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The effect of thermal exposure on the γ′ characteristics in a Ni-base superalloy
Journal of Alloys and Compounds 368 (2004) 144–151
The effect of thermal exposure on the ␥ characteristics in a Ni-base superalloy R. Sharghi-Moshatghin∗ , S. Asgari Department of Material Science and Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran Received 16 January 2003; received in revised form 2 July 2003; accepted 2 July 2003
Abstract In this investigation, changes in ␥ characteristics in superalloy IN-738LC during aging are presented. The SEM studies revealed that coarsening kinetics of ␥ follows a linear law at different aging time for different temperatures. Whereas when coarsening of secondary ␥ is studied, it was found that at the early stage of aging, volume fraction of secondary ␥ is high, leading to short inter-particle distances. In this condition interfacial energy is dominant and variation of [r 3 − r03 ] as a function of aging time is linear. As the coarsening proceeds, volume fraction of secondary ␥ decreases and elastic interaction energy becomes dominant. In such case a deviation in variation of [r3 − r03 ] versus aging time was observed. © 2003 Published by Elsevier B.V. Keywords: Ni-base superalloy; Secondary ␥ ; Coarsening; Aging
1. Introduction Ni-base superalloys are the most complex and the most widely used material for manufacturing of critical gas turbine components such as rotating blades. It is well known that these materials own their high temperature strength from the fine particles of L12 type ordered ␥ [Ni3 (Al, Ti)] phase precipitated coherently with the matrix [1]. The mechanical properties of a given alloy are dependent upon such factors as volume fraction, particle size, coarsening rate and composition of ␥ phase [2]. Therefore knowledge about the influence of thermal exposure on the ␥ characteristics would be valuable for realistic estimation of service life of these components. This would help to avoid any premature retirement and, more importantly, premature failure of these components during service by setting an optimum time between overhauls (TBO) [3]. Superalloy IN-738LC with its good high temperature properties is extensively used for manufacturing of gas turbine blades. This material has been the subject of investigations since 30 years ago. However, a few papers have been published [4,5] regarding coarsening of ␥ precipitates ∗
Corresponding author. Fax: +98-21-600-5717. E-mail address: [email protected] (R. Sharghi-Moshatghin).
0925-8388/$ – see front matter © 2003 Published by Elsevier B.V. doi:10.1016/S0925-8388(03)00699-6
in this alloy. Stevens and Flewitt [4], studied only coarsening of secondary ␥ by using TEM replica technique. They found that kinetics of secondary ␥ follows a linear law also their experimental results showed that, secondary ␥ disappear after 1200 h aging at 850 ◦ C. Footner and Richards [5] studied only coarsening of primary ␥ In this study coarsening of primary and secondary ␥ precipitates in superalloy IN-738LC have been studied. Also using high resolution Field Emission Scanning Electron Microscope (FESEM), the ␥ characteristics such as size, inter-particle spacing and volume fraction have been quantified during aging.
2. Experimental procedure The material used in this study was supplied by Ross and Chaterall Co., UK. The chemical composition of the alloy is shown in Table 1. The material after casting under vacuum was subjected to standard heat treatment (SHT), 1120 ◦ C/2 h/air cool + 845 ◦ C/24 h/air cool. Samples of the size of 10 mm × 10 mm × 5 mm were prepared from the material and isothermally aged at 800, 850 and 900 ◦ C in an atmospheric furnace. Samples were removed from furnace during aging at each temperature, air cooled and sectioned. Each sample was prepared mechanically, and then was polished electrolytically in a solution of 45% butanol, 45%
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151
145
Table 1 Chemical composition of superalloy IN-738LC (wt.%)
Min Max
Ni
C
Co
Cr
Mo
W
Ta
Nb
Ai
Ti
B
Zr
Bal Bal
0.09 0.13
8.00 9.00
15.7 16.3
1.5 2.0
2.4 2.8
1.5 2.0
0.6 1.1
3.2 3.7
3.2 3.7
0.007 0.012
0.03 0.08
acetic acid and 10% perchloric acid, at 20–25 V for 25 s. Microstructural studies were carried out using a high resolution Field Emission Scanning Electron Microscope. Total weight fraction of ␥ was also established using the electrolytic extraction technique described by Kriege and Baris [6]. The particle size and statistical dispersion were obtained from SEM images employing an image analyzing system. In this study in order to obtain reliable results more than 100 particles were studied in different areas of each sample. In this system due to random and duplex distribution of ␥ precipitates, the number of precipitates in the certain area will alter the average size of precipitates. Then in order to decrease the errors in calculation, the number of precipitates should be included in calculations. In this case the average size of precipitates can be expressed as: n (ds,i + ac,i ) D = i=1 (1) Ns + N c where ds,i is the average diameter of secondary (spherical) ␥ , and ac,i the average of cubic side lengths of the primary ␥ . Same areas of samples in each aging condition were selected, and diameter of all spherical as well as cube sides of cuboid particles were measured and value of D calculated for different conditions using Eq. (1). It should be mentioned that for cuboids precipitates, shortest and longest lengths
were measured and the average of these measurements calculated as a representative size of cuboids precipitates.
3. Results Fig. 1 shows the microstructure of the material in SHT condition. As it can be seen standard heat treatment produces a bimodal distribution of ␥ precipitates in spheroidal and cuboidal forms having average size of 86 nm in diameter (d) and 550 nm in edge length (a), respectively. Figs. 2–4 show SEM images of samples aged at 800, 850 and 900 ◦ C for different aging times. Average size of ␥ precipitates and inter-particles spacing for each condition are also presented in Table 2. Comparing SEM images with the data in Table 2 imply that precipitates coarsen and interparticle spacing increase during aging at each temperature. Total volume fraction of precipitates (primary plus secondary) in SHT condition was measured to be 46%, then area fraction of primary ␥ was determined from the images to be 13% and by subtracting this value from the total amount, the area fraction of secondary ␥ was calculated to be 33%. Also total volume fraction of ␥ was measured during aging at each temperature by extraction method and the results are presented in Fig. 5. It is evident from Fig. 5, that the total volume fraction of ␥ is almost constant during aging.
Fig. 1. Microstructure of material in SHT condition.
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Fig. 2. SEM images of samples aged at 800 ◦ C for: (a) 500 h, (b) 1000 h, (c) 2000 h and (d) 3000 h.
Variation of area fraction of primary and secondary ␥ with the aging time is shown in Fig. 6. As it can be seen volume fraction of secondary ␥ decreases, whereas volume fraction of primary ␥ increases with aging time. Variation of overall particle size [(D/2)3 − (D0 /2)3 ] with aging time at different temperatures is presented in Fig. 7. As it seen during aging, coarsening kinetics follows a linear law at all temperatures. The increase in mean radius of the secondary ␥ precipitates, [r 3 −r03 ] as a function of aging time is presented in Fig. 8. It is evident from this figure that in the early stages of aging, the variation of [r3 − r03 ] as a function of aging time, can be approximated by a linear law, which then depart from the linear behavior at longer aging times.
Size distribution of secondary ␥ during aging is presented in Fig. 9. It can be seen that in the early stage of aging, size distribution of precipitates becomes broaden that is attributed to the coarsening of precipitates, whereas in later stages no broadening was observed and distribution becomes more uniform.
4. Discussion There are number of factors that may affect the coarsening of precipitates, and are not considered in so-called LSW theory [7]. Of different factors, elastic strain due to
Table 2 ␥ particle and inter-particle size in SHT and different aging conditions Temperature (◦ C) 800 Aging time (h) Primary ␥ (a) (nm) Secondary ␥ (D) (nm) Inter-particle spacing (nm)
500 660 150 65
850 1000 740 168 75
3000 810 172 89
500 720 176 71
900 2000 830 232 131
5000 910 390 170
150 760 220 116
500 835 290 142
1000 950 370 180
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151
147
Fig. 3. SEM images of samples aged at 850 ◦ C for: (a) 500 h, (b) 1000 h, (c) 2000 h and (d) 5000 h.
precipitate/matrix mismatch is of crucial importance [2,7,8]. The total energy of the system (Et ) containing coherent second phase precipitates can be expressed as [8]: Et = Es + Ee
(2)
where Et , Es and Ee are total energy, surface energy and elastic energy of the system, respectively. When a precipitate is coherent with a surrounding matrix, like ␥ /␥ system in Ni-base superalloy, the lattice mismatch between the precipitate and matrix causes elastic strain fields form around the precipitates. Therefore elastic interaction arises from overlapping of the elastic strain field around the coherent precipitates [9]. This would happen when the inter-particle spacing is short enough or volume fraction of precipitates is high. In this case elastic energy term (Ee ) in Eq. (2), consists of two energies: Ee = Em + Eint
(3)
where Em and Eint are elastic energies due to lattice mismatch and interaction of elastic strain fields around the precipitates, respectively. Energetically during coarsening the system tends to decrease total energy (Et ). In the early stage
of coarsening because of high volume fraction of fine precipitates, interfacial energy is dominant in such case driving force for coarsening is reduction in interfacial energy, and the system tends to reduces its total energy by decreasing interfacial energy. In this condition Ostwald ripening takes place and growth kinetic of ␥ would follow a linear equation predicted by LSW theory, expressed by following equation: r3 − r03 = Kt
(4)
and K=
8ΓVm DCm 9RT
(5)
where r is the particle radii for the secondary ␥ at the time t, r0 the particle radii at time zero (t = 0), K the rate constant and is defined by Eq. (5), where Γ is the interfacial energy between precipitates and matrix, D the diffusion constant, Cm the concentration of solute in the matrix in equilibrium with an infinitely large particle, Vm the molar volume of the precipitates, R the gas constant, T the absolute temperature. Experimental results show that in the early stages of aging, there is a linear correlation between [r3 − r03 ] and aging time which is consistent with above discussion.
148
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151
Fig. 4. SEM images of samples aged at 850 ◦ C for: (a) 100 h, (b) 500 h, (c) 750 h and (d) 1000 h.
Fig. 5. Variation of total volume fraction of ␥ as a function of aging time at 850 ◦ C.
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151 0. 6 Primary γ' Secondaryγ'
Volume Fraction of γ '
0. 5
0. 4
0. 3
0. 2
0. 1
0. 0
0
500
1000
1500
2000
2500
3000
3500
Aging Time (hrs)
Fig. 6. Area fraction of primary and secondary ␥ as a function of aging time at 850 ◦ C.
Also as it could be seen from Fig. 8, at longer aging times the growth rate of ␥ tended to decrease and depart from that linear correlation. As the coarsening proceeds, the elastic energy associated with each precipitate grows as r3 , whereas the interfacial energy associated with each precipitate grows as r2 [10]. In such condition elastic interaction energy in Eq. (3) and term Ee in Eq. (2) will be greater than interfacial energy (Es ) and therefore elastic energy becomes dominant in late stage of coarsening. Therefore, as the coarsening proceeds in this system, the elastic energy becomes progressively more important in controlling the behavior of the coarsening precipitates, so in such a system at later stages of aging any deviation from interfacial energy driven coarsening might be evident [10]. The differences in the results obtained in this study and previously reported results [4] are attributed to the different volume fraction of secondary ␥ in these systems.
1.40E+07
T=850˚C T=800˚C
1.20E+07
[(D/2)3 - (D/2)3 ] (nm) 3
T=900˚C 1.00E+07 8.00E+06 6.00E+06 4.00E+06 2.00E+06 0.00E+00 0
1000
2000
149
3000
4000
5000
6000
Aging Time (h)
Fig. 7. Correlation between [(D/2)3 − (D0 /2)3 ] and aging time at different temperature.
Fig. 8. Correlation between [r 3 − r03 ] and aging time at 850 ◦ C.
150
40
35
30
35
30
25 30
15
10
20 15
20
15
10
10
5
5
5
0
0 0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.2
2
0.4
0.6
0.8
1
(b)
r / r
1.2
1.4
1.6
1.8
2
0.2
0.4
0.6
0.8
(c)
r / r
20
20
15
10
15
10
5
5
0 0.2
0.4
0.6
0.8
1
1.2 1.4
1.6
1.8
2
0 0.2
(d)
r / r
(e)
0.4
0.6
0.8
1
1.2
1
r / r
25
25
Frequency (%)
0.4
Frequency(%)
0.2
(a)
25
Frequency (%)
Frequency(%)
20
1.4
1.6
1.8
2
r / r
Fig. 9. Size distribution of secondary ␥ during aging at 850 ◦ C for: (a) SHT, (b) 500 h, (c) 1000 h, (d) 2000 h and (e) 3000 h.
1.2
1.4
1.6
1.8
2
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151
Frequency(%)
25
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151
When the amount of ␥ is increased inter-particle distances become short. The experimental and theoretical works of Doi et al. [8] indicate that the elastic interaction energies are greatly affected by the distance between the precipitates, and as the distance between precipitates become short, the elastic interaction between them becomes noticeable. In such case variation of [r 3 − r03 ] as a function of aging time deviate from linear behavior, which is consistent with experimental results, obtained in this study. Concept of bifurcation for the coarsening of coherent precipitates in elastically stressed system was proposed by [11] for the first time. According to this concept in the early stage of coarsening, driving force for coarsening is only surface energy, in such case Ostwald ripening takes place and large precipitates coarsen at the expense of smaller precipitates. As the precipitates coarsen as a result of elastic energies, slowing down of coarsening kinetic and formation of uniform structure will be observed. From experimental results presented in Fig. 9, it could be seen that in the early stages of aging, size distribution of particles broaden whereas in later stages size distribution of ␥ becomes uniform and no further broadening observed. These results show that coarsening rate slow down in later stage of aging. Also Stevens and Flewitt [4] reported that after 1200 h aging at 850 ◦ C, secondary ␥ disappear, whereas experimental results presented in Fig. 3 show that even after 3000 h aging at 850 ◦ C, secondary ␥ has not disappeared.
5. Conclusion 1. When overall particles including primary as well as secondary ␥ precipitates are considered, coarsening kinetics follow a linear law at different temperatures during aging. Whereas when only secondary ␥ precipitates are considered, at the early stage of coarsening the kinetics follows a linear law and depart at longer aging times.
151
2. In the early stages of aging, driving force for coarsening of secondary ␥ precipitates is reduction in interfacial energy. In this case variation of [r 3 − r03 ] as a function of aging time is linear. 3. Strain field around coherent precipitates, causes deviation in variation of [r3 − r03 ] as a function of time in longer aging times. 4. Particle size distribution becomes broaden in the early stage of aging where as it becomes uniform in longer aging times. It shows that in the early stage of aging coarsening of precipitates takes place whereas in longer aging times there is a decrease in coarsening rate. Acknowledgements The authors would like to thank Imperial College London for the Microscope facilities. Also Mavadkaran Eng. Company in Iran is acknowledged for the supplying of material.
References [1] C.T. Sims, N.S. Stoloff, W.C. Hagel, Superalloy II, Wiley, New York, 1987, pp. 97–131. [2] A. Baladan, J. Mater. Sci. 37 (2002) 2379–2405. [3] V.P. Swaminathan, N.S. Cheruvu, Internal Report, Material Engineering Department, Gas Turbine Materials, Southwest Research Institute, 1985. [4] R.A. Stevens, P.E.J. Flewitt, Mater. Sci. Eng. 37 (1979) 234–247. [5] P.K. Footner, B.P. Richards, J. Mater. Sci. 17 (1982) 2141–2153. [6] O.H. Kreige, J.M. Baris, Trans. ASM 62 (1969) 195–202. [7] C.S. Jayanth, P. Nash, J. Mater. Sci. 24 (1989) 3041–3052. [8] M. Doi, T. Miyazaki, T. Wakatsuki, Mater. Sci. Eng. 67 (1984) 247– 253. [9] T. Miyazaki, H. Imamura, H. Mori, T. Kozaki, J. Mater. Sci. 16 (1981) 1197–1203. [10] A.C. Lund, P.W. Voorhees, Acta Mater. 50 (2002) 2585–2589. [11] W.C. Johnson, A. Cahn, Acta Metall. 32 (1984) 465–476.
The effect of thermal exposure on the ␥ characteristics in a Ni-base superalloy R. Sharghi-Moshatghin∗ , S. Asgari Department of Material Science and Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran Received 16 January 2003; received in revised form 2 July 2003; accepted 2 July 2003
Abstract In this investigation, changes in ␥ characteristics in superalloy IN-738LC during aging are presented. The SEM studies revealed that coarsening kinetics of ␥ follows a linear law at different aging time for different temperatures. Whereas when coarsening of secondary ␥ is studied, it was found that at the early stage of aging, volume fraction of secondary ␥ is high, leading to short inter-particle distances. In this condition interfacial energy is dominant and variation of [r 3 − r03 ] as a function of aging time is linear. As the coarsening proceeds, volume fraction of secondary ␥ decreases and elastic interaction energy becomes dominant. In such case a deviation in variation of [r3 − r03 ] versus aging time was observed. © 2003 Published by Elsevier B.V. Keywords: Ni-base superalloy; Secondary ␥ ; Coarsening; Aging
1. Introduction Ni-base superalloys are the most complex and the most widely used material for manufacturing of critical gas turbine components such as rotating blades. It is well known that these materials own their high temperature strength from the fine particles of L12 type ordered ␥ [Ni3 (Al, Ti)] phase precipitated coherently with the matrix [1]. The mechanical properties of a given alloy are dependent upon such factors as volume fraction, particle size, coarsening rate and composition of ␥ phase [2]. Therefore knowledge about the influence of thermal exposure on the ␥ characteristics would be valuable for realistic estimation of service life of these components. This would help to avoid any premature retirement and, more importantly, premature failure of these components during service by setting an optimum time between overhauls (TBO) [3]. Superalloy IN-738LC with its good high temperature properties is extensively used for manufacturing of gas turbine blades. This material has been the subject of investigations since 30 years ago. However, a few papers have been published [4,5] regarding coarsening of ␥ precipitates ∗
Corresponding author. Fax: +98-21-600-5717. E-mail address: [email protected] (R. Sharghi-Moshatghin).
0925-8388/$ – see front matter © 2003 Published by Elsevier B.V. doi:10.1016/S0925-8388(03)00699-6
in this alloy. Stevens and Flewitt [4], studied only coarsening of secondary ␥ by using TEM replica technique. They found that kinetics of secondary ␥ follows a linear law also their experimental results showed that, secondary ␥ disappear after 1200 h aging at 850 ◦ C. Footner and Richards [5] studied only coarsening of primary ␥ In this study coarsening of primary and secondary ␥ precipitates in superalloy IN-738LC have been studied. Also using high resolution Field Emission Scanning Electron Microscope (FESEM), the ␥ characteristics such as size, inter-particle spacing and volume fraction have been quantified during aging.
2. Experimental procedure The material used in this study was supplied by Ross and Chaterall Co., UK. The chemical composition of the alloy is shown in Table 1. The material after casting under vacuum was subjected to standard heat treatment (SHT), 1120 ◦ C/2 h/air cool + 845 ◦ C/24 h/air cool. Samples of the size of 10 mm × 10 mm × 5 mm were prepared from the material and isothermally aged at 800, 850 and 900 ◦ C in an atmospheric furnace. Samples were removed from furnace during aging at each temperature, air cooled and sectioned. Each sample was prepared mechanically, and then was polished electrolytically in a solution of 45% butanol, 45%
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151
145
Table 1 Chemical composition of superalloy IN-738LC (wt.%)
Min Max
Ni
C
Co
Cr
Mo
W
Ta
Nb
Ai
Ti
B
Zr
Bal Bal
0.09 0.13
8.00 9.00
15.7 16.3
1.5 2.0
2.4 2.8
1.5 2.0
0.6 1.1
3.2 3.7
3.2 3.7
0.007 0.012
0.03 0.08
acetic acid and 10% perchloric acid, at 20–25 V for 25 s. Microstructural studies were carried out using a high resolution Field Emission Scanning Electron Microscope. Total weight fraction of ␥ was also established using the electrolytic extraction technique described by Kriege and Baris [6]. The particle size and statistical dispersion were obtained from SEM images employing an image analyzing system. In this study in order to obtain reliable results more than 100 particles were studied in different areas of each sample. In this system due to random and duplex distribution of ␥ precipitates, the number of precipitates in the certain area will alter the average size of precipitates. Then in order to decrease the errors in calculation, the number of precipitates should be included in calculations. In this case the average size of precipitates can be expressed as: n (ds,i + ac,i ) D = i=1 (1) Ns + N c where ds,i is the average diameter of secondary (spherical) ␥ , and ac,i the average of cubic side lengths of the primary ␥ . Same areas of samples in each aging condition were selected, and diameter of all spherical as well as cube sides of cuboid particles were measured and value of D calculated for different conditions using Eq. (1). It should be mentioned that for cuboids precipitates, shortest and longest lengths
were measured and the average of these measurements calculated as a representative size of cuboids precipitates.
3. Results Fig. 1 shows the microstructure of the material in SHT condition. As it can be seen standard heat treatment produces a bimodal distribution of ␥ precipitates in spheroidal and cuboidal forms having average size of 86 nm in diameter (d) and 550 nm in edge length (a), respectively. Figs. 2–4 show SEM images of samples aged at 800, 850 and 900 ◦ C for different aging times. Average size of ␥ precipitates and inter-particles spacing for each condition are also presented in Table 2. Comparing SEM images with the data in Table 2 imply that precipitates coarsen and interparticle spacing increase during aging at each temperature. Total volume fraction of precipitates (primary plus secondary) in SHT condition was measured to be 46%, then area fraction of primary ␥ was determined from the images to be 13% and by subtracting this value from the total amount, the area fraction of secondary ␥ was calculated to be 33%. Also total volume fraction of ␥ was measured during aging at each temperature by extraction method and the results are presented in Fig. 5. It is evident from Fig. 5, that the total volume fraction of ␥ is almost constant during aging.
Fig. 1. Microstructure of material in SHT condition.
146
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Fig. 2. SEM images of samples aged at 800 ◦ C for: (a) 500 h, (b) 1000 h, (c) 2000 h and (d) 3000 h.
Variation of area fraction of primary and secondary ␥ with the aging time is shown in Fig. 6. As it can be seen volume fraction of secondary ␥ decreases, whereas volume fraction of primary ␥ increases with aging time. Variation of overall particle size [(D/2)3 − (D0 /2)3 ] with aging time at different temperatures is presented in Fig. 7. As it seen during aging, coarsening kinetics follows a linear law at all temperatures. The increase in mean radius of the secondary ␥ precipitates, [r 3 −r03 ] as a function of aging time is presented in Fig. 8. It is evident from this figure that in the early stages of aging, the variation of [r3 − r03 ] as a function of aging time, can be approximated by a linear law, which then depart from the linear behavior at longer aging times.
Size distribution of secondary ␥ during aging is presented in Fig. 9. It can be seen that in the early stage of aging, size distribution of precipitates becomes broaden that is attributed to the coarsening of precipitates, whereas in later stages no broadening was observed and distribution becomes more uniform.
4. Discussion There are number of factors that may affect the coarsening of precipitates, and are not considered in so-called LSW theory [7]. Of different factors, elastic strain due to
Table 2 ␥ particle and inter-particle size in SHT and different aging conditions Temperature (◦ C) 800 Aging time (h) Primary ␥ (a) (nm) Secondary ␥ (D) (nm) Inter-particle spacing (nm)
500 660 150 65
850 1000 740 168 75
3000 810 172 89
500 720 176 71
900 2000 830 232 131
5000 910 390 170
150 760 220 116
500 835 290 142
1000 950 370 180
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151
147
Fig. 3. SEM images of samples aged at 850 ◦ C for: (a) 500 h, (b) 1000 h, (c) 2000 h and (d) 5000 h.
precipitate/matrix mismatch is of crucial importance [2,7,8]. The total energy of the system (Et ) containing coherent second phase precipitates can be expressed as [8]: Et = Es + Ee
(2)
where Et , Es and Ee are total energy, surface energy and elastic energy of the system, respectively. When a precipitate is coherent with a surrounding matrix, like ␥ /␥ system in Ni-base superalloy, the lattice mismatch between the precipitate and matrix causes elastic strain fields form around the precipitates. Therefore elastic interaction arises from overlapping of the elastic strain field around the coherent precipitates [9]. This would happen when the inter-particle spacing is short enough or volume fraction of precipitates is high. In this case elastic energy term (Ee ) in Eq. (2), consists of two energies: Ee = Em + Eint
(3)
where Em and Eint are elastic energies due to lattice mismatch and interaction of elastic strain fields around the precipitates, respectively. Energetically during coarsening the system tends to decrease total energy (Et ). In the early stage
of coarsening because of high volume fraction of fine precipitates, interfacial energy is dominant in such case driving force for coarsening is reduction in interfacial energy, and the system tends to reduces its total energy by decreasing interfacial energy. In this condition Ostwald ripening takes place and growth kinetic of ␥ would follow a linear equation predicted by LSW theory, expressed by following equation: r3 − r03 = Kt
(4)
and K=
8ΓVm DCm 9RT
(5)
where r is the particle radii for the secondary ␥ at the time t, r0 the particle radii at time zero (t = 0), K the rate constant and is defined by Eq. (5), where Γ is the interfacial energy between precipitates and matrix, D the diffusion constant, Cm the concentration of solute in the matrix in equilibrium with an infinitely large particle, Vm the molar volume of the precipitates, R the gas constant, T the absolute temperature. Experimental results show that in the early stages of aging, there is a linear correlation between [r3 − r03 ] and aging time which is consistent with above discussion.
148
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151
Fig. 4. SEM images of samples aged at 850 ◦ C for: (a) 100 h, (b) 500 h, (c) 750 h and (d) 1000 h.
Fig. 5. Variation of total volume fraction of ␥ as a function of aging time at 850 ◦ C.
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151 0. 6 Primary γ' Secondaryγ'
Volume Fraction of γ '
0. 5
0. 4
0. 3
0. 2
0. 1
0. 0
0
500
1000
1500
2000
2500
3000
3500
Aging Time (hrs)
Fig. 6. Area fraction of primary and secondary ␥ as a function of aging time at 850 ◦ C.
Also as it could be seen from Fig. 8, at longer aging times the growth rate of ␥ tended to decrease and depart from that linear correlation. As the coarsening proceeds, the elastic energy associated with each precipitate grows as r3 , whereas the interfacial energy associated with each precipitate grows as r2 [10]. In such condition elastic interaction energy in Eq. (3) and term Ee in Eq. (2) will be greater than interfacial energy (Es ) and therefore elastic energy becomes dominant in late stage of coarsening. Therefore, as the coarsening proceeds in this system, the elastic energy becomes progressively more important in controlling the behavior of the coarsening precipitates, so in such a system at later stages of aging any deviation from interfacial energy driven coarsening might be evident [10]. The differences in the results obtained in this study and previously reported results [4] are attributed to the different volume fraction of secondary ␥ in these systems.
1.40E+07
T=850˚C T=800˚C
1.20E+07
[(D/2)3 - (D/2)3 ] (nm) 3
T=900˚C 1.00E+07 8.00E+06 6.00E+06 4.00E+06 2.00E+06 0.00E+00 0
1000
2000
149
3000
4000
5000
6000
Aging Time (h)
Fig. 7. Correlation between [(D/2)3 − (D0 /2)3 ] and aging time at different temperature.
Fig. 8. Correlation between [r 3 − r03 ] and aging time at 850 ◦ C.
150
40
35
30
35
30
25 30
15
10
20 15
20
15
10
10
5
5
5
0
0 0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.2
2
0.4
0.6
0.8
1
(b)
r / r
1.2
1.4
1.6
1.8
2
0.2
0.4
0.6
0.8
(c)
r / r
20
20
15
10
15
10
5
5
0 0.2
0.4
0.6
0.8
1
1.2 1.4
1.6
1.8
2
0 0.2
(d)
r / r
(e)
0.4
0.6
0.8
1
1.2
1
r / r
25
25
Frequency (%)
0.4
Frequency(%)
0.2
(a)
25
Frequency (%)
Frequency(%)
20
1.4
1.6
1.8
2
r / r
Fig. 9. Size distribution of secondary ␥ during aging at 850 ◦ C for: (a) SHT, (b) 500 h, (c) 1000 h, (d) 2000 h and (e) 3000 h.
1.2
1.4
1.6
1.8
2
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151
Frequency(%)
25
R. Sharghi-Moshatghin, S. Asgari / Journal of Alloys and Compounds 368 (2004) 144–151
When the amount of ␥ is increased inter-particle distances become short. The experimental and theoretical works of Doi et al. [8] indicate that the elastic interaction energies are greatly affected by the distance between the precipitates, and as the distance between precipitates become short, the elastic interaction between them becomes noticeable. In such case variation of [r 3 − r03 ] as a function of aging time deviate from linear behavior, which is consistent with experimental results, obtained in this study. Concept of bifurcation for the coarsening of coherent precipitates in elastically stressed system was proposed by [11] for the first time. According to this concept in the early stage of coarsening, driving force for coarsening is only surface energy, in such case Ostwald ripening takes place and large precipitates coarsen at the expense of smaller precipitates. As the precipitates coarsen as a result of elastic energies, slowing down of coarsening kinetic and formation of uniform structure will be observed. From experimental results presented in Fig. 9, it could be seen that in the early stages of aging, size distribution of particles broaden whereas in later stages size distribution of ␥ becomes uniform and no further broadening observed. These results show that coarsening rate slow down in later stage of aging. Also Stevens and Flewitt [4] reported that after 1200 h aging at 850 ◦ C, secondary ␥ disappear, whereas experimental results presented in Fig. 3 show that even after 3000 h aging at 850 ◦ C, secondary ␥ has not disappeared.
5. Conclusion 1. When overall particles including primary as well as secondary ␥ precipitates are considered, coarsening kinetics follow a linear law at different temperatures during aging. Whereas when only secondary ␥ precipitates are considered, at the early stage of coarsening the kinetics follows a linear law and depart at longer aging times.
151
2. In the early stages of aging, driving force for coarsening of secondary ␥ precipitates is reduction in interfacial energy. In this case variation of [r 3 − r03 ] as a function of aging time is linear. 3. Strain field around coherent precipitates, causes deviation in variation of [r3 − r03 ] as a function of time in longer aging times. 4. Particle size distribution becomes broaden in the early stage of aging where as it becomes uniform in longer aging times. It shows that in the early stage of aging coarsening of precipitates takes place whereas in longer aging times there is a decrease in coarsening rate. Acknowledgements The authors would like to thank Imperial College London for the Microscope facilities. Also Mavadkaran Eng. Company in Iran is acknowledged for the supplying of material.
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