the alloy is found to be ~ 0.35 depending on strain rate and temperature. The observed efficiency of power dissipation (ƞ) for this alloy is ~ 0.5 and hence indicates availability of a moderately good hot working domain in the alloy. It has been reported by Remi and Pineau [43] that the ductility in the Co-xNi-15Cr-5Mo alloy (x = 20 - 45 mass %) improved owing to the FCC ( γ ) → HCP ( ε ) transformation, which partially occurred during plastic deformation. Also, in superplastic materials like Ti6Al4V or AA7475, ‘m’ reaches values above 0.5 and as high as 0.9 [44]. In the present study, deformation in the temperature range of 1323 - 1500 K and strain rate range of 0.1 - 1 s-1 is found to be safe for the alloy. It may be noted that, the deformation with these parameters is practically possible at industrial scale. Activation energy (Q) for deformation of the alloy is found to be similar to three cobalt based superalloys Co-28Cr-9W-0.17N alloy with 453 kJ.mol-1 , Co-29Cr-9W with 445 kJ.mol-1 and Co-33Ni-20Cr-10Mo alloy with 562 kJ.mol-1 [45]. Hence, activation energy for hot deformation for this alloy indicates that, deformation may be through volume diffusion process, where dislocation motion plays an important role [46, 47]. Constitutive equation formulated for the alloy was found to estimate the flow stress of the alloy reasonably well. Favre et al. [48] have proposed that selfheating and metadynamic recrystallization occur jointly which when taken into account during modeling the DRX can result in improving prediction of the flow stresses for high strain rates. 5.0.

Conclusions Hot isothermal compression testing of Co-20Cr-15W-10Ni alloy was carried out in the temperature range of 1323 - 1573 K and strain rate in the range of 0.01 - 10 s-1. Following conclusions are derived from the study:1. Microstructures consisting of predominantly DRX grains of size ranging from 20 - 40 µm were observed after hot isothermal deformation from an initial grain size was of the order of 100 µm. Size of DRX grains is found to decrease with increase in strain rate and vice versa. 2. Formation of DRX grains begins at 1323 K and indicates the minimum temperature of deformation to trigger DRX. 3. At high strain rates and low temperatures, necklace type partially recrystallized grains along with coarse grains were observed which correspond to the instability regime of the processing map. Whereas at high strain rate and high temperature instability domain, the microstructures

19

reveal a mixture of fine and coarse grains along with a high volume fraction of twins which may result in flow localization type of instability. 4. Using processing maps, the safe working range for the alloy is in the temperature range of 1323 - 1500 K and strain rate range of 0.1 - 1 s-1, which is the DRX domain for this alloy. 5. The recrystallized grain size (D DRX ) for the alloy is found to be inversely dependent on the deformation temperature compensated strain rate (Z) which is a characteristic of DRX phenomenon. For the present alloy, this dependence is found to be ‘ ln D DRX = 5.459 − 0.05214 ln Z ’. 6. Constitutive equation has been established for the alloy and is given as ‘ ε& = 2.504 × 1010 [sinh(ασ )]0.952 exp[− 421000 / R * T ] ’

Acknowledgments: The authors thank Dr. Vinod Kumar, RDCIS, SAIL, Ranchi for extending support in compression testing. The authors are also thankful to GM, MMA and DD, MME for the encouragement and support provided during this work. The authors are thankful to Director, VSSC for granting permission to publish this work. References: 1. Geddes B, Leon H, Huang X. Superalloys: Alloying and Performance- ASM handbook, Metals Park, Ohio, 2010. 2. Lee B S, Matsumoto H, Chiba A. Fractures in tensile deformation of biomedical Co-Cr-Mo-Ni alloys. Mater Let 2011; 65: 843–6. 3. Yukawa N, Sato K. The correlation between microstructure and stress rupture properties of a Co-Cr-Ni-W (H-25) alloy. Trans Japan Inst Met 1968; 9: 680–6. 4. Wlodek S T. Embrittlement of a Co-Cr-W (L-605) alloy. Trans ASM 1963; 56: 287–303. 5. Teague J, Cerreta E, Stout M, Tensile properties and microstructure of Haynes 25 alloy after aging at elevated temperatures for extended times. Metal Mater Trans A 2004; 35A:2767–81. 6. ASTM E 209-00 (2010): Standard Practice for Compression Tests of Metallic Materials at Elevated Temperatures with Conventional or Rapid Heating Rates and Strain Rates. 7. Prasad Y V R K, Gegel H L, Doraivelu S M, Malas J C, Morgan J T, Lark K A, Barker D R. Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242. Metal Trans A 1984; 15A: 1883-92. 8. Ziegler, H. In Progress in Solid Mechanics; Sneddon, I.N., Hill, R., Eds.; John Wiley: New York, NY, USA, 1965; pp. 91–193. 9. Narayana Murty S V S, Nageswara Rao, Kashyap B P. On the relationship between the intrinsic hot workability parameters of DMM and PRM. Scand J Metal 2003; 32: 185-93. 10. Narayana Murty S V S, Nageswara Rao B, Kashyap B P. Instability criteria for hot deformation of materials. Int Mat Rev 2000; 45: 15-26. 11. Narayana Murty S V S, Nageswara Rao B. Ziegler’s criterion on the instability regions in processing maps. J Mater Sci Let 1998; 17: 1203-5. 12. Narayana Murty S V S, Nageswara Rao B On the dynamic material model for the hot deformation of materials. J Mater Sci Let 1999; 18: 1757-8. 13. Narayana Murty S V S, Nageswara Rao, Kashyap B P. Identification of flow instabilities during hot working of powder metallurgy superalloy IN100. Pow Metal 2001; 44: 165-70. 14. Narayana Murty S V S, Nageswara Rao, Kashyap B P. Hot working characteristics of powder metallurgy NIMONIC AP-1 superalloy. Pow Metal 2001; 44: 267-73. 15. Narayana Murty S V S, Nageswara Rao, Kashyap B P. Identification of flow instabilities in the processing maps of AISI 304 stainless steel. J Mat Proc Tech 2005; 166: 268-78. 16. Narayana Murty S V S, Nageswara Rao, Kashyap B P. On the hot working characteristics of 20

2014 Al-20vol% Al2O3 metal matrix composites. J Mat Proc Tech 2005; 166: 279-85. 17. Narayana Murty S V S, Nageswara Rao, Kashyap B P. Development of a processing map for the hot working of Ti-25Al-15Nb. Z Metallkd 2000; 91: 769-74. 18. Narayana Murty S V S, Nageswara Rao, Kashyap B P. On the hot workability of ELI grade titanium alloy Ti-6Al-4V. Z Metallkd 2001; 92: 473-6. 19. Narayana Murty S V S, Nageswara Rao, Kashyap B P. Development and Validation of a Processing Map for Zirconium alloys. Mod Sim Mat Sci Eng 2002; 10: 503-20. 20. Narayana Murty S V S, Nageswara Rao B. On the development of instability criteria during hot working with reference to IN 718. Mater Sci Eng A 1998; 254: 76-82. 21. Narayana Murty S V S, Nageswara Rao B, Kashyap B P. Development and validation of a processing map for AFNOR 7020 aluminum alloy. Mater Sci Tech 2004; 20: 772-82. 22. Sellars C M, Modeling an interdisciplinary activity. In Yue S, Proc Int Conf Mat Model Hot Rolling Steel. 1990, CIMM, Hamilton. 23. Gupta R K, Narayana Murty S V S, Bhanu Pant, Vijaya Agarwala, Sinha P P. Hot workability of γ+α2 Titanium Aluminide : Development of processing map and constitutive equations, Mater Sci Eng A 2012; 551: 169-86. 24. Favre J, Koizumi Y, Chiba A, Fabregue D, Maire E. Deformation Behavior and Dynamic Recrystallization of Biomedical Co-Cr-W-Ni (L-605) Alloy. Metal Mater Trans 2013; 44A: 2819-29. 25. Nayan N, Gurao N P, Narayana Murty S V S, Jha A K, Bhanu Pant, Koshy M George, Microstructure and micro-texture evolution during large strain deformation of Inconel alloy IN718. Mat Char 2015; 110: 236-41. 26. Kapoor R, Paul B, Raveendra S, Samajdar I, Chakravartty J K. Metal Mater Trans 2009; 40A: 818-27. 27. Paul B, Kapoor R, Chakravartty J K, Bidaye A C, Sharma I G, Suri A K. Scripta Mater 2009; 60: 104-7. 28. Zhang P, Hu C, Zhu Q, Ding C G, Qin H Y. Hot compression deformation and constitutive modeling of GH4698 alloy. Mater Des 2015; 65: 1153–60. 29. Herchenvoeder R B, Ebihara W T. In- Process Metallurgy of Wrought Cobalt-Base Alloys. Met Eng Quart 1969; 4: 313-24. 30. Gupta R K, Karthikeyan M K, Bhatia D N, Ghosh B R, Sinha P P. Effect of microstructure on mechanical properties of refractory Co-Cr-W-Ni alloy. Met Sci Heat Treat 2008; 50: 175–9. 31. Koizumi Y, Nukaya T, Suzuki S, Otomo T, Kurosu S, Li Y, Matsumoto H, Sato K, Tanaka Y, Chiba A. Suzuki segregation in Co–Ni-based superalloy at 973 K: An experimental and computational study by phase-field simulation. Acta Mater 2012; 60(7): 2901-15. 32. Benson M L, Reetz B, Liaw P K, Reimers W, Choo H, Brown D W, Saleh T A, Klarstrom D L. Phase-transformation and subgrain-deformation characteristics in a cobalt-based superalloy. Mater Sci Eng A 2011; 528(4-5): 1987-93. 33. Sorensen D, Li B Q, Gerberich W W, Mkhoyan K A. Investigation of secondary hardening in Co–35Ni–20Cr–10Mo alloy using analytical scanning transmission electron microscopy. Acta Mater 2014; 63: 63–72. 34. Prasad Y V R K, Rao K P, Sasidhar S. Hot working guide: A compendium of processing maps. 2nd Ed. ASM International; 2015, p. 606-608. 35. Ueki M, Horie S, Nakamura T. Factors affecting dynamic recrystallization of metals and alloys. Mater Sci Tech 1987; 3: 329-37. 36. Luton M J, Sellars C M. Dynamic recrystallization in nickel and nickel-iron alloys during high temperature deformation, Acta Metall 1969; 17:1033-43. 37. Sah J P, Richardson G J, Sellars C M. Grain-size effects during dynamic recrystallization of nickel. Metal Sci 1974; 8: 325-331. 21

38. Jonas J J, Sellars C M, Tegart W J M. Strength and structure under hot- working conditions. Met Rev 1969; 14:1-25. 39. Chakravartty J K, Kapoor R, Banerjee S. Characterization of hot-deformation behavior of Zircaloy-2: A comparison between kinetic analysis and processing maps. Z Metallkde 2005; 96: 645-52. 40. Seshacharyulu T, Medeiros S C, Frazier W G, Prasad Y V R K. Microstructural mechanisms during hot working of commercial grade Ti–6Al–4V with lamellar starting structure. Mater Sci Eng A 2002; 325: 112-25. 41. Chen X M, Hu C, Lin Y C, Wen D X, Zhang J L, He M. Dynamic recrystallization behavior of a typical nickel-based superalloy during hot deformation. Mater Des 2014; 57: 568-77. 42. Dieter G E, Kuhn H A, Semiatin S L. Handbook of workability and process design, Metals Park, Ohio: ASM International; 2003, p.27-29. 43. Remy R, Pineau A. Twinning and strain-induced FCC → HCP transformation on the mechanical properties of Co–xNi–15Cr–5Mo alloys. Mater Sci Eng A 1976; 26: 123-32. 44. Chokshi A H, Mukherjee A K, Langdon T G. Superplasticity in advanced materials. Mater Sci Eng Res 1993; 10: 237-74. 45. Yamanaka K, Mori M, Chiba A. Effects of nitrogen on microstructural evolution of biomedical Co–Cr–W alloys during hot deformation and subsequent cooling. Mater Des 2014; 57: 421-5. 46. Kim Y W, Boyer R R. Microstructure/property relationships in Titanium Aluminides & alloys, Warrendale: The minerals, metals & materials society, Warrendale; 1991, p. 337-344. 47. Kim Y W. Effects of microstructure on the deformation and fracture of γ-TiAl alloys. Mater Sci Eng A 1995; 192,193: 519-33. 48. Favre J, Fabregue D, Yamanaka K, Chiba A. Modeling dynamic recrystallization of L-605 cobalt superalloy. DOI: 10.1016/j.msea.2015.12.003.

Appendix-A Input power to a work piece is dissipated by two complementary processes: a significant protion as heat through plastic deformation and the other part in bringing about microstructural changes. The total power dissipated can be calculated as : ε&

σ

0

0

P = σε& = ∫ σdε& + ∫ ε&dσ = G + J

(A1)

The first integral is defined as G content and represents the main power input dissipated in the form of a temperature rise. The second integral is defined as J co-content and is related to the power dissipated by metallurgical processes. The power partitioning between G and J is given through the following equation, dJ ε&dσ d (ln σ ) = = = m (strain rate sensitivity) dG σdε& d (ln ε& )

(A2)

At a given deformation temperature and strain J=

m σε& m +1

The efficiency of dissipation η is obtained by comparing its dissipation through the microstructural changes with that occurred in an ideal dissipation, and is given by: η=

J 2m = J max m + 1

(A3)

where J max = σ ε& when m = 1 2

22

Deformation processing should be focused on the regions of maximum efficiency of power dissipation, unless structural instabilities like flow localization, etc. occur. The location of regions of microstructural instability is based on principles of maximum rate of entropy production [7] and is found by mapping the instability parameter, ξ ( ε& ), where: ξ (ε& ) =

∂ ln[ m /( m + 1)] +m 1.2 (in the high stress regime), then Eq. (B3) reduces to Z = ε& exp( Q / RT ) = A 2 exp (ασ )

(B4) (B5)

Assuming the hot deformation of the present alloy comes under high stress regime, from Eq. (B5), ε& exp (Q / RT ) = A 2 exp (ασ )

ln ε& + Q / RT = ln A 2 + ασ

(B6)

at constant temperature,

ln ε& = ln A 2 + ασ + C

(B7) where C is constant. From Eq. (B6) and (B7), by linear regression of the relation of ‘ ln ε& vs σ ’ at different temperatures, an optimum value of α is determined.

24

Substituting the values of α and flow stress and utilizing Eq. (B2), activation energy Q is determined. Value of Q is found to be varying (marginally) with temperature (due to change in α , σ , ε& and T in Eq. (B2). Average value of Q can be taken for further calculation, since it is found to be in narrow range and it leads to practical estimation for all deformation conditions. The minimum value of Q indicates the initial feasibility of deformation and highest value of Q ensures the continuation of deformation of material. Taking the natural logarithm each side of Eq. (B3), ln Z = ln A + n ln[sinh(ασ )] (B8) Substituting Q and strain rates at different temperatures into Eq. (B3), the values of Z and ln Z of alloy under different conditions are obtained. Based on the peak stresses, the relationship between ‘ ln Z ’ and ‘ ln[sinh(ασ )] ’ can be plotted. The slope of the plot corresponding to the value of stress exponent ‘n’ in Eq. (B4) is determined and the intercept corresponding to ln A is determined.

25