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Microstructure evolution and analysis of a single crystal nickel-based superalloy during compressive creep
Materials Science and Engineering A 528 (2011) 4988–4993
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Microstructure evolution and analysis of a single crystal nickel-based superalloy during compressive creep Tian Sugui a,∗ , Zhang Shu a,b , Liang Fushun a , Li Anan a , Li Jingjing a a b
Shenyang University of Technology, Shenyang 110870, China Shenyang University of Chemical Technology, Shenyang 110142, China
a r t i c l e
i n f o
Article history: Received 17 October 2010 Received in revised form 28 January 2011 Accepted 6 March 2011 Available online 11 March 2011 Keywords: Single crystal nickel-based superalloy Compressive creep Microstructure evolution FEM analysis Driving force
a b s t r a c t During compressive creep, the cubical ␥ phase in [0 0 1] orientation single crystal nickel-based superalloy is transformed into the rafted structure along the direction parallel to the applied stress axis. By means of the elastic stress–strain finite element method (FEM), the von Mises stress distributions of the cubical ␥ /␥ phases are calculated for investigating the influence of the applied stress on the stress distribution and the directional coarsening regularity of ␥ phase. Results show that the stress distribution of the cubical ␥/␥ phases may be changed by the applied compressive stress, and the coarsening orientation of ␥ phase is related to the von Mises stress distribution of the ␥ matrix channel. Thereinto, under the action of applied compressive stress, the bigger von Mises stress produced on (0 0 1) plane of the cubical ␥ phase is thought to be a main reason of the microstructure evolution. The expression of the driving force for the elements diffusion and the directional growing of ␥ phase during compressive creep are also proposed. © 2011 Elsevier B.V. All rights reserved.
1. Introduction One of the most striking characteristics of single crystal nickelbased superalloys during high temperature tensile/compressive creep is the rapid directional coarsening of the cubic ␥ -Ni3 Al precipitates to form preferentially orientated rafts structure, and the configuration of the directional coarsening is related to the direction of the applied load and misfit between the ␥/␥ phases [1]. The cubical ␥ phase in single crystal superalloys with negative misfits during tensile creep is transformed into the N-type rafted structure along the direction vertical to the stress axis. And it is considered that the driving force of the ␥ phase directional coarsening is proportional to the applied load, the lattice mismatch of ␥/␥ phases and strain energy density [2]. Dislocation model proposed by Tien and Buffiere may explain the regularity of ␥ phase directional coarsening [3,4]. Actually, the evolution regularity of ␥ phase in single crystal nickel-based superalloys during creep depends on the change of the misfit stress distribution originated from the applied load [5]. The change regularity of the misfit stress and strain energy density in the cubical ␥/␥ phases can be calculated by means of the finite element method (FEM) [5–8], for analyzing the evolution regularity of ␥ phase in superalloys during creep.
∗ Corresponding author. Tel.: +86 24 25494089; fax: +86 24 25496768; mobile: +86 13889121677. E-mail address: [email protected] (T. Sugui). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.03.035
Although the ␥ directional coarsening behavior of the [0 0 1] orientation single crystal superalloy during tensile creep has been extensively investigated [9], but few literatures report the microstructure evolution behavior of ␥ phase of the superalloy during compressive creep, and the evolution regularity of the cubical ␥ phase in the alloy in three-dimensional space during compressive creep is still unclear. In the paper, by means of measuring the creep curve and microstructure observation, the microstructure evolution of a [0 0 1] orientation single crystal nickel-based superalloy during compressive creep is investigated for constituting the existence mode of the rafted ␥ phase in three-dimensional space. Moreover, the von Mises stress distribution and strain energy density on the interfaces of the cubical ␥/␥ phases is calculated by means of the finite element method, for analyzing the evolution regularity of ␥ phase in the single crystal nickel-based superalloy with [0 0 1] orientation during compressive creep.
2. Experimental procedure A single crystal nickel-based superalloy had been produced by means of the selecting crystal method in a directional solidification vacuum furnace under a high temperature gradient. The nominal chemical composition of the superalloy is Ni–6.0Cr–4.0Co–4.0W–5.5Mo–6.0Al–7.0Ta (wt.%). The longitudinal orientation of the specimen was within 7◦ deviation from [0 0 1]. The heat treatment regimes of the alloy are
T. Sugui et al. / Materials Science and Engineering A 528 (2011) 4988–4993
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o
T -- 1040 C
0.8
σ --180 MPa
Strain ε (%)
0.6
0.4
0.2
0.0
0
6
12
18
24
30
Time, (h) Fig. 1. Compressive creep curve of the alloy at 1040 ◦ C/180 MPa.
Fig. 3. Morphologies of the rafted ␥ phase on different crystal planes after the alloy crept for 30 h at 180 MPa/1040 ◦ C. (a) Schematic diagram showing the applied stress direction, (b) morphology on (0 0 1) plane vertical to stress axis, (c) and (d) morphologies on (1 0 0) and (0 1 0) planes, respectively.
Fig. 2. Microstructure of cubic ␥ phase after the alloy fully heat treated.
given as follows: 1280 ◦ C × 2 h + 1300 ◦ C × 4 h, A.C. + 1040 ◦ C × 4 h, A.C. + 870 ◦ C × 24 h, A.C. The alloy is placed in the reverse-stretching device, and crept for 30 h under the applied compressive stress of 180 MPa at 1040 ◦ C. Then the specimen was cut into the rectangle of 4 mm × 4 mm × 8 mm along the specific crystal planes, for observing the microstructure under SEM to constitute the existence mode of ␥ phase in three-dimensional space. The influences of the applied stress on the von Mises stress distribution and strain energy density within the ␥/␥ phases are calculated by means of the FEM for analyzing the evolution regularity of ␥ phase in single crystal nickel-based superalloys during compressive creep. 3. Microstructure evolution of the alloy during compressive creep The compressive creep curve of the alloy crept for 30 h under the applied stress of 180 MPa at 1040 ◦ C is shown in Fig. 1. It indicates that the alloy displays a bigger strain at the moment of applying load, and then the strain rate of the alloy decreases for entering the steady state stage as the creep goes on. The strain feature of the alloy during compressive creep obeys the parabolic law, and the only small strain of about 0.53% occurs after the alloy is crept for 30 h. After fully heat treated, the microstructure of the alloy consists of the cubical ␥ phase embedded coherently in the ␥ matrix phase, and the morphology of the alloy on (1 0 0) crystal plane is shown in Fig. 2, which indicates that the edge size of the cubical ␥ phase is about 0.4 m, the size of the matrix channel is about 0.1 m, and the volume fraction of the cubical ␥ phase is about 65%.
After the alloy is crept for 30 h under the applied compressive stress of 180 MPa at 1040 ◦ C, the morphology of the cubical ␥ phase on the different crystal planes in the alloy is shown in Fig. 3. Thereinto, the direction of the applied stress on the cubic single cell is schematically shown in Fig. 3(a), after the alloy is compressive crept for 30 h, the morphology of the rafted ␥ phase on (0 0 1), (1 0 0) and (0 1 0) planes are shown in Fig. 3(b)–(d), respectively. After the sample is eroded, the ␥ phase displays the black regions due to the dissolution of them, and the ␥ matrix phase displays the gray color. It is understood from Fig. 3(b) that the ␥ phase on the (0 0 1) plane displays the disc-like morphology, but the ␥ phase on the (1 0 0) and (0 1 0) planes displays the rafted structure along the direction parallel to [0 0 1] stress axis, as shown in Fig. 3(c) and (d). This indicates that, during compressive creep, the ␥ phase in the [0 0 1] orientation single crystal nickel-based superalloy has been transformed into the needle-like rafted structure along the direction parallel to the stress axis. Therefore, the ␥ phase on the (0 0 1) plane displays the disc-like morphology in the cross-section of the needle-like rafted structure, and the ␥ matrix phase is continuously filled between the needle-like ␥ rafts, which results in the better ductility of the alloy. After fully heat treated, the schematic diagram of the ␥ phase embedded coherently in the ␥ matrix phase of the [0 0 1] orientation single crystal nickel-based superalloy is shown in Fig. 4(a). Fig. 4(b) shows the orientations of coordinate axes. After compressive crept, the schematic diagram of the ␥ phase transformed into the needle-like ␥ rafted structure along the direction parallel to [0 0 1] orientation is shown in Fig. 4(c). 4. Model and data The schematic diagram of the applied compressive stress along [0 0 1] orientation on the cell is shown in Fig. 5(a). One eighth of the cubical ␥ precipitates and the surrounding matrix are selected due to symmetry, and the finite element meshwork of the cubical ␥/␥ phases in three-dimensional space are shown in Fig. 5(b). The dark region in the meshwork denotes the cubical ␥ phase, the white region denotes the ␥ matrix phase, and the volume fraction of the cubical ␥ phase is calculated to be about 65%. After fully heat treated, the microstructure of the [0 0 1] orientation single crystal nickel-based superalloy consists of the cubical ␥ phase embedded coherently in the ␥ matrix, and aligned regu-
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Fig. 4. Schematic diagram of the ␥ phase located in 3-D space. (a) After fully heat treated, the cubic ␥ phase embedded coherently in ␥ matrix, (b) orientations of coordinate axes, (c) after compressive crept, the needle-like rafted ␥ phase in 3-D space.
Fig. 5. Schematic diagram of the finite element meshwork of the cubical ␥/␥ phases, due to symmetry, giving only one eighth of the precipitates and surrounding matrix. (a) Schematic diagram of the applied compressive stress along [0 0 1] orientation on the cell and (b) the founded finite element meshwork of the cubical ␥/␥ phases in three-dimensional space.
larly along 1 0 0 orientation (the picture omitted) [10]. The model of the single crystal nickel-based superalloy, possessing a negative misfit (˛␥ > ˛␥ ), is used to study the directional coarsening behavior of the cubical ␥/␥ phases. It is thought according to the stress analysis of the ␥/␥ interfaces that the ␥ matrix near the interface is subjected to a compressive stress, and the ␥ phase near the interface is subjected to a tensile stress. The gradient of the misfits stress from the center to edge in the coherent interfaces increases, and there is the same gradient of coherent misfit stress at the ␥/␥ interfaces for both horizontal and vertical channels. When applied no stress, the equilibrium of the stress distribution is kept due to the symmetrical stress state on the different planes of the cubical ␥/␥ phases. The misfit of the ␥/␥ phases in the alloy at 1040 ◦ C is calculated to be ı = 2(a␥’ − a␥ )/(a␥’ + a␥ ) = − 0.36 % according to the thermal expansion coefficients of the ␥ and ␥ phases [9]. When applied compressive stress along [0 0 1] orientation, the von Mises stress in the cubical ␥/␥ phases consists of the superposition of the initial thermal mismatch stress and applied stress in the finite element calculation of the stress–strain in the elasticity range. The calculation formula of the von Mises stress is given as follows [9]: von =
1 2
2
2
2
1/2
2 2 2 (xx − yy ) + (yy − zz ) + (zz − xx ) + 6(xy + yz + zx )
(1)
The value of the strain energy density (U) is expressed as: U=
1 xx εxx + yy εyy + zz εzz + xy εxy + yz εyz + zx εzx 2
(2)
Here, ij is the stress components of three-dimensional symmetry, and εij is the strain components corresponding to ij [11–14]. The generalized finite element model of the elastic stress–strain may simulate the stress distribution in the actual crystal with a small strain, the constraint conditions in the model are defined as ux = 0 at x = 0, uy = 0 at y = 0, uz = 0 at z = 0, and all the nodes on the plane x = 1, y = 1 and z = 1 have the common unknown displacement values which are indicated by ux , uy , and uz , respectively. 5. Results and discussion 5.1. Influence of the applied load on stress distribution of the cubic / phases Because of the applied compressive stress, a change in the stress distribution of the coherent ␥/␥ phases may result in the evolution the ␥ phase. Therefore, the analysis of the stress and strain is a significant event for understanding the regularity of ␥ rafting in the alloy. Under the applied compressive stress of 180 MPa at 1040 ◦ C along [0 0 1] orientation, the von Mises stress distributions in (1/2) cubic ␥ phase and (1/8) ␥ matrix phase are calculated by means of the elastic stress–strain finite element method, as shown in Fig. 6. It indicates that the bigger von Mises stress is distributed on (0 0 1) planes of the cubical ␥ phase, and the lower von Mises stress is distributed on the (1 0 0) and (0 1 0) plane, as shown in Fig. 6(a). The von Mises stress on (1/8) ␥ matrix phase near the ␥ phase is shown in Fig. 6(b), indicating that the biggest von Mises stress occurs in
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Fig. 6. After compressive crept for 10 h at 1040 ◦ C/180 MPa, distribution of the von Mises stress on the matrix and cubical ␥ /␥ phases. (a) (1/2) cubical ␥ phase and (b) (1/8) ␥ matrix.
Fig. 7. Distribution of von Mises stress in ␥ and ␥ phases when applied the compressive stress of 180 MPa at 1040 ◦ C. (a) ␥ matrix and (b) ␥ precipitate.
the intersecting regions of the different crystal planes, the smallest von Mises stress appears on (0 0 1) plane, and the bigger von Mises stress appears on the (1 0 0) and (0 1 0) planes. The strain energy density (U) on the cubical ␥/␥ phases has a similar distribution feature. Intercepting Fig. 6(a) along the black line joining points a and b, the contours of the von Mises equivalent stress distribution in the cross-section of ␥ and ␥ phases is obtained, as shown in Fig. 7. It may be understood from Fig. 7(a) that the smaller von Mises stress displays in the horizontal matrix channel, and the contours of the bigger von Mises stress of about 385 MPa displays in the upright matrix channel. But for the cubical ␥ phase, the smaller von Mises stress of about 140 MPa appears on the region a in the upright interface, and the bigger von Mises stress about 213 MPa occurs on the region b in the horizontal interface, as shown in Fig. 7(b). It is thought by analysis that, when applied the compressive stress along the [0 0 1] orientation, the von Mises stress in the upright matrix channel increases, due to the superposition effect of the applied stress component and the misfit stress of ␥ matrix near the interface, to produce the compressive lattice strain of ␥ matrix phase, which results in the compressive lattice strain of the ␥ phase near the ␥ matrix phase. However, for the horizontal matrix channel, when applied the compressive stress along [0 0 1] orientation, the expanding lattice strain of ␥ matrix phase occurs along the [1 0 0] and [0 1 0] directions on (0 0 1) plane, besides the compressive lattice strain of ␥ matrix phase occurs on (1 0 0) and (0 1 0) planes along [0 0 1] orientation, which results in the same lattice strain occurred in the planes of the cubical ␥ phase. If it is thought that the lattice strain in the interfaces of the cubical ␥ phase is attributed to the effect of the principal stress
components parallel to the interfaces, the change of the misfit stress in the interfaces of ␥/␥ phases may be evaluated according to the values and symbols of the principal stress components in the cubical ␥ phase, which may analyze the directional growth regularity of the cubical ␥ phase. In the stress analysis at the applied stress range, the ij component may be omitted due to the smaller value and no change of them, and the [0 1 0] and [0 0 1] directions are denoted by the letters y and z, respectively. It indicates according to Figs. 6 and 7 that the bigger von Mises stress displays in the regions a and b in the cubical ␥ phase. When applied no external stress, the principal stress components parallel to the crystal planes are z = y = x = 85 MPa, which denotes that the lattice misfits stress between the ␥ and ␥ phases is mis = 85 MPa. With the increase of the applied stress, the principal stress components in the regions a and b are changed, as shown in Fig. 8, and = ji − mis . In the stress analysis, ␥ i > 0 denotes that the lattice in cubical ␥ phase bears a tensile tension stress, ␥ i < 0 denotes that the lattice in the cubical ␥ phase bears a compressive stress. And as the applied stress increases, the change amplitude ( i ) of the principal stress component parallel to the crystal planes may express the amplitude of the tensile/compressive strain of the lattice along the various directions. It can be seen from Fig. 8 that various values of the principal stress components are displayed in the regions a and b as the applied stress increases to 180 MPa. In the cubical ␥ phase, the principal stress component ( z␥ ) parallel to the (0 1 0) plane decreases from 85 to −115 MPa, and = −200 MPa, which indicates that the lattice of the ␥ phase in the crystal plane bears a compressive stress, as shown in Fig. 8(a). Compared to the region a, the principal stress component ( y␥ ) parallel to (0 0 1) plane in the region b of
T. Sugui et al. / Materials Science and Engineering A 528 (2011) 4988–4993
100 0
Stress component, MPa
Stress component, MPa
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σyγ σzγ
-100
σyγ ' σzγ '
-200 -300
(a) 0
30
60
90
120
150
100
0
-100
-200
180
(b) 0
30
60
90
120
150
180
External stress, σ MPa
External stress, σ MPa
Fig. 8. Relationship between the principal stress component and applied compressive stress in the different regions. (a) Region a and (b) region b.
5.2. Influence of applied stress on strain energy density The influence of the applied stress on the strain energy density (U) of the different regions in the cubical ␥ phase at 1040 ◦ C is shown in Fig. 9. Because the direction of the applied stress is the same as that of the original misfit stress in the region b, the superposing role of the applied stress and misfit stress results in the linear increase of the strain energy (U). Moreover, the direction of the applied stress is inverse to that of the original misfit stress in the region a, and the counteracting role of them results in that no obvious change of the strain energy (U) is detected at the applied lower stress range. However, when the applied stress is more than 60 MPa, the strain energy density (U) in the region b increases linearly with the applied stress, and compared to the region a, the bigger strain energy is displayed in the region b, as shown in Fig. 9. Therefore, it may be concluded that the change of the strain energy density in the different regions results in the directional diffusion of the elements and the directional growth of the ␥ phase along the crystal plane having the bigger strain energy.
3
0.45
Strain energy density,J/m
the cubical ␥ phase increases from 85 to 96 MPa, and = 11 MPa, as shown in Fig. 8(b), which indicates that the lattice on the (0 0 1) plane of the cubical ␥ phase in the region b produces the expanding strain. In the model alloy, the elements Al, Ta are ␥ phase former, have the bigger atomic radius, and the elements Mo, Cr are ␥ matrix phase former. Under the applied compressive stress, the elements Al, Ta in the lattice of the cubical ␥ phase bears a lateral extruded stress to repel them into the adjoining matrix channels, which makes them to be supersaturated in concentration. Meanwhile, the ␥ chemical potentials i of the elements Al and Ta are enhanced to a larger value in the lateral channels than in the horizontal chan␥ ␥ nels (i [l] > i [h]). The difference in the chemical potentials of the elements Al and Ta in both channels may drive the directional diffusion of them to the horizontal channels from the lateral ones. During creep under the applied compressive stress, compared to (1 0 0) and (0 1 0) planes of the cubical ␥ phase, the bigger lattice expanding strain occurs on (0 0 1) plane under the action of the principal stress components, which may trap the Al, Ta atoms with bigger radius to promote the directional growth of ␥ phase into the strip-like P-type rafted structure along the [0 0 1] orientation. This decreases the volume fraction of the ␥ matrix phase on the (0 0 1) planes, so that the elements Mo and Cr become supersaturated in ␥ ␥ concentration (j [l] > j [h]). With the directional growth of the ␥ phase along the [0 0 1] orientation, the supersaturated Mo and Cr elements segregated in the horizontal channels are repelled to diffuse to the lateral channels of ␥ matrix according to the equilibrium distribution principle of the solute atoms in dual phase alloys.
1 -- Region a 2 -- Region b o T -- 1040 C
0.30
2 0.15
1
(b)
0.00 0
30
60
90
120
150
180
External stress,MPa Fig. 9. Relationships between the strain energy density and applied compressive stress at the different regions of ␥ phase.
5.3. Driving forces of elements diffusion and directional coarsening of phase During creep at high temperature, the lattice strain in the cubical ␥/␥ phases of alloy increases with the applied stress, and some dislocations are activated in the ␥ matrix channels, which may accelerate the processes of both the element diffusing and the ␥ phase directional growing due to the piping effect of dislocations [10]. It may be thought that the change of the lattice strain energy is equivalent to the change of the interatomic potential energy, therefore, the changes of the interatomic potential energy, the interfacial energy and the misfit stress on the ␥/␥ interface are the driving forces for promoting the element diffusing and ␥ phase directional growing, the formula of the driving forces is given as follows: F = W + |Gs | + |ı|
(3)
After fully heat treated, the microstructure of the superalloy consists of the cubical ␥ phase embedded coherently in the ␥ matrix phase, and arranged along 1 0 0 orientation as shown in Fig. 3(a). It may be considered that the edge length of the cubical ␥ phase is 2r (mm), the width of the ␥ matrix channel is 0.1r (mm), and then the total interfacial area of the cubical ␥ /␥ phases in the superalloy containing n × n × n cubic ␥ particles along [1 0 0], [0 1 0] and [0 0 1] directions may be calculated. Therefore, the driving forces for promoting the elements diffusion and the directional growth of ␥ phase may be expressed as: F=
2A E 1− + 10r 2 n3 ˝ + 3˛0 (E + a )
B 2E
(a − mis )2
(4)
where A and B are constants, E is the elastic modulus, ˛0 is the average lattice parameter of ␥ and ␥ phases at the stress-free state, a is the applied stress, mis is the misfit stress, and ˝ is the interface energy per unit area. The change of the lattice strain energy
T. Sugui et al. / Materials Science and Engineering A 528 (2011) 4988–4993
originated from the applied stress is denoted in the first part, the second part is defined as the change of the interfacial energy before and after the alloy crept, and the third part is defined as the change of the misfit stress caused by the applied stress, which includes the role of the dislocation movement for promoting the element diffusion due to the piping effect [15]. Namely, the formula (4) indicates that the strain energy of ␥/␥ phases in the alloy increases with the applied stress for promoting the dislocation movement, which may accelerate the processes of the element diffusion and the ␥ phase directional coarsening. This is in good agreement with the experimental results stated above. 6. Conclusions (1) After fully heat treated, the microstructure of the [0 0 1] orientation single crystal nickel-based superalloy consists of the cubical ␥ phase embedded coherently in the ␥ matrix phase, and arranged regularly along 1 0 0 orientation. During creep under the applied compressive stress, the cubical ␥ phase in the alloy is transformed into the P-type rafted structure along the direction parallel to the stress axis, and the ␥ matrix phase is continuously filled in between the rafted ␥ phase. (2) During creep under the applied compressive stress, compared to (1 0 0) and (0 1 0) planes of the cubical ␥ phase, the bigger lattice expanding strain occurs on (0 0 1) plane under the action of the principal stress components, which may trap the Al, Ta atoms, which are ␥ phase former with bigger radius, to promote the directional growth of ␥ phase into the strip-like P-type rafted structure along the [0 0 1] orientation. (3) When applied compressive stress along [0 0 1] orientation, compared to [0 1 0] and [1 0 0] channels, the bigger von Mises stress occurs to the [0 0 1] channel to cause the change of the
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strain energy density in the different matrix channels. This promotes the elements diffusion and the directional growth of ␥ phase in the alloy. Thereinto, the change of the atomic potential energy, interfacial energy and lattice misfit stress is thought to be the driving forces for promoting the elements diffusion and directional coarsening of ␥ phase. Acknowledgements Sponsorship of this research by the National Natural Science Foundation of China under Grant no. 50571070 and Education Ministry Foundation of China under Grant no. 20092102110003 is gratefully acknowledged. References [1] H. Feng, H. Biermann, H. Mughrabi, Metall. Mater. Trans. A 31 (2000) 585–593. [2] X.F. Yu, S.G. Tian, H.Q. Du, H.C. Yu, M.G. Wang, L.J. Shang, S.S. Cui, Mater. Sci. Eng. A 506 (2009) 80–86. [3] L. Zhou, S.X. Li, C.R. Chen, Z. Metallkd 4 (2002) 315–322. [4] J.K. Tien, S.M. Copley, Metall. Trans. 2 (1971) 543–553. [5] T.M. Pollock, A.S. Argon, Acta Metall. Mater. 42 (1994) 1859–1874. [6] H.A. Kuhn, H. Biermann, T. Ungar, Acta Metall. Mater. 39 (1991) 2783–2794. [7] H. Biermann, M. Strehler, H. Mughrabi, Metall. Mater. Trans. A 27 (1996) 1003–1010. [8] F.R.N. Nabarro, Metall. Mater. Trans. A 27 (1996) 513–530. [9] S.G. Tian, C.R. Chen, J.H. Zhang, H.C. Yang, X. Wu, Y.B. Xu, Z.Q. Hu, Mater. Sci. Technol. 17 (2001) 736–744. [10] S.G. Tian, J.H. Zhang, H.C. Yang, Y.B. Xu, Z.Q. Hu, J. Aeronaut. Mater. 20 (2000) 1–7. [11] Y.H. Sha, C.R. Chen, J.H. Zhang, Y.B. Xu, Z.Q. Hu, Acta Metall. Sin. 36 (1999) 254–261. [12] L. Zhou, X.L. Yu, Trans. Shenyang Ligong Univ. 27 (2008) 1–4. [13] L. Shui, T. Jin, S.G. Tian, Z.Q. Hu, Rare Met. Mater. Eng. 38 (2009) 826–829. [14] L. Shui, Y.H. Yang, J.J. Yu, Mater. Mech. Eng. 33 (2009) 6–9. [15] S.G. Tian, J.H. Zhang, H.C. Yang, Z.Q. Hu, Mater. Sci. Technol. 16 (2000) 451–456.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Microstructure evolution and analysis of a single crystal nickel-based superalloy during compressive creep Tian Sugui a,∗ , Zhang Shu a,b , Liang Fushun a , Li Anan a , Li Jingjing a a b
Shenyang University of Technology, Shenyang 110870, China Shenyang University of Chemical Technology, Shenyang 110142, China
a r t i c l e
i n f o
Article history: Received 17 October 2010 Received in revised form 28 January 2011 Accepted 6 March 2011 Available online 11 March 2011 Keywords: Single crystal nickel-based superalloy Compressive creep Microstructure evolution FEM analysis Driving force
a b s t r a c t During compressive creep, the cubical ␥ phase in [0 0 1] orientation single crystal nickel-based superalloy is transformed into the rafted structure along the direction parallel to the applied stress axis. By means of the elastic stress–strain finite element method (FEM), the von Mises stress distributions of the cubical ␥ /␥ phases are calculated for investigating the influence of the applied stress on the stress distribution and the directional coarsening regularity of ␥ phase. Results show that the stress distribution of the cubical ␥/␥ phases may be changed by the applied compressive stress, and the coarsening orientation of ␥ phase is related to the von Mises stress distribution of the ␥ matrix channel. Thereinto, under the action of applied compressive stress, the bigger von Mises stress produced on (0 0 1) plane of the cubical ␥ phase is thought to be a main reason of the microstructure evolution. The expression of the driving force for the elements diffusion and the directional growing of ␥ phase during compressive creep are also proposed. © 2011 Elsevier B.V. All rights reserved.
1. Introduction One of the most striking characteristics of single crystal nickelbased superalloys during high temperature tensile/compressive creep is the rapid directional coarsening of the cubic ␥ -Ni3 Al precipitates to form preferentially orientated rafts structure, and the configuration of the directional coarsening is related to the direction of the applied load and misfit between the ␥/␥ phases [1]. The cubical ␥ phase in single crystal superalloys with negative misfits during tensile creep is transformed into the N-type rafted structure along the direction vertical to the stress axis. And it is considered that the driving force of the ␥ phase directional coarsening is proportional to the applied load, the lattice mismatch of ␥/␥ phases and strain energy density [2]. Dislocation model proposed by Tien and Buffiere may explain the regularity of ␥ phase directional coarsening [3,4]. Actually, the evolution regularity of ␥ phase in single crystal nickel-based superalloys during creep depends on the change of the misfit stress distribution originated from the applied load [5]. The change regularity of the misfit stress and strain energy density in the cubical ␥/␥ phases can be calculated by means of the finite element method (FEM) [5–8], for analyzing the evolution regularity of ␥ phase in superalloys during creep.
∗ Corresponding author. Tel.: +86 24 25494089; fax: +86 24 25496768; mobile: +86 13889121677. E-mail address: [email protected] (T. Sugui). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.03.035
Although the ␥ directional coarsening behavior of the [0 0 1] orientation single crystal superalloy during tensile creep has been extensively investigated [9], but few literatures report the microstructure evolution behavior of ␥ phase of the superalloy during compressive creep, and the evolution regularity of the cubical ␥ phase in the alloy in three-dimensional space during compressive creep is still unclear. In the paper, by means of measuring the creep curve and microstructure observation, the microstructure evolution of a [0 0 1] orientation single crystal nickel-based superalloy during compressive creep is investigated for constituting the existence mode of the rafted ␥ phase in three-dimensional space. Moreover, the von Mises stress distribution and strain energy density on the interfaces of the cubical ␥/␥ phases is calculated by means of the finite element method, for analyzing the evolution regularity of ␥ phase in the single crystal nickel-based superalloy with [0 0 1] orientation during compressive creep.
2. Experimental procedure A single crystal nickel-based superalloy had been produced by means of the selecting crystal method in a directional solidification vacuum furnace under a high temperature gradient. The nominal chemical composition of the superalloy is Ni–6.0Cr–4.0Co–4.0W–5.5Mo–6.0Al–7.0Ta (wt.%). The longitudinal orientation of the specimen was within 7◦ deviation from [0 0 1]. The heat treatment regimes of the alloy are
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o
T -- 1040 C
0.8
σ --180 MPa
Strain ε (%)
0.6
0.4
0.2
0.0
0
6
12
18
24
30
Time, (h) Fig. 1. Compressive creep curve of the alloy at 1040 ◦ C/180 MPa.
Fig. 3. Morphologies of the rafted ␥ phase on different crystal planes after the alloy crept for 30 h at 180 MPa/1040 ◦ C. (a) Schematic diagram showing the applied stress direction, (b) morphology on (0 0 1) plane vertical to stress axis, (c) and (d) morphologies on (1 0 0) and (0 1 0) planes, respectively.
Fig. 2. Microstructure of cubic ␥ phase after the alloy fully heat treated.
given as follows: 1280 ◦ C × 2 h + 1300 ◦ C × 4 h, A.C. + 1040 ◦ C × 4 h, A.C. + 870 ◦ C × 24 h, A.C. The alloy is placed in the reverse-stretching device, and crept for 30 h under the applied compressive stress of 180 MPa at 1040 ◦ C. Then the specimen was cut into the rectangle of 4 mm × 4 mm × 8 mm along the specific crystal planes, for observing the microstructure under SEM to constitute the existence mode of ␥ phase in three-dimensional space. The influences of the applied stress on the von Mises stress distribution and strain energy density within the ␥/␥ phases are calculated by means of the FEM for analyzing the evolution regularity of ␥ phase in single crystal nickel-based superalloys during compressive creep. 3. Microstructure evolution of the alloy during compressive creep The compressive creep curve of the alloy crept for 30 h under the applied stress of 180 MPa at 1040 ◦ C is shown in Fig. 1. It indicates that the alloy displays a bigger strain at the moment of applying load, and then the strain rate of the alloy decreases for entering the steady state stage as the creep goes on. The strain feature of the alloy during compressive creep obeys the parabolic law, and the only small strain of about 0.53% occurs after the alloy is crept for 30 h. After fully heat treated, the microstructure of the alloy consists of the cubical ␥ phase embedded coherently in the ␥ matrix phase, and the morphology of the alloy on (1 0 0) crystal plane is shown in Fig. 2, which indicates that the edge size of the cubical ␥ phase is about 0.4 m, the size of the matrix channel is about 0.1 m, and the volume fraction of the cubical ␥ phase is about 65%.
After the alloy is crept for 30 h under the applied compressive stress of 180 MPa at 1040 ◦ C, the morphology of the cubical ␥ phase on the different crystal planes in the alloy is shown in Fig. 3. Thereinto, the direction of the applied stress on the cubic single cell is schematically shown in Fig. 3(a), after the alloy is compressive crept for 30 h, the morphology of the rafted ␥ phase on (0 0 1), (1 0 0) and (0 1 0) planes are shown in Fig. 3(b)–(d), respectively. After the sample is eroded, the ␥ phase displays the black regions due to the dissolution of them, and the ␥ matrix phase displays the gray color. It is understood from Fig. 3(b) that the ␥ phase on the (0 0 1) plane displays the disc-like morphology, but the ␥ phase on the (1 0 0) and (0 1 0) planes displays the rafted structure along the direction parallel to [0 0 1] stress axis, as shown in Fig. 3(c) and (d). This indicates that, during compressive creep, the ␥ phase in the [0 0 1] orientation single crystal nickel-based superalloy has been transformed into the needle-like rafted structure along the direction parallel to the stress axis. Therefore, the ␥ phase on the (0 0 1) plane displays the disc-like morphology in the cross-section of the needle-like rafted structure, and the ␥ matrix phase is continuously filled between the needle-like ␥ rafts, which results in the better ductility of the alloy. After fully heat treated, the schematic diagram of the ␥ phase embedded coherently in the ␥ matrix phase of the [0 0 1] orientation single crystal nickel-based superalloy is shown in Fig. 4(a). Fig. 4(b) shows the orientations of coordinate axes. After compressive crept, the schematic diagram of the ␥ phase transformed into the needle-like ␥ rafted structure along the direction parallel to [0 0 1] orientation is shown in Fig. 4(c). 4. Model and data The schematic diagram of the applied compressive stress along [0 0 1] orientation on the cell is shown in Fig. 5(a). One eighth of the cubical ␥ precipitates and the surrounding matrix are selected due to symmetry, and the finite element meshwork of the cubical ␥/␥ phases in three-dimensional space are shown in Fig. 5(b). The dark region in the meshwork denotes the cubical ␥ phase, the white region denotes the ␥ matrix phase, and the volume fraction of the cubical ␥ phase is calculated to be about 65%. After fully heat treated, the microstructure of the [0 0 1] orientation single crystal nickel-based superalloy consists of the cubical ␥ phase embedded coherently in the ␥ matrix, and aligned regu-
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Fig. 4. Schematic diagram of the ␥ phase located in 3-D space. (a) After fully heat treated, the cubic ␥ phase embedded coherently in ␥ matrix, (b) orientations of coordinate axes, (c) after compressive crept, the needle-like rafted ␥ phase in 3-D space.
Fig. 5. Schematic diagram of the finite element meshwork of the cubical ␥/␥ phases, due to symmetry, giving only one eighth of the precipitates and surrounding matrix. (a) Schematic diagram of the applied compressive stress along [0 0 1] orientation on the cell and (b) the founded finite element meshwork of the cubical ␥/␥ phases in three-dimensional space.
larly along 1 0 0 orientation (the picture omitted) [10]. The model of the single crystal nickel-based superalloy, possessing a negative misfit (˛␥ > ˛␥ ), is used to study the directional coarsening behavior of the cubical ␥/␥ phases. It is thought according to the stress analysis of the ␥/␥ interfaces that the ␥ matrix near the interface is subjected to a compressive stress, and the ␥ phase near the interface is subjected to a tensile stress. The gradient of the misfits stress from the center to edge in the coherent interfaces increases, and there is the same gradient of coherent misfit stress at the ␥/␥ interfaces for both horizontal and vertical channels. When applied no stress, the equilibrium of the stress distribution is kept due to the symmetrical stress state on the different planes of the cubical ␥/␥ phases. The misfit of the ␥/␥ phases in the alloy at 1040 ◦ C is calculated to be ı = 2(a␥’ − a␥ )/(a␥’ + a␥ ) = − 0.36 % according to the thermal expansion coefficients of the ␥ and ␥ phases [9]. When applied compressive stress along [0 0 1] orientation, the von Mises stress in the cubical ␥/␥ phases consists of the superposition of the initial thermal mismatch stress and applied stress in the finite element calculation of the stress–strain in the elasticity range. The calculation formula of the von Mises stress is given as follows [9]: von =
1 2
2
2
2
1/2
2 2 2 (xx − yy ) + (yy − zz ) + (zz − xx ) + 6(xy + yz + zx )
(1)
The value of the strain energy density (U) is expressed as: U=
1 xx εxx + yy εyy + zz εzz + xy εxy + yz εyz + zx εzx 2
(2)
Here, ij is the stress components of three-dimensional symmetry, and εij is the strain components corresponding to ij [11–14]. The generalized finite element model of the elastic stress–strain may simulate the stress distribution in the actual crystal with a small strain, the constraint conditions in the model are defined as ux = 0 at x = 0, uy = 0 at y = 0, uz = 0 at z = 0, and all the nodes on the plane x = 1, y = 1 and z = 1 have the common unknown displacement values which are indicated by ux , uy , and uz , respectively. 5. Results and discussion 5.1. Influence of the applied load on stress distribution of the cubic / phases Because of the applied compressive stress, a change in the stress distribution of the coherent ␥/␥ phases may result in the evolution the ␥ phase. Therefore, the analysis of the stress and strain is a significant event for understanding the regularity of ␥ rafting in the alloy. Under the applied compressive stress of 180 MPa at 1040 ◦ C along [0 0 1] orientation, the von Mises stress distributions in (1/2) cubic ␥ phase and (1/8) ␥ matrix phase are calculated by means of the elastic stress–strain finite element method, as shown in Fig. 6. It indicates that the bigger von Mises stress is distributed on (0 0 1) planes of the cubical ␥ phase, and the lower von Mises stress is distributed on the (1 0 0) and (0 1 0) plane, as shown in Fig. 6(a). The von Mises stress on (1/8) ␥ matrix phase near the ␥ phase is shown in Fig. 6(b), indicating that the biggest von Mises stress occurs in
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Fig. 6. After compressive crept for 10 h at 1040 ◦ C/180 MPa, distribution of the von Mises stress on the matrix and cubical ␥ /␥ phases. (a) (1/2) cubical ␥ phase and (b) (1/8) ␥ matrix.
Fig. 7. Distribution of von Mises stress in ␥ and ␥ phases when applied the compressive stress of 180 MPa at 1040 ◦ C. (a) ␥ matrix and (b) ␥ precipitate.
the intersecting regions of the different crystal planes, the smallest von Mises stress appears on (0 0 1) plane, and the bigger von Mises stress appears on the (1 0 0) and (0 1 0) planes. The strain energy density (U) on the cubical ␥/␥ phases has a similar distribution feature. Intercepting Fig. 6(a) along the black line joining points a and b, the contours of the von Mises equivalent stress distribution in the cross-section of ␥ and ␥ phases is obtained, as shown in Fig. 7. It may be understood from Fig. 7(a) that the smaller von Mises stress displays in the horizontal matrix channel, and the contours of the bigger von Mises stress of about 385 MPa displays in the upright matrix channel. But for the cubical ␥ phase, the smaller von Mises stress of about 140 MPa appears on the region a in the upright interface, and the bigger von Mises stress about 213 MPa occurs on the region b in the horizontal interface, as shown in Fig. 7(b). It is thought by analysis that, when applied the compressive stress along the [0 0 1] orientation, the von Mises stress in the upright matrix channel increases, due to the superposition effect of the applied stress component and the misfit stress of ␥ matrix near the interface, to produce the compressive lattice strain of ␥ matrix phase, which results in the compressive lattice strain of the ␥ phase near the ␥ matrix phase. However, for the horizontal matrix channel, when applied the compressive stress along [0 0 1] orientation, the expanding lattice strain of ␥ matrix phase occurs along the [1 0 0] and [0 1 0] directions on (0 0 1) plane, besides the compressive lattice strain of ␥ matrix phase occurs on (1 0 0) and (0 1 0) planes along [0 0 1] orientation, which results in the same lattice strain occurred in the planes of the cubical ␥ phase. If it is thought that the lattice strain in the interfaces of the cubical ␥ phase is attributed to the effect of the principal stress
components parallel to the interfaces, the change of the misfit stress in the interfaces of ␥/␥ phases may be evaluated according to the values and symbols of the principal stress components in the cubical ␥ phase, which may analyze the directional growth regularity of the cubical ␥ phase. In the stress analysis at the applied stress range, the ij component may be omitted due to the smaller value and no change of them, and the [0 1 0] and [0 0 1] directions are denoted by the letters y and z, respectively. It indicates according to Figs. 6 and 7 that the bigger von Mises stress displays in the regions a and b in the cubical ␥ phase. When applied no external stress, the principal stress components parallel to the crystal planes are z = y = x = 85 MPa, which denotes that the lattice misfits stress between the ␥ and ␥ phases is mis = 85 MPa. With the increase of the applied stress, the principal stress components in the regions a and b are changed, as shown in Fig. 8, and = ji − mis . In the stress analysis, ␥ i > 0 denotes that the lattice in cubical ␥ phase bears a tensile tension stress, ␥ i < 0 denotes that the lattice in the cubical ␥ phase bears a compressive stress. And as the applied stress increases, the change amplitude ( i ) of the principal stress component parallel to the crystal planes may express the amplitude of the tensile/compressive strain of the lattice along the various directions. It can be seen from Fig. 8 that various values of the principal stress components are displayed in the regions a and b as the applied stress increases to 180 MPa. In the cubical ␥ phase, the principal stress component ( z␥ ) parallel to the (0 1 0) plane decreases from 85 to −115 MPa, and = −200 MPa, which indicates that the lattice of the ␥ phase in the crystal plane bears a compressive stress, as shown in Fig. 8(a). Compared to the region a, the principal stress component ( y␥ ) parallel to (0 0 1) plane in the region b of
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100 0
Stress component, MPa
Stress component, MPa
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σyγ σzγ
-100
σyγ ' σzγ '
-200 -300
(a) 0
30
60
90
120
150
100
0
-100
-200
180
(b) 0
30
60
90
120
150
180
External stress, σ MPa
External stress, σ MPa
Fig. 8. Relationship between the principal stress component and applied compressive stress in the different regions. (a) Region a and (b) region b.
5.2. Influence of applied stress on strain energy density The influence of the applied stress on the strain energy density (U) of the different regions in the cubical ␥ phase at 1040 ◦ C is shown in Fig. 9. Because the direction of the applied stress is the same as that of the original misfit stress in the region b, the superposing role of the applied stress and misfit stress results in the linear increase of the strain energy (U). Moreover, the direction of the applied stress is inverse to that of the original misfit stress in the region a, and the counteracting role of them results in that no obvious change of the strain energy (U) is detected at the applied lower stress range. However, when the applied stress is more than 60 MPa, the strain energy density (U) in the region b increases linearly with the applied stress, and compared to the region a, the bigger strain energy is displayed in the region b, as shown in Fig. 9. Therefore, it may be concluded that the change of the strain energy density in the different regions results in the directional diffusion of the elements and the directional growth of the ␥ phase along the crystal plane having the bigger strain energy.
3
0.45
Strain energy density,J/m
the cubical ␥ phase increases from 85 to 96 MPa, and = 11 MPa, as shown in Fig. 8(b), which indicates that the lattice on the (0 0 1) plane of the cubical ␥ phase in the region b produces the expanding strain. In the model alloy, the elements Al, Ta are ␥ phase former, have the bigger atomic radius, and the elements Mo, Cr are ␥ matrix phase former. Under the applied compressive stress, the elements Al, Ta in the lattice of the cubical ␥ phase bears a lateral extruded stress to repel them into the adjoining matrix channels, which makes them to be supersaturated in concentration. Meanwhile, the ␥ chemical potentials i of the elements Al and Ta are enhanced to a larger value in the lateral channels than in the horizontal chan␥ ␥ nels (i [l] > i [h]). The difference in the chemical potentials of the elements Al and Ta in both channels may drive the directional diffusion of them to the horizontal channels from the lateral ones. During creep under the applied compressive stress, compared to (1 0 0) and (0 1 0) planes of the cubical ␥ phase, the bigger lattice expanding strain occurs on (0 0 1) plane under the action of the principal stress components, which may trap the Al, Ta atoms with bigger radius to promote the directional growth of ␥ phase into the strip-like P-type rafted structure along the [0 0 1] orientation. This decreases the volume fraction of the ␥ matrix phase on the (0 0 1) planes, so that the elements Mo and Cr become supersaturated in ␥ ␥ concentration (j [l] > j [h]). With the directional growth of the ␥ phase along the [0 0 1] orientation, the supersaturated Mo and Cr elements segregated in the horizontal channels are repelled to diffuse to the lateral channels of ␥ matrix according to the equilibrium distribution principle of the solute atoms in dual phase alloys.
1 -- Region a 2 -- Region b o T -- 1040 C
0.30
2 0.15
1
(b)
0.00 0
30
60
90
120
150
180
External stress,MPa Fig. 9. Relationships between the strain energy density and applied compressive stress at the different regions of ␥ phase.
5.3. Driving forces of elements diffusion and directional coarsening of phase During creep at high temperature, the lattice strain in the cubical ␥/␥ phases of alloy increases with the applied stress, and some dislocations are activated in the ␥ matrix channels, which may accelerate the processes of both the element diffusing and the ␥ phase directional growing due to the piping effect of dislocations [10]. It may be thought that the change of the lattice strain energy is equivalent to the change of the interatomic potential energy, therefore, the changes of the interatomic potential energy, the interfacial energy and the misfit stress on the ␥/␥ interface are the driving forces for promoting the element diffusing and ␥ phase directional growing, the formula of the driving forces is given as follows: F = W + |Gs | + |ı|
(3)
After fully heat treated, the microstructure of the superalloy consists of the cubical ␥ phase embedded coherently in the ␥ matrix phase, and arranged along 1 0 0 orientation as shown in Fig. 3(a). It may be considered that the edge length of the cubical ␥ phase is 2r (mm), the width of the ␥ matrix channel is 0.1r (mm), and then the total interfacial area of the cubical ␥ /␥ phases in the superalloy containing n × n × n cubic ␥ particles along [1 0 0], [0 1 0] and [0 0 1] directions may be calculated. Therefore, the driving forces for promoting the elements diffusion and the directional growth of ␥ phase may be expressed as: F=
2A E 1− + 10r 2 n3 ˝ + 3˛0 (E + a )
B 2E
(a − mis )2
(4)
where A and B are constants, E is the elastic modulus, ˛0 is the average lattice parameter of ␥ and ␥ phases at the stress-free state, a is the applied stress, mis is the misfit stress, and ˝ is the interface energy per unit area. The change of the lattice strain energy
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originated from the applied stress is denoted in the first part, the second part is defined as the change of the interfacial energy before and after the alloy crept, and the third part is defined as the change of the misfit stress caused by the applied stress, which includes the role of the dislocation movement for promoting the element diffusion due to the piping effect [15]. Namely, the formula (4) indicates that the strain energy of ␥/␥ phases in the alloy increases with the applied stress for promoting the dislocation movement, which may accelerate the processes of the element diffusion and the ␥ phase directional coarsening. This is in good agreement with the experimental results stated above. 6. Conclusions (1) After fully heat treated, the microstructure of the [0 0 1] orientation single crystal nickel-based superalloy consists of the cubical ␥ phase embedded coherently in the ␥ matrix phase, and arranged regularly along 1 0 0 orientation. During creep under the applied compressive stress, the cubical ␥ phase in the alloy is transformed into the P-type rafted structure along the direction parallel to the stress axis, and the ␥ matrix phase is continuously filled in between the rafted ␥ phase. (2) During creep under the applied compressive stress, compared to (1 0 0) and (0 1 0) planes of the cubical ␥ phase, the bigger lattice expanding strain occurs on (0 0 1) plane under the action of the principal stress components, which may trap the Al, Ta atoms, which are ␥ phase former with bigger radius, to promote the directional growth of ␥ phase into the strip-like P-type rafted structure along the [0 0 1] orientation. (3) When applied compressive stress along [0 0 1] orientation, compared to [0 1 0] and [1 0 0] channels, the bigger von Mises stress occurs to the [0 0 1] channel to cause the change of the
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strain energy density in the different matrix channels. This promotes the elements diffusion and the directional growth of ␥ phase in the alloy. Thereinto, the change of the atomic potential energy, interfacial energy and lattice misfit stress is thought to be the driving forces for promoting the elements diffusion and directional coarsening of ␥ phase. Acknowledgements Sponsorship of this research by the National Natural Science Foundation of China under Grant no. 50571070 and Education Ministry Foundation of China under Grant no. 20092102110003 is gratefully acknowledged. References [1] H. Feng, H. Biermann, H. Mughrabi, Metall. Mater. Trans. A 31 (2000) 585–593. [2] X.F. Yu, S.G. Tian, H.Q. Du, H.C. Yu, M.G. Wang, L.J. Shang, S.S. Cui, Mater. Sci. Eng. A 506 (2009) 80–86. [3] L. Zhou, S.X. Li, C.R. Chen, Z. Metallkd 4 (2002) 315–322. [4] J.K. Tien, S.M. Copley, Metall. Trans. 2 (1971) 543–553. [5] T.M. Pollock, A.S. Argon, Acta Metall. Mater. 42 (1994) 1859–1874. [6] H.A. Kuhn, H. Biermann, T. Ungar, Acta Metall. Mater. 39 (1991) 2783–2794. [7] H. Biermann, M. Strehler, H. Mughrabi, Metall. Mater. Trans. A 27 (1996) 1003–1010. [8] F.R.N. Nabarro, Metall. Mater. Trans. A 27 (1996) 513–530. [9] S.G. Tian, C.R. Chen, J.H. Zhang, H.C. Yang, X. Wu, Y.B. Xu, Z.Q. Hu, Mater. Sci. Technol. 17 (2001) 736–744. [10] S.G. Tian, J.H. Zhang, H.C. Yang, Y.B. Xu, Z.Q. Hu, J. Aeronaut. Mater. 20 (2000) 1–7. [11] Y.H. Sha, C.R. Chen, J.H. Zhang, Y.B. Xu, Z.Q. Hu, Acta Metall. Sin. 36 (1999) 254–261. [12] L. Zhou, X.L. Yu, Trans. Shenyang Ligong Univ. 27 (2008) 1–4. [13] L. Shui, T. Jin, S.G. Tian, Z.Q. Hu, Rare Met. Mater. Eng. 38 (2009) 826–829. [14] L. Shui, Y.H. Yang, J.J. Yu, Mater. Mech. Eng. 33 (2009) 6–9. [15] S.G. Tian, J.H. Zhang, H.C. Yang, Z.Q. Hu, Mater. Sci. Technol. 16 (2000) 451–456.