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Tensile properties and temperature-dependent yield strength prediction of GH4033 wrought superalloy
Materials Science & Engineering A 676 (2016) 165–172
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Tensile properties and temperature-dependent yield strength prediction of GH4033 wrought superalloy Jianzuo Ma a, Weiguo Li a,n, Xianhe Zhang a, Haibo Kou a, Jiaxing Shao a, Peiji Geng a, Yong Deng a, Daining Fang b a b
State Key Laboratory of Coal Mine Disaster Dynamics and Control and College of Aerospace Engineering, Chongqing University, Chongqing 400030, China LTCS and College of Engineering, Peking University, Beijing 100871, China
art ic l e i nf o
a b s t r a c t
Article history: Received 19 April 2016 Received in revised form 26 August 2016 Accepted 27 August 2016 Available online 28 August 2016
The tensile properties of superalloy GH4033 have been evaluated at temperatures ranging from room temperature to 1000 °C. Fracture surfaces and precipitation were observed using a field-emission scanning electron microscope (FE-SEM). The alloy mainly consisted of γ’ precipitate particles homogeneously dispersed in the γ matrix interior. The effects of dynamic strain aging and precipitation on the strength were verified. A temperature-dependent yield strength model was developed to describe the temperature and precipitation effects on the alloy's yield behaviour. The model is able to consider the effect of precipitation strengthening on the yield strength. The yield behaviour of the precipitationstrengthened superalloy was demonstrated to be adequately predictable over a wide range of temperatures. Note that this model reflects the quantitative relationship between the yield strength of the precipitation-strengthened superalloy and the temperature, the elastic modulus, the specific heat capacity at constant pressure, Poisson's ratio, the precipitate particle size and the volume fraction of the particles. & 2016 Elsevier B.V. All rights reserved.
Keywords: GH4033 Tensile properties Temperature dependence Yield strength prediction
1. Introduction Superalloys are extensively used in structural applications at elevated temperatures because of their favourable mechanical properties, good corrosion resistance, and long-term structural stability under severe conditions [1,2]. The typical applications of superalloys are in turbine engines, chemical plants, heat treatment equipment and jet engines [3,4]. To obtain the mechanical properties required for operational conditions up to very high temperatures in service, precipitation strengthening is commonly used as one of the major strengthening mechanisms for superalloys [5,6]. Over the past several decades, there have been a large amount of researches on the impact of precipitate particles on the properties of superalloy at different temperatures [7–11]. For instance, the contributions of different microstructural features and distributions of γ’ precipitates to the total strength in a polycrystalline Ni-Co-based disk superalloy (TMW-4M3 alloy) were analysed by Osada [7]. Suzuki [8] studied the high-temperature strength and deformation behaviour of γ/γ’ two-phase Co-Al-Wbased alloys. Francis [9] studied the effect of the γ’ precipitate size on the deformation behaviour of a polycrystalline nickel-based n
Corresponding author. E-mail address: [email protected] (W. Li).
http://dx.doi.org/10.1016/j.msea.2016.08.105 0921-5093/& 2016 Elsevier B.V. All rights reserved.
superalloy by neutron diffraction and electron microscopy. Li [10] investigated the influence of the microstructure on the dwell fatigue crack growth behaviour of an advanced nickel-based superalloy at 700 °C. The temperature dependence of the tensile behaviour and the effects of strain rate of the nickel-based alloy Haynes 230 studied by K. Hrutkay [11] via tensile tests in the temperature range of 25 °C to 950 °C at strain rates of 10 3 s 1, 10 4 s 1, and 10 5 s 1. Most of the previous studies concentrated on describing the factors influencing the strengthening of superalloys at elevated temperatures from phenomenological and experimental perspectives [12–15]. The temperature-dependent yield strength as one of the most important properties of plastic materials is normally obtained from tensile tests [16]. Tensile tests for determining yield strength of metallic materials at different temperatures are quite inconvenient. To determine the yield strength of metallic materials under different temperatures more conveniently, our research team has established a temperature-dependent yield strength model [17], which develops a quantitative relationship between the yield strength and the temperature, the elastic modulus, the specific heat at constant pressure and Poisson's ratio. In particular, the contribution of precipitate particles on the yield strength should also be considered for precipitation-strengthened superalloys [18]. γ’ shearing is well established as the main contributor to the strength of polycrystalline superalloys [18]. Recently,
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quantitative insights on the interactions between the yield strength and precipitated phase characteristics have been widely introduced. Toshio Osada [19] studied the factors influencing the mechanical properties of a polycrystalline nickel-cobalt-based superalloy, indicating that the precipitated phase has the greatest influence on the yield strength increment of the alloy. The kinetics of the formation of the sigma phase in the high strength nickelbased superalloys UDIMET 720 (U720) and UDIMET 720Li (U720Li) were characterized by R.C. Reed [20] using a combination of electrolytic extraction and quantitative X-ray diffraction (XRD) involving the Rietveld method. The yield strength of the nickelbased alloy 718Plus was predicted by M.R. Ahmadi [21] based on a thermo-kinetic precipitation simulation and the precipitation strengthening of γ’ has the largest effect on the final yield strength of this alloy during aging. As for theoretical studies, Kozar et al. [22] proposed a strength model for polycrystalline γ-γ’ superalloys including grain sizes and unimodal, bimodal, or trimodal distributions of precipitates. Good predictions were obtained for subsolvus heat-treatment conditions (fine grain and low tertiary γ’ volume fraction). However, this model displayed the opposite strengthening effects under supersolvus conditions (coarse grain and higher tertiary γ’ volume fraction), which was mentioned in a later study [23]. An extended model was then proposed by E.I. Galindo-Nava [23] that accounted for multimodal particle size distributions, where the strengthening contributions of different particle sizes were weighted according to the relative number of each size particle in the alloy, similar to the study by D.M. Collins and H.J. Stone [24]. These models mainly focused on alloys produced by powder metallurgy due to the higher homogeneity of the final microstructure than that of alloys produced by the cast-andwrought route. In this study, the microstructural characteristics of GH4033 alloy were investigated by field-emission scanning electron microscope (FE-SEM). GH4033 alloy is similar to Nimonic 80A [1]. The UNS equivalent of this Chinese grade alloy is NO7080. The tensile properties of GH4033 were tested at different temperatures. In addition, a new temperature-dependent yield strength model for precipitation-strengthened superalloys was developed based on the experimental analysis of the typical precipitationstrengthened superalloy GH4033. This model considers the influence of precipitate particles on the yield strength based on a temperature-dependent yield strength model [17] and the AshbyOrowan model [5]. We experimentally validated this model with both our test results and the results from the literature. The predicted yield strength was remarkably consistent with the experimental data. This model is useful for the design and application of precipitation-strengthened superalloys.
2. Experimental procedure The material used in the present study is GH4033 without any protective coating. The chemical composition of this material is shown in Table 1. The superalloy GH4033 was supplied by Handan Iron & Steel Group Company. Proportional tensile specimens with a gage length of 30 mm were machined, the shape and size of which are shown in Fig. 1. The apparatus equipped with a high-temperature furnace was Table 1 Details of the chemical composition of GH4033 (wt%). Element
C
Cr
Ni
Al
Ti
Fe
Mn
Si
Value
0.03 0.08
19.0 22.0
Bal.
0.60 1.00
2.40 2.80
r 4.00
r 0.35
r 0.65
Fig. 1. Sketch of proportional tensile specimen (unit: mm).
Fig. 2. Photograph of the apparatus for high-temperature mechanical testing.
developed for high-temperature mechanical testing, as shown in Fig. 2. The test apparatus is a stroke displacement and load speed control system. Tests were performed under vacuum by a computer-interfaced universal testing machine (WDW-100, Fangrui Technology Co., Ltd., Changchun, China). The total pressure was vacuumed to 20 Pa before heating. Test temperatures were controlled with an accuracy of 73 °C. The specimen was held at each testing temperature for 10 min, prior to tensile testing. The tests were carried out by controlling the stroke displacement. The beam speed of the test machine was 0.2 mm min 1. Microstructural analyses focused mainly on distribution of precipitates in GH4033. The microstructural characteristics of GH4033 were assessed using a field-emission scanning electron microscope (FE-SEM). The metallographic specimens were mechanically polished and then electrolytically etched with a solution of 12% phosphate, 40% nitric acid and 48% sulfuric acid, as referred to in Ref [1]. In the Ref [1], the microstructures of GH4033 after service exposure for 1600 engine operating hours were investigated.
3. Results and discussion 3.1. Tensile properties Fig. 3 shows the stress-strain curves of the specimens derived from tensile test, and Table 2 presents some mechanical properties of GH4033 obtained experimentally at different temperatures. Table 2 clearly shows that the magnitude of yield strength and ultimate strength gradually reduced with the increasing temperature, as anticipated. Fig. 3 shows that all of the curves rise rapidly until yield, but the behaviours after yielding between room
J. Ma et al. / Materials Science & Engineering A 676 (2016) 165–172
temperature (25 °C) and 1000 °C are different. The tensile stress continues to rise with the increase in strain until fracture in the temperature range of 25 °C to 700 °C. At room temperature and 200 °C, the alloy exhibits obvious work hardening. Serrated flow is clearly observed at temperatures of 400 °C and 600 °C, indicating the occurrence of dynamic strain aging (DSA) [25], which may occur in susceptible materials due to the diffusion of either interstitial or substitutional solute elements. Thus, DSA impedes the movement of dislocations in the vicinity of the grain boundaries [26]. The work-hardening of the alloy during plastic deformation showing a reduced failure strain was produced because of the reduced dislocation mobility during DSA, as seen in this investigation. Smooth flow occurred at temperatures of 700 °C and 800 °C. The stress dropped rapidly beyond a maximum point with
Fig. 3. Stress-strain curves at different temperatures.
Table 2 The tensile properties of GH4033 at different temperatures.
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the increase in strain at 800 °C. However, the stress dropped slowly after yielding at 1000 °C, and the curve can be described as a type of dynamic recrystallization. Similar observations were reported in Ref.[27]. 3.2. Microstructure Figs. 4 and 5 show the microstructures of the specimens after tensile tests at different temperatures. The grain size was approximately 55 mm. After tensile testing at 800 °C, the average grain size showed no remarkable variation (see Fig. 4). The formation of voids on the grain boundaries (in Fig. 4(a)) is possibly because of excessive erosion by electrolyte,. The alloy mainly consisted of γ’ precipitate particles dispersed homogeneously in the γ matrix interior (see Fig. 5). The γ’ precipitates are spherical with an average size of approximately 27 nm, and they were considered as the original microstructural feature without service, as reported in Ref. [1]. As the main strengthening precipitates, the evolution of γ’ phase was investigated after thermal exposure by Tong, et al. [1]. It indicated that the coarsening of γ’ precipitates occurred with exposure time, and was accelerated with increasing the exposure temperature. The size of γ’ precipitates with exposure time at 650 °C and 700 °C could be expressed as:
T = 650°C , x¯ 3 − x¯ 03 = 8.4t
(1)
T = 700°C , x¯ 3 − x¯ 03 = 240.9t
(2)
where T is the temperature in Celsius, t is the thermal exposure time in hour, x¯ is the average size of γ’ precipitates in nm at time t, x¯ 0 is the initial size of γ’ precipitates in nm. The volume fraction of γ’ precipitate was approximately 9.5%, as reported in Ref. [1]. No significant changes in the average γ’ precipitate size when the specimens underwent tensile testing in the temperature range of 25 °C to 800 °C, as shown in Fig. 5. However, the coarsening of γ’ precipitates was observed after long-term thermal exposure at 700 °C for 1500 h, as reported in Ref. [1]. 3.3. Yield strength prediction
Temperature (°C) Tensile properties
25 200 400 600 700 800 1000
Yield strength (MPa)
Ultimate strength (MPa)
Elongation (%)
585 564 545 526 497 467 121
878 874 816 685 663 467 121
29.1 31.6 23.7 12.4 11.9 4.2 40.7
The yield strength at different temperatures is one of the most important mechanical properties for superalloys employed at high temperatures. In general, the temperature-dependent yield strength of superalloy is obtained from tensile tests [9,10]. The yield strength of GH4033 obtained from testing is shown in Table 2 as a function of the testing temperature. The evaluation of experimental data reveals that alloy GH4033 is capable of maintaining relatively high tensile strength up to 700 °C, and followed by a reduction at temperatures approaching 1000 °C. The operating temperature of GH4033 as turbine blade in service is below
Fig. 4. The grain microstructures of GH4033 after tensile testing at (a) 25 °C and (b) 800 °C.
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Fig. 5. The γ’ morphologies in GH4033 after tensile testing at (a) 25 °C, (b) 600 °C and (c) 800 °C.
0.5 ⎡ T ⎛ ⎞⎤ ∫T Cp( T )dT ⎟⎥ ⎢ 1 + μ T0 ET ⎜ 0 σy( T ) = ⎢ ⎜ 1 − Tm ⎟⎥ σy( T0) ⎢ 1 + μ T ET0 ⎜ Cp( T )dT ⎟⎥ ∫ ⎝ ⎠⎦ T ⎣ 0
(
)
(
)
(3)
Fig. 6. Critical resolved shear stress vs. temperature T for single-phase γ’ [32].
70 Critical re-solved shear stress (MPa)
700 °C. The strengthening mechanism of yield strength in superalloys is well established [23]. The complex distributions of precipitates (γ’) in face-centred cubic matrix (γ) allow superalloys to reach high yield strengths at temperatures up to 700 °C [28]. The yield strength in superalloys includes four strengthening contributions [23]: (i) Grain boundary; (ii) solid solution in γ; (iii) precipitation shearing; and (iv) Orowan by-passing. If the γ’ precipitates have higher strength and hardness than the matrix γ, with sufficient spacing between precipitate particles or those particles have no coherent relationship with the matrix, the dislocations can’t cut through such particles, only by-passing them. This by-passing mechanism was firstly proposed by Orowan [29]. It is generally believed that the Orowan strengthening model is suitable for austenitic superalloys [30]. The Orowan strengthening model is quite practical for some nickel-based superalloys with volume fraction of precipitates less than 30% [31]. In addition, the temperature-dependent critical resolved shear stress (CRSS) of single-phase γ’ and single-phase γ were measured by Astrid Nitz and Eckhard Nembach [32], as shown in Figs. 6 and 7, respectively. The compositions of single-phase γ’ and single-phase γ are listed in Table 3 [32]. The experimental results showed that the CRSS of the single-phase γ’ increased linearly with temperatures between 100 °C and 800 °C. The CRSS of the single-phase γ decreased in this temperature range. Based on the above analysis, we can assume that the Orowan by-passing mechanism plays an increasingly dominant role as the temperature increases in the alloy GH4033. Generally, the tensile tests for determining yield strength of metallic materials at different temperatures are quite inconvenient [16]. To avoid the need to perform temperature-dependent yield strength experiments, which are difficult to conduct, a theoretical model [17] was proposed by our research team to compute the temperature-dependent yield strength for metallic materials at arbitrary temperatures based on a type of equivalence between heat energy and distortional strain energy. The model of the temperature-dependent yield strength can be expressed as [17]:
60 50 40 30 20 10 0 100
where T is the temperature in Celsius, σy( T ) is the yield strength in Mpa at temperature T , and σy( T0) is the value of the yield strength in Mpa at an arbitrary reference temperature T0 . ET and μT are the Young's modulus in Gpa and Poisson's ratio at temperature T , respectively. ET0 and μT are the Young's modulus in Mpa and 0
Poisson's ratio at an arbitrary reference temperature T0 , respectively. CP is the specific heat capacity at constant pressure in J/(kg K), and Tm is the melting point of metallic materials in Celsius. If the yield strength of a metallic material at any temperature is known, the yield strength at all temperatures can be predicted theoretically by the model (Eq. (3)) without any fitting parameters.
Single-Phase γ
200
300 400 500 600 o Temperature T ( C)
700
800
Fig. 7. Critical resolved shear stress vs. temperature T for single-phase γ [32].
Table 3 Compositions of the single-phase γ’ and single-phase γ (wt%). [32]. Element
Ni
Co
Cr
Al
Ti
Mo
Fe
single-phase γ’ single-phase γ
65.8 39.5
8.3 27.3
2.1 26.0
19.0 2.94
4.2 0.37
0.5 2.61
0.0 1.30
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The excellent agreement between the model's yield strength predictions and experimental results has been confirmed for some types of metallic materials [17], such as acicular ferrite steel, mild steel, Q345, S690, HRBF500, etc. However, large quantities of precipitate particles exist in precipitation-strengthened superalloys [1–5]. In addition, many studies have demonstrated that the presence of precipitate particles has an important influence on the yield strength [7–11,23]. Hence, considering the effect of precipitation on the yield strength is necessary. The mechanism of precipitation strengthening, known as the Orowan type, was extended by Ashby [33] for random arrangements of particles. Precipitation strengthening σp was quantified using a modified form of the Ashby-Orowan equation [5].
σp =
0.3Gbf 0.5 ⎛⎜ x¯ ⎞⎟ ln ⎝ 2b ⎠ x¯
(4)
where G is the shear modulus in Gpa, b is the Burgers vector in nm, f is the volume fraction of particles, and x¯ is the average particle size in nm. To combine the Ashby-Orowan equation, the yield strength can be expressed as [34]
σy = σ0 + ksσp
(5)
where ks is a constant, and σ0 is frictional stress. G , f and x¯ in Eq. (4) are represented by the temperature-dependent parameters G(T ), f (T ) and x¯ (T ). Refer to the model (5), a new temperature-dependent yield strength for precipitationstrengthened superalloys can be obtained as 0.5 ⎡ T ⎛ ⎞⎤ ∫T Cp( T )dT ⎟⎥ ⎢ 1 + μ T0 ET ⎜ 0 σy( T ) = ⎢ ⎜ 1 − Tm ⎟⎥ ⎢ 1 + μ T ET0 ⎜ Cp( T )dT ⎟⎥ ∫ ⎝ ⎠⎦ T0 ⎣
(
)
(
)
σ ( T0) + ks( T )
0.3G( T )bf 0.5 ( T ) ⎛ x¯ ( T ) ⎞ ⎟⎟ ln⎜⎜ x¯ ( T ) ⎝ 2b ⎠
169
value of ks( T ) is assumed to increase linearly with the increasing temperature in the stage of stable organization, ks( T ) = T /800. The Burgers vector b¼0.25 nm was used based on the data reported for similar steel grades [5,13–15]. The Young's moduli of GH4033 at different temperatures were obtained from a material handbook [37], as shown in Table 4. Using the proposed temperature-dependent yield strength model account of precipitation strengthening, the temperature-dependent yield strength of GH4033 was predicted, as shown in Fig. 8. The specific heat capacities used in the calculations were obtained from a material handbook [37]. The effect of the temperature-dependent Poisson's ratio on the yield strength is neglected. Fig. 8 shows the comparison between the theoretical predictions of the yield strength and the experimental results for GH4033. The Poisson's ratio is μ ¼0.3. The original micro-structural γ’ precipitates in GH4033 are approximately 27 nm in diameter. The same particle size from 20 °C to 800 °C is assumed because of the short thermal exposure time in test. The volume fractions of γ’ precipitate was approximately 9.5%, as reported in Ref. [1]. The proposed temperature-dependent yield strength model for precipitation-strengthened superalloy can accurately predict the yield strength of GH4033 at different temperatures. The good agreement between the experimental and theoretical results is striking. The parameters used in the model are determined by materials properties taken from the experiments and the literature. The proposed temperature-dependent yield strength model (Eq. (6)) can also be used to predict the yield strength of other precipitation-strengthened superalloys. Comparisons between the predicted yield strength and the experimental data for other typical precipitation-strengthened superalloys are shown in Figs. 9–11. The Young's moduli of typical superalloys at different temperatures are obtained from a material handbook [37] and shown in Table 5. Fig. 9 shows the comparison between the yield strength
(6)
where ks( T ) is the influence coefficient of precipitation strengthening at temperature T relative to T0 , G( T ), f ( T ) and x¯ ( T ) are the shear modulus in Gpa, the volume fraction of particles and the average particle size in nm at temperature T , respectively. In the model (Eq. (6)), a quantitative relationship is established between the yield strength of the precipitation-strengthened superalloy and the temperature, the elastic modulus, the specific heat capacity at constant pressure, Poisson's ratio, the precipitate particle size and the volume fraction of particles. The macroscopic quantities and the microscopic quantities of the superalloy are used in this model to determine the quantitative relationship between the yield strength and the temperature. The temperaturedependent yield strength of precipitation-strengthened superalloys can be theoretically predicted by the model (Eq. (6)). The microstructure of GH4033 is relatively stable within the application temperature range, as shown in Fig. 5. The volume fraction of precipitate particles is stable in a large temperature range [4–10,35]. However, the volume fraction of precipitate particles decreases as a result of precipitate particle dissolution when a critical temperature is exceeded [4,36]. In this study, the temperature-dependent yield strength of GH4033 was predicted before its failure mechanism changed significantly above 800 °C [36]. Choosing room temperature as the reference temperature T0 , the σy( T0) in Eq. (6) has included strengthening contributions of grain boundary, solid solution in γ, precipitation shearing, and Orowan by-passing at room temperature. The difficulty of measuring each strengthening contributions is ingenious solved by introducing parameter σy( T0). The increasingly dominant role of Orowan by-passing is reflected by ks( T ). The
Table 4 The Young's modulus of GH4033 at different temperatures [37]. Temperature (°C)
25
200
400
600
700
800
E(T) of GH4033 (GPa)
220.5
210.7
198.9
185.2
176.4
167.5
Fig. 8. Temperature-dependent yield strength of GH4033.
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Table 5 The Young's modulus of typical superalloys at different temperatures [37].
Fig. 9. Temperature-dependent yield strength of GH4037.
Temperature (°C)
25
200
400
600
700
800
E(T) of GH4037 (GPa) E(T) of GH80A (GPa) E(T) of GH738 (GPa)
225.4 222 224
– 214 213
– 200 200
186 189 185
173.8 179 178
166.9 165 169
predicted by the model (Eq. (6)) and the experimental data for GH4037. The experimental yield strength of GH4037 is taken from handbook [38]. The γ’ precipitates in GH4037 are spherical with an average size of 100 nm, and the volume fraction of γ’ particles is approximately 20% [6]. Fig. 10 shows the comparison between the values predicted by the model (Eq. (6)) and the experimental data for GH80A. The experimental yield strength of GH80A is taken from handbook [38]. The average size of γ’ precipitate in GH80A is approximately 100 nm, and the volume fraction of γ’ particles is approximately 17% [39]. Fig. 11 shows the comparison between the predicted yield strength obtained by the model (Eq. (6)) and the experimental data of GH738. The experimental yield strength of GH738 is taken from handbook [38]. The average size of γ’ precipitate in GH738 is approximately 65 nm, and the volume fraction of γ’ particles is approximately 24% [40]. The temperature effects on yield strength are assumed to be dominated by Orowan type precipitation strengthening and elastic modulus in the range of temperatures between 25 °C and 800 °C. The predicted yield strength from the proposed model is highly consistent with both our experimental data and data from other studies, as shown in Figs. 8–11. When the elastic modulus, the precipitate particle size and the volume fraction of particles at different temperatures are known, the new temperature-dependent yield strength model can precisely predict the yield strength of a precipitation-strengthened superalloy at different temperatures, avoiding the need to perform high-temperature yield strength tests. Above 800 °C, the predicted values usually deviate from the experimental results. This might be because the change in the deformation mechanism has occurred with the increasing temperature [21–24]. 3.4. Fractography
Fig. 10. Temperature-dependent yield strength of GH80A.
The fracture surfaces of tensile-tested specimens were observed by SEM and are shown in Fig. 12. Below 200 °C, dimples and grain boundary cracks were seen on the fracture surfaces of the tested specimens. The full of dimples on the fracture surface as shown in Fig. 12(a) indicate that the fracture mode for these specimens was completely ductile. Failure occurred in a mixed intergranular and transgranular mode in the range of temperatures between 400 °C and 700 °C. The typical fracture surface is shown in Fig. 12(b, c and d). The percentages of intergranular fracture increased with the increase in temperature. At 800 °C, the fracture was completely brittle, and intergranular fracture was dominant. The change in the failure behaviour could be dictated by the interaction between the dislocation movement and the γ’ precipitates [41]. While a large number of micropores exist on the fracture surfaces at 1000 °C, the tensile fracture mode was interpreted as the micropore aggregation type.
4. Conclusions
Fig. 11. Temperature-dependent yield strength of GH738.
The microstructural characteristics and mechanical properties of the GH4033 superalloy were investigated at temperatures ranging from room temperature to 1000 °C. Based on the results
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Fig. 12. The SEM micrographs of GH4033 after tensile testing at (a) 200 °C, (b) 400 °C, (c) 600 °C, (d) 700 °C, (e) 800 °C and (f) 1000 °C.
presented in this study, the significant conclusions are presented below. 1) The tensile strength of GH4033 gradually reduced with the increasing temperature, as expected. The stress-strain curves of the GH4033 superalloy show different characteristics at different temperatures due to the combined effects of work hardening, dynamic strain aging and dynamic recrystallization. GH4033 has superior strength and high ductility at temperatures below 700 °C, and the yield strength and tensile strength drop rapidly at 800 °C and 1000 °C. 2) The alloy mainly consisted of γ’ precipitate particles homogeneously dispersed in the γ matrix interior. No significant changes in the average γ’ precipitate size occurred when the specimens underwent tensile testing in the range of temperatures between 25 °C and 800 °C. 3) A temperature-dependent yield strength model was developed to calculate the yield stress as a function of the temperature. The model was shown to be able to consider the effect of precipitation strengthening on the yield strength. The yield behaviour of the precipitation-strengthened superalloy can be adequately predicted over a wide range of temperatures. If the yield
strength of a precipitation-strengthened superalloy at a reference temperature is known, the yield strength can be predicted theoretically at a wide range of temperatures, avoiding the need to perform high-temperature yield strength tests. 4) Dimpled microstructures indicating ductile failures were seen in the alloy below 200 °C. However, a combination of intergranular and transgranular modes was observed in the range of temperatures between 400 °C and 700 °C. At 800 °C, the fracture was completely brittle, and intergranular fracture was dominant. While a large number of micropores existed on the fracture surfaces at 1000 °C, the tensile fracture mode was interpreted as micropore aggregation type.
Acknowledgement This work was supported by the National Natural Science Foundation of China under Grants nos. 11672050, 11602041 and 11472066, the Program for New Century Excellent Talents in University under Grant no. ncet-13-0634, the China Postdoctoral Science Foundation under Grant no. 2016M592636, the Postdoctoral Science Foundation of Chongqing under Grant no. xm2015079, and the Scientific and
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Technological Research Program of the Chongqing Municipal Education Commission under Grants nos. KJ1503104 and KJ1503109.
References [1] J.Y. Tong, X.F. Ding, M.L. Wang, Y.R. Zheng, K. Yagi, Q. Feng, Evaluation of a serviced turbine blade made of GH4033 wrought superalloy, Mater. Sci. Eng. A 618 (2014) 605–613. [2] D. Nunes, M. Vilarigues, J.B. Correia, P.A. Carvalho, Nickel–carbon nanocomposites: Synthesis, structural changes and strengthening mechanisms, Acta Mater. 60 (2012) 737–747. [3] B. Larrouy, P. Villechaise, J. Cormier, O. Berteaux, Grain boundary-slip bands interactions: Impact on the fatigue crack initiation in a polycrystalline forged Ni-based superalloy, Acta Mater. 99 (2015) 325–336. [4] L.Q. Chen, Q. Cheng, F.X. Zhu, Y. Zhao, in: T.M.S. Fernand Marquis (Ed.), Grain Growth behavior of a NI-CR based Superalloy GH4033 in reheating process prior to Hot rolling, The 8th Pacific RIM International Congress on Advanced Materials and processing, The Minerals, Metals & Materials Society, 2013, pp. 369–377. [5] V.C. Olalla, V. Bliznuk, N. Sanchez, P. Thibaux, L.A.I. Kestens, R.H. Petrov, Analysis of the strengthening mechanisms in pipeline steels as a function of the hot rolling parameters, Mater. Sci. Eng. A 604 (2014) 46–56. [6] X.Z. Lv, F. Sun, J.Y. Tong, Q. Feng, J.X. Zhang, Paired dislocations and their interactions with γ’ particles in polycrystalline superalloy GH4037, J. Mater. Eng. Perform. 24 (2015) 143–148. [7] T. Osada, Y.F. Gu, N. Nagashima, Y. Yuan, T. Yokokawa, H. Harada, Optimum microstructure combination for maximizing tensile strength in a polycrystalline superalloy with a two-phase structure, Acta Mater. 61 (2013) 1820–1829. [8] A. Suzuki, T.M. Pollock, High-temperature strength and deformation of γ/γ’ two-phase Co-Al-W-base alloys, Acta Mater. 56 (2008) 1288–1297. [9] E.M. Francis, B.M.B. Grant, J. Quinta da Fonseca, P.J. Phillips, M.J. Mills, M. R. Daymond, M. Preuss, High-temperature deformation mechanisms in a polycrystalline nickel-base superalloy studied by neutron diffraction and electron microscopy, Acta Mater. 74 (2014) 18–29. [10] H.Y. Li, J.F. Sun, M.C. Hardy, H.E. Evans, S.J. Williams, T.J.A. Doel, P. Bowen, Effects of microstructure on high temperature dwell fatigue crack growth in a coarse grain PM nickel based superalloy, Acta Mater. 90 (2015) 355–369. [11] K. Hrutkay, D. Kaoumi, Tensile deformation behavior of a nickel based superalloy at different temperatures, Mater. Sci. Eng. A 599 (2014) 196–203. [12] X.D. Lu, J.H. Du, Q. Deng, J.Y. Zhuang, Stress rupture properties of GH4169 superalloy, J. Mater. Res. Technol. 3 (2014) 107–113. [13] F.P. Yuan, X.L. Wu, Size effect and boundary type on the strengthening of nanoscale domains in pure nickel, Mater. Sci. Eng. A 648 (2015) 243–251. [14] K.G. Wang, Z. Guo, W. Sha, M.E. Glicksman, K. Rajan, Property predictions using microstructural modeling, Acta Mater. 53 (2005) 3395–3402. [15] D. Nunes, M. Vilarigues, J.B. Correia, P.A. Carvalho, Nickel-carbon nanocomposites: Synthesis, structural changes and strengthening mechanisms, Acta Mater. 60 (2012) 737–747. [16] J.Z. Xiao, Y.Y. Dai, Y. Zhao, Z.J. Chen, X.F. Wang, Stress-Strain relationship of HRBF500 at high temperatures, J. Build. Mater. 11 (2008) 277–282. [17] W.G. Li, X.H. Zhang, H.B. Kou, R.Z. Wang, D.N. Fang, Theoretical prediction of temperature-dependent yield strength for metallic materials, Int J. Mech. Sci. 105 (2016) 273–278. [18] A.J. Ardell, V. Munjal, D.J. Chellman, Precipitation hardening of Ni-Al alloys containing large volume fractions of γ’, Metall. Trans. A 7 (1976) 1263–1268. [19] T. Osada, N. Nagashima, Y. Gu, Y. Yuan, T. Yokokawa, H. Harada, Factors contributing to the strength of a polycrystalline nickel-cobalt base superalloy, Scr.
Mater. 64 (2011) 892–895. [20] R.C. Reed, M.P. Jackson, Y.S. Na, Characterization and modelling of the precipitation of the sigma phase in UDIMET 720 and UDIMET 720Li, Metall. Mater. Trans. A 30 (1999) 521–533. [21] M. Ahmadi, E. Povoden-Karadeniz, L. Whitmore, M. Stockinger, A. Falahati, E. Kozeschnik, Yield strength prediction in Ni-base alloy 718Plus based on thermo-kinetic precipitation simulation, Mater. Sci. Eng. A 608 (2014) 114–122. [22] R. Kozar, A. Suzuki, W. Milligan, J. Schirra, M. Savage, T. Pollock, Strengthening mechanisms in polycrystalline multimodal nickel-base superalloys, Metall. Mater. Trans. A 40 (2009) 1588–1603. [23] E.I. Galindo-Nava, L.D. Connor, C.M.F. Rae, On the prediction of the yield stress of unimodal and multimodal γ’ Nickel-base superalloys, Acta Mater. 98 (2015) 377–390. [24] D. Collins, H. Stone, A modelling approach to yield strength optimisation in a nickel-base superalloy, Int. J. Plast. 54 (2014) 96–112. [25] M.C. Rezende, L.S. Araújo, S.B. Gabriel, J. Dille, L.H. de Almeida, Oxidation assisted intergranular cracking under loading at dynamic strain aging temperatures in Inconel 718 superalloy, J. Alloy. Compd. 643 (2015) S256–S259. [26] A.K. Roy, V. Virupaksha, Performance of alloy 800H for high-temperature heat exchanger applications, Mater. Sci. Eng. A 452 (2007) 665–672. [27] X.H. Xiong, D.M. Quan, P.D. Dai, Z.P. Wang, Q.X. Zhang, Z.F. Yue, Tensile behavior of nickel-base single-crystal superalloy DD6, Mater. Sci. Eng. A 636 (2015) 608–612. [28] R. Reed, The Superalloys: Fundamentals and Applications, Cambridge University Press, Cambridge, 2006. [29] E..Orowan, in: T.I.o.Metals(Ed.), Proceedings of the Symposium on Internal Stresses in Metals and Alloys, the Institue of Metals, London, 1948, pp. 451453. [30] C.T. Sims, W.C. Hagel, The Superalloys, first ed., John Wiley & Sons, New York, 1972. [31] J.T. Guo, Meterials Science and Engineering for Superalloys, first ed., Science Press, Beijing, 2008. [32] A. Nitz, E. Nembach, The critical resolved shear stress of a superalloy as a combination of those of its γ matrix and γ’ precipitates, Metall. Mater. Trans. A 29A (1998) 799–807. [33] M.F. Ashby, in: G.A.Breach (Eds.), Proceedings of the Metallurgical Society Conference Oxide Dispersion Strengthening, NewYork, 1966, pp. 143–205. [34] M.J. Peet, 6-Bainitic steels and alloys for power plants, Structural Alloys for, Power Plants, Camb. (2014) 153–187. [35] Z. Zhu, H. Basoalto, N. Warnken, R.C. Reed, A model for the creep deformation behaviour of nickel-based single crystal superalloys, Acta Mater. 60 (2012) 4888–4900. [36] Y.N. Fan, H.J. Shi, W.H. Qiu, Constitutive modeling of creep behavior in single crystal superalloys: Effects of rafting at high temperatures, Mater. Sci. Eng. A 644 (2015) 225–233. [37] J.R. An, L.G. Tian, Metal Materials Handbook, first ed., Chemical Industry Press, Beijing, 2008. [38] Y. Gan, Z.L. Tian, H. Dong, D. Feng, X.L. Wang, Steel Materials Handbook, first ed., Chemical Industry Press, Beijing, 2009. [39] T.T. Ge, J.X. Dong, M.C. Zhang, L. Zheng, S.W. Gao, Microstructure characteristics of GH80A superalloy and thermodynamic calculation on precipitated phases, Rare Met. Mater. Eng. 40 (2011) 1178–1183. [40] Y.Y. Shi, S.Y. Jiao, J.X. Dong, M.C. Zhang, Classical precipitation dynamic model of γ’ phase of nickel-based superalloys and applications, Acta Metall. Sin. 48 (2012) 661–670. [41] Z.H. Zhong, Y.F. Gu, Y. Yuan, Microstructural stability and mechanical properties of a newly developed Ni-Fe-base superalloy, Mater. Sci. Eng. A 622 (2015) 101–107.
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Tensile properties and temperature-dependent yield strength prediction of GH4033 wrought superalloy Jianzuo Ma a, Weiguo Li a,n, Xianhe Zhang a, Haibo Kou a, Jiaxing Shao a, Peiji Geng a, Yong Deng a, Daining Fang b a b
State Key Laboratory of Coal Mine Disaster Dynamics and Control and College of Aerospace Engineering, Chongqing University, Chongqing 400030, China LTCS and College of Engineering, Peking University, Beijing 100871, China
art ic l e i nf o
a b s t r a c t
Article history: Received 19 April 2016 Received in revised form 26 August 2016 Accepted 27 August 2016 Available online 28 August 2016
The tensile properties of superalloy GH4033 have been evaluated at temperatures ranging from room temperature to 1000 °C. Fracture surfaces and precipitation were observed using a field-emission scanning electron microscope (FE-SEM). The alloy mainly consisted of γ’ precipitate particles homogeneously dispersed in the γ matrix interior. The effects of dynamic strain aging and precipitation on the strength were verified. A temperature-dependent yield strength model was developed to describe the temperature and precipitation effects on the alloy's yield behaviour. The model is able to consider the effect of precipitation strengthening on the yield strength. The yield behaviour of the precipitationstrengthened superalloy was demonstrated to be adequately predictable over a wide range of temperatures. Note that this model reflects the quantitative relationship between the yield strength of the precipitation-strengthened superalloy and the temperature, the elastic modulus, the specific heat capacity at constant pressure, Poisson's ratio, the precipitate particle size and the volume fraction of the particles. & 2016 Elsevier B.V. All rights reserved.
Keywords: GH4033 Tensile properties Temperature dependence Yield strength prediction
1. Introduction Superalloys are extensively used in structural applications at elevated temperatures because of their favourable mechanical properties, good corrosion resistance, and long-term structural stability under severe conditions [1,2]. The typical applications of superalloys are in turbine engines, chemical plants, heat treatment equipment and jet engines [3,4]. To obtain the mechanical properties required for operational conditions up to very high temperatures in service, precipitation strengthening is commonly used as one of the major strengthening mechanisms for superalloys [5,6]. Over the past several decades, there have been a large amount of researches on the impact of precipitate particles on the properties of superalloy at different temperatures [7–11]. For instance, the contributions of different microstructural features and distributions of γ’ precipitates to the total strength in a polycrystalline Ni-Co-based disk superalloy (TMW-4M3 alloy) were analysed by Osada [7]. Suzuki [8] studied the high-temperature strength and deformation behaviour of γ/γ’ two-phase Co-Al-Wbased alloys. Francis [9] studied the effect of the γ’ precipitate size on the deformation behaviour of a polycrystalline nickel-based n
Corresponding author. E-mail address: [email protected] (W. Li).
http://dx.doi.org/10.1016/j.msea.2016.08.105 0921-5093/& 2016 Elsevier B.V. All rights reserved.
superalloy by neutron diffraction and electron microscopy. Li [10] investigated the influence of the microstructure on the dwell fatigue crack growth behaviour of an advanced nickel-based superalloy at 700 °C. The temperature dependence of the tensile behaviour and the effects of strain rate of the nickel-based alloy Haynes 230 studied by K. Hrutkay [11] via tensile tests in the temperature range of 25 °C to 950 °C at strain rates of 10 3 s 1, 10 4 s 1, and 10 5 s 1. Most of the previous studies concentrated on describing the factors influencing the strengthening of superalloys at elevated temperatures from phenomenological and experimental perspectives [12–15]. The temperature-dependent yield strength as one of the most important properties of plastic materials is normally obtained from tensile tests [16]. Tensile tests for determining yield strength of metallic materials at different temperatures are quite inconvenient. To determine the yield strength of metallic materials under different temperatures more conveniently, our research team has established a temperature-dependent yield strength model [17], which develops a quantitative relationship between the yield strength and the temperature, the elastic modulus, the specific heat at constant pressure and Poisson's ratio. In particular, the contribution of precipitate particles on the yield strength should also be considered for precipitation-strengthened superalloys [18]. γ’ shearing is well established as the main contributor to the strength of polycrystalline superalloys [18]. Recently,
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quantitative insights on the interactions between the yield strength and precipitated phase characteristics have been widely introduced. Toshio Osada [19] studied the factors influencing the mechanical properties of a polycrystalline nickel-cobalt-based superalloy, indicating that the precipitated phase has the greatest influence on the yield strength increment of the alloy. The kinetics of the formation of the sigma phase in the high strength nickelbased superalloys UDIMET 720 (U720) and UDIMET 720Li (U720Li) were characterized by R.C. Reed [20] using a combination of electrolytic extraction and quantitative X-ray diffraction (XRD) involving the Rietveld method. The yield strength of the nickelbased alloy 718Plus was predicted by M.R. Ahmadi [21] based on a thermo-kinetic precipitation simulation and the precipitation strengthening of γ’ has the largest effect on the final yield strength of this alloy during aging. As for theoretical studies, Kozar et al. [22] proposed a strength model for polycrystalline γ-γ’ superalloys including grain sizes and unimodal, bimodal, or trimodal distributions of precipitates. Good predictions were obtained for subsolvus heat-treatment conditions (fine grain and low tertiary γ’ volume fraction). However, this model displayed the opposite strengthening effects under supersolvus conditions (coarse grain and higher tertiary γ’ volume fraction), which was mentioned in a later study [23]. An extended model was then proposed by E.I. Galindo-Nava [23] that accounted for multimodal particle size distributions, where the strengthening contributions of different particle sizes were weighted according to the relative number of each size particle in the alloy, similar to the study by D.M. Collins and H.J. Stone [24]. These models mainly focused on alloys produced by powder metallurgy due to the higher homogeneity of the final microstructure than that of alloys produced by the cast-andwrought route. In this study, the microstructural characteristics of GH4033 alloy were investigated by field-emission scanning electron microscope (FE-SEM). GH4033 alloy is similar to Nimonic 80A [1]. The UNS equivalent of this Chinese grade alloy is NO7080. The tensile properties of GH4033 were tested at different temperatures. In addition, a new temperature-dependent yield strength model for precipitation-strengthened superalloys was developed based on the experimental analysis of the typical precipitationstrengthened superalloy GH4033. This model considers the influence of precipitate particles on the yield strength based on a temperature-dependent yield strength model [17] and the AshbyOrowan model [5]. We experimentally validated this model with both our test results and the results from the literature. The predicted yield strength was remarkably consistent with the experimental data. This model is useful for the design and application of precipitation-strengthened superalloys.
2. Experimental procedure The material used in the present study is GH4033 without any protective coating. The chemical composition of this material is shown in Table 1. The superalloy GH4033 was supplied by Handan Iron & Steel Group Company. Proportional tensile specimens with a gage length of 30 mm were machined, the shape and size of which are shown in Fig. 1. The apparatus equipped with a high-temperature furnace was Table 1 Details of the chemical composition of GH4033 (wt%). Element
C
Cr
Ni
Al
Ti
Fe
Mn
Si
Value
0.03 0.08
19.0 22.0
Bal.
0.60 1.00
2.40 2.80
r 4.00
r 0.35
r 0.65
Fig. 1. Sketch of proportional tensile specimen (unit: mm).
Fig. 2. Photograph of the apparatus for high-temperature mechanical testing.
developed for high-temperature mechanical testing, as shown in Fig. 2. The test apparatus is a stroke displacement and load speed control system. Tests were performed under vacuum by a computer-interfaced universal testing machine (WDW-100, Fangrui Technology Co., Ltd., Changchun, China). The total pressure was vacuumed to 20 Pa before heating. Test temperatures were controlled with an accuracy of 73 °C. The specimen was held at each testing temperature for 10 min, prior to tensile testing. The tests were carried out by controlling the stroke displacement. The beam speed of the test machine was 0.2 mm min 1. Microstructural analyses focused mainly on distribution of precipitates in GH4033. The microstructural characteristics of GH4033 were assessed using a field-emission scanning electron microscope (FE-SEM). The metallographic specimens were mechanically polished and then electrolytically etched with a solution of 12% phosphate, 40% nitric acid and 48% sulfuric acid, as referred to in Ref [1]. In the Ref [1], the microstructures of GH4033 after service exposure for 1600 engine operating hours were investigated.
3. Results and discussion 3.1. Tensile properties Fig. 3 shows the stress-strain curves of the specimens derived from tensile test, and Table 2 presents some mechanical properties of GH4033 obtained experimentally at different temperatures. Table 2 clearly shows that the magnitude of yield strength and ultimate strength gradually reduced with the increasing temperature, as anticipated. Fig. 3 shows that all of the curves rise rapidly until yield, but the behaviours after yielding between room
J. Ma et al. / Materials Science & Engineering A 676 (2016) 165–172
temperature (25 °C) and 1000 °C are different. The tensile stress continues to rise with the increase in strain until fracture in the temperature range of 25 °C to 700 °C. At room temperature and 200 °C, the alloy exhibits obvious work hardening. Serrated flow is clearly observed at temperatures of 400 °C and 600 °C, indicating the occurrence of dynamic strain aging (DSA) [25], which may occur in susceptible materials due to the diffusion of either interstitial or substitutional solute elements. Thus, DSA impedes the movement of dislocations in the vicinity of the grain boundaries [26]. The work-hardening of the alloy during plastic deformation showing a reduced failure strain was produced because of the reduced dislocation mobility during DSA, as seen in this investigation. Smooth flow occurred at temperatures of 700 °C and 800 °C. The stress dropped rapidly beyond a maximum point with
Fig. 3. Stress-strain curves at different temperatures.
Table 2 The tensile properties of GH4033 at different temperatures.
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the increase in strain at 800 °C. However, the stress dropped slowly after yielding at 1000 °C, and the curve can be described as a type of dynamic recrystallization. Similar observations were reported in Ref.[27]. 3.2. Microstructure Figs. 4 and 5 show the microstructures of the specimens after tensile tests at different temperatures. The grain size was approximately 55 mm. After tensile testing at 800 °C, the average grain size showed no remarkable variation (see Fig. 4). The formation of voids on the grain boundaries (in Fig. 4(a)) is possibly because of excessive erosion by electrolyte,. The alloy mainly consisted of γ’ precipitate particles dispersed homogeneously in the γ matrix interior (see Fig. 5). The γ’ precipitates are spherical with an average size of approximately 27 nm, and they were considered as the original microstructural feature without service, as reported in Ref. [1]. As the main strengthening precipitates, the evolution of γ’ phase was investigated after thermal exposure by Tong, et al. [1]. It indicated that the coarsening of γ’ precipitates occurred with exposure time, and was accelerated with increasing the exposure temperature. The size of γ’ precipitates with exposure time at 650 °C and 700 °C could be expressed as:
T = 650°C , x¯ 3 − x¯ 03 = 8.4t
(1)
T = 700°C , x¯ 3 − x¯ 03 = 240.9t
(2)
where T is the temperature in Celsius, t is the thermal exposure time in hour, x¯ is the average size of γ’ precipitates in nm at time t, x¯ 0 is the initial size of γ’ precipitates in nm. The volume fraction of γ’ precipitate was approximately 9.5%, as reported in Ref. [1]. No significant changes in the average γ’ precipitate size when the specimens underwent tensile testing in the temperature range of 25 °C to 800 °C, as shown in Fig. 5. However, the coarsening of γ’ precipitates was observed after long-term thermal exposure at 700 °C for 1500 h, as reported in Ref. [1]. 3.3. Yield strength prediction
Temperature (°C) Tensile properties
25 200 400 600 700 800 1000
Yield strength (MPa)
Ultimate strength (MPa)
Elongation (%)
585 564 545 526 497 467 121
878 874 816 685 663 467 121
29.1 31.6 23.7 12.4 11.9 4.2 40.7
The yield strength at different temperatures is one of the most important mechanical properties for superalloys employed at high temperatures. In general, the temperature-dependent yield strength of superalloy is obtained from tensile tests [9,10]. The yield strength of GH4033 obtained from testing is shown in Table 2 as a function of the testing temperature. The evaluation of experimental data reveals that alloy GH4033 is capable of maintaining relatively high tensile strength up to 700 °C, and followed by a reduction at temperatures approaching 1000 °C. The operating temperature of GH4033 as turbine blade in service is below
Fig. 4. The grain microstructures of GH4033 after tensile testing at (a) 25 °C and (b) 800 °C.
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Fig. 5. The γ’ morphologies in GH4033 after tensile testing at (a) 25 °C, (b) 600 °C and (c) 800 °C.
0.5 ⎡ T ⎛ ⎞⎤ ∫T Cp( T )dT ⎟⎥ ⎢ 1 + μ T0 ET ⎜ 0 σy( T ) = ⎢ ⎜ 1 − Tm ⎟⎥ σy( T0) ⎢ 1 + μ T ET0 ⎜ Cp( T )dT ⎟⎥ ∫ ⎝ ⎠⎦ T ⎣ 0
(
)
(
)
(3)
Fig. 6. Critical resolved shear stress vs. temperature T for single-phase γ’ [32].
70 Critical re-solved shear stress (MPa)
700 °C. The strengthening mechanism of yield strength in superalloys is well established [23]. The complex distributions of precipitates (γ’) in face-centred cubic matrix (γ) allow superalloys to reach high yield strengths at temperatures up to 700 °C [28]. The yield strength in superalloys includes four strengthening contributions [23]: (i) Grain boundary; (ii) solid solution in γ; (iii) precipitation shearing; and (iv) Orowan by-passing. If the γ’ precipitates have higher strength and hardness than the matrix γ, with sufficient spacing between precipitate particles or those particles have no coherent relationship with the matrix, the dislocations can’t cut through such particles, only by-passing them. This by-passing mechanism was firstly proposed by Orowan [29]. It is generally believed that the Orowan strengthening model is suitable for austenitic superalloys [30]. The Orowan strengthening model is quite practical for some nickel-based superalloys with volume fraction of precipitates less than 30% [31]. In addition, the temperature-dependent critical resolved shear stress (CRSS) of single-phase γ’ and single-phase γ were measured by Astrid Nitz and Eckhard Nembach [32], as shown in Figs. 6 and 7, respectively. The compositions of single-phase γ’ and single-phase γ are listed in Table 3 [32]. The experimental results showed that the CRSS of the single-phase γ’ increased linearly with temperatures between 100 °C and 800 °C. The CRSS of the single-phase γ decreased in this temperature range. Based on the above analysis, we can assume that the Orowan by-passing mechanism plays an increasingly dominant role as the temperature increases in the alloy GH4033. Generally, the tensile tests for determining yield strength of metallic materials at different temperatures are quite inconvenient [16]. To avoid the need to perform temperature-dependent yield strength experiments, which are difficult to conduct, a theoretical model [17] was proposed by our research team to compute the temperature-dependent yield strength for metallic materials at arbitrary temperatures based on a type of equivalence between heat energy and distortional strain energy. The model of the temperature-dependent yield strength can be expressed as [17]:
60 50 40 30 20 10 0 100
where T is the temperature in Celsius, σy( T ) is the yield strength in Mpa at temperature T , and σy( T0) is the value of the yield strength in Mpa at an arbitrary reference temperature T0 . ET and μT are the Young's modulus in Gpa and Poisson's ratio at temperature T , respectively. ET0 and μT are the Young's modulus in Mpa and 0
Poisson's ratio at an arbitrary reference temperature T0 , respectively. CP is the specific heat capacity at constant pressure in J/(kg K), and Tm is the melting point of metallic materials in Celsius. If the yield strength of a metallic material at any temperature is known, the yield strength at all temperatures can be predicted theoretically by the model (Eq. (3)) without any fitting parameters.
Single-Phase γ
200
300 400 500 600 o Temperature T ( C)
700
800
Fig. 7. Critical resolved shear stress vs. temperature T for single-phase γ [32].
Table 3 Compositions of the single-phase γ’ and single-phase γ (wt%). [32]. Element
Ni
Co
Cr
Al
Ti
Mo
Fe
single-phase γ’ single-phase γ
65.8 39.5
8.3 27.3
2.1 26.0
19.0 2.94
4.2 0.37
0.5 2.61
0.0 1.30
J. Ma et al. / Materials Science & Engineering A 676 (2016) 165–172
The excellent agreement between the model's yield strength predictions and experimental results has been confirmed for some types of metallic materials [17], such as acicular ferrite steel, mild steel, Q345, S690, HRBF500, etc. However, large quantities of precipitate particles exist in precipitation-strengthened superalloys [1–5]. In addition, many studies have demonstrated that the presence of precipitate particles has an important influence on the yield strength [7–11,23]. Hence, considering the effect of precipitation on the yield strength is necessary. The mechanism of precipitation strengthening, known as the Orowan type, was extended by Ashby [33] for random arrangements of particles. Precipitation strengthening σp was quantified using a modified form of the Ashby-Orowan equation [5].
σp =
0.3Gbf 0.5 ⎛⎜ x¯ ⎞⎟ ln ⎝ 2b ⎠ x¯
(4)
where G is the shear modulus in Gpa, b is the Burgers vector in nm, f is the volume fraction of particles, and x¯ is the average particle size in nm. To combine the Ashby-Orowan equation, the yield strength can be expressed as [34]
σy = σ0 + ksσp
(5)
where ks is a constant, and σ0 is frictional stress. G , f and x¯ in Eq. (4) are represented by the temperature-dependent parameters G(T ), f (T ) and x¯ (T ). Refer to the model (5), a new temperature-dependent yield strength for precipitationstrengthened superalloys can be obtained as 0.5 ⎡ T ⎛ ⎞⎤ ∫T Cp( T )dT ⎟⎥ ⎢ 1 + μ T0 ET ⎜ 0 σy( T ) = ⎢ ⎜ 1 − Tm ⎟⎥ ⎢ 1 + μ T ET0 ⎜ Cp( T )dT ⎟⎥ ∫ ⎝ ⎠⎦ T0 ⎣
(
)
(
)
σ ( T0) + ks( T )
0.3G( T )bf 0.5 ( T ) ⎛ x¯ ( T ) ⎞ ⎟⎟ ln⎜⎜ x¯ ( T ) ⎝ 2b ⎠
169
value of ks( T ) is assumed to increase linearly with the increasing temperature in the stage of stable organization, ks( T ) = T /800. The Burgers vector b¼0.25 nm was used based on the data reported for similar steel grades [5,13–15]. The Young's moduli of GH4033 at different temperatures were obtained from a material handbook [37], as shown in Table 4. Using the proposed temperature-dependent yield strength model account of precipitation strengthening, the temperature-dependent yield strength of GH4033 was predicted, as shown in Fig. 8. The specific heat capacities used in the calculations were obtained from a material handbook [37]. The effect of the temperature-dependent Poisson's ratio on the yield strength is neglected. Fig. 8 shows the comparison between the theoretical predictions of the yield strength and the experimental results for GH4033. The Poisson's ratio is μ ¼0.3. The original micro-structural γ’ precipitates in GH4033 are approximately 27 nm in diameter. The same particle size from 20 °C to 800 °C is assumed because of the short thermal exposure time in test. The volume fractions of γ’ precipitate was approximately 9.5%, as reported in Ref. [1]. The proposed temperature-dependent yield strength model for precipitation-strengthened superalloy can accurately predict the yield strength of GH4033 at different temperatures. The good agreement between the experimental and theoretical results is striking. The parameters used in the model are determined by materials properties taken from the experiments and the literature. The proposed temperature-dependent yield strength model (Eq. (6)) can also be used to predict the yield strength of other precipitation-strengthened superalloys. Comparisons between the predicted yield strength and the experimental data for other typical precipitation-strengthened superalloys are shown in Figs. 9–11. The Young's moduli of typical superalloys at different temperatures are obtained from a material handbook [37] and shown in Table 5. Fig. 9 shows the comparison between the yield strength
(6)
where ks( T ) is the influence coefficient of precipitation strengthening at temperature T relative to T0 , G( T ), f ( T ) and x¯ ( T ) are the shear modulus in Gpa, the volume fraction of particles and the average particle size in nm at temperature T , respectively. In the model (Eq. (6)), a quantitative relationship is established between the yield strength of the precipitation-strengthened superalloy and the temperature, the elastic modulus, the specific heat capacity at constant pressure, Poisson's ratio, the precipitate particle size and the volume fraction of particles. The macroscopic quantities and the microscopic quantities of the superalloy are used in this model to determine the quantitative relationship between the yield strength and the temperature. The temperaturedependent yield strength of precipitation-strengthened superalloys can be theoretically predicted by the model (Eq. (6)). The microstructure of GH4033 is relatively stable within the application temperature range, as shown in Fig. 5. The volume fraction of precipitate particles is stable in a large temperature range [4–10,35]. However, the volume fraction of precipitate particles decreases as a result of precipitate particle dissolution when a critical temperature is exceeded [4,36]. In this study, the temperature-dependent yield strength of GH4033 was predicted before its failure mechanism changed significantly above 800 °C [36]. Choosing room temperature as the reference temperature T0 , the σy( T0) in Eq. (6) has included strengthening contributions of grain boundary, solid solution in γ, precipitation shearing, and Orowan by-passing at room temperature. The difficulty of measuring each strengthening contributions is ingenious solved by introducing parameter σy( T0). The increasingly dominant role of Orowan by-passing is reflected by ks( T ). The
Table 4 The Young's modulus of GH4033 at different temperatures [37]. Temperature (°C)
25
200
400
600
700
800
E(T) of GH4033 (GPa)
220.5
210.7
198.9
185.2
176.4
167.5
Fig. 8. Temperature-dependent yield strength of GH4033.
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Table 5 The Young's modulus of typical superalloys at different temperatures [37].
Fig. 9. Temperature-dependent yield strength of GH4037.
Temperature (°C)
25
200
400
600
700
800
E(T) of GH4037 (GPa) E(T) of GH80A (GPa) E(T) of GH738 (GPa)
225.4 222 224
– 214 213
– 200 200
186 189 185
173.8 179 178
166.9 165 169
predicted by the model (Eq. (6)) and the experimental data for GH4037. The experimental yield strength of GH4037 is taken from handbook [38]. The γ’ precipitates in GH4037 are spherical with an average size of 100 nm, and the volume fraction of γ’ particles is approximately 20% [6]. Fig. 10 shows the comparison between the values predicted by the model (Eq. (6)) and the experimental data for GH80A. The experimental yield strength of GH80A is taken from handbook [38]. The average size of γ’ precipitate in GH80A is approximately 100 nm, and the volume fraction of γ’ particles is approximately 17% [39]. Fig. 11 shows the comparison between the predicted yield strength obtained by the model (Eq. (6)) and the experimental data of GH738. The experimental yield strength of GH738 is taken from handbook [38]. The average size of γ’ precipitate in GH738 is approximately 65 nm, and the volume fraction of γ’ particles is approximately 24% [40]. The temperature effects on yield strength are assumed to be dominated by Orowan type precipitation strengthening and elastic modulus in the range of temperatures between 25 °C and 800 °C. The predicted yield strength from the proposed model is highly consistent with both our experimental data and data from other studies, as shown in Figs. 8–11. When the elastic modulus, the precipitate particle size and the volume fraction of particles at different temperatures are known, the new temperature-dependent yield strength model can precisely predict the yield strength of a precipitation-strengthened superalloy at different temperatures, avoiding the need to perform high-temperature yield strength tests. Above 800 °C, the predicted values usually deviate from the experimental results. This might be because the change in the deformation mechanism has occurred with the increasing temperature [21–24]. 3.4. Fractography
Fig. 10. Temperature-dependent yield strength of GH80A.
The fracture surfaces of tensile-tested specimens were observed by SEM and are shown in Fig. 12. Below 200 °C, dimples and grain boundary cracks were seen on the fracture surfaces of the tested specimens. The full of dimples on the fracture surface as shown in Fig. 12(a) indicate that the fracture mode for these specimens was completely ductile. Failure occurred in a mixed intergranular and transgranular mode in the range of temperatures between 400 °C and 700 °C. The typical fracture surface is shown in Fig. 12(b, c and d). The percentages of intergranular fracture increased with the increase in temperature. At 800 °C, the fracture was completely brittle, and intergranular fracture was dominant. The change in the failure behaviour could be dictated by the interaction between the dislocation movement and the γ’ precipitates [41]. While a large number of micropores exist on the fracture surfaces at 1000 °C, the tensile fracture mode was interpreted as the micropore aggregation type.
4. Conclusions
Fig. 11. Temperature-dependent yield strength of GH738.
The microstructural characteristics and mechanical properties of the GH4033 superalloy were investigated at temperatures ranging from room temperature to 1000 °C. Based on the results
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Fig. 12. The SEM micrographs of GH4033 after tensile testing at (a) 200 °C, (b) 400 °C, (c) 600 °C, (d) 700 °C, (e) 800 °C and (f) 1000 °C.
presented in this study, the significant conclusions are presented below. 1) The tensile strength of GH4033 gradually reduced with the increasing temperature, as expected. The stress-strain curves of the GH4033 superalloy show different characteristics at different temperatures due to the combined effects of work hardening, dynamic strain aging and dynamic recrystallization. GH4033 has superior strength and high ductility at temperatures below 700 °C, and the yield strength and tensile strength drop rapidly at 800 °C and 1000 °C. 2) The alloy mainly consisted of γ’ precipitate particles homogeneously dispersed in the γ matrix interior. No significant changes in the average γ’ precipitate size occurred when the specimens underwent tensile testing in the range of temperatures between 25 °C and 800 °C. 3) A temperature-dependent yield strength model was developed to calculate the yield stress as a function of the temperature. The model was shown to be able to consider the effect of precipitation strengthening on the yield strength. The yield behaviour of the precipitation-strengthened superalloy can be adequately predicted over a wide range of temperatures. If the yield
strength of a precipitation-strengthened superalloy at a reference temperature is known, the yield strength can be predicted theoretically at a wide range of temperatures, avoiding the need to perform high-temperature yield strength tests. 4) Dimpled microstructures indicating ductile failures were seen in the alloy below 200 °C. However, a combination of intergranular and transgranular modes was observed in the range of temperatures between 400 °C and 700 °C. At 800 °C, the fracture was completely brittle, and intergranular fracture was dominant. While a large number of micropores existed on the fracture surfaces at 1000 °C, the tensile fracture mode was interpreted as micropore aggregation type.
Acknowledgement This work was supported by the National Natural Science Foundation of China under Grants nos. 11672050, 11602041 and 11472066, the Program for New Century Excellent Talents in University under Grant no. ncet-13-0634, the China Postdoctoral Science Foundation under Grant no. 2016M592636, the Postdoctoral Science Foundation of Chongqing under Grant no. xm2015079, and the Scientific and
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Technological Research Program of the Chongqing Municipal Education Commission under Grants nos. KJ1503104 and KJ1503109.
References [1] J.Y. Tong, X.F. Ding, M.L. Wang, Y.R. Zheng, K. Yagi, Q. Feng, Evaluation of a serviced turbine blade made of GH4033 wrought superalloy, Mater. Sci. Eng. A 618 (2014) 605–613. [2] D. Nunes, M. Vilarigues, J.B. Correia, P.A. Carvalho, Nickel–carbon nanocomposites: Synthesis, structural changes and strengthening mechanisms, Acta Mater. 60 (2012) 737–747. [3] B. Larrouy, P. Villechaise, J. Cormier, O. Berteaux, Grain boundary-slip bands interactions: Impact on the fatigue crack initiation in a polycrystalline forged Ni-based superalloy, Acta Mater. 99 (2015) 325–336. [4] L.Q. Chen, Q. Cheng, F.X. Zhu, Y. Zhao, in: T.M.S. Fernand Marquis (Ed.), Grain Growth behavior of a NI-CR based Superalloy GH4033 in reheating process prior to Hot rolling, The 8th Pacific RIM International Congress on Advanced Materials and processing, The Minerals, Metals & Materials Society, 2013, pp. 369–377. [5] V.C. Olalla, V. Bliznuk, N. Sanchez, P. Thibaux, L.A.I. Kestens, R.H. Petrov, Analysis of the strengthening mechanisms in pipeline steels as a function of the hot rolling parameters, Mater. Sci. Eng. A 604 (2014) 46–56. [6] X.Z. Lv, F. Sun, J.Y. Tong, Q. Feng, J.X. Zhang, Paired dislocations and their interactions with γ’ particles in polycrystalline superalloy GH4037, J. Mater. Eng. Perform. 24 (2015) 143–148. [7] T. Osada, Y.F. Gu, N. Nagashima, Y. Yuan, T. Yokokawa, H. Harada, Optimum microstructure combination for maximizing tensile strength in a polycrystalline superalloy with a two-phase structure, Acta Mater. 61 (2013) 1820–1829. [8] A. Suzuki, T.M. Pollock, High-temperature strength and deformation of γ/γ’ two-phase Co-Al-W-base alloys, Acta Mater. 56 (2008) 1288–1297. [9] E.M. Francis, B.M.B. Grant, J. Quinta da Fonseca, P.J. Phillips, M.J. Mills, M. R. Daymond, M. Preuss, High-temperature deformation mechanisms in a polycrystalline nickel-base superalloy studied by neutron diffraction and electron microscopy, Acta Mater. 74 (2014) 18–29. [10] H.Y. Li, J.F. Sun, M.C. Hardy, H.E. Evans, S.J. Williams, T.J.A. Doel, P. Bowen, Effects of microstructure on high temperature dwell fatigue crack growth in a coarse grain PM nickel based superalloy, Acta Mater. 90 (2015) 355–369. [11] K. Hrutkay, D. Kaoumi, Tensile deformation behavior of a nickel based superalloy at different temperatures, Mater. Sci. Eng. A 599 (2014) 196–203. [12] X.D. Lu, J.H. Du, Q. Deng, J.Y. Zhuang, Stress rupture properties of GH4169 superalloy, J. Mater. Res. Technol. 3 (2014) 107–113. [13] F.P. Yuan, X.L. Wu, Size effect and boundary type on the strengthening of nanoscale domains in pure nickel, Mater. Sci. Eng. A 648 (2015) 243–251. [14] K.G. Wang, Z. Guo, W. Sha, M.E. Glicksman, K. Rajan, Property predictions using microstructural modeling, Acta Mater. 53 (2005) 3395–3402. [15] D. Nunes, M. Vilarigues, J.B. Correia, P.A. Carvalho, Nickel-carbon nanocomposites: Synthesis, structural changes and strengthening mechanisms, Acta Mater. 60 (2012) 737–747. [16] J.Z. Xiao, Y.Y. Dai, Y. Zhao, Z.J. Chen, X.F. Wang, Stress-Strain relationship of HRBF500 at high temperatures, J. Build. Mater. 11 (2008) 277–282. [17] W.G. Li, X.H. Zhang, H.B. Kou, R.Z. Wang, D.N. Fang, Theoretical prediction of temperature-dependent yield strength for metallic materials, Int J. Mech. Sci. 105 (2016) 273–278. [18] A.J. Ardell, V. Munjal, D.J. Chellman, Precipitation hardening of Ni-Al alloys containing large volume fractions of γ’, Metall. Trans. A 7 (1976) 1263–1268. [19] T. Osada, N. Nagashima, Y. Gu, Y. Yuan, T. Yokokawa, H. Harada, Factors contributing to the strength of a polycrystalline nickel-cobalt base superalloy, Scr.
Mater. 64 (2011) 892–895. [20] R.C. Reed, M.P. Jackson, Y.S. Na, Characterization and modelling of the precipitation of the sigma phase in UDIMET 720 and UDIMET 720Li, Metall. Mater. Trans. A 30 (1999) 521–533. [21] M. Ahmadi, E. Povoden-Karadeniz, L. Whitmore, M. Stockinger, A. Falahati, E. Kozeschnik, Yield strength prediction in Ni-base alloy 718Plus based on thermo-kinetic precipitation simulation, Mater. Sci. Eng. A 608 (2014) 114–122. [22] R. Kozar, A. Suzuki, W. Milligan, J. Schirra, M. Savage, T. Pollock, Strengthening mechanisms in polycrystalline multimodal nickel-base superalloys, Metall. Mater. Trans. A 40 (2009) 1588–1603. [23] E.I. Galindo-Nava, L.D. Connor, C.M.F. Rae, On the prediction of the yield stress of unimodal and multimodal γ’ Nickel-base superalloys, Acta Mater. 98 (2015) 377–390. [24] D. Collins, H. Stone, A modelling approach to yield strength optimisation in a nickel-base superalloy, Int. J. Plast. 54 (2014) 96–112. [25] M.C. Rezende, L.S. Araújo, S.B. Gabriel, J. Dille, L.H. de Almeida, Oxidation assisted intergranular cracking under loading at dynamic strain aging temperatures in Inconel 718 superalloy, J. Alloy. Compd. 643 (2015) S256–S259. [26] A.K. Roy, V. Virupaksha, Performance of alloy 800H for high-temperature heat exchanger applications, Mater. Sci. Eng. A 452 (2007) 665–672. [27] X.H. Xiong, D.M. Quan, P.D. Dai, Z.P. Wang, Q.X. Zhang, Z.F. Yue, Tensile behavior of nickel-base single-crystal superalloy DD6, Mater. Sci. Eng. A 636 (2015) 608–612. [28] R. Reed, The Superalloys: Fundamentals and Applications, Cambridge University Press, Cambridge, 2006. [29] E..Orowan, in: T.I.o.Metals(Ed.), Proceedings of the Symposium on Internal Stresses in Metals and Alloys, the Institue of Metals, London, 1948, pp. 451453. [30] C.T. Sims, W.C. Hagel, The Superalloys, first ed., John Wiley & Sons, New York, 1972. [31] J.T. Guo, Meterials Science and Engineering for Superalloys, first ed., Science Press, Beijing, 2008. [32] A. Nitz, E. Nembach, The critical resolved shear stress of a superalloy as a combination of those of its γ matrix and γ’ precipitates, Metall. Mater. Trans. A 29A (1998) 799–807. [33] M.F. Ashby, in: G.A.Breach (Eds.), Proceedings of the Metallurgical Society Conference Oxide Dispersion Strengthening, NewYork, 1966, pp. 143–205. [34] M.J. Peet, 6-Bainitic steels and alloys for power plants, Structural Alloys for, Power Plants, Camb. (2014) 153–187. [35] Z. Zhu, H. Basoalto, N. Warnken, R.C. Reed, A model for the creep deformation behaviour of nickel-based single crystal superalloys, Acta Mater. 60 (2012) 4888–4900. [36] Y.N. Fan, H.J. Shi, W.H. Qiu, Constitutive modeling of creep behavior in single crystal superalloys: Effects of rafting at high temperatures, Mater. Sci. Eng. A 644 (2015) 225–233. [37] J.R. An, L.G. Tian, Metal Materials Handbook, first ed., Chemical Industry Press, Beijing, 2008. [38] Y. Gan, Z.L. Tian, H. Dong, D. Feng, X.L. Wang, Steel Materials Handbook, first ed., Chemical Industry Press, Beijing, 2009. [39] T.T. Ge, J.X. Dong, M.C. Zhang, L. Zheng, S.W. Gao, Microstructure characteristics of GH80A superalloy and thermodynamic calculation on precipitated phases, Rare Met. Mater. Eng. 40 (2011) 1178–1183. [40] Y.Y. Shi, S.Y. Jiao, J.X. Dong, M.C. Zhang, Classical precipitation dynamic model of γ’ phase of nickel-based superalloys and applications, Acta Metall. Sin. 48 (2012) 661–670. [41] Z.H. Zhong, Y.F. Gu, Y. Yuan, Microstructural stability and mechanical properties of a newly developed Ni-Fe-base superalloy, Mater. Sci. Eng. A 622 (2015) 101–107.