Materials and Design 32 (2011) 1872–1879

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Materials and Design

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Hot compressive deformation behavior of a new hot isostatically pressed Ni–Cr–Cobased powder metallurgy superalloy

Kai Wu a,⇑, Guoquan Liu a,b, Benfu Hu a, Feng Li c, Yiwen Zhang d,e, Yu Tao e, Jiantao Liu e

a School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, Chinab State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, Chinac Department of Materials Science and Metallurgy, University of Cambridge, Cambridgeshire CB 3QZ, United Kingdomd School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, Chinae High Temperature Materials Research Institution, CISRI, Beijing 100081, China

a r t i c l e i n f o

Article history:Received 29 August 2010Accepted 6 December 2010Available online 13 December 2010

Keywords:A. Non-ferrous metals and alloysC. ForgingF. Plastic behavior

0261-3069/$ - see front matter Crown Copyright � 2doi:10.1016/j.matdes.2010.12.014

⇑ Corresponding author. Address: XueYuan Road 3Science and Technology Beijing, Beijing 100083, China+86 10 62327283.

E-mail address: wk-ustb@163.com (K. Wu).

a b s t r a c t

The hot compressive deformation behavior of a new hot isostatically pressed Ni–Cr–Co based powdermetallurgy (P/M) superalloy was studied in the temperature range of 950–1150 �C and strain rate rangeof 0.0003–1 s�1 using Gleeble-1500 thermal simulator. The dynamic recrystallization-time–temperature(RTT) curve was developed and the constitutive equation of flow stress during hot deformation wasestablished. The results show that the flow stress decreases with increasing deformation temperatureand decreasing strain rate. The flow stress represents as the characteristic of dynamic crystallization withthe increasing of strain at the deformation temperatures lower than 1100 �C and strain rates higher than0.0003 s�1. The beginning time of dynamic crystallization has no linear relationship with deformationtemperature in the condition of strain rate lower than 0.01 s�1. Besides, the experiments verify thatthe hyperbolic sine model including the variable of strain reflects the changing law of flow stress duringthe hot deformation process.

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1. Introduction

The c0 precipitate strengthened Ni–Cr–Co based superalloycombines excellent oxidation resistance with mechanical proper-ties at high temperatures. The powder metallurgy (P/M) route hasbeen found to be attractive for the manufacture of turbine com-ponents in Ni–Cr–Co based superalloys [1,2]. While hot isostaticpressing (HIP) and other techniques are developed for powderconsolidation, the need for a subsequent isothermal forging pro-cess is well recognized because deformation processing at ele-vated temperatures helps in mitigating the undesirable effect ofprior particle boundaries (PPB) [3,4]. The trial and error methodsare generally employed in selecting the hot deformation process-ing parameters while the recently developed technique of numer-ical simulation is found to be very useful in optimizingworkability and controlling microstructure [5,6]. Based on thepublished chemical compositions of the typical third generationP/M superalloys [7–9], a new Ni–Cr–Co based P/M superalloywas designed with the aid of the thermodynamic calculation re-sults [10] and d-electron theory [11,12]. Compared with the first

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and second generations P/M superalloys, the new alloy is de-signed for thermal stability in long time service condition andcontrols the precipitation of topologically close packed (TCP)phases. It produces the mass ratios of Al/Ti and Nb/Ta to be ofunity, in order to achieve the desired combination of properties[13]. It also adds a certain amount of Hf, to enhance the compre-hensive performance [14]. The alloy possesses heat resistingproperties up to about 760 �C. The excellent working andmechanical properties make it a potential material for gas turbineapplications as well as high-temperature attaching parts. Therelated researches on the isothermal forging process [9,15] indi-cated that the hot deformation process of the third generationP/M superalloys became more difficult because more alloying ele-ments were added in. Meanwhile the mechanical properties ofsuperalloys are highly sensitive to the microstructural evolutionduring hot deformation. So the hot deformation behavior of thethird generation P/M superalloys is one of the most important re-search topics in recent years.

Constitutive equation can be used to describe the change offlow stress with the variation of processing parameters such asdeformation strain, temperature and strain rate [16]. It is one ofthe most important inputs for the numerical simulation of isother-mal forging. Bruni et al. [17] studied the flow behavior of Nimonic115 with the variation of processing parameters and established aconstitutive model of flow stress. Thomasa et al. [18] discussed the

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K. Wu et al. / Materials and Design 32 (2011) 1872–1879 1873

dependence of peak stress on the strain rate and temperature, onthe basis of constitutive equation which normalized the stress bythe Young modulus. Alniak and Bedir [19] developed a new strainrate equation for peak flow strength prediction of Rene 95. Liu et al.[20] investigated the influence of deformation temperature andstrain rate on the peak stress of Haynes 230 by the Zener–Hollo-mon parameter. Wang et al. [21] obtained a power exponent rela-tionship between peak strain and Zener–Hollomon parameter forsuperalloy 718. Cai et al. [22] had done the kinetic analysis of aNi-base superalloy both by the constitutive equation of peak stressand corresponding Zener–Hollomon parameters. However, theestablished constitutive equations for Ni-base superalloys in theseabove literatures were limited to peak stress or steady state stress,while neglecting the effect of deformation strain. It led to the devi-ation from the actual condition and could not reflect the change offlow stress during the isothermal forging process. In this study, thehot compressive deformation behavior was studied in differentdeformation conditions using Gleeble-1500 thermal simulator.Flow stress was analyzed in terms of strain rate and temperaturesensitivities. The dynamic RTT curve and the constitutive equationincluding the variable of strain were developed. All of these pro-vided a theoretical and experimental reference for the optimiza-tion design and numerical simulation of isothermal forgingprocess.

2. Experiments

The hot isostatically pressed (HIPed) Ni–Cr–Co based P/Msuperalloy was selected as the experimental material with the fol-lowing chemical composition: Cr 12.92, Co 20.83, Mo 2.64, W 3.85,Al 3.57, Ti 3.53, Nb 1.51, Ta 1.65, C 0.048, B 0.027, Zr 0.043, Hf 0.2,Ni-base. The details of the preparation procedures were as fol-lowed: the vacuum induction melting (VIM) and electroslagremelting (ESR) methods were used for alloy smelting; the plasmarotating electrode process (PREP) was used for powder prepara-tion, and the vibration screening and electrostatic separationmethods were combined to remove inclusions and produce pow-der with particle size of 50–150 lm. The powder particles wereencapsulated in AISI 304 stainless steel capsules and sealed aftervacuum degassing. The capsules were then HIPed in a single stageat 1180 �C for 4 h at a pressure of 120 MPa. The HIPed rods werethen skinned to remove the stainless steel encapsulation. Hot

Fig. 1. Microstructure of HIPed Ni–Cr–Co based P/M superalloy exhibiting auniform dispersion of a few undeformed powder particles (arrows) in a recrystal-lization-grained matrix.

compression tests were conducted using a Gleeble-1500 thermalsimulator at the temperatures of 950 �C, 1000 �C, 1050 �C,1100 �C and 1150 �C and in the strain rate range of 0.0003–1 s�1

with 8 mm diameter, 15 mm high cylindrical specimens. All spec-imens were heated to the deformation temperatures at a heatingrate of 10 �C s�1 and held for 5 min in order to gain the uniformmicrostructure before the hot compression test. Then they weredeformed to a true strain of 0.7 and water cooled to freeze themicrostructure. The load-stroke data obtained in compressionwere processed to obtain true stress–true strain curves using stan-dard equations. The microstructure of as-HIPed sample was ob-served using an Olympus optical microscope and with thechemical etchant of CuCl2 (10 g) + HCl (50 mL) + H2O (50 mL), theetching time of 30 s. Grain sizes were determined according toASTM E112 linear intercept procedures using circular grid overlays[23]. Besides, the microstructure of as-HIPed sample was observedusing a XL30TMP scanning electron microscope (SEM), and thechemical composition analysis of carbides was performed using aPhoenix energy dispersive spectroscopy (EDS). For SEM and EDSstudies, the preparation method of sample started with electropol-ishing with 20% sulfuric–methanol and followed by electrolyticetching in a CrO3–H3PO4–sulfuric acid solution.

Fig. 2. SEM micrographs of HIPed Ni–Cr–Co based P/M superalloy showing cuboidalc0 precipitates (second electron image) (a) and white carbides (back-scatteredelectron image) (b).

1874 K. Wu et al. / Materials and Design 32 (2011) 1872–1879

3. Results and discussion

3.1. Initial microstructure

The typical microstructure of as-HIPed Ni–Cr–Co based P/Msuperalloy is shown in Fig. 1. It consists primarily of recrystallized

Fig. 3. EDS results from the carbides at the grain boundaries showing Cr, Mo and Wcomposition (b).

grains with a uniform dispersion of a few apparently undeformedpowder particles that have retained as-cast dendritic structure.The HIP process carrying out at 1180 �C reduces carbide precipita-tion at PPBs but gives a coarse grain structure. The grain size isabout ASTM 7-8. SEM examination of the specimen revealed cubo-dial c0 precipitates (Fig. 2a) and carbide particles, mainly at the

rich composition (a) and the carbides in the matrix showing Ti, Ta and Nb rich

K. Wu et al. / Materials and Design 32 (2011) 1872–1879 1875

grain boundaries (Fig. 2b). The microstructure of Fig. 2b reveals aprior particle boundary (PPB) network by the large primary c0 pre-cipitates and white carbides. The volume fraction of c0 phase isestimated to be 55%. The EDS recorded at the carbides at the grainboundaries show that the carbides are Cr, Mo and W based(Fig. 3a), while the carbides in the matrix are Ti, Ta and Nb based(Fig. 3b).

3.2. Flow stress curves

The true stress–true strain curves of the Ni–Cr–Co based P/Msuperalloy recorded at various temperatures from 950 to 1150 �Cunder strain rates from 0.0003 to 1 s�1 are shown in Fig. 4. Theseflow stress curves exhibit a flow softening feature, which is moresignificant at lower temperatures and higher strain rates. The basicchanging trends of flow stress are as follows: the stress increasesrapidly with increasing strain at first, then decreases when peak

Fig. 4. True stress–true strain flow curves for the Ni–Cr–Co based P/M superalloy und0.001 s�1 and (e) 0.0003 s�1.

Fig. 5. Peak strain (a) and dynamic RTT curve (b) of the Ni–Cr–Co

stress is reached and it is almost unchanged under certain valuesof strain finally. It means that a typical flow stress curve is com-posed of three stages: stage I (work hardening stage), stage II (soft-ening stage) and stage III (steady stage). This is a combinationeffect of work hardening, which is primarily caused by second or-der pyramidal slip system dislocation motion, and thermally acti-vated softening. In the stage I, the initial rapid rise in stress isassociated with an increase in dislocation density and the forma-tion of poorly developed subgrain boundaries, as a result of workhardening and dynamic recovery. As the Ni–Cr–Co based P/Msuperalloy has low stacking fault energy, the dynamic recoveryproceeds slowly. The high dislocation density stimulates the occur-rence of dynamic recrystallization once a critical strain (usuallyless than 0.1) is exceeded, then the flow stress decreases whichmeans the coming of stage II. In this stage, the dislocations areannihilated in large numbers through the migration of a high angleboundary and the stress drops steeply. Finally, stage III (steady

er different temperatures with strain rates: (a) 1 s�1, (b) 0.1 s�1, (c) 0.01 s�1, (d)

based P/M superalloy under different deformation conditions.

1876 K. Wu et al. / Materials and Design 32 (2011) 1872–1879

stage): the stress becomes steady when a new balance betweensoftening and hardening is obtained [24–26]. From the experimen-tal results (shown in Fig. 4), it can be found that the flow stress rep-resents as the characteristic of dynamic crystallization with theincreasing of strain at the deformation temperatures lower than1100 �C and strain rates higher than 0.0003 s�1.

Besides, the variation of flow stress with deformation tempera-tures and strain rates also can be seen in Fig. 4. For a constantstrain rate, the lower the deformation temperature, the higherthe flow stress. Because with the increase of deformation temper-ature, the atoms in the superalloy become more active, the bindingforce between atoms decreases and more slip systems start. Thedislocations also become more active which means they can over-come the pinning effect and accomplish the activities such as thecross-slip of screw dislocation and the climb of edge dislocation.Meanwhile the nucleation rate and growth rate of dynamic recrys-tallized grain also increase, so the softening effect strengthens,leading to the decrease of flow stress [27]. For a constant deforma-tion temperature, the higher strain rate, the higher the flow stress.Because higher strain rate provides shorter time for energy accu-mulation and dynamic recrystallization cannot occur completely.Thereby, it increases the critical shear stress for starting the slipsystems during hot deformation, and resulting in the increase offlow stress. So the effect of deformation temperature and strainrate on flow stress can be explained by the terms of dynamicrecrystallization and dislocation mechanism.

3.3. Dynamic RTT curve

Dynamic recrystallization-time–temperature (RTT) curve is akind of curve which can characterize the relationship between dy-namic recrystallization, time and deformation temperature.According to the true stress–true strain curves of Fig. 4, a criticaldeformation strain ec is needed for the occurrence of dynamicrecrystallization. Generally, ec is almost equal to the peak strainep. The beginning time t of dynamic crystallization is defined asthe following equation [28]:

t ¼ ep

_eð1Þ

The values of ep are obtained from Fig. 4, then t can be calcu-lated by Eq. (1). The peak strain and dynamic RTT curve of theNi–Cr–Co based P/M superalloy under different deformation condi-tions are shown in Fig. 5.

Fig. 6. Relations of r with ln _e: (a) and ln r with ln _e and (b

Fig. 5a shows that when the strain rate is 0.1 s�1, the peak strainep decreases with increasing deformation temperature. While thefluctuating changes of ep with increasing deformation temperatureoccur when the strain rates are no more than 0.01 s�1. When thestrain rates are 0.01 s�1 and 0.001 s�1, the peak strain ep has themaximum value at 1050 �C. But the peak strain ep has the maxi-mum value at 1000 �C if the strain rate is 0.0003 s�1. Taking intoaccount the occurrence of dynamic recrystallization and theneeded pressure for hot compressive deformation, when the strainrate ranges from 0.01 s�1 to 0.001 s�1, the avoided deformationtemperature is 1050 �C. And when the strain rate is 0.0003 s�1,the hot deformation should be carried out at the temperature high-er than 1000 �C because higher deformation temperature can mit-igate the amount of PPB to some extent [4].

Fig. 5b shows that the beginning time t of dynamic crystalliza-tion is very short (<1.5 s) if the hot deformation is performed at rel-atively high strain rate (0.1 s�1). It happens in an instant and theeffect of strain rate on dynamic recrystallization is more significantthan deformation temperature. Taking into account the occurrenceof dynamic recrystallization is a thermally activated process, strainrate also has important effect on the thermal activation energy. Ifstrain rate decreases, dynamic recrystallization delays and the dif-ference of t under different deformation temperatures is largerwhen comparing with higher strain rate condition. When the strainrate is 0.0003 s�1, the values of t are 73–305 s at 950–1150 �C.While the range of t is 0.72–1.47 s at the strain rate of 0.1 s�1. Soit means that the effect of deformation temperature on dynamicrecrystallization becomes more significant with decreasing strainrate. Besides, the beginning time t of dynamic crystallization forthe new Ni–Cr–Co based P/M superalloy has no linear relationshipwith deformation temperature in the condition of strain rate lowerthan 0.01 s�1. On the one hand, when the superalloy deforms at thestrain rate of 0.1 s�1, the deformation time is short. The higher thedeformation temperature, the easier it is to satisfy the thermalactivation condition, so the occurrence of dynamic recrystallizationbecomes easier. On the other hand, if the superalloy deforms at rel-atively lower strain rate, due to the prolonged deformation time,the phenomena of grain growth [19,20], c0 dissolution and coars-ening [9,15] shall happen, which leads to the fluctuating changesof ep with increasing deformation temperature.

3.4. Constitutive equation

From the analysis of flow curves of the Ni–Cr–Co based P/Msuperalloy (Fig. 4), it is found that the main factors affecting flow

) at e = 0.3 under different deformation temperatures.

K. Wu et al. / Materials and Design 32 (2011) 1872–1879 1877

stress are deformation temperature, strain rate and strain, and theeffect of the former two are more significant. As both hot deforma-tion and creep belong to a thermally activated process, hot defor-mation can be regarded as the extension of creep under thecondition with larger strain rate and higher stress. Therefore, theflow stress mainly depends on deformation temperature and strain

Fig. 7. Relations of ln[sinh (ar)] with ln _e at different deformation temperat

Fig. 8. Relations between material parameters and the change

rate, and there exists dynamic balance between strain hardeningand dynamic softening.

In this study, the researches [29,30] on the constitutive equa-tion between strain rate, temperature with flow stress are summa-rized as below.

The hyperbolic sine model:

ures (a) and ln[sinh (ar)] with l/T at different strain rates (b) at e = 0.3.

s of strain: (a) a � e, (b) n � e, (c) Q � e and (d) ln A � e.

1878 K. Wu et al. / Materials and Design 32 (2011) 1872–1879

_e ¼ A½sinhðarÞ�n expð�Q=RTÞ ð2Þ

The power function model:

_e ¼ A1rn1 ðlow stress; ar < 0:8Þ ð3Þ

The exponential function model

_e ¼ A2 expðbrÞ ðhigh stress; ar > 1:2 ð4Þ

In which, A, A1, A2, n, n1, a and b are the material constantswhich are independent of temperature and a = b/n1, R is the uni-versal gas constant (8.31 J mol�1 K�1), T is the absolute tempera-ture (K), Q is the activation energy of hot deformation (kJ mol�1)which reflects the difficult degree of hot deformation.

Many studies [31–33] show that Eq. (2) can be used to describethe conventional hot deformation process of materials, and alsocan be simplified to Eqs. 3 and 4 under different stress conditions.As we know, dynamic changes of microstructure and flow stresswith the variation of strain are obvious during hot deformation.However, it is commonly accepted that the effect of strain on theflow stress is not be considered in Eq. (2). Therefore, this study as-sumes that A, n a and Q are the material constants which dependon the strain. Then the constitutive equation of the Ni–Cr–Co basedP/M superalloy is established using the hyperbolic sine model ofEq. (2).

Taking the logarithm of both sides of Eqs. (3) and (4) gives

ln r ¼ ln _en1� ln A1

n1ð5Þ

r ¼ ln _eb� ln A2

bð6Þ

The corresponding flow stress with the strain ranges from 0.05to 0.7 is selected from the flow stress curves of Fig. 4. The values ofb and n1 can be obtained by Eqs. (5) and (6) from the slope of thelines in the r – ln _e and ln r – ln _e plots respectively. Then, furtherwork on the relations of a with strain can be done. Fig. 6 showsboth the experimental data and regression results at the strain of0.3. Obviously, r with ln _e and ln r with ln _e have good linear rela-tionship, and the correlation coefficients are 0.981–0.993.

Fig. 9. Comparisons between predicted and measured flow curves at strain ra

As the value of Q is independent of temperature, taking the log-arithm of both sides of Eq. (2) gives

ln _e ¼ ln A� Q=ðRTÞ þ n ln½sinhðarÞ� ð7Þ

For the given strain rate conditions, differentiating Eq. (7) gives

Q ¼ R@ ln _e

@ ln sinhðarÞ

� �T

@ ln sinhðarÞ@ðl=TÞ

� �_e

ð8Þ

By substituting the values of the flow stress and strain rate forall the tested temperatures into Eq. (7), the relations of ln[sin-h (ar)] with ln _e and ln[sinh (ar)] with l/T can be obtained, asshown in Fig. 7. From this kind of figure, the values of n and Acan be easily obtained, and Q can be calculated by Eq. (8) under dif-ferent strain.

These four material parameters with the variation of strain areshown in Fig. 8. It is found that their values change with the increas-ing strain, which may be related to the development of dynamicrecrystallization, the occurrence of grain refinement and so on. Themain reasons for the change of Q can be considered as follows: Inthe initial stage, only a small number of soft-oriented slip systemsand grain take part in the deformation, so the value of Q is relativelyhigh. While with the increase of deformation strain, grain rotationoccurs and more slip systems are activated, leading to the decreaseof Q. Herein, the relations of these material parameters with a func-tion of strain are fitted and shown in Eqs. (9)–(12).

a ¼ 0:00347� 0:00202eþ 0:01378e2 � 0:01496e3

þ 0:00789e4 ð9Þ

n ¼ 4:513� 2:041e� 2:160e2 þ 8:863e3 � 6:102e4 ð10Þ

Q ¼ 811:3� 86:25e� 1401e2 þ 2502e3 � 1634e4 ð11Þ

ln A ¼ 69:16� 8:202e� 121:4e2 þ 216:2e3 � 141:3e4 ð12Þ

The values of a, n Q and ln A can be expressed as 4th order poly-nomial functions, as shown in Fig. 8. It is easy to find that theregression curves fit the experimental data very well and the val-ues of mean square deviation are 0.0004–0.0034.

tes of: (a) 1 s�1, (b) 0.1 s�1, (c) 0.01 s�1, (d) 0.001 s�1 and (e) 0.0003 s�1.

K. Wu et al. / Materials and Design 32 (2011) 1872–1879 1879

Substituting the values of a, n, Q and ln A into Eq. (2), the flowstress constitutive equation of hot compressive deformation forthe Ni–Cr–Co based P/M superalloy can be expressed as follows:

r ¼ 1a

arcsin h explne� ln _Aþ Q=RT

n

!" #ð13Þ

Finally, the value of flow stress can be obtained by substitutingstrain, deformation temperature and strain rate values into Eq.(13). Then the calculated data are compared with the experimentalflow curves, in order to verify the developed constitutive equationof the Ni–Cr–Co based P/M superalloy. Fig. 9 shows comparisonsbetween predicted data and measured flow curves under differentstrain rates. The mean relative error is 3.8%. It can be easily foundthat the proposed deformation constitutive equation gives a goodestimate of flow stress for the Ni–Cr–Co based P/M superalloy,and can be used for the numerical simulation of isothermal forgingprocess.

4. Conclusions

The hot compressive deformation behavior of a new hot isostat-ically pressed Ni–Cr–Co based P/M superalloy has been investi-gated in the temperature range of 950–1150 �C and strain raterange of 0.0003–1 s�1 using Gleeble-1500 thermal simulator. Thefollowing conclusions have been drawn from the results of thisinvestigation:

(1) The true stress–true strain curves of the Ni–Cr–Co based P/Msuperalloy shows the typical characteristics of dynamicrecrystallization and dynamic recovery. The flow stressdecreases with increasing deformation temperature anddecreasing strain rate. The flow stress represents as the char-acteristic of dynamic crystallization with the increasing ofstrain at the deformation temperatures lower than 1100 �Cand strain rates higher than 0.0003s�1.

(2) The beginning time of dynamic crystallization for the Ni–Cr–Co based P/M superalloy has no linear relationship withdeformation temperature in the condition of strain ratelower than 0.01s�1.

(3) Based on the hyperbolic sine model, the constitutiveequation of flow stress including the variable of strain isestablished. The comparisons between the predicted andexperimental results show that the proposed deformationconstitutive equation can give a good estimate of flow stressfor the Ni–Cr–Co based P/M superalloy, and can be used forthe numerical simulation of isothermal forging process.

Acknowledgements

This work was financially supported by National Pre-researchFunds and High Technology Research and Development Programof China (No. 2007AA03A223).

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