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Creep strength of a tungsten–rhenium–hafnium carbide alloy from 2200 to 2400 K
Materials Science and Engineering A265 (1999) 174 – 178
Creep strength of a tungsten–rhenium–hafnium carbide alloy from 2200 to 2400 K John J. Park * Los Alamos National Laboratory, MS E508, Los Alamos, NM 87545, USA Received 17 June 1998; received in revised form 16 November 1998
Abstract The high–temperature creep behavior of tungsten– 4 wt.% rhenium-0.32 wt.% hafnium carbide (W-4Re-0.32HfC) was evaluated at temperatures ranging from 2200 to 2400 K and stresses ranging from 40 to 70 MPa in a vacuum less than 1.33 ×10 – 6 MPa (1.0× 10 – 8 torr). The effects of temperature and stress on the steady – state creep rate were determined. The stress exponent for creep was 5.2, and the activation energy for creep was 594 kJ mol − 1. The creep strength of W-4Re-0.32HfC was compared with that of pure tungsten (W) and tungsten–5 wt.% rhenium (W – 5Re) at a creep rate of 10 − 6 s − 1 as a function of temperature. The temperature-compensated creep rate of W–4Re–0.32HfC was approximately two orders of magnitude less than that of pure W and one order of magnitude less than that of W – 5Re. The creep strength of W – 4Re – 0.32HfC was correlated with its microstructural development during the high-temperature deformation. Transmission electron microscope (TEM) study of the creep tested samples revealed that the high creep strength of this alloy resulted from finely dispersed submicron-sized HfC particles. The strengthening effect of the HfC particles could be attributed to direct and indirect particle strengthening. Direct particle strengthening was caused by the retardation of subboundary dislocation movement by direct particle/dislocation interaction. Indirect particle strengthening was caused by the formation of subgrains, which in turn reduces the distance that dislocations can move before being immobilized at subgrain or grain boundaries. The strengthening effect of HfC particles was reduced as HfC particle diameter increased. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Steady-state creep; W–4Re–0.32Hfc; Tungsten
1. Introduction Future thermionic energy conversion systems will be expected to operate at temperatures greater than 1500 K for several years. Because of the high operating temperatures and an extremely small distance between an emitter and a collector (0.2 – 0.6 mm), the creep resistance of emitter material is very critical to the performance of the energy conversion system. Tungsten alloys have good thermionic properties as well as hightemperature mechanical properties and, thus, have been considered as primary candidate materials for thermionic emitters. Pure tungsten (W) is very brittle at room temperature and is very hard to fabricate into desired forms. Exten-
* Corresponding author. Tel.: +1-505-6658247; fax: + 1-5056678919. E-mail address: [email protected] (J.J. Park)
sive alloying studies have focused on tungsten to increase its ductility. Studies revealed that the addition of rhenium increased room temperature ductility and the high-temperature creep strength of tungsten [1]. Strengthening tungsten with fine precipitates of secondphase particles has been very effective in improving high-temperature tensile and creep properties at temperatures above 0.5 Tm (Tm is the melting temperature of tungsten) [2]. Among various potential strengtheners, hafnium carbide (HfC) possesses the highest melting point, the highest thermodynamic stability, and the lowest vapor pressure. It was found that hafnium carbide is the most effective strengthener to improve the high-temperature strength of tungsten without adversely affecting the room temperature ductility [3]. Therefore, it is advantageous to develop W–Re–HfC alloys for space power applications [4,5]. The objectives of this research were: (1) to study the creep behavior of W–4Re–0.32HfC in detail by mea-
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 8 ) 0 1 1 3 4 - 4
J.J. Park / Materials Science and Engineering A265 (1999) 174–178
suring the stress exponent and activation energy; (2) to compare the creep strength of W – 4Re – 0.32HfC with that of pure W and W – 5Re; and (3) to determine the strengthening mechanism of dispersed HfC particles in tungsten at temperatures greater than 2200 K.
2. Experimental procedures The material studied in this research was arc-melted and swaged W–4 wt.% Re – 0.32 wt.% HfC (W–4Re– 0.32HfC), which was supplied by the National Aeronautics and Space Administration, Lewis Research Center. As-received material was in the form of 25.4 mm diameter rods. Plate-type specimens with a gauge section of 12.7× 3.2 mm and a thickness of 0.75 mm were prepared by electrical discharge machining. The specimens were first mechanically polished with abrasive papers and then lapped with alumina powders. After the mechanical polishing, specimens were chemically polished in a 10% NaOH solution to ensure smooth surfaces. Prior to testing, all the specimens were annealed at 2500 K for 1 h to produce recrystallized grains. The average grain size after annealing, as determined by the intercept method, was 97 mm, with a standard deviation of 8.5%. The specimens were tested under engineering stresses from 40 to 70 MPa, with 10 MPa intervals, at 2200, 2300, and 2400 K on a custom-built ultrahigh-temperature, ultrahigh vacuum (UHV) creep test station. Specimens were heated by passing alternating current through them. A mechanical pump, a sorption pump, and an ion pump ensured a maximum pressure inside the vacuum chamber of less than 1.33× 10 – 6 Pa (1× 10 – 8 torr) during the creep tests. The specimen temperature was measured with a microoptical disappearing filament pyrometer that was calibrated with a standard tungsten ribbon filament lamp provided by the National Institute of Standards and Technology. The blackbody temperature of the specimen was verified using high-temperature emissivity data from a sample with the same alloy composition. The maximum uncertainty of the measured temperature was 9 5 K for the entire temperature range used in the present research. The load was applied to the specimen through stainless steel bellows that were attached to the UHV chamber, and corrections were made for changes in the spring force of the bellows caused by the extension of the load column. Specimen elongation was measured in terms of the motion of the load train, with a linear variable differential transformer that interfaced with a data acquisition system, making it possible to measure the creep strains to within 9 0.03%. The specimens were examined before and after the creep tests with a transmission electron microscope (TEM) to characterize the strengthening effect of HfC
175
particles in the W–Re matrix. Samples for the TEM study were removed from the uniformly deformed region of the specimens after the tests. The thicknesses of the samples were then reduced to approximately 120 mm. From these samples, disk-shaped blanks with a diameter of 3 mm were produced with an ultrasonic cutter, and both sides of the blanks were ground to a thickness of 70 mm. The blanks were dimpled to a thickness of 30 mm at the center using a 6-mm diamond paste for 2 h and were then polished with a 1-mm diamond paste for 5 min. After the mechanical thinning procedures were complete, the specimen blanks were ion-milled at an angle of 15–20° for 10–15 h. The samples were then examined with a high resolution TEM at magnifications of 5000, 15 000, 30 000, 60 000, and 100 000 times at 200 kV.
3. Results and discussion Fig. 1 shows the engineering strain–time creep curve of W–4Re–0.32HfC at 2200 K and 40 MPa, respectively which is typical of creep curves obtained from the present study. It shows the three regions of a creep curve normally observed: primary, secondary or steadystate, and tertiary creep regions. The steady-state creep rates, which were our primary interest, were obtained from the application of the least-squares and linear regression methods to the raw data obtained from the secondary creep region of the creep curves. The effects of stress and temperature on the steady-state creep rate of W–4Re–0.32HfC were obtained by analyzing these creep curves. Fig. 2 shows the stress dependence of the steady-state creep rate (SSCR) of W–4Re–0.32HfC at different temperatures. Three straight parallel lines were obtained from these log–log plots, implying that the steady-state creep rate and the applied stress have a
Fig. 1. Engineering strain – time creep curve for W – 4Re–0.32HfC at 2200 K and 40 MPa.
J.J. Park / Materials Science and Engineering A265 (1999) 174–178
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Fig. 2. Stress dependence of steady-state creep rate (SSCR) for W– 4Re – 0.32HfC.
power-law relationship. The stress exponent for creep deformation, n, was obtained from the slope of each straight line, and a least-squares analysis yielded an n value of 5.2. Fig. 3 shows the temperature dependence of the steady-state creep rate at each stress level for W–4Re– 0.32HfC. The activation energies for creep, Qc, measured from the slopes of each line ranged from 577 to 611 kJ mol − 1, with an average value of 594 kJ mol − 1. This is in agreement with the observations made by Barrett et al. [6] that the activation energy for creep is not sensitive to the applied stress. The steady-state creep rate is a function of both stress and temperature, which can be expressed as o; s =B ·
s E
n
· exp −
Qc , RT
(1)
where o; s is the steady-state creep rate, B is a constant, s is the engineering stress, E is Young’s modulus at the test temperature, R is the universal gas constant, and T is the absolute temperature in K. Young’s modulus for W–4Re–0.32HfC (E= − 0.123T +553.78 at temperatures between 2000–2500 K) was calculated from the values reported by Ayres et al. [7] for a W–Re alloy, assuming that hafnium carbide has no effect on Young’s modulus. Eq. (1) is in accordance with the equation for the steady-state creep rate of common metallic materials proposed by Mukherjee et al. [8] and Weertman [9]. After substituting the obtained values of n and Q from this research, B can be determined, and the creep rate at any given stress and temperature can be found. Based on the results obtained from this research, the material constant B was determined to be 5.45×1027 by the multiple linear regression method. Therefore, Eq. (1) can be rewritten o; s = 5.45× 1027 ·
s E
5.2
· exp −
142000 . RT
(2)
This equation can be used to calculate the steady-state creep rate of W–4Re–0.32HfC at a given temperature (2200–2400 K) and applied stress as long as the powerlaw creep is valid. For example, according to this equation, a thermionic emitter made of W–4Re– 0.32HfC would have a steady-state creep rate of 5.24× 10 – 12 s − 1 at 2200 K and 5 MPa. According to LIFE-4 [10], a code that was developed to simulate the performance of thermionic fuel elements, typical temperature and pressure on the emitter is 1800 K and 1–4 MPa, respectively. If an emitter made of W–4Re–0.32HfC was operated, for example, at 2200 K and 5 MPa, it would take 60 years to reach a creep strain of 1%, without the primary creep strain and elastic strain being considered. The primary creep strain is very small, as shown in Fig. 1, and so is the elastic strain in general. The emitter creep strain of 1% is an arbitrary number. Actual tolerable creep strain depends on many parameters; however, it is much higher than 1%. The lifetime of the emitter is designed to be 7 years at normal operating temperature and pressure. Thus, W–4Re– 0.32HfC has a more than adequate lifetime for an emitter material. One of the most frequently used parameters in comparing the creep properties of different materials is the temperature-compensated creep rate, i.e. the ZenerHolloman parameter [11], which is expressed as Z= o; s exp
Fig. 3. Temperature dependence of steady-state creep rate (SSCR) for W– 4Re – 0.32HfC.
Qc s =B · RT E
n
(3)
The Z values of W–4Re–0.32HfC, W–5Re [1], and pure W [12] were plotted logarithmically against the normalized stress (s/E) in Fig. 4. This figure clearly shows the creep strength advantage of W–4Re–
J.J. Park / Materials Science and Engineering A265 (1999) 174–178
177
Fig. 4. Temperature-compensated (TC) creep rates (Z =o; s exp(Qc/ RT)) for pure W, W –5Re, and W–4Re–0.32HfC.
Fig. 6. Subboundary dislocation structure observed in W–4Re– 0.32HfC.
0.32HfC over W– 5Re and pure W. At the same normalized stress, the temperature-compensated creep rate of W–4Re–0.32HfC is approximately two orders of magnitude less than that of pure W and one order of magnitude less than W – 5Re. Typical TEM micrographs of creep tested W–4Re– 0.32HfC are shown in Figs. 5 and 6. These micrographs show that subgrains were formed and that dislocation tangles [13] were no longer observed. Subgrains consisted of dislocation networks (Fig. 5) and dislocation walls (Fig. 6). Fig. 5 shows the interaction between subboundaries and HfC particles. It can be seen that HfC particles tend to retard the movement of subboundary dislocations. The two typical TEM microstructural features observed in the creep tested specimens were the formation of subgrains and the interaction between HfC particles and subboundary dislocations. The strengthening effect of HfC particles in W–4Re–0.32HfC is therefore attributed to two
causes: direct particle strengthening and indirect particle strengthening. Direct particle strengthening arises from the retardation of subboundary dislocation movement by direct particle/dislocation interaction. Indirect particle strengthening arises from the formation of subgrains caused by the stabilization of subgrain structure, which in turn reduces the distance that dislocations can move before being immobilized at subgrain or grain boundaries. The HfC particle size measurement by the TEM revealed that the HfC particle size increases as the test temperature increases (Table 1). The driving force for precipitation growth is the reduction of the total surface energy of the precipitates. Lifshitz et al. [14] derived a diffusion controlled particle growth theory for ideal spherical particles r 3 − r 30 = kt,
(4)
where r is the average particle radius at time t, r0 is the average particle radius at the onset of coarsening, and k is the rate constant given by Table 1 HfC particle size in W–4Re–0.32HfC after creep tests
Fig. 5. Interaction between a dislocation network and an HfC particle in W – 4Re – 0.32HfC.
Temperature (K)
Stress (MPa)
˚) Particle radius (A
2200 2200 2200 2200 2300 2300 2300 2400 2400 2400 2400
40 50 60 70 40 50 70 40 50 60 70
388 346 328 298 512 428 402 814 785 751 687
J.J. Park / Materials Science and Engineering A265 (1999) 174–178
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(3) At the same normalized stress, the temperaturecompensated creep rate of W–4Re–0.32HfC is approximately two orders of magnitude less than that of pure W and one order of magnitude less than that of W–5Re. (4) The high creep strength of W–4Re–0.32HfC is associated with direct and indirect particle strengthening. Direct particle strengthening is caused by the retardation of subboundary dislocation movement by direct particle/ dislocation interaction. Indirect particle strengthening is caused by the formation of subgrains, which in turn reduces the distance that dislocations can move before being immobilized at subgrain or grain boundaries. (5) The creep strength increment of W–4Re–0.32HfC decreases as the HfC particle diameter increases. Fig. 7. Creep strength increment for W–4Re–0.32HfC as a function of HfC particle diameter.
k=
2 m
8gDCeV , 9RT
(5)
where g is the interfacial free energy of the particle matrix interface, D is the diffusion coefficient of solute in the matrix, Ce is the concentration of solute in the matrix in equilibrium with a particle of infinite size, and Vm is the molar volume of the particle. The k value can be considered as a measurement of the thermodynamic instability of particles. The higher the k value, the faster the particles coarsen. From these equations, it can be seen that the coarsening of precipitates in solid matrices tends to increase with increasing exposure time and temperature. In order to evaluate the HfC strengthening effect in the tungsten–rhenium matrix, the creep strength of W–4Re–0.32HfC was subtracted from that of W–5Re; the results are shown as a function of HfC particle size in Fig. 7. As the particle size increases, the creep strength increment decreases, and when the particle diameter ˚ , the strengthening effect of HfC is exceeds 4000 A predicted to be negligible. For a given particle volume fraction, particle coarsening results in a decrease in the total number of particles and, hence, an increase in interparticle spacing. The particle growth reduces not only the pinning effect of particles on dislocation but also the retarding effect of particles on the growth of subgrains, hence reducing both the direct and indirect particle strengthening effects of HfC particles with increasing temperature. 4. Summary of results The following summaries were made from the present research on the creep behavior of the arc-melted and swaged W–4Re– 0.32HfC between 2200 and 2400 K: (1) The stress exponent for creep is 5.2. (2) The activation energy for creep is 594 kJ mol − 1.
Acknowledgements This research was performed at Arizona State University and was sponsored by the Wright Research and Development Center (WRDC), Wright-Patterson Air Force Base, Ohio, under contract number F33615-91-C2109. References [1] D.A. Robins, Discussion to properties of refractory alloys containing rhenium, Trans. ASM 52 (1960) 943. [2] P.L. Raffo, W.D. Klopp, Mechanical properties of solid solution and carbide-strengthened arc-melted tungsten alloys, NASA Technical Note D-3248, Lewis Research Center, Cleveland, Ohio, 1966. [3] W.D. Klopp, W.R. Witzke, Mechanical properties of arc-melted tungsten – rhenium – hafnium – carbon alloys, NASA Technical Note D-5348, Lewis Research Center, Cleveland, Ohio, 1969. [4] J.J. Park, D.L. Jacobson, Creep behavior of tungsten –4 rhenium– 0.32 hafnium carbide, in: A. Bose, R.J. Dowding (Eds.), Proceedings of the International Conference on Tungsten and Tungsten Alloys, MPIF, Princeton, NJ, 1992, p. 241. [5] J.J. Park, D.L. Jacobson, Steady-state creep rates of W–4Re– 0.32HfC, in: B.D. Bryskin (Ed.), Proceedings of the International Symposium on Rhenium and Rhenium Alloys, TMS, Warrendale, PA, 1997, p. 327. [6] C.R. Barrett, A.J. Ardell, O.D. Sherby, Influence of modulus on the temperature dependence of the activation energy for creep at high temperature, Trans. TMS-AIME 230 (1964) 200. [7] R.A. Ayres, G.W. Shannette, D.F. Stein, Elastic constants of tungsten – rhenium alloys, J. Appl. Phys. 46 (1975) 1526. [8] A.K. Mukherjee, J.E. Bird, J.E. Dorn, Experimental correlations for high temperature creep, Trans. ASM 62 (1969) 155. [9] J. Weertman, Steady state creep through dislocation climb, J. Appl. Phys. 28 (1957) 362. [10] T. Roth (Ed.), LIFE-4 Programmers’ Manual, Westinghouse Electric Corporation report WARD-94000-12 Rev. 0, 1983. [11] C. Zener, J.H. Holoman, Effect of strain rate upon plastic flow of steel, J. Appl. Phys. 15 (1944) 22. [12] J.W. Pugh, L.H. Amra, D.T. Hurd, Properties of tungsten–rhenium lamp wire, Trans. ASM 55 (1962) 451. [13] O.D. Sherby, P.M. Burke, Mechanical behavior of crystalline solids at elevated temperatures, Prog. Mater. Sci. 13 (1967) 325. [14] I.M. Lifshitz, V.V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19 (1961) 35.
Creep strength of a tungsten–rhenium–hafnium carbide alloy from 2200 to 2400 K John J. Park * Los Alamos National Laboratory, MS E508, Los Alamos, NM 87545, USA Received 17 June 1998; received in revised form 16 November 1998
Abstract The high–temperature creep behavior of tungsten– 4 wt.% rhenium-0.32 wt.% hafnium carbide (W-4Re-0.32HfC) was evaluated at temperatures ranging from 2200 to 2400 K and stresses ranging from 40 to 70 MPa in a vacuum less than 1.33 ×10 – 6 MPa (1.0× 10 – 8 torr). The effects of temperature and stress on the steady – state creep rate were determined. The stress exponent for creep was 5.2, and the activation energy for creep was 594 kJ mol − 1. The creep strength of W-4Re-0.32HfC was compared with that of pure tungsten (W) and tungsten–5 wt.% rhenium (W – 5Re) at a creep rate of 10 − 6 s − 1 as a function of temperature. The temperature-compensated creep rate of W–4Re–0.32HfC was approximately two orders of magnitude less than that of pure W and one order of magnitude less than that of W – 5Re. The creep strength of W – 4Re – 0.32HfC was correlated with its microstructural development during the high-temperature deformation. Transmission electron microscope (TEM) study of the creep tested samples revealed that the high creep strength of this alloy resulted from finely dispersed submicron-sized HfC particles. The strengthening effect of the HfC particles could be attributed to direct and indirect particle strengthening. Direct particle strengthening was caused by the retardation of subboundary dislocation movement by direct particle/dislocation interaction. Indirect particle strengthening was caused by the formation of subgrains, which in turn reduces the distance that dislocations can move before being immobilized at subgrain or grain boundaries. The strengthening effect of HfC particles was reduced as HfC particle diameter increased. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Steady-state creep; W–4Re–0.32Hfc; Tungsten
1. Introduction Future thermionic energy conversion systems will be expected to operate at temperatures greater than 1500 K for several years. Because of the high operating temperatures and an extremely small distance between an emitter and a collector (0.2 – 0.6 mm), the creep resistance of emitter material is very critical to the performance of the energy conversion system. Tungsten alloys have good thermionic properties as well as hightemperature mechanical properties and, thus, have been considered as primary candidate materials for thermionic emitters. Pure tungsten (W) is very brittle at room temperature and is very hard to fabricate into desired forms. Exten-
* Corresponding author. Tel.: +1-505-6658247; fax: + 1-5056678919. E-mail address: [email protected] (J.J. Park)
sive alloying studies have focused on tungsten to increase its ductility. Studies revealed that the addition of rhenium increased room temperature ductility and the high-temperature creep strength of tungsten [1]. Strengthening tungsten with fine precipitates of secondphase particles has been very effective in improving high-temperature tensile and creep properties at temperatures above 0.5 Tm (Tm is the melting temperature of tungsten) [2]. Among various potential strengtheners, hafnium carbide (HfC) possesses the highest melting point, the highest thermodynamic stability, and the lowest vapor pressure. It was found that hafnium carbide is the most effective strengthener to improve the high-temperature strength of tungsten without adversely affecting the room temperature ductility [3]. Therefore, it is advantageous to develop W–Re–HfC alloys for space power applications [4,5]. The objectives of this research were: (1) to study the creep behavior of W–4Re–0.32HfC in detail by mea-
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 8 ) 0 1 1 3 4 - 4
J.J. Park / Materials Science and Engineering A265 (1999) 174–178
suring the stress exponent and activation energy; (2) to compare the creep strength of W – 4Re – 0.32HfC with that of pure W and W – 5Re; and (3) to determine the strengthening mechanism of dispersed HfC particles in tungsten at temperatures greater than 2200 K.
2. Experimental procedures The material studied in this research was arc-melted and swaged W–4 wt.% Re – 0.32 wt.% HfC (W–4Re– 0.32HfC), which was supplied by the National Aeronautics and Space Administration, Lewis Research Center. As-received material was in the form of 25.4 mm diameter rods. Plate-type specimens with a gauge section of 12.7× 3.2 mm and a thickness of 0.75 mm were prepared by electrical discharge machining. The specimens were first mechanically polished with abrasive papers and then lapped with alumina powders. After the mechanical polishing, specimens were chemically polished in a 10% NaOH solution to ensure smooth surfaces. Prior to testing, all the specimens were annealed at 2500 K for 1 h to produce recrystallized grains. The average grain size after annealing, as determined by the intercept method, was 97 mm, with a standard deviation of 8.5%. The specimens were tested under engineering stresses from 40 to 70 MPa, with 10 MPa intervals, at 2200, 2300, and 2400 K on a custom-built ultrahigh-temperature, ultrahigh vacuum (UHV) creep test station. Specimens were heated by passing alternating current through them. A mechanical pump, a sorption pump, and an ion pump ensured a maximum pressure inside the vacuum chamber of less than 1.33× 10 – 6 Pa (1× 10 – 8 torr) during the creep tests. The specimen temperature was measured with a microoptical disappearing filament pyrometer that was calibrated with a standard tungsten ribbon filament lamp provided by the National Institute of Standards and Technology. The blackbody temperature of the specimen was verified using high-temperature emissivity data from a sample with the same alloy composition. The maximum uncertainty of the measured temperature was 9 5 K for the entire temperature range used in the present research. The load was applied to the specimen through stainless steel bellows that were attached to the UHV chamber, and corrections were made for changes in the spring force of the bellows caused by the extension of the load column. Specimen elongation was measured in terms of the motion of the load train, with a linear variable differential transformer that interfaced with a data acquisition system, making it possible to measure the creep strains to within 9 0.03%. The specimens were examined before and after the creep tests with a transmission electron microscope (TEM) to characterize the strengthening effect of HfC
175
particles in the W–Re matrix. Samples for the TEM study were removed from the uniformly deformed region of the specimens after the tests. The thicknesses of the samples were then reduced to approximately 120 mm. From these samples, disk-shaped blanks with a diameter of 3 mm were produced with an ultrasonic cutter, and both sides of the blanks were ground to a thickness of 70 mm. The blanks were dimpled to a thickness of 30 mm at the center using a 6-mm diamond paste for 2 h and were then polished with a 1-mm diamond paste for 5 min. After the mechanical thinning procedures were complete, the specimen blanks were ion-milled at an angle of 15–20° for 10–15 h. The samples were then examined with a high resolution TEM at magnifications of 5000, 15 000, 30 000, 60 000, and 100 000 times at 200 kV.
3. Results and discussion Fig. 1 shows the engineering strain–time creep curve of W–4Re–0.32HfC at 2200 K and 40 MPa, respectively which is typical of creep curves obtained from the present study. It shows the three regions of a creep curve normally observed: primary, secondary or steadystate, and tertiary creep regions. The steady-state creep rates, which were our primary interest, were obtained from the application of the least-squares and linear regression methods to the raw data obtained from the secondary creep region of the creep curves. The effects of stress and temperature on the steady-state creep rate of W–4Re–0.32HfC were obtained by analyzing these creep curves. Fig. 2 shows the stress dependence of the steady-state creep rate (SSCR) of W–4Re–0.32HfC at different temperatures. Three straight parallel lines were obtained from these log–log plots, implying that the steady-state creep rate and the applied stress have a
Fig. 1. Engineering strain – time creep curve for W – 4Re–0.32HfC at 2200 K and 40 MPa.
J.J. Park / Materials Science and Engineering A265 (1999) 174–178
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Fig. 2. Stress dependence of steady-state creep rate (SSCR) for W– 4Re – 0.32HfC.
power-law relationship. The stress exponent for creep deformation, n, was obtained from the slope of each straight line, and a least-squares analysis yielded an n value of 5.2. Fig. 3 shows the temperature dependence of the steady-state creep rate at each stress level for W–4Re– 0.32HfC. The activation energies for creep, Qc, measured from the slopes of each line ranged from 577 to 611 kJ mol − 1, with an average value of 594 kJ mol − 1. This is in agreement with the observations made by Barrett et al. [6] that the activation energy for creep is not sensitive to the applied stress. The steady-state creep rate is a function of both stress and temperature, which can be expressed as o; s =B ·
s E
n
· exp −
Qc , RT
(1)
where o; s is the steady-state creep rate, B is a constant, s is the engineering stress, E is Young’s modulus at the test temperature, R is the universal gas constant, and T is the absolute temperature in K. Young’s modulus for W–4Re–0.32HfC (E= − 0.123T +553.78 at temperatures between 2000–2500 K) was calculated from the values reported by Ayres et al. [7] for a W–Re alloy, assuming that hafnium carbide has no effect on Young’s modulus. Eq. (1) is in accordance with the equation for the steady-state creep rate of common metallic materials proposed by Mukherjee et al. [8] and Weertman [9]. After substituting the obtained values of n and Q from this research, B can be determined, and the creep rate at any given stress and temperature can be found. Based on the results obtained from this research, the material constant B was determined to be 5.45×1027 by the multiple linear regression method. Therefore, Eq. (1) can be rewritten o; s = 5.45× 1027 ·
s E
5.2
· exp −
142000 . RT
(2)
This equation can be used to calculate the steady-state creep rate of W–4Re–0.32HfC at a given temperature (2200–2400 K) and applied stress as long as the powerlaw creep is valid. For example, according to this equation, a thermionic emitter made of W–4Re– 0.32HfC would have a steady-state creep rate of 5.24× 10 – 12 s − 1 at 2200 K and 5 MPa. According to LIFE-4 [10], a code that was developed to simulate the performance of thermionic fuel elements, typical temperature and pressure on the emitter is 1800 K and 1–4 MPa, respectively. If an emitter made of W–4Re–0.32HfC was operated, for example, at 2200 K and 5 MPa, it would take 60 years to reach a creep strain of 1%, without the primary creep strain and elastic strain being considered. The primary creep strain is very small, as shown in Fig. 1, and so is the elastic strain in general. The emitter creep strain of 1% is an arbitrary number. Actual tolerable creep strain depends on many parameters; however, it is much higher than 1%. The lifetime of the emitter is designed to be 7 years at normal operating temperature and pressure. Thus, W–4Re– 0.32HfC has a more than adequate lifetime for an emitter material. One of the most frequently used parameters in comparing the creep properties of different materials is the temperature-compensated creep rate, i.e. the ZenerHolloman parameter [11], which is expressed as Z= o; s exp
Fig. 3. Temperature dependence of steady-state creep rate (SSCR) for W– 4Re – 0.32HfC.
Qc s =B · RT E
n
(3)
The Z values of W–4Re–0.32HfC, W–5Re [1], and pure W [12] were plotted logarithmically against the normalized stress (s/E) in Fig. 4. This figure clearly shows the creep strength advantage of W–4Re–
J.J. Park / Materials Science and Engineering A265 (1999) 174–178
177
Fig. 4. Temperature-compensated (TC) creep rates (Z =o; s exp(Qc/ RT)) for pure W, W –5Re, and W–4Re–0.32HfC.
Fig. 6. Subboundary dislocation structure observed in W–4Re– 0.32HfC.
0.32HfC over W– 5Re and pure W. At the same normalized stress, the temperature-compensated creep rate of W–4Re–0.32HfC is approximately two orders of magnitude less than that of pure W and one order of magnitude less than W – 5Re. Typical TEM micrographs of creep tested W–4Re– 0.32HfC are shown in Figs. 5 and 6. These micrographs show that subgrains were formed and that dislocation tangles [13] were no longer observed. Subgrains consisted of dislocation networks (Fig. 5) and dislocation walls (Fig. 6). Fig. 5 shows the interaction between subboundaries and HfC particles. It can be seen that HfC particles tend to retard the movement of subboundary dislocations. The two typical TEM microstructural features observed in the creep tested specimens were the formation of subgrains and the interaction between HfC particles and subboundary dislocations. The strengthening effect of HfC particles in W–4Re–0.32HfC is therefore attributed to two
causes: direct particle strengthening and indirect particle strengthening. Direct particle strengthening arises from the retardation of subboundary dislocation movement by direct particle/dislocation interaction. Indirect particle strengthening arises from the formation of subgrains caused by the stabilization of subgrain structure, which in turn reduces the distance that dislocations can move before being immobilized at subgrain or grain boundaries. The HfC particle size measurement by the TEM revealed that the HfC particle size increases as the test temperature increases (Table 1). The driving force for precipitation growth is the reduction of the total surface energy of the precipitates. Lifshitz et al. [14] derived a diffusion controlled particle growth theory for ideal spherical particles r 3 − r 30 = kt,
(4)
where r is the average particle radius at time t, r0 is the average particle radius at the onset of coarsening, and k is the rate constant given by Table 1 HfC particle size in W–4Re–0.32HfC after creep tests
Fig. 5. Interaction between a dislocation network and an HfC particle in W – 4Re – 0.32HfC.
Temperature (K)
Stress (MPa)
˚) Particle radius (A
2200 2200 2200 2200 2300 2300 2300 2400 2400 2400 2400
40 50 60 70 40 50 70 40 50 60 70
388 346 328 298 512 428 402 814 785 751 687
J.J. Park / Materials Science and Engineering A265 (1999) 174–178
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(3) At the same normalized stress, the temperaturecompensated creep rate of W–4Re–0.32HfC is approximately two orders of magnitude less than that of pure W and one order of magnitude less than that of W–5Re. (4) The high creep strength of W–4Re–0.32HfC is associated with direct and indirect particle strengthening. Direct particle strengthening is caused by the retardation of subboundary dislocation movement by direct particle/ dislocation interaction. Indirect particle strengthening is caused by the formation of subgrains, which in turn reduces the distance that dislocations can move before being immobilized at subgrain or grain boundaries. (5) The creep strength increment of W–4Re–0.32HfC decreases as the HfC particle diameter increases. Fig. 7. Creep strength increment for W–4Re–0.32HfC as a function of HfC particle diameter.
k=
2 m
8gDCeV , 9RT
(5)
where g is the interfacial free energy of the particle matrix interface, D is the diffusion coefficient of solute in the matrix, Ce is the concentration of solute in the matrix in equilibrium with a particle of infinite size, and Vm is the molar volume of the particle. The k value can be considered as a measurement of the thermodynamic instability of particles. The higher the k value, the faster the particles coarsen. From these equations, it can be seen that the coarsening of precipitates in solid matrices tends to increase with increasing exposure time and temperature. In order to evaluate the HfC strengthening effect in the tungsten–rhenium matrix, the creep strength of W–4Re–0.32HfC was subtracted from that of W–5Re; the results are shown as a function of HfC particle size in Fig. 7. As the particle size increases, the creep strength increment decreases, and when the particle diameter ˚ , the strengthening effect of HfC is exceeds 4000 A predicted to be negligible. For a given particle volume fraction, particle coarsening results in a decrease in the total number of particles and, hence, an increase in interparticle spacing. The particle growth reduces not only the pinning effect of particles on dislocation but also the retarding effect of particles on the growth of subgrains, hence reducing both the direct and indirect particle strengthening effects of HfC particles with increasing temperature. 4. Summary of results The following summaries were made from the present research on the creep behavior of the arc-melted and swaged W–4Re– 0.32HfC between 2200 and 2400 K: (1) The stress exponent for creep is 5.2. (2) The activation energy for creep is 594 kJ mol − 1.
Acknowledgements This research was performed at Arizona State University and was sponsored by the Wright Research and Development Center (WRDC), Wright-Patterson Air Force Base, Ohio, under contract number F33615-91-C2109. References [1] D.A. Robins, Discussion to properties of refractory alloys containing rhenium, Trans. ASM 52 (1960) 943. [2] P.L. Raffo, W.D. Klopp, Mechanical properties of solid solution and carbide-strengthened arc-melted tungsten alloys, NASA Technical Note D-3248, Lewis Research Center, Cleveland, Ohio, 1966. [3] W.D. Klopp, W.R. Witzke, Mechanical properties of arc-melted tungsten – rhenium – hafnium – carbon alloys, NASA Technical Note D-5348, Lewis Research Center, Cleveland, Ohio, 1969. [4] J.J. Park, D.L. Jacobson, Creep behavior of tungsten –4 rhenium– 0.32 hafnium carbide, in: A. Bose, R.J. Dowding (Eds.), Proceedings of the International Conference on Tungsten and Tungsten Alloys, MPIF, Princeton, NJ, 1992, p. 241. [5] J.J. Park, D.L. Jacobson, Steady-state creep rates of W–4Re– 0.32HfC, in: B.D. Bryskin (Ed.), Proceedings of the International Symposium on Rhenium and Rhenium Alloys, TMS, Warrendale, PA, 1997, p. 327. [6] C.R. Barrett, A.J. Ardell, O.D. Sherby, Influence of modulus on the temperature dependence of the activation energy for creep at high temperature, Trans. TMS-AIME 230 (1964) 200. [7] R.A. Ayres, G.W. Shannette, D.F. Stein, Elastic constants of tungsten – rhenium alloys, J. Appl. Phys. 46 (1975) 1526. [8] A.K. Mukherjee, J.E. Bird, J.E. Dorn, Experimental correlations for high temperature creep, Trans. ASM 62 (1969) 155. [9] J. Weertman, Steady state creep through dislocation climb, J. Appl. Phys. 28 (1957) 362. [10] T. Roth (Ed.), LIFE-4 Programmers’ Manual, Westinghouse Electric Corporation report WARD-94000-12 Rev. 0, 1983. [11] C. Zener, J.H. Holoman, Effect of strain rate upon plastic flow of steel, J. Appl. Phys. 15 (1944) 22. [12] J.W. Pugh, L.H. Amra, D.T. Hurd, Properties of tungsten–rhenium lamp wire, Trans. ASM 55 (1962) 451. [13] O.D. Sherby, P.M. Burke, Mechanical behavior of crystalline solids at elevated temperatures, Prog. Mater. Sci. 13 (1967) 325. [14] I.M. Lifshitz, V.V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19 (1961) 35.