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Internal stress superplasticity in the NiAl–Mo eutectic alloy
Acta mater. 49 (2001) 1717–1724 www.elsevier.com/locate/actamat
INTERNAL STRESS SUPERPLASTICITY IN THE NiAl–Mo EUTECTIC ALLOY R. S. SUNDAR†, K. KITAZONO, E. SATO‡ and K. KURIBAYASHI The Institute of Space and Astronautical Science, Sagamihara, Kanagawa 229-8510, Japan ( Received 6 September 2000; received in revised form 16 February 2001; accepted 16 February 2001 )
Abstract—Internal stress superplasticity (ISS) in a NiAl–Mo based eutectic alloy was investigated by conducting thermal cycling creep tests. The alloy was annealed at high temperatures to spheroidize the refractory metal phase. Under thermal cycling creep conditions, the alloy exhibited characteristics of ISS, that is, at low stresses, the thermal cycling creep rates were much higher than the isothermal creep rates and the corresponding stress exponent was close to 1. These results were compared quantitatively with the predictions of a theoretical model of ISS. The experimental thermal cycling creep rates agreed with the predicted values within an error less than one order of magnitude. Superplastic elongation of >200% without fracture was attained during a thermal cycling tensile creep test. 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Intermetallic; Composites; Creep; Internal stress superplasticity
1. INTRODUCTION
NiAl based intermetallics are attractive candidates for high temperature structural applications because of their high melting point, low density, good thermal conductivity and good oxidation resistance [1, 2]. However, poor damage tolerance at ambient temperatures and inadequate strength at high temperatures have prevented their commercial applications. Among several attempts to improve the above properties through alloying and thermomechanical processing [1, 2], it was recently shown that two-phase NiAl– Cr/Mo based eutectic alloys [3–5] have better fracture toughness and higher creep resistance than binary NiAl. Fracture toughness of polycrystalline NiAl is 5–6 MPa m1/2 [6, 7], while that of the NiAl–Cr/Mo eutectic alloys is 15–20 MPa m1/2 [3, 8, 9]. The extrinsic toughening mechanisms like crack trapping, crack deflection, interface debonding and crack bridging are responsible for the improvement in toughness. When compared to NiAl, the improvement in creep strength (in terms of stress required to produce a creep rate of 10⫺6 s⫺1 at 1300K) in the NiAl–Mo alloy is nearly two-fold, while that in NiAl–Cr is more than five-fold [9]. The presence of a semi-coherent interface between the constituent phases (NiAl † Present address: Chrysalis Technologies Incorporated, Richmond, VA 23234, USA. ‡ To whom all correspondence should be addressed. Tel.: +81-42-759-8263; Fax: +81-42-759-8461. E-mail address: [email protected] (E. Sato)
and refractory metal phase) and the fine nature of the eutectic mixture are reasons for improvement in the high temperature deformation resistance. In addition, since the refractory metal phase is thermodynamically in equilibrium with the matrix, these materials have good microstructural stability at high temperatures. Successful application of any new material requires identification of processing routes, which can produce defect free material in a required shape at a competitive cost. Forming NiAl eutectic alloys and other intermetallic alloys by internal stress superplasticity (ISS) is promising, as these materials are difficult to form through conventional processing routes. Furthermore, in view of their high temperature applications, processing intermetallics through ISS is attractive, since it does not require a fine grain size as in conventional superplastic forming. ISS is defined as the ability of a material to undergo large deformation in a viscous manner under the simultaneous application of a small applied stress and thermal cycling [10]. Under these conditions, the material experiences high internal stresses and deforms with an average strain rate which is linearly proportional to the applied stress. The corresponding deformation rate is much faster than the isothermal creep rate at a corresponding equivalent temperature. Depending on the means of internal stress generation, ISS can be broadly classified into three groups, namely transformation superplasticity, composite coefficients of thermal expansion (CTE)-mismatch superplasticity and anisotropic CTE-mismatch super-
1359-6454/01/$20.00 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 0 1 ) 0 0 0 8 8 - X
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plasticity. Transformation superplasticity has been reported in metallic materials [11–14], that undergo phase transformation during thermal cycling. The internal stress is generated in the material due to transformation mismatch strain between the parent and the product phase. On the other hand, composite CTE-mismatch superplasticity has been reported in dual phase materials such as metal matrix composites [14, 15], eutectic alloys [16, 17] and superalloys [18], where the difference in CTEs of the constituent phases is responsible for the generation of internal stresses. Anisotropic CTE-mismatch superplasticity has been reported in metals like a-U and Zn [19–21] which exhibit anisotropic thermal expansion behavior. Here, internal stress is generated in the material due to anisotropic thermal expansion behavior of adjacent grains. Transformation superplasticity in intermetallicbased alloys has been reported in super a2-alloy [22] and NiAl/ZrO2 composite [23]. Exploring the possibility of forming intermetallic based alloys via composite CTE-mismatch superplasticity is important since most of the promising intermetallic based alloys are duel phase materials [3–5]. Recently we have studied the thermal cycling creep behavior of NiAl– Cr eutectic alloy [24]. In that paper, although linear creep behavior during thermal cycling was demonstrated, the superplastic tensile elongation was not examined. In addition, the volume fraction of Cr particles (32%) is too large to apply rigorously a CTEmismatch superplasticity model [25]. In this paper, we have explored the possibilities of forming NiAl– Mo eutectic alloys via ISS. A detailed analysis based on the theoretical model is also performed for this material with a Mo volume fraction of 9%.
roidize the Mo phase in the eutectic mixture. Metallographic examinations were made in the as-cast and heat-treated samples [Figs 1(a) and (b)], after etching with a solution containing 10% HNO3+10% HF+80% H2O with a scanning electron microscope. The particle size and volume fraction of phases present in the alloy after heat treatment were estimated through image analysis. 2.2. Creep tests Hollow cylindrical compression samples, of 10 mm outer diameter, 8 mm inner diameter and 15 mm in length, were machined from the heat treated blocks by electro-discharge machining. Hollow compression samples are favored for thermal cycling creep experiments to minimize the difference in temperature and in heating and cooling rate between the surface and interior of the samples. Compression creep tests under thermal cycling and isothermal conditions were performed in a servo-hydraulic testing machine equipped with an induction heating facility. In order to minimize oxidation of the samples, all the creep experiments
2. EXPERIMENTAL
2.1. Materials The NiAl–Mo alloy was prepared by consumable electrode arc melting of the high purity elemental metals. The composition of the alloys was Ni–46at.% Al–9at.% Mo. Impurity levels in the alloy were Fe 0.01at.%, Si 0.02at.%, O 0.003at.%, Co 0.007at.% and Cu 0.001at.%. The microstructure of the alloy in the as-cast condition consisted of primary NiAl and fine fibrous eutectic mixture. The diffusional accommodation around the second phase is important to achieve large elongation. It has been shown [17] that diffusional accommodation around the precipitate during thermal cycling is much easier for a globular structure than for elongated particles. Hence, the alloy was heat-treated to spheroidize the eutectic Mo phase. Since the microstructure of NiAl–Mo alloy is quite stable against spheroidization, it requires static annealing after forging to break down the fibrous structure [26]. However, in the present study, a high temperature and long time heat treatment was given at 1848 K for 360 ks under an Ar atmosphere to sphe-
Fig. 1. Scanning electron micrographs of the NiAl-Mo alloy: (a) as-cast condition exhibiting a primary NiAl and eutectic mixture of the NiAl and Mo phases; and (b) after spheroidization heat-treatment at 1848K for 360 ks. The heat treatment was successful in converting the morphology of the Mo phase from fibrous to globular.
SUNDAR et al.: INTERNAL STRESS SUPERPLASTICITY
were performed in a vacuum evacuated by a rotary pump. The specimens were heated by a high frequency induction coil and cooled naturally. The temperature of the sample was controlled through a Rtype thermocouple, which was spot-welded on the surface. The maximum controlling error, which occurred at points where heating was reversed to cooling, was ±3K. Thermal cycling creep tests were performed mainly in the temperature range of 1248–1448 K and over a range of stress levels. In all the above experiments, the temperature profile was triangular wave similar to that shown in Fig. 2 of Ref. [16], and the temperature amplitude and heating/cooling rates of thermal cycling were fixed at 200 K and 10 K/s, respectively. The triangular wave, without isothermal holding, is preferred to eliminate thermal ratcheting effects [27], which occur during the isothermal holding at the maximum temperature. The thermal cycling creep rates were measured after sufficient periods to reach steady state conditions. On average, it took between 1.5 and 2 h, that is, 150–200 cycles, under low applied stresses, and between a quarter and a half hour, that is, 25–50 cycles, under high applied stresses. To compare the thermal cycling creep behavior with the isothermal creep behavior, the equivalent temperature, Teq, of the triangular wave is defined as [16]:
冉
冊
Q 1 exp ⫺ = nRTeq Tmax⫺Tmin
冕 冉 冊
Tmax
exp ⫺
Q dT, nRT
Tmin
(1)
where Tmax and Tmin are the maximum and minimum temperatures during thermal cycling, n and Q are the stress exponent and the apparent activation energy for steady state creep under isothermal condition, respectively. The equivalent temperature, Teq, for the 1248–1448K thermal cycling is calculated as 1350K, using Q = 297 kJ/mol and n = 7.0 which are reported in Section 3.2. The isothermal creep experiments were carried out at 1348K, which is close to Teq above. A tensile creep test was performed to confirm the ability of the material to undergo large elongation under thermal cycling conditions. Tensile samples of 9 mm diameter and 15 mm gauge length were machined from the heat-treated ingot. In order to achieve large elongation in reasonable time, the tensile thermal cycling creep test was done at high temperature range namely, 1323–1523K in a vacuum evacuated by a rotary pump. The temperature profile was triangular waveform and having a heating and cooling rate of 10K/s. During testing, temperature of the sample was monitored through three R-type thermocouples, which were spot-welded at the center and the
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two shoulders of the specimen. Due to the large size of the specimen, the maximum controlling error was ±10K. For comparison, an isothermal tensile creep test was done at 1523K. Additional compressive thermal cycling creep experiments were performed at a constant stress level of 15 MPa, with a fixed heating and cooling rate of 10K/s, at a fixed equivalent temperature of 1350K and with different temperature amplitudes of 150, 200, 250, 300 and 350K. The temperature ranges of 1274– 1424, 1248–1448, 1222–1472, 1196–1496 and 1169– 1519K were selected in such a way that the corresponding equivalent temperature was equal to 1350K. 3. RESULTS
3.1. Microstructure The alloy studied in the present investigation was hypoeutectic and contained fine fibrous eutectic mixture and primary NiAl phase in the as-cast condition (Fig. 1(a)). The microstructure of the heat-treated alloy is shown in Fig. 1(b). Annealing at 1848K for 360 ks spheroidized most of the Mo fibers in the eutectic mixture. The volume fraction of primary NiAl phase, F, was estimated to be equal to 12.4% and that of the Mo phase 9.7%. The Mo particles were seen at the grain boundaries and inside the grains, whose volume fraction ratio was estimated to be 1:12 through microstructural observations. Since the internal stress generated by particles at the grain boundaries is easily accommodated by fast grain boundary diffusion [16], only the volume fraction of the Mo particles within the grain, f=8.9%, is considered for theoretical calculation. The average size of Mo particles inside the grain was 1.5 µm. During thermal cycling, the primary NiAl phase at 18 µm acts as a non-deforming particle embedded in a superplastically-deforming eutectic matrix. The average matrix grain size of the alloy was 120 µm, which is too large for conventional fine grain superplasticity. 3.2. Isothermal creep behavior The isothermal creep results at 1348K are presented in Fig. 2. Here, the strain rate is plotted against stress on a double logarithmic scale. The stress exponent for steady state creep is about 7, which indicates the operation of a dislocation creep mechanism. Creep behavior of NiAl–Mo alloy in the literature is limited to that of directionally-solidified alloy at 1300K, which shows a stress exponent (about 6) close to our data [9]. Direct comparison of creep rates is not valid since their alloy shows much better creep resistance than ours due to the directionallysolidified microstructure. Single deformation behavior for a wide range of temperature in these NiAl–Mo alloys is reasonably considered to be similar to that of coarse grain NiAl alloy but differently to that in ODS NiAl alloy [28]. The values of the stress exponents in these NiAl–Mo alloys are slightly
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Fig. 2. Stress dependence of steady state isothermal creep rate of the NiAl-Mo alloy at 1248K with the same scale as Fig. 4.
Fig. 3. Arrhenius plot showing the temperature dependence of the steady state isothermal creep rate of the NiAl-Mo alloy.
larger than that of the coarse grain NiAl alloy, 4.5 [28], possibly because of the interaction between the Mo phases and the dislocations. The activation energy under isothermal conditions is estimated through a temperature change test at a fixed stress of 33 MPa. The strain rate is plotted against 1/RT in a semi-logarithmic graph (Fig. 3), where R is the universal gas constant. From the slope of the line the activation energy for isothermal creep rate is estimated to be 297 kJ/mol, which matches well with the activation energy for lattice diffusion of Ni in NiAl, 308 kJ/mol [29]. 3.3. Thermal cycling creep behavior Thermal cycling creep results are presented in Fig. 4. For comparison, the estimated isothermal creep
Fig. 4. Thermal cycling creep rates as a function of applied stress in the NiAl-Mo alloy. The temperature was cycled between 1248 and 1448K. Estimated isothermal creep rate at 1350K which corresponds to the equivalent temperature is also shown for comparison. The broken line shows theoretical values calculated using equations (3) and (5).
rates at the equivalent temperature, 1350K, using the data at 1348K and Q = 297 kJ/mol, is also shown in the figure. At low stresses, thermal cycling creep rates are several orders of magnitude higher than those of the isothermal creep rates. Moreover, the stress exponent value at the low stress level is close to 1. This region is considered to be an ISS region. With increasing stress, the stress exponent value for the thermal cycling creep tends to depart from 1. The above trend agrees well with other studies [14–18] of composite CTE-mismatch superplasticity. A tensile creep experiment was performed under the thermal cycling condition of 1323–1523K. By assuming uniform deformation and constant volume
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during the deformation, a constant stress of 10 MPa was maintained on the specimen by adjusting the load. The test was stopped when the controlling thermocouples at the shoulders of the sample were moved out of the heating zone. The average strain rate during the above tensile test was 10⫺5 s⫺1. For comparison, a tensile creep test under an isothermal condition was done at 1523K at the same strain rate (stress level of 27 MPa). Photographs of the specimen (a) undeformed, (b) deformed under thermal cycling condition and (c) deformed under isothermal conditions are shown in Fig. 5. Under the thermal cycling condition, elongation close to 210% was achieved without fracture. The specimen showed a shallow necking, which was formed due to the difference in temperature between the center and edges of the specimen. On the other hand, the sample deformed under the isothermal condition developed a neck after 20% elongation and ultimately the sample failed at 60% elongation. After the tests, the tensile samples were sectioned parallel to the tensile axis and observed under an optical microscope. The sample deformed under isothermal conditions exhibits large cavities below the fracture surface [Fig. 6(a)]. In general, cavities were observed at or near the grain boundaries. On the other hand, any cavities were not found in the sample deformed under the thermal cycling creep condition [Fig. 6(b)]. The above result indicates the beneficial effect of thermal cycling in achieving large elongation without developing cavities. The temperature amplitude dependence of ISS was studied by carrying out thermal cycling creep tests at a constant stress level and equivalent temperature. The result is shown in Fig. 7. For comparison purposes, the isothermal creep rate, which corresponds to zero temperature amplitude is also included in the figure. The results clearly show that the larger the temperature amplitude, the higher the strain rate of ISS is.
Fig. 5. Photograph of the tensile creep tested samples: (a) undeformed condition; (b) after thermal cycling creep at 13231523K under a stress of 10 MPa; and (c) after isothermal creep at 1523K under a stress of 27 MPa. Total elongation of 210% was recorded under thermal cycling condition without fracture (b), while the isothermal tested sample failed after 60% of deformation (c).
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Fig. 6. Optical micrographs of gauge sections of the deformed tensile samples: (a) deformed under isothermal condition (area near the fracture surface); and (b) deformed under thermally cycling creep condition. Large cavities are present in the isothermally tested sample (a), while in the sample tested under thermal cycling conditions, even after a large elongation, apparent cavities are not present (b).
Fig. 7. Effect of temperature amplitude on the thermal cycling creep rate. The test was carried out at a stress level of 15 MPa and the heating and cooling rates were fixed at 10 K/s. The solid line is the curve fitted using equation (7).
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SUNDAR et al.: INTERNAL STRESS SUPERPLASTICITY 4. DISCUSSION
The thermal cycling strain rates of NiAl–Mo alloy at low stresses are higher (more than several orders of magnitude) than the isothermal creep rates. As the stress increases, the thermal cycling creep rate increases at a rate faster than the linear behavior and approaches the isothermal creep rates. These results imply that enhancement of creep rate by thermal cycling takes place at low stress levels, where the internal stress caused by the difference in thermal expansion of the constituent phases are relatively larger than the applied stress. Based on micromechanics, Sato and Kuribayashi [25] proposed a quantitative model for ISS in a creeping matrix with rigid inclusions. Although there is another qualitative model of ISS [20] available in the literature, the above model is very attractive, as it does not need any fitting parameters for predicting the thermal cycling strain rate from the isothermal creep rate equation. The above model has been shown to predict thermal cycling creep behavior of Al alloys and Ti matrix composites [14, 16, 17]. In this section, first, we will briefly outline the model and then will compare the theoretical predictions and the experimental results. In the model [25], it is assumed that the material consists of a matrix, uniformly dispersed with spherical inclusions of radius a and volume fraction f, with a difference in thermal expansion coefficient of ⌬a. During thermal cycling, while the inclusion is treated as elastic, the matrix deforms by power law creep of the form: ⑀˙ = Bsn
(2)
where ⑀˙ , B and s are steady state creep rate, temperature dependent constant and stress, respectively. Here, the effect of the interaction between the inclusions and dislocations are included in equation (2), that is, equation (2) does not express the deformation behavior of the monolithic matrix material. Though this treatment is not rigorous, the model is able to treat only two factors: deformation behavior of the matrix and the strain mismatch effect, and the former consists of the deformation of the monolithic matrix and inclusion–dislocation interaction. When the material is subjected to a temperature change with a rate T˙ and if the inclusion is not restrained by the matrix, the inclusion would dilate (or shrink) isotropically against the matrix with a strain rate of ⌬aT˙. This volumetric strain cannot be accommodated by the fast interface diffusion between the matrix and the inclusions. It can be accommodated by the volume diffusion in the matrix, though its rate is, in normal cases, negligibly slow (the relaxation time is calculated as 9.5 s, see Appendix A). Therefore, it must be accommodated by a heterogeneous plastic flow of the matrix (plastic
accommodation). On the other hand, the strain mismatch caused by macroscopic flow of the matrix due to the applied stress, which has only a shear component, can be accommodated by fast interface diffusion (the relaxation time is calculated as 0.70 s, see Appendix A). When these two accommodation processes, plastic accommodation for volumetric strain mismatch and interface diffusion for shear strain mismatch, take place, simultaneously, a quasi-steady state is achieved where the stress and the strain rate distributions remain unchanged except the change caused by isothermal creep rate due to the temperature change. Using the above analysis [25], the volume averaged uniaxial strain rate during thermal cycling under an applied stress sA is given by: ⑀¯˙model = |⌬aT˙|1⫺1/n
B1/n 2n(n + 4) 1⫺f1/n s , (low sA) 1⫺f 21/n5 (1⫺f)f1/n A (3)
and ⑀¯˙model =
B sn (high sA) (1⫺f)n A
(4)
The model predicts that under an applied stress much higher than the internal stress, the thermal cycling creep rate coincides with the isothermal creep rate [equation (4)] and at low stresses, it is proportional to the applied stress [equation (3)]. Under typical ISS conditions, that is, at low applied stresses during thermal cycling, the primary NiAl phase deforms with slower strain rate than the eutectic NiAl–Mo phase with volume fraction 12.4%. For example, under 5 MPa at 1350K, coarse grain pure NiAl is estimated to deform below 1×10⫺7 s⫺1 [28]. The present material is, therefore, considered to be a composite consisting of a superplastically deforming eutectic mixture with a stress exponent of 1 and nondeforming NiAl particles. In this configuration also, the thermal strain mismatch arises during thermal cycling creep, but in the matrix with a stress exponent of 1, ISS is not generated. In deriving equation (3), we use the non-linearity of equation (1), that is, n>1. On the other hand, the strain mismatch caused by the macroscopic flow of the eutectic matrix cannot be accommodated by interface diffusion around the NiAl particles since the particle size of 18 µm results in the negligible accommodation rate. In this case, the strengthening effect through load transfer to the particles takes place, which has been analyzed extensively by the sear-lag model [30], the self-consistent potential method [31] and FEM [32]. In the present case, since the eutectic matrix deforms with a stress exponent of 1, a simple analysis using elastic analogy is rigorously applicable and the reduced creep rate of
SUNDAR et al.: INTERNAL STRESS SUPERPLASTICITY
the material, ⑀¯˙th, from that of the eutectic matrix, ⑀¯˙model, is given by the following formula [33]: ⑀¯˙th =
1⫺F ⑀¯˙ . 1⫺F + F/S∗ model
(5)
Here S∗ has a value of 2/5 for non-elongated particle, and F denotes the particle volume fraction. The theoretical prediction by equations (3) and (5) for the present alloy is shown in Fig. 4 as a broken line. The following values are utilized for the calculation: F = 0.124, f = 0.089, n = 7.0, B = 2.8×10⫺17 MPa⫺7s⫺1 (from Fig. 4) and ⌬a = 9.3×10⫺6 K⫺1. The value of ⌬a is calculated using aNiAl = 15.1×10⫺6K⫺1 at 1100–1800K [1] and aMo = 5.8×10⫺6 K⫺1 at 1273K [34]. The power law equation of n = 7 for the matrix deformation under the thermal cycling condition at low applied stresses is justified because the equivalent stresses in the matrix during thermal cycling is so high that they are in the power law creep region (see Appendix B in Ref. [16]). The theoretical creep rates are within one order of magnitude of the experimental creep rates. The theoretical model treats only the quasi-steady state during heating and cooling, but in actual experiment, a stationary internal stress distribution is achieved after a certain period after each temperature reversal [16]. Therefore, the experimental strain rate cannot exceed the theoretical prediction and the difference becomes larger with small temperature amplitude, as clearly shown in Fig. 7. Assuming that all the difference between the experimental and theoretical creep rates is caused by the transient phenomena, the above data are analyzed by the following equation: ⑀¯˙∗ = ⑀˙ iso + (⑀¯˙th⫺⑀˙ iso)[1⫺exp(⫺C|T˙ |t)].
(6)
The above equation considers that the instantaneous strain rate ⑀˙ ∗ increases exponentially with time t after each temperature reversal with a constant C, from the isothermal creep rate ⑀˙ iso to that of theoretical stationary creep rate ⑀¯˙th predicted by the micro-mechanics model [equation (5)]. The average strain rate during thermal cycling in the temperature range is ⌬T then given by:
冕
⌬T
1 1 (⑀¯˙ ⫺⑀˙ )[1 ⑀˙ ∗d(|T˙ |t)⬇⑀¯˙th⫺ ⑀¯˙ = ⌬T C⌬T th iso 0
(7)
⫺exp(⫺C⌬T)].
The solid line in Fig. 7 is the fitted curve of the above equation with 1/C⬇410K⫺1. It indicates that after each temperature reversal, the quasi-steady state stress and strain rate distributions are achieved in a transient time, (C|T˙ |)⫺1, of 41 s.
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5. SUMMARY
ISS in NiAl–Mo alloy was investigated by conducting thermal cycling creep experiments. At low stress levels, the thermal cycling creep rates were much higher than the isothermal creep rates and the corresponding stress exponent in this region was close to 1. This region is identified as an ISS region. At high stress levels, the thermal cycling creep rates were close to the isothermal creep rates. Superplastic elongation of >200% was achieved during a tensile creep test in the superplastic region. The present result was compared with the prediction of a micromechanics model and the experimental creep rates in the ISS region were found to be within one order of magnitude of the model prediction. REFERENCES 1. Miracle, D. B. and Darolia, R., in Intermetallic Compounds: Vol. 2, Practice, eds. J. H. Westbrook and R. L. Fleischer. John Wiley & Sons, New York, 1994, p. 53. 2. Noebe, R. D., Bowman, R. R. and Nathal, M. V., Int. Mater. Rev., 1993, 38, 193. 3. Johnson, D. R., Chen, X. F., Oliver, B. F., Noebe, R. D. and Whittenberger, J. D., Intermetallics, 1995, 3, 99. 4. Misra, A., Wu, Z. L., Kush, M. T. and Gibala, R., Mater. Sci. Engng, 1997, A239/240, 75. 5. Johnson, D. R., Joslin, S. M., Reviere, R. D., Oliver, B. F. and Noebe, R. D., in Processing and Fabrication of Advanced Materials for High Temperature Applications– II, eds. V. A. Ravi and T. S. Srivatsan. TMS, Warrendale, 1993, p. 77. 6. Reuss, S. and Vehoff, H., Scripta metall., 1990, 24, 1021. 7. Lewandowski, J. J., Michal, G. M., Locci, I. and Rigney, J. D., MRS Symp. Proc., 1990, 341, 1. 8. Heredia, F. E., He, M. Y., Lucas, G. E., Evans, A. G., Deve, H. E. and Konitzer, D., Acta. metall., 1993, 41, 505. 9. Johnson, D. R., Oliver, B. F., Noebe, R. D. and Whittenberger, J. D., Intermetallics, 1995, 3, 493. 10. Sherby, O. D. and Wadsworth, J., Mater. Sci. Technol., 1985, 1, 925. 11. de Jong, M. and Rathenau, G. W., Acta metall., 1961, 9, 714. 12. Greenwood, G. W. and Johnson, R. H., Proc. R. Soc. London, 1965, 283A, 403. 13. Zwigl, P. and Dunand, D. C., Metall. Trans., 1998, 29A, 565. 14. Dunand, D. C. and Bedell, C. M., Acta metall., 1996, 44, 1063. 15. Wu, M. Y. and Sherby, O. D., Scripta Metall., 1984, 18, 773. 16. Kitazono, K. and Sato, E., Acta mater., 1998, 46, 207. 17. Kitazono, K. and Sato, E., Acta mater., 1999, 47, 135. 18. Kitazono, K., Sato, E. and Kuribayashi, K., Scripta mater., 1999, 41, 263. 19. Lobb, R. C., Sykes, E. C. and Johnson, R. H., Metal Sci. J., 1972, 6, 33. 20. Wu, M. Y., Wadsworth, J. and Sherby, O. D., Metall. Trans., 1987, 18A, 451. 21. Kitazono, K., Hirasaka, R., Sato, E., Kuribayashi, K. and Motegi, T., Acta mater., 2001, 49, 473. 22. Schuh, C. and Dunand, D. C., Acta. mater., 1998, 46, 5663. 23. Zwigl, P. and Dunand, D. C., in Superplasticity and Superplastic Forming 1998, supplemental volume, eds. A. K. Ghosh and T. R. Bieler. TMS, Warrendale, 1998, p. 40. 24. Sundar, R. S., Kitazono, K., Sato, E. and Kuribayashi, K., Intermetallics, 2001, 9, 279. 25. Sato, E. and Kuribayashi, K., Acta metall. mater, 1993, 41, 1759.
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APPENDIX A
The relaxation times for the two kinds of diffusional accommodation are calculated in order to confirm that in the present experimental condition, the volumetric strain mismatch (thermal expansion) is not accommodated by volume diffusion but is accommodated by plastic accommodation, and the shear strain mismatch (matrix flow) is accommodated by interface diffusion. They are given by: 4a3kT 1 8⫺10n∗ + = 0.70 s, ti = 2 ∗ 3p Didq G G(7⫺5n) (A1)
(interface diffusion [35]) kTa2 (G∗(1 + n)) + (2G(2⫺2n∗)) = 9.5 s, tv = 4Dvq GG∗(1 + n∗) (A2)
(volume diffusion [36]) where Di, Dv, n, n∗, G, G∗, q, d, k and a are the interface diffusion constant, the volume diffusion constant, the Poisson ratios of the matrix and the inclusion, the shear moduli of the matrix and the inclusion, atomic volume of NiAl, interface thickness, Boltzman’s constant and the radius of the inclusion, respectively. The following values are used for the above calculations: Dv = 4.46×10⫺4exp((⫺308 ⫺16 kJ/mol)/(RT)) = 4.92×10 m2/s [29], Di = Dgb (from Coble creep) = 1.9×10⫺6exp((⫺143 kJ/mol)/ (RT)) = 5.44×10⫺12 m2/s [28], n = 0.307 + 2.15× 10⫺5T = 0.336 [1], n∗ = 0.362 [28], G = 5.68×1010 Pa [1], G∗ = 9.69×1010 Pa [37], a = 0.75×10⫺6 m, q = 1.2×10⫺29 m3 [28], d = 2b; where b is Burgers vector (2.9×10⫺10 m). When the creep of the material is limited by relaxation kinetics caused by interface diffusion around spherical inclusions under uniaxial stress, the steady state creep rate is given by [38]: ⑀˙ =
5(1⫺n) 2tiG(7⫺5n)
(A3)
The relaxation limited creep is calculated as 3.9×10⫺2 s⫺1 at a stress of 5 MPa, which is far greater than that of the isothermal creep rate (2.1×10⫺12 s⫺1) and the thermal cycling creep rate (2.0×10⫺6 s⫺1) (Fig. 4).
INTERNAL STRESS SUPERPLASTICITY IN THE NiAl–Mo EUTECTIC ALLOY R. S. SUNDAR†, K. KITAZONO, E. SATO‡ and K. KURIBAYASHI The Institute of Space and Astronautical Science, Sagamihara, Kanagawa 229-8510, Japan ( Received 6 September 2000; received in revised form 16 February 2001; accepted 16 February 2001 )
Abstract—Internal stress superplasticity (ISS) in a NiAl–Mo based eutectic alloy was investigated by conducting thermal cycling creep tests. The alloy was annealed at high temperatures to spheroidize the refractory metal phase. Under thermal cycling creep conditions, the alloy exhibited characteristics of ISS, that is, at low stresses, the thermal cycling creep rates were much higher than the isothermal creep rates and the corresponding stress exponent was close to 1. These results were compared quantitatively with the predictions of a theoretical model of ISS. The experimental thermal cycling creep rates agreed with the predicted values within an error less than one order of magnitude. Superplastic elongation of >200% without fracture was attained during a thermal cycling tensile creep test. 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Intermetallic; Composites; Creep; Internal stress superplasticity
1. INTRODUCTION
NiAl based intermetallics are attractive candidates for high temperature structural applications because of their high melting point, low density, good thermal conductivity and good oxidation resistance [1, 2]. However, poor damage tolerance at ambient temperatures and inadequate strength at high temperatures have prevented their commercial applications. Among several attempts to improve the above properties through alloying and thermomechanical processing [1, 2], it was recently shown that two-phase NiAl– Cr/Mo based eutectic alloys [3–5] have better fracture toughness and higher creep resistance than binary NiAl. Fracture toughness of polycrystalline NiAl is 5–6 MPa m1/2 [6, 7], while that of the NiAl–Cr/Mo eutectic alloys is 15–20 MPa m1/2 [3, 8, 9]. The extrinsic toughening mechanisms like crack trapping, crack deflection, interface debonding and crack bridging are responsible for the improvement in toughness. When compared to NiAl, the improvement in creep strength (in terms of stress required to produce a creep rate of 10⫺6 s⫺1 at 1300K) in the NiAl–Mo alloy is nearly two-fold, while that in NiAl–Cr is more than five-fold [9]. The presence of a semi-coherent interface between the constituent phases (NiAl † Present address: Chrysalis Technologies Incorporated, Richmond, VA 23234, USA. ‡ To whom all correspondence should be addressed. Tel.: +81-42-759-8263; Fax: +81-42-759-8461. E-mail address: [email protected] (E. Sato)
and refractory metal phase) and the fine nature of the eutectic mixture are reasons for improvement in the high temperature deformation resistance. In addition, since the refractory metal phase is thermodynamically in equilibrium with the matrix, these materials have good microstructural stability at high temperatures. Successful application of any new material requires identification of processing routes, which can produce defect free material in a required shape at a competitive cost. Forming NiAl eutectic alloys and other intermetallic alloys by internal stress superplasticity (ISS) is promising, as these materials are difficult to form through conventional processing routes. Furthermore, in view of their high temperature applications, processing intermetallics through ISS is attractive, since it does not require a fine grain size as in conventional superplastic forming. ISS is defined as the ability of a material to undergo large deformation in a viscous manner under the simultaneous application of a small applied stress and thermal cycling [10]. Under these conditions, the material experiences high internal stresses and deforms with an average strain rate which is linearly proportional to the applied stress. The corresponding deformation rate is much faster than the isothermal creep rate at a corresponding equivalent temperature. Depending on the means of internal stress generation, ISS can be broadly classified into three groups, namely transformation superplasticity, composite coefficients of thermal expansion (CTE)-mismatch superplasticity and anisotropic CTE-mismatch super-
1359-6454/01/$20.00 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 0 1 ) 0 0 0 8 8 - X
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plasticity. Transformation superplasticity has been reported in metallic materials [11–14], that undergo phase transformation during thermal cycling. The internal stress is generated in the material due to transformation mismatch strain between the parent and the product phase. On the other hand, composite CTE-mismatch superplasticity has been reported in dual phase materials such as metal matrix composites [14, 15], eutectic alloys [16, 17] and superalloys [18], where the difference in CTEs of the constituent phases is responsible for the generation of internal stresses. Anisotropic CTE-mismatch superplasticity has been reported in metals like a-U and Zn [19–21] which exhibit anisotropic thermal expansion behavior. Here, internal stress is generated in the material due to anisotropic thermal expansion behavior of adjacent grains. Transformation superplasticity in intermetallicbased alloys has been reported in super a2-alloy [22] and NiAl/ZrO2 composite [23]. Exploring the possibility of forming intermetallic based alloys via composite CTE-mismatch superplasticity is important since most of the promising intermetallic based alloys are duel phase materials [3–5]. Recently we have studied the thermal cycling creep behavior of NiAl– Cr eutectic alloy [24]. In that paper, although linear creep behavior during thermal cycling was demonstrated, the superplastic tensile elongation was not examined. In addition, the volume fraction of Cr particles (32%) is too large to apply rigorously a CTEmismatch superplasticity model [25]. In this paper, we have explored the possibilities of forming NiAl– Mo eutectic alloys via ISS. A detailed analysis based on the theoretical model is also performed for this material with a Mo volume fraction of 9%.
roidize the Mo phase in the eutectic mixture. Metallographic examinations were made in the as-cast and heat-treated samples [Figs 1(a) and (b)], after etching with a solution containing 10% HNO3+10% HF+80% H2O with a scanning electron microscope. The particle size and volume fraction of phases present in the alloy after heat treatment were estimated through image analysis. 2.2. Creep tests Hollow cylindrical compression samples, of 10 mm outer diameter, 8 mm inner diameter and 15 mm in length, were machined from the heat treated blocks by electro-discharge machining. Hollow compression samples are favored for thermal cycling creep experiments to minimize the difference in temperature and in heating and cooling rate between the surface and interior of the samples. Compression creep tests under thermal cycling and isothermal conditions were performed in a servo-hydraulic testing machine equipped with an induction heating facility. In order to minimize oxidation of the samples, all the creep experiments
2. EXPERIMENTAL
2.1. Materials The NiAl–Mo alloy was prepared by consumable electrode arc melting of the high purity elemental metals. The composition of the alloys was Ni–46at.% Al–9at.% Mo. Impurity levels in the alloy were Fe 0.01at.%, Si 0.02at.%, O 0.003at.%, Co 0.007at.% and Cu 0.001at.%. The microstructure of the alloy in the as-cast condition consisted of primary NiAl and fine fibrous eutectic mixture. The diffusional accommodation around the second phase is important to achieve large elongation. It has been shown [17] that diffusional accommodation around the precipitate during thermal cycling is much easier for a globular structure than for elongated particles. Hence, the alloy was heat-treated to spheroidize the eutectic Mo phase. Since the microstructure of NiAl–Mo alloy is quite stable against spheroidization, it requires static annealing after forging to break down the fibrous structure [26]. However, in the present study, a high temperature and long time heat treatment was given at 1848 K for 360 ks under an Ar atmosphere to sphe-
Fig. 1. Scanning electron micrographs of the NiAl-Mo alloy: (a) as-cast condition exhibiting a primary NiAl and eutectic mixture of the NiAl and Mo phases; and (b) after spheroidization heat-treatment at 1848K for 360 ks. The heat treatment was successful in converting the morphology of the Mo phase from fibrous to globular.
SUNDAR et al.: INTERNAL STRESS SUPERPLASTICITY
were performed in a vacuum evacuated by a rotary pump. The specimens were heated by a high frequency induction coil and cooled naturally. The temperature of the sample was controlled through a Rtype thermocouple, which was spot-welded on the surface. The maximum controlling error, which occurred at points where heating was reversed to cooling, was ±3K. Thermal cycling creep tests were performed mainly in the temperature range of 1248–1448 K and over a range of stress levels. In all the above experiments, the temperature profile was triangular wave similar to that shown in Fig. 2 of Ref. [16], and the temperature amplitude and heating/cooling rates of thermal cycling were fixed at 200 K and 10 K/s, respectively. The triangular wave, without isothermal holding, is preferred to eliminate thermal ratcheting effects [27], which occur during the isothermal holding at the maximum temperature. The thermal cycling creep rates were measured after sufficient periods to reach steady state conditions. On average, it took between 1.5 and 2 h, that is, 150–200 cycles, under low applied stresses, and between a quarter and a half hour, that is, 25–50 cycles, under high applied stresses. To compare the thermal cycling creep behavior with the isothermal creep behavior, the equivalent temperature, Teq, of the triangular wave is defined as [16]:
冉
冊
Q 1 exp ⫺ = nRTeq Tmax⫺Tmin
冕 冉 冊
Tmax
exp ⫺
Q dT, nRT
Tmin
(1)
where Tmax and Tmin are the maximum and minimum temperatures during thermal cycling, n and Q are the stress exponent and the apparent activation energy for steady state creep under isothermal condition, respectively. The equivalent temperature, Teq, for the 1248–1448K thermal cycling is calculated as 1350K, using Q = 297 kJ/mol and n = 7.0 which are reported in Section 3.2. The isothermal creep experiments were carried out at 1348K, which is close to Teq above. A tensile creep test was performed to confirm the ability of the material to undergo large elongation under thermal cycling conditions. Tensile samples of 9 mm diameter and 15 mm gauge length were machined from the heat-treated ingot. In order to achieve large elongation in reasonable time, the tensile thermal cycling creep test was done at high temperature range namely, 1323–1523K in a vacuum evacuated by a rotary pump. The temperature profile was triangular waveform and having a heating and cooling rate of 10K/s. During testing, temperature of the sample was monitored through three R-type thermocouples, which were spot-welded at the center and the
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two shoulders of the specimen. Due to the large size of the specimen, the maximum controlling error was ±10K. For comparison, an isothermal tensile creep test was done at 1523K. Additional compressive thermal cycling creep experiments were performed at a constant stress level of 15 MPa, with a fixed heating and cooling rate of 10K/s, at a fixed equivalent temperature of 1350K and with different temperature amplitudes of 150, 200, 250, 300 and 350K. The temperature ranges of 1274– 1424, 1248–1448, 1222–1472, 1196–1496 and 1169– 1519K were selected in such a way that the corresponding equivalent temperature was equal to 1350K. 3. RESULTS
3.1. Microstructure The alloy studied in the present investigation was hypoeutectic and contained fine fibrous eutectic mixture and primary NiAl phase in the as-cast condition (Fig. 1(a)). The microstructure of the heat-treated alloy is shown in Fig. 1(b). Annealing at 1848K for 360 ks spheroidized most of the Mo fibers in the eutectic mixture. The volume fraction of primary NiAl phase, F, was estimated to be equal to 12.4% and that of the Mo phase 9.7%. The Mo particles were seen at the grain boundaries and inside the grains, whose volume fraction ratio was estimated to be 1:12 through microstructural observations. Since the internal stress generated by particles at the grain boundaries is easily accommodated by fast grain boundary diffusion [16], only the volume fraction of the Mo particles within the grain, f=8.9%, is considered for theoretical calculation. The average size of Mo particles inside the grain was 1.5 µm. During thermal cycling, the primary NiAl phase at 18 µm acts as a non-deforming particle embedded in a superplastically-deforming eutectic matrix. The average matrix grain size of the alloy was 120 µm, which is too large for conventional fine grain superplasticity. 3.2. Isothermal creep behavior The isothermal creep results at 1348K are presented in Fig. 2. Here, the strain rate is plotted against stress on a double logarithmic scale. The stress exponent for steady state creep is about 7, which indicates the operation of a dislocation creep mechanism. Creep behavior of NiAl–Mo alloy in the literature is limited to that of directionally-solidified alloy at 1300K, which shows a stress exponent (about 6) close to our data [9]. Direct comparison of creep rates is not valid since their alloy shows much better creep resistance than ours due to the directionallysolidified microstructure. Single deformation behavior for a wide range of temperature in these NiAl–Mo alloys is reasonably considered to be similar to that of coarse grain NiAl alloy but differently to that in ODS NiAl alloy [28]. The values of the stress exponents in these NiAl–Mo alloys are slightly
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Fig. 2. Stress dependence of steady state isothermal creep rate of the NiAl-Mo alloy at 1248K with the same scale as Fig. 4.
Fig. 3. Arrhenius plot showing the temperature dependence of the steady state isothermal creep rate of the NiAl-Mo alloy.
larger than that of the coarse grain NiAl alloy, 4.5 [28], possibly because of the interaction between the Mo phases and the dislocations. The activation energy under isothermal conditions is estimated through a temperature change test at a fixed stress of 33 MPa. The strain rate is plotted against 1/RT in a semi-logarithmic graph (Fig. 3), where R is the universal gas constant. From the slope of the line the activation energy for isothermal creep rate is estimated to be 297 kJ/mol, which matches well with the activation energy for lattice diffusion of Ni in NiAl, 308 kJ/mol [29]. 3.3. Thermal cycling creep behavior Thermal cycling creep results are presented in Fig. 4. For comparison, the estimated isothermal creep
Fig. 4. Thermal cycling creep rates as a function of applied stress in the NiAl-Mo alloy. The temperature was cycled between 1248 and 1448K. Estimated isothermal creep rate at 1350K which corresponds to the equivalent temperature is also shown for comparison. The broken line shows theoretical values calculated using equations (3) and (5).
rates at the equivalent temperature, 1350K, using the data at 1348K and Q = 297 kJ/mol, is also shown in the figure. At low stresses, thermal cycling creep rates are several orders of magnitude higher than those of the isothermal creep rates. Moreover, the stress exponent value at the low stress level is close to 1. This region is considered to be an ISS region. With increasing stress, the stress exponent value for the thermal cycling creep tends to depart from 1. The above trend agrees well with other studies [14–18] of composite CTE-mismatch superplasticity. A tensile creep experiment was performed under the thermal cycling condition of 1323–1523K. By assuming uniform deformation and constant volume
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during the deformation, a constant stress of 10 MPa was maintained on the specimen by adjusting the load. The test was stopped when the controlling thermocouples at the shoulders of the sample were moved out of the heating zone. The average strain rate during the above tensile test was 10⫺5 s⫺1. For comparison, a tensile creep test under an isothermal condition was done at 1523K at the same strain rate (stress level of 27 MPa). Photographs of the specimen (a) undeformed, (b) deformed under thermal cycling condition and (c) deformed under isothermal conditions are shown in Fig. 5. Under the thermal cycling condition, elongation close to 210% was achieved without fracture. The specimen showed a shallow necking, which was formed due to the difference in temperature between the center and edges of the specimen. On the other hand, the sample deformed under the isothermal condition developed a neck after 20% elongation and ultimately the sample failed at 60% elongation. After the tests, the tensile samples were sectioned parallel to the tensile axis and observed under an optical microscope. The sample deformed under isothermal conditions exhibits large cavities below the fracture surface [Fig. 6(a)]. In general, cavities were observed at or near the grain boundaries. On the other hand, any cavities were not found in the sample deformed under the thermal cycling creep condition [Fig. 6(b)]. The above result indicates the beneficial effect of thermal cycling in achieving large elongation without developing cavities. The temperature amplitude dependence of ISS was studied by carrying out thermal cycling creep tests at a constant stress level and equivalent temperature. The result is shown in Fig. 7. For comparison purposes, the isothermal creep rate, which corresponds to zero temperature amplitude is also included in the figure. The results clearly show that the larger the temperature amplitude, the higher the strain rate of ISS is.
Fig. 5. Photograph of the tensile creep tested samples: (a) undeformed condition; (b) after thermal cycling creep at 13231523K under a stress of 10 MPa; and (c) after isothermal creep at 1523K under a stress of 27 MPa. Total elongation of 210% was recorded under thermal cycling condition without fracture (b), while the isothermal tested sample failed after 60% of deformation (c).
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Fig. 6. Optical micrographs of gauge sections of the deformed tensile samples: (a) deformed under isothermal condition (area near the fracture surface); and (b) deformed under thermally cycling creep condition. Large cavities are present in the isothermally tested sample (a), while in the sample tested under thermal cycling conditions, even after a large elongation, apparent cavities are not present (b).
Fig. 7. Effect of temperature amplitude on the thermal cycling creep rate. The test was carried out at a stress level of 15 MPa and the heating and cooling rates were fixed at 10 K/s. The solid line is the curve fitted using equation (7).
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SUNDAR et al.: INTERNAL STRESS SUPERPLASTICITY 4. DISCUSSION
The thermal cycling strain rates of NiAl–Mo alloy at low stresses are higher (more than several orders of magnitude) than the isothermal creep rates. As the stress increases, the thermal cycling creep rate increases at a rate faster than the linear behavior and approaches the isothermal creep rates. These results imply that enhancement of creep rate by thermal cycling takes place at low stress levels, where the internal stress caused by the difference in thermal expansion of the constituent phases are relatively larger than the applied stress. Based on micromechanics, Sato and Kuribayashi [25] proposed a quantitative model for ISS in a creeping matrix with rigid inclusions. Although there is another qualitative model of ISS [20] available in the literature, the above model is very attractive, as it does not need any fitting parameters for predicting the thermal cycling strain rate from the isothermal creep rate equation. The above model has been shown to predict thermal cycling creep behavior of Al alloys and Ti matrix composites [14, 16, 17]. In this section, first, we will briefly outline the model and then will compare the theoretical predictions and the experimental results. In the model [25], it is assumed that the material consists of a matrix, uniformly dispersed with spherical inclusions of radius a and volume fraction f, with a difference in thermal expansion coefficient of ⌬a. During thermal cycling, while the inclusion is treated as elastic, the matrix deforms by power law creep of the form: ⑀˙ = Bsn
(2)
where ⑀˙ , B and s are steady state creep rate, temperature dependent constant and stress, respectively. Here, the effect of the interaction between the inclusions and dislocations are included in equation (2), that is, equation (2) does not express the deformation behavior of the monolithic matrix material. Though this treatment is not rigorous, the model is able to treat only two factors: deformation behavior of the matrix and the strain mismatch effect, and the former consists of the deformation of the monolithic matrix and inclusion–dislocation interaction. When the material is subjected to a temperature change with a rate T˙ and if the inclusion is not restrained by the matrix, the inclusion would dilate (or shrink) isotropically against the matrix with a strain rate of ⌬aT˙. This volumetric strain cannot be accommodated by the fast interface diffusion between the matrix and the inclusions. It can be accommodated by the volume diffusion in the matrix, though its rate is, in normal cases, negligibly slow (the relaxation time is calculated as 9.5 s, see Appendix A). Therefore, it must be accommodated by a heterogeneous plastic flow of the matrix (plastic
accommodation). On the other hand, the strain mismatch caused by macroscopic flow of the matrix due to the applied stress, which has only a shear component, can be accommodated by fast interface diffusion (the relaxation time is calculated as 0.70 s, see Appendix A). When these two accommodation processes, plastic accommodation for volumetric strain mismatch and interface diffusion for shear strain mismatch, take place, simultaneously, a quasi-steady state is achieved where the stress and the strain rate distributions remain unchanged except the change caused by isothermal creep rate due to the temperature change. Using the above analysis [25], the volume averaged uniaxial strain rate during thermal cycling under an applied stress sA is given by: ⑀¯˙model = |⌬aT˙|1⫺1/n
B1/n 2n(n + 4) 1⫺f1/n s , (low sA) 1⫺f 21/n5 (1⫺f)f1/n A (3)
and ⑀¯˙model =
B sn (high sA) (1⫺f)n A
(4)
The model predicts that under an applied stress much higher than the internal stress, the thermal cycling creep rate coincides with the isothermal creep rate [equation (4)] and at low stresses, it is proportional to the applied stress [equation (3)]. Under typical ISS conditions, that is, at low applied stresses during thermal cycling, the primary NiAl phase deforms with slower strain rate than the eutectic NiAl–Mo phase with volume fraction 12.4%. For example, under 5 MPa at 1350K, coarse grain pure NiAl is estimated to deform below 1×10⫺7 s⫺1 [28]. The present material is, therefore, considered to be a composite consisting of a superplastically deforming eutectic mixture with a stress exponent of 1 and nondeforming NiAl particles. In this configuration also, the thermal strain mismatch arises during thermal cycling creep, but in the matrix with a stress exponent of 1, ISS is not generated. In deriving equation (3), we use the non-linearity of equation (1), that is, n>1. On the other hand, the strain mismatch caused by the macroscopic flow of the eutectic matrix cannot be accommodated by interface diffusion around the NiAl particles since the particle size of 18 µm results in the negligible accommodation rate. In this case, the strengthening effect through load transfer to the particles takes place, which has been analyzed extensively by the sear-lag model [30], the self-consistent potential method [31] and FEM [32]. In the present case, since the eutectic matrix deforms with a stress exponent of 1, a simple analysis using elastic analogy is rigorously applicable and the reduced creep rate of
SUNDAR et al.: INTERNAL STRESS SUPERPLASTICITY
the material, ⑀¯˙th, from that of the eutectic matrix, ⑀¯˙model, is given by the following formula [33]: ⑀¯˙th =
1⫺F ⑀¯˙ . 1⫺F + F/S∗ model
(5)
Here S∗ has a value of 2/5 for non-elongated particle, and F denotes the particle volume fraction. The theoretical prediction by equations (3) and (5) for the present alloy is shown in Fig. 4 as a broken line. The following values are utilized for the calculation: F = 0.124, f = 0.089, n = 7.0, B = 2.8×10⫺17 MPa⫺7s⫺1 (from Fig. 4) and ⌬a = 9.3×10⫺6 K⫺1. The value of ⌬a is calculated using aNiAl = 15.1×10⫺6K⫺1 at 1100–1800K [1] and aMo = 5.8×10⫺6 K⫺1 at 1273K [34]. The power law equation of n = 7 for the matrix deformation under the thermal cycling condition at low applied stresses is justified because the equivalent stresses in the matrix during thermal cycling is so high that they are in the power law creep region (see Appendix B in Ref. [16]). The theoretical creep rates are within one order of magnitude of the experimental creep rates. The theoretical model treats only the quasi-steady state during heating and cooling, but in actual experiment, a stationary internal stress distribution is achieved after a certain period after each temperature reversal [16]. Therefore, the experimental strain rate cannot exceed the theoretical prediction and the difference becomes larger with small temperature amplitude, as clearly shown in Fig. 7. Assuming that all the difference between the experimental and theoretical creep rates is caused by the transient phenomena, the above data are analyzed by the following equation: ⑀¯˙∗ = ⑀˙ iso + (⑀¯˙th⫺⑀˙ iso)[1⫺exp(⫺C|T˙ |t)].
(6)
The above equation considers that the instantaneous strain rate ⑀˙ ∗ increases exponentially with time t after each temperature reversal with a constant C, from the isothermal creep rate ⑀˙ iso to that of theoretical stationary creep rate ⑀¯˙th predicted by the micro-mechanics model [equation (5)]. The average strain rate during thermal cycling in the temperature range is ⌬T then given by:
冕
⌬T
1 1 (⑀¯˙ ⫺⑀˙ )[1 ⑀˙ ∗d(|T˙ |t)⬇⑀¯˙th⫺ ⑀¯˙ = ⌬T C⌬T th iso 0
(7)
⫺exp(⫺C⌬T)].
The solid line in Fig. 7 is the fitted curve of the above equation with 1/C⬇410K⫺1. It indicates that after each temperature reversal, the quasi-steady state stress and strain rate distributions are achieved in a transient time, (C|T˙ |)⫺1, of 41 s.
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5. SUMMARY
ISS in NiAl–Mo alloy was investigated by conducting thermal cycling creep experiments. At low stress levels, the thermal cycling creep rates were much higher than the isothermal creep rates and the corresponding stress exponent in this region was close to 1. This region is identified as an ISS region. At high stress levels, the thermal cycling creep rates were close to the isothermal creep rates. Superplastic elongation of >200% was achieved during a tensile creep test in the superplastic region. The present result was compared with the prediction of a micromechanics model and the experimental creep rates in the ISS region were found to be within one order of magnitude of the model prediction. REFERENCES 1. Miracle, D. B. and Darolia, R., in Intermetallic Compounds: Vol. 2, Practice, eds. J. H. Westbrook and R. L. Fleischer. John Wiley & Sons, New York, 1994, p. 53. 2. Noebe, R. D., Bowman, R. R. and Nathal, M. V., Int. Mater. Rev., 1993, 38, 193. 3. Johnson, D. R., Chen, X. F., Oliver, B. F., Noebe, R. D. and Whittenberger, J. D., Intermetallics, 1995, 3, 99. 4. Misra, A., Wu, Z. L., Kush, M. T. and Gibala, R., Mater. Sci. Engng, 1997, A239/240, 75. 5. Johnson, D. R., Joslin, S. M., Reviere, R. D., Oliver, B. F. and Noebe, R. D., in Processing and Fabrication of Advanced Materials for High Temperature Applications– II, eds. V. A. Ravi and T. S. Srivatsan. TMS, Warrendale, 1993, p. 77. 6. Reuss, S. and Vehoff, H., Scripta metall., 1990, 24, 1021. 7. Lewandowski, J. J., Michal, G. M., Locci, I. and Rigney, J. D., MRS Symp. Proc., 1990, 341, 1. 8. Heredia, F. E., He, M. Y., Lucas, G. E., Evans, A. G., Deve, H. E. and Konitzer, D., Acta. metall., 1993, 41, 505. 9. Johnson, D. R., Oliver, B. F., Noebe, R. D. and Whittenberger, J. D., Intermetallics, 1995, 3, 493. 10. Sherby, O. D. and Wadsworth, J., Mater. Sci. Technol., 1985, 1, 925. 11. de Jong, M. and Rathenau, G. W., Acta metall., 1961, 9, 714. 12. Greenwood, G. W. and Johnson, R. H., Proc. R. Soc. London, 1965, 283A, 403. 13. Zwigl, P. and Dunand, D. C., Metall. Trans., 1998, 29A, 565. 14. Dunand, D. C. and Bedell, C. M., Acta metall., 1996, 44, 1063. 15. Wu, M. Y. and Sherby, O. D., Scripta Metall., 1984, 18, 773. 16. Kitazono, K. and Sato, E., Acta mater., 1998, 46, 207. 17. Kitazono, K. and Sato, E., Acta mater., 1999, 47, 135. 18. Kitazono, K., Sato, E. and Kuribayashi, K., Scripta mater., 1999, 41, 263. 19. Lobb, R. C., Sykes, E. C. and Johnson, R. H., Metal Sci. J., 1972, 6, 33. 20. Wu, M. Y., Wadsworth, J. and Sherby, O. D., Metall. Trans., 1987, 18A, 451. 21. Kitazono, K., Hirasaka, R., Sato, E., Kuribayashi, K. and Motegi, T., Acta mater., 2001, 49, 473. 22. Schuh, C. and Dunand, D. C., Acta. mater., 1998, 46, 5663. 23. Zwigl, P. and Dunand, D. C., in Superplasticity and Superplastic Forming 1998, supplemental volume, eds. A. K. Ghosh and T. R. Bieler. TMS, Warrendale, 1998, p. 40. 24. Sundar, R. S., Kitazono, K., Sato, E. and Kuribayashi, K., Intermetallics, 2001, 9, 279. 25. Sato, E. and Kuribayashi, K., Acta metall. mater, 1993, 41, 1759.
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APPENDIX A
The relaxation times for the two kinds of diffusional accommodation are calculated in order to confirm that in the present experimental condition, the volumetric strain mismatch (thermal expansion) is not accommodated by volume diffusion but is accommodated by plastic accommodation, and the shear strain mismatch (matrix flow) is accommodated by interface diffusion. They are given by: 4a3kT 1 8⫺10n∗ + = 0.70 s, ti = 2 ∗ 3p Didq G G(7⫺5n) (A1)
(interface diffusion [35]) kTa2 (G∗(1 + n)) + (2G(2⫺2n∗)) = 9.5 s, tv = 4Dvq GG∗(1 + n∗) (A2)
(volume diffusion [36]) where Di, Dv, n, n∗, G, G∗, q, d, k and a are the interface diffusion constant, the volume diffusion constant, the Poisson ratios of the matrix and the inclusion, the shear moduli of the matrix and the inclusion, atomic volume of NiAl, interface thickness, Boltzman’s constant and the radius of the inclusion, respectively. The following values are used for the above calculations: Dv = 4.46×10⫺4exp((⫺308 ⫺16 kJ/mol)/(RT)) = 4.92×10 m2/s [29], Di = Dgb (from Coble creep) = 1.9×10⫺6exp((⫺143 kJ/mol)/ (RT)) = 5.44×10⫺12 m2/s [28], n = 0.307 + 2.15× 10⫺5T = 0.336 [1], n∗ = 0.362 [28], G = 5.68×1010 Pa [1], G∗ = 9.69×1010 Pa [37], a = 0.75×10⫺6 m, q = 1.2×10⫺29 m3 [28], d = 2b; where b is Burgers vector (2.9×10⫺10 m). When the creep of the material is limited by relaxation kinetics caused by interface diffusion around spherical inclusions under uniaxial stress, the steady state creep rate is given by [38]: ⑀˙ =
5(1⫺n) 2tiG(7⫺5n)
(A3)
The relaxation limited creep is calculated as 3.9×10⫺2 s⫺1 at a stress of 5 MPa, which is far greater than that of the isothermal creep rate (2.1×10⫺12 s⫺1) and the thermal cycling creep rate (2.0×10⫺6 s⫺1) (Fig. 4).