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Tension–compression creep asymmetry in a turbine disc superalloy: roles of internal stress and thermal ageing
Acta Materialia 52 (2004) 1761–1772 www.actamat-journals.com
Tension–compression creep asymmetry in a turbine disc superalloy: roles of internal stress and thermal ageing S.K. Sondhi 1, B.F. Dyson, M. McLean
*
Department of Materials, Imperial College London, Exhibition Road London SW7 2AZ, UK Received 27 August 2003; received in revised form 29 November 2003; accepted 12 December 2003
Abstract The tension and compression creep behaviour of an as-received and pre-aged IN100 disc alloy have been characterised in order to validate a previous hypothesis that the unusual response of low and even negative initial creep rates in tension was caused by the presence of an internal stress field within the alloy. Absolute values of initial creep rates in compression were found to be much greater than in tension and this asymmetric creep response is conclusive proof of the presence of an internal compressive stress field in the alloy matrix. The asymmetry was virtually removed by pre-ageing prior to creep and this is attributed to the decay of the internal stress. These features have been simulated using a microstructure-based creep model incorporating an evolving internal stress field. The model also simulates the additional (and complicating) reduction in general creep strength that is thought to be due to coarsening and dissolution of the smallest particles of the tri-modal c0 distribution in the alloy. The net consequence of these two competing thermal processes is that the short-term creep response is dominated by the initial magnitude of the internal stress field whereas coarsening and dissolution of the smallest c0 particles determines the long-term behaviour. 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nickel alloys; Creep; Internal stress; Tension–compression asymmetry
1. Introduction Although the nickel-base superalloy IN100 was originally developed for use in the cast form to produce turbine blades, it is now also used for making turbine discs by a powder metallurgical route. Since these two engine components experience very different operating conditions, the microstructures required to optimise their engineering performance differ considerably. Turbine blades, manufactured by investment casting a high carbon (0.18 wt%) version of this alloy, are heat-treated to give a large grain size for maximum creep resistance. A low carbon (0.07 wt%) variant, produced as powder by gas atomisation is forged into turbine discs. The discs are solution heat-treated below the c0 solvus temperature to *
Corresponding author. Tel.: +44-2075946812; fax: +442075843194. E-mail address: [email protected] (M. McLean). 1 Now at: National Metallurgical Laboratory, Jamshedpur 831007, India.
obtain a fine grain size and heat-treated to produce a fine c0 distribution required for high yield strength and long fatigue life. At present, turbine discs operate at temperatures where creep deformation is insignificant. However, the operating temperatures of turbine discs are expected to rise to levels where creep deformation, and, in particular its interaction with low cycle fatigue, can no longer be ignored. The present study addresses this projected application by: (a) characterising the creep behaviour of the IN100 disc alloy at temperatures around 700 C, and (b) modifying an existing quantitative microstructurespecific model to simulate the creep behaviour. A preliminary study of uniaxial tensile creep of this alloy had revealed an atypical creep curve shape at 704 C [1] compared to blade alloys at higher temperatures. The creep strain rates were extremely low for prolonged periods, taking more than half of the rupture life to accumulate 0.5% strain. Indeed, at the lowest test stress of 400 MPa the initial creep rates were negative for 100 h while loaded in tension. The material also shrank when aged at 704 C with no applied stress.
1359-6454/$30.00 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2003.12.017
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Various mechanisms have been proposed for negative creep observed in nickel-base superalloys. In a few superalloys the nickel/chromium matrix undergoes an ordering transformation leading to a decrease in the lattice parameter [2,3], the associated volumetric change manifesting itself as a linear shrinkage of a test piece. However, such ordering transformations are restricted to temperatures below 600 C whereas the present alloy exhibits shrinkage at 704 C. Negative creep has also been attributed to a decrease in c0 volume fraction with increasing temperature [4]. However, this can only occur in a superalloy with large positive misfit (ac0 > ac ) heated well above its final ageing temperature. IN100 does not have the prerequisite large positive misfit [5] and exhibits negative creep below the final ageing temperature of 732 C. Reppich [6,7] investigated negative creep in a number of superalloys, attributing it to solid-state phase transformations involving carbides; the associated volumetric changes can cause shrinkage. However, they do not interact with the creep process, so that the strains due to phase transformations and creep can simply be added [7]. Since the maximum shrinkage observed by Reppich was 0.1% over hundreds of hours, its addition to the creep strain has little effect on the overall shape of the creep curve. This contrasts with our recent work [1] where the initial tensile creep rates in IN100 were highly suppressed. None of these previous explanations can explain the low and negative creep strains observed in IN100. It was proposed that these results are consistent with a compressive internal stress in the matrix of this two-phase alloy [1], with compensating tensile stresses within the particles. A possible source of such an internal stress field is a volumetric mismatch between matrix and coherent precipitate particles. The objective of the work presented below was to extend the characterisation of tensile creep behaviour previously reported [1] and to carry out a series of diagnostic tests to confirm or disprove the existence of the internal stress field that was proposed. A compressive internal stress within the matrix should result in an asymmetrical creep response – suppressing creep in tension but enhancing creep in compression. A comparison of the creep responses in tensile and compressive loading therefore constitutes an unambiguous test of the presence of an internal stress field. Furthermore, tension and compression creep tests have also been performed on pre-aged material, since any thermally induced attenuation of an internal stress field should reduce this asymmetry. A microstructure-based creep model, modified to include the effects of an evolving internal stress, is used to simulate the shapes of creep curves in both the
as-received and pre-aged material under tension and compression.
2. Experimental procedure 2.1. Alloy composition and heat treatment The nominal chemical composition of the low carbon variant of IN100 is given in Table 1. The material was supplied by Pratt & Whitney, USA, in the form of rods, 11 mm in diameter and 130 mm in length, machined from a commercially heat-treated turbine disc. The commercial heat treatment was designed to obtain a fine grain size, so the material was solution heat-treated below the c0 solvus temperature at 1143 C for 2 h followed by an oil-quench. It was subsequently aged at 982 C for 1 h and 732 C for 8 h. Because of the sub-solvus heat treatment, some of the primary c0 remains un-dissolved and inhibits grain growth. This, coupled with the subsequent two-stage ageing, results in a tri-modal distribution of c0 particles. Material subject to this heat treatment will subsequently be described as being in the as-received condition. 2.2. Microstructural characterisation The microstructure was characterised using scanning electron microscopy. To observe the precipitate dispersion, specimens were electro-polished using a solution containing 45% butanol, 45% acetic acid and 10% perchloric acid. The electro-polishing was carried out at 25 V for 25 s. Subsequently, the samples were electroetched using the same solution but at a lower voltage of 5 V for 2–3 s. For grain size measurement the samples were etched for 1 min using a solution of 5.5 g of CuSO4 in 100 ml of hydrochloric acid and 100 ml of ethanol. 2.3. Creep and yield tests Creep and yield tests in tension were carried out in accordance with the British Standard BS 4 A4 Part 1 which specifies the test procedures as well as the testpiece specifications for both tests. Section 1 of this standard deals with the yield test whereas Section 3 provides relevant details for the creep test. In all cases, cylindrical testpieces were used. Compression yield tests were carried out in accordance with British Standard BS EN 24506. No British Standard is available for compression creep testing and an in-house method was used. Cylindrical specimens with a height to diameter ratio of
Table 1 Chemical composition of the present IN100 disc alloy (in wt%) Al
B
C
Co
Cr
Fe
Mo
Si
Ti
V
W
Zr
Ni
5
.02
.07
18
12
.09
3.1
.03
4.3
.75
.02
.07
Rest
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1.5 and minimum diameter 5.5 mm were used. For the creep and yield tests in tension, strain was measured by linear transducers attached to extensometers that were clamped to the ridges on the testpiece. In the case of compression tests, the extensometer was attached to the plates that are compressing the testpiece, adjacent to the specimen. The yield tests were carried at a constant strain rate of 1 103 per second.
3. Results 3.1. Microstructural examination The typical microstructure of the as-received material in Fig. 1(a) clearly shows a significant amount of pri-
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mary c0 at the grain boundaries. The diameter of the primary c0 varies from 1 to 2 lm and the average grain size is 5 lm. Fig. 1(b), at a higher magnification, reveals two further distinct populations of the c0 precipitate. The secondary c0 particles have diameters of 150–250 nm, whilst the smallest tertiary c0 particles are 10–20 nm in size. The distribution of the secondary and the tertiary c0 was found to be relatively uniform in all the samples examined. Fig. 1(c) shows the microstructure of this alloy after 1000 h of ageing at 704 C. The tertiary c0 particles have significantly increased in size, and their number density has clearly reduced; the size of the larger precipitate is almost unaffected. 3.2. Creep test results at 704 C – as-received material Creep tests were carried out on the as-received material in both tension and compression. Tensile creep curves, at all five stress levels between 400 and 738 MPa, have the same unusual shape and these are presented in Fig. 2(a) in a normalised form for ease of comparison.
Fig. 1. Typical microstructure of IN100 disc alloy (a) and (b) as received at two different magnifications and (c) after 600 h at 704 C at the same magnification as (b).
Fig. 2. (a) Normalised creep curves for IN100 disc alloy at 704 C. The test stress varies from 400 to 738 MPa. (b) Initial stages of the creep curve at 400 MPa.
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There is no evidence of primary creep. In all cases, the initial creep rates are extremely low and there is a long period of apparent inactivity. This is followed by a steep rise in creep rates leading to rupture. The initial creep rates are smaller at lower applied stresses and are negative at the lowest test stress of 400 MPa considered. The initial part of the 400 MPa creep curve, magnified in Fig. 2(b), shows a negative strain rates that extends for the first 100 h developing a maximum negative strain is 0.01%. To gain a better understanding of this unusual phenomenon, dimensional changes were monitored in a creep testpiece at 704 C, in the absence of any applied stress. The results, in Fig. 3, show a continuous shrinkage for more than some 500 h. The maximum magnitude of shrinkage in the absence of an applied stress is 0.1%; approximately 10 times the extent of negative creep observed when tested at 400 MPa. Compression creep tests were carried out at the two extreme stress levels of 400 and 738 MPa. The compression creep curves are presented along with the corresponding tensile data in Fig. 4. The compression creep curves have been inverted for ease of comparison. It is important to recall that all the creep tests were carried out under constant load, rather than constant stress. For a constant load test in tension, the cross-sectional area decreases with increasing axial strain, leading to progressively increasing stresses and strain rates. This geometrical effect is quite the opposite in a constant load compression test and would decrease creep rates. In reality, initial creep strain rates in compression are much higher than in tension, at both stress levels considered. There is an initial rapid accumulation of strain in compression, followed by a decrease to a minimum strain rate. In the later stages, tensile creep curves show a rapid acceleration in strain rates while the compressive creep rates undergo only slight increases over long periods. Thus, there is a large asymmetry in the creep
Fig. 4. Tension and compression creep curves for the as-received material at 704 C: (a) 400 MPa, (b) 738 MPa. The compression creep curves have been inverted for ease of comparison.
behaviour of this alloy in both the initial and final stages of lifetime. 3.3. Creep test results at 704 C – after ageing
Fig. 3. Shrinkage profile during thermal ageing at 704 C, in absence of any externally applied stress.
Cylindrical blanks were aged for 600 h at 704 C in air and then air-cooled prior to testpiece manufacture. Creep testing in tension was at 400 and 738 MPa. The tensile creep curves of the aged material are presented in Fig. 5, along with the corresponding test results for the as-received material. The aged material exhibits consistently higher creep rates throughout the tests and this leads to shorter rupture lives. At the lower test stress of 400 MPa, the rupture life of the aged material is approximately 27% less than that of the as-received alloy. The loss of rupture life is more severe at the higher test stress of 738 MPa, with the lifetime being reduced after ageing to less than one-third of that of the as-received alloy. The aged material was also creep tested in compression at 704 C at 738 MPa. The data are presented in
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Fig. 5. Effect of thermal ageing on the tensile creep response at 704 C: (a) 400 MPa, (b) 738 MPa.
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Fig. 7. (a) Tension and compression creep response of the IN100 disc alloy at 704 C and 738 MPa; in the as-received condition and after thermal ageing for 600 h at the test temperature. (b) Initial stages of the same.
aged material are 3–4 times higher than in the asreceived material. The tension and compression creep curves for the asreceived and pre-aged material are compared in Fig. 7(a) with the initial stages of the same curves presented in Fig. 7(b). Clearly, the initial creep rates of the pre-aged materials are similar in tension and compression. The large asymmetry in the initial creep rates, that was present in the as-received material, has been almost completely removed by thermal ageing. In contrast, the asymmetry in the later stages of the creep curve is present in the as-received as well as the pre-aged material. Fig. 6. Effect of thermal ageing on the compressive creep response at 704 C and 738 MPa.
Fig. 6, along with the corresponding test results for the as-received material. In the initial stages, the aged material exhibits lower initial strain rates than the asreceived material. However, there is a cross-over of the two creep curves and the long-term creep rates of the
4. Discussion 4.1. Tension–compression asymmetry in creep It is clear from Fig. 4 that the compressive creep response of the as-received material is quite different from that observed in tension. The initial creep rates in
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compression are much greater than in tension, in spite of the fact that geometrical changes in constant load conditions would decrease the stress in compression and increase the stress in tension leading to the opposite effect. The asymmetry cannot therefore be a testing artefact and must be a consequence of an anisotropic material response. The asymmetric initial creep rates in tension and compression are qualitatively consistent with the presence of volumetric changes due to carbide transformations as proposed by Reppich [7]. However, this hypothesis has three quantitative implications: (a) Measured displacements in a tensile creep testpiece will always be a linear sum of the intrinsic creep displacements and the uniaxial component of volumetric shrinkage associated with any microstructural transformation, such as carbide formation or c0 precipitation. (b) The uniaxial component of volumetric shrinkage can be measured independently by an isothermal ageing test in the absence of an applied stress. (c) Any difference between the displacements measured during compressive and tensile creep tests will simply be twice the current amount of linear shrinkage. However, in the experiments on IN100 described above, the difference between the tensile and compressive creep strains is far greater than twice the observed shrinkage obtained without stress. Consequently, the two phenomena (creep and shrinkage) cannot be independent processes. Rather, creep is being significantly influenced by the mechanism causing of the shrinkage. In other words, there must therefore be a coupling between the mechanism attenuating the volume mismatch and the creep mechanism which is not a simple summation of the dimensional changes. The asymmetric initial creep rates shown in Fig. 4 are also consistent with the presence of the internal stress field hypothesised in our preliminary work in tension [1]. To be consistent with the tension–compression data in Fig. 4, such a field would require the stress within the matrix to be compressive with a compensating tensile stress within the particles. So, a compressive internal stress within the matrix opposes an applied tensile stress but reinforces an applied compressive stress – provided of course that the rate controlling creep process is occurring within the matrix, not in the particles. Regardless of the detailed creep mechanism, or the functional form of the creep rate equation, creep rates in compression will be greater than in tension when there is a compressive internal stress. The reverse is true when the internal stress field is reversed. 4.2. Possible origin of internal stress It has not been possible in the present work to identify the exact origin of the internal stress field in this alloy. However, there is a body of literature on their
possible presence in nickel-based superalloys. Although it has been reported that the difference in lattice parameters of the c matrix and coherent c0 precipitate can be accommodated by a tetragonal distortion of the softer face centred cubic matrix [8], it is more likely that the volume misfit on precipitation will be relatively symmetric and hydrostatic on the scale of the particles. When the lattice parameter of the particle is smaller than that of the matrix, this distortion leads to a compressive internal stress within the matrix. Consequently, the particles are in tension and the relative magnitudes of misfit stresses will be determined by the extent of lattice mismatch and their respective volume fractions. Lattice parameter mismatch has previously been linked to compressive internal stress within the matrix phases of SRR99 and CMSX4 [8–10]. Although there have been no similar measurements on IN100, it is speculated that such lattice parameter (i.e. volume) mismatch leads to the internal stress fields deduced in the present study. As discussed in Section 1, the complex heat treatment of this disc alloy results in a tri-modal c0 distribution, the smallest particles of which are precipitated at 732 C. Whether or not all the particles contribute equally to the internal stress field is unknown but clearly the lower the temperature of precipitation, the less chance there will be for recovery processes to attenuate its magnitude. Such an internal stress should have a wavelength similar to the inter-particle spacing with highest magnitudes being near the matrix–particle interface. The internal stress is generated by a combination of volume misfit and coherency constraints between the particle and matrix lattices. In our analysis it is implicitly assumed that the initially coherent particles quickly become semi-coherent, so allowing attenuation of the volume mismatch by stress-directed diffusion of vacancies between the particle/matrix interfaces and grain boundaries. 4.3. Magnitude of the internal stress It is useful to estimate the magnitude of the internal stress field more directly. Room temperature yield data for the IN100 alloy are presented in Appendix A for constant strain rate tests in both tension and compression. Fig. 10 shows that there is a large asymmetry in the yield response with the 0.02% yield in compression occurring approximately 340 MPa below that in tension, which means that the mean compressive internal stress within the matrix at room temperature is of the order of 170 MPa. Available literature [9,10] indicates that the lattice mismatch in superalloys remains almost unchanged between room temperature and 700–800 C, and becomes more negative as the temperature is further increased. Therefore, the internal stress at 704 C is expected to be close to its room temperature value of 170 MPa but will increase at higher temperatures.
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One could also try to estimate the magnitude of internal stress at 704 C from dimensional changes during thermal ageing in the absence of an applied stress. Although there is no externally applied stress, the presence of an internal stress can induce stress-directed diffusion. This mass transport leads to a relaxation of the internal stress due to volumetric mismatch, manifesting itself in the form of testpiece shrinkage. Assuming the rate of decrease of internal stress is proportional to the magnitude of the internal stress, consistent with a diffusioncontrolled relaxation mechanism, a classical exponential decay is observed (Fig. 3). Within the elastic limits, the initial magnitude of internal stress will be given by 1 E e1 sh ; where E is YoungÕs modulus and esh the shrinkage at infinite time. The maximum accumulated shrinkage without applied stress was slightly less than 0.1%. Using an elastic modulus value of 175 GPa [11] at 704 C, the shrinkage data suggest a value of 160 MPa for the compressive internal stress, which is very close to the value obtained from the room temperature yield data analysis. Because of the progressive decay of the driving force for stress relaxation, it is unlikely that the full shrinkage has been achieved. Consequently, 160 MPa will be a lower limit of the true internal stress. Alternatively, an Eshelby-type analysis could be attempted to estimate the stresses generated by the particle/matrix volume misfit. This is complicated by the high volume fraction and tri-modal distribution of the particles. A full stress analysis accounting for the overlap of stress fields is beyond the scope of this study. 4.4. Effect of thermal ageing Fig. 3 also shows that the relief of internal stress is almost complete after 600 h of thermal ageing at 704 C. Accordingly, this particular pre-ageing treatment was selected for investigating the creep response in the absence of an internal stress. Comparison of the tensile creep curves of as-received and pre-aged materials in Fig. 5 showed the tensile creep rates to be consistently much higher after ageing, leading to a reduction in creep life. The loss of tensile creep life is most severe at the higher test stress. This decrease in lifetime could possibly be due to the loss of internal stress; however, coarsening of the tertiary c0 particles during thermal ageing may also be a contributory factor. Available experimental data on the coarsening kinetics in these superalloys [12,13] indicate that there should be little change in the size of primary and secondary c0 precipitate during the present ageing treatment. However, the size of the tertiary c0 will increase by 70–80% during pre-ageing. There may even be a decrease in the volume fraction of the smallest c0 , similar to the observations made by Steven and Flewitt [14] for the IN738 superalloy. These predictions are consistent with the experimental observations made in the present study (Fig. 1(c)). Hence
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significant coarsening and dissolution of the smallest c0 precipitate during the ageing may influence the creep strength of this superalloy. Diagnostic compression creep testing on the same batch of pre-aged material, shown in Fig. 6, was designed to clarify the relative roles of microstructural weakening and loss of internal stress. Any loss of compressive internal stress in the matrix due to ageing lowers the effective applied stress when tested in compression, leading to lower strain rates, but increases the effective stress in tension to give higher strain rates. Thus relaxation of the internal stress should decrease, or even eliminate, the tension–compression creep asymmetry. This kinematic behaviour of an internal-stress field contrasts with the isotropic consequences of coarsening of strengthening particles, which will affect creep response in tension and compression in the same way. The compression creep data in Fig. 6 are in accord with this prediction: the initial creep rates of pre-aged material are indeed lower than in the as-received material. The overall result of the tension and compression tests – that pre-ageing elevates the initial creep rates in tension but lowers them in compression is, to us, unambiguous proof of the presence of the internal stress field in the as-received alloy. However, the long-term creep rates of the pre-aged material are higher than those of the as-received material in compression as well as in tension. Therefore, the influence of the internal stress alone is limited to the initial stages of creep and the long-term creep response is governed by the inherent strength of the material. This agrees with the work of Ashby [15] on the non-homogeneous plastic deformation of two-phase alloys, which suggests that internal stress fields influence mechanical behaviour only up to 1–2% strain. We conclude therefore that microstructural weakening is indeed taking place in parallel with the attenuation of the internal stress field. It is also worth noting that initial creep rates of the pre-aged material are very similar in tension and compression (Fig. 7). The later divergence in the creep rates of the pre-aged material is due to: (a) geometrical effects of constant load tests, and (b) cavitation damage being operative in tension but not in compression. The tensile and compressive yield stresses after ageing are also very close, although they are higher than at room temperature (Table 2). Clearly, the asymmetry in creep and yield, as observed in the unaged material, is removed after thermal ageing. The tertiary c0 particles are in the size range where resistance to particle cutting increases with increasing particle size. Since there is significant increase during ageing in the size of the tertiary particles, but not the primary and secondary, this should lead to the observed increase in yield stress. This contrasts with the creep behaviour where creep deformation is predominantly confined to the matrix. However, the effects of heat treatment on both yield stress
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and creep behaviour indicate that a combination of the attenuation of internal stress and a change in the tertiary particle size, modifying the creep and yield stress, accounts for the observed behaviour. 4.5. Illustrative calculations using a constitutive creep model The quantitative implications of the competing and interacting phenomena identified by the present set of diagnostic tests are important in developing a constitutive creep model. A physically based approach, developed at Imperial College for engineering alloys with unimodal particle strengthening, has been modified to incorporate the effect of internal stresses in an alloy with a tri-modal particle distribution. The details of this model can be found elsewhere [16]; it is, however, summarised in Appendix B, with appropriate modifications, along with some relevant example calculations using a set of semi-empirical model parameters. Illustrative calculations in Appendix B clearly show that a compressive internal stress within the matrix leads to higher strain rates in compression than in tension (Fig. 12). Calculations also show the changes in creep response due to: (a) changing magnitude of internal stress, and (b) microstructural weakening due to particle coarsening (Figs. 13 and 14). The model has been used to simulate a number of the experimental results. 1. Dimensional changes in this material due to thermal ageing. The specimen shrinkage during thermal aging at 704 C in the absence of an applied stress (Fig. 3) has been simulated as a zero-applied stress creep test on a material that has a compressive internal stress of 160 MPa. The model predictions are presented in Fig. 8 along with the experimental data. Experimental data and the predicted fit show excellent agreement.
Fig. 8. A comparison of the model predictions for shrinkage during thermal ageing, using the present creep model, with the experimental data.
2. A comparison of the compressive creep curves, before and after ageing. Fig. 6 showed a cross-over in the two strain trajectories in the early stages of the creep curves. The creep response of the as-received material was calculated using the parameter set presented in Table 3 with an initial internal stress of 160 MPa. The thermal ageing was assumed to remove this internal stress and weaken the material by way of lowering the value of r0 . Accordingly, the creep response of the preaged material has been modelled using the same parameter set except that: (a) there was no internal stress at the beginning of the test, and (b) r0 was lowered from 70 to 65 MPa to simulate the coarsening of the tertiary c0 . The model predictions for the pre-aged and the unaged materials are presented in Fig. 9(a) and show similar trends as the experimental data, Fig. 6. The pre-aged material has lower initial creep rates but higher longterm creep rates and a cross-over in strain trajectory which occurs at a similar time scale as observed in the
Fig. 9. Model predictions of creep response; before and after thermal ageing. (a) The initial stages of compressive creep curves showing the experimentally observed cross-over, and (b) complete creep curves in tension and compression.
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experimental data. The illustrative calculations in Appendix B show that the cross-over of the compression creep curves can not be explained by considering the decay of internal stress or the microstructural weakening in isolation. It is therefore concluded that the thermal ageing treatment used in the present study, does indeed cause a microstructural weakening of the material as well as relieving the compressive internal stress. 3. Tension–compression asymmetry. Example calculations presented in Appendix B clearly show how the tension–compression asymmetry in the initial stages can result from the presence of an internal stress. There is also an asymmetry in the later stages of the creep curves, with the creep rates in tension undergoing a large increase while the compressive creep rates are almost constant. This asymmetry is present in the as-received as well as the pre-aged material. The complete creep curves under tension and compression, at 704 C and 738 MPa were presented in Fig. 7(a) and these creep curves have been modelled by taking into account the effect of cavitation damage that is present in tension but not in compression. The incorporation of cavitation damage in the present model is presented in Appendix B. The model predictions, presented in Fig. 9(b), and the experimental data show good quantitative agreement.
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Acknowledgements The work described in this paper was carried out as apart of DARPA Accelerated Insertion of Materials programme in conjunction with Pratt & Whitney and GE Aircraft Engines. The creep and tensile testing was carried out in the accredited testing laboratory of Incotest. The authors are particularly grateful to Dr. Hector Basoalto and Mr. Reza Sharghi-Moshtaghin for advice and information on modelling and microstructural characterisation, respectively. Appendix A A.1. Yield tests in tension and compression Room temperature yield tests were carried out in both tension and compression to estimate the magnitude of the internal stress field. The alloy was tested in two conditions: (a) as-received, and (b) aged for 600 h at 704 C. The stress–strain curves are shown in Fig. 10 with the compression test strains being inverted for ease of comparison. All data have been converted to true stress versus true strain to remove any geometrically induced asymmetry. The 0.02% yield stress values for all conditions are listed in Table 2.
5. Conclusions 1. A commercially heat-treated IN100 disc alloy exhibits a large tension–compression asymmetry, having greater creep resistance in tension than in compression. 2. Comparison of tensile and compressive creep of asreceived and pre-aged IN100 is consistent with plastic deformation being largely confined to the matrix where there is a a compressive internal stress. This accounts for the tension–compression asymmetry and the unusual tensile creep response. It is speculated that the internal stress field originates from a volumetric mismatch between c and c0 . 3. The large tension–compression creep asymmetry present in the as-received material can be relieved by thermal ageing; it is proposed that this is due to relief of the initial internal stress. 4. The complicated tension and compression creep response in as-received and pre-aged alloy has been simulated by using a simple constitutive equationset which linearly superimposes volumetric- and shear-induced internal stresses. 5. Only the short-term creep performance depends on the presence of the internal stress field; long-term behaviour is determined by the coarsening rate of the smallest c0 particles.
Fig. 10. Yield test data for IN100 disc alloy in tension and compression; in the as-received and pre-aged conditions.
Table 2 0.02% Yield stress data for IN100 disc alloy
0.02% YS (MPa)
As received
Pre-aged
Tension
Compression
Tension
Compression
1130
790
1140
1180
1770
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Appendix B B.1. Computer simulations of creep behaviour The creep test data presented above demonstrate unambiguously that there must be a compressive internal stress within the c matrix. Although its origins have only been surmised, it is possible to simulate its impact on creep behaviour in tension and compression by extending a microstructure-based creep model that has been developed at Imperial College for unimodal precipitation-strengthened alloys [16]. Within this model, the uniaxial creep rate e_ creep is expressed as r rk _ecreep ¼ e_ 00 exp½Qj=v =RT sinh ; ðB:1Þ r0 where e_ 00 is a variable rate parameter that depends upon particle volume fraction and mobile dislocation density; Qj=v is the combined activation energy for diffusion and thermal jog formation; r is the applied stress; rk an internal stress; T is the absolute temperature; and r0 is a normalising stress that is dependent upon particle dispersion and varies inversely with the inter-particle spacing. There are four key features of the model: 1. The magnitude of e_ 00 is independent of the state of particle dispersion and depends only upon its volume fraction, which is usually a function only of temperature. 2. The mobile dislocation density, q, embedded within e_ 00 is not a constant during creep but increases progressively as strain accumulates, thereby weakening the material. 3. r0 is inversely proportional to inter-particle spacing and therefore to the average size of the particles for a given volume fraction. The microstructural weakening of the alloy due to thermally induced particle coarsening manifests itself in the reduction of r0 . Its presence within the argument of the sinh function ensures that there is a large and stress dependent, but scalar (stress-state independent), increase in creep rate with time. 4. The magnitude of rk is a measure of the straininduced stress redistribution between matrix and particles because of the requirement to maintain compatibility of strain between the inelastically deforming matrix and elastically deforming particles. Two situations can be envisaged at the start of creep: • In a well-annealed alloy rk ¼ 0 at t ¼ 0 and the subsequent build-up of rk with creep strain will oppose the applied stress (i.e. the effective stress in the matrix becomes lower than the applied stress) resulting in a reduction in creep rate. This is the underlying mechanism of primary creep in this creep model. • If the alloy had been pre-strained in tension, then rk > 0 at t ¼ 0 and the initial creep rate is lower. Because the internal stress fields are kinematic in nature, a build-up of rk during creep in compression will
have the opposite sign to that generated in tension. The initial creep rate on tensile reloading will now be greater than was the case when the internal stress was initially zero. This is important in appreciating the significance of the tension–compression tests performed in the present work. Since changes always occur in both q and rk during creep (as they are both strain-induced) and changes may occur in inter-particle spacing k (and therefore r0 ) due to particle coarsening, it is vital to know their evolution kinetics. These may be written as [16] q_ ¼ C e_ creep ; h rk i r_ k ¼ h0 1 e_ creep ; rH k3 k30 ¼ kt:
ðB:2Þ ðB:3Þ ðB:4Þ
The relationship of the individual model parameters to the microstructural features is described elsewhere [16]. This creep model has been extended to accommodate the presence of an initial internal stress in the following way. The internal stress due to a volumetric mismatch has been approximated as an initial non-zero value of rk . Furthermore, this is assumed to be directly additive to the internal stress build-up due to stress transfer during creep. Eq. (B.3) represents only the generation and dynamic recovery of internal stress and ignores the normally small contributions of thermal recovery. However, one does need to consider the thermal recovery of internal stress when the creep strain rate, the driving force for dynamic recovery, is extremely low. Thermal recovery of strain-compatibility-induced internal stresses in particle-strengthened alloys has been discussed and quantified by Ashby and Derby [17] and we adopt the same approach. While the transport path for the straincompatibility-induced internal stresses is of the order of particle size; the path for volume-difference-induced internal stresses should be related to the nearest vacancy source/sinks such as grain boundaries. Eq. (B.3) may therefore be modified to accommodate the thermal recovery of internal stresses: h rk i r_ k ¼ h0 1 ðB:5Þ e_ creep E_ethermal ; rH e_ thermal ¼ A exp½QD =RT rk ;
ðB:6Þ
E is YoungÕs modulus, ethermal is the dimensional change associated with thermal recovery of internal stresses, and QD is the activation energy associated with selfdiffusion. The pre-exponent A should be similar to the term observed by Ashby and Derby [17] and varies as 1=d 2 where d is the grain size. It may be noted that the rate of thermal recovery has presently been taken to be same for both types of internal stresses; the individual kinetics may, however, be quite different.
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The dimensional change associated with the thermal recovery of internal stress, ethermal , is normally small compared to the total creep strain and therefore can be neglected. However, when the creep rates are very low and internal stresses are present in the material, e_ thermal , can no longer be ignored. Evolution of the overall dimensional change may be written as e_ total ¼ e_ creep þ e_ thermal :
ðB:7Þ
It may appear at first glance that the two terms in Eq. (B.7) are independent of each other. That is not the case, however, as the evolution of internal stress has a strong and direct influence on the creep strain rate by way of changing the effective applied stress. The tension–compression creep data for this alloy also suggest the presence of creep cavitation as a microstructural damage. This will elevate the strain rates in a tensile creep test but will not operate in compression. This can be simulated following the approach of Ashby and Dyson [18] in the following way: r rk 0 e_ creep ¼ e_ 0 exp½Qj=v =RT sinh ; ðB:8Þ r0 ð1 Dc Þ 1 D_ c ¼ e_ creep ; 3ef
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When there is no initial internal stress and the tests are carried out under constant stress, the model predictions are identical for tension and compression; the effect of cavitation damage has been ignored. For the constant load tests, the initial creep rates are identical in tension and compression. However, the accumulation of strain increases the stress in tension while lowering it in compression and leads to diverging creep rates in the later stages. These creep curves are presented in Fig. 11. To illustrate the individual influence of internal stress and particle coarsening, all of the following calculations in this section: (a) ignore the cavitation damage, and (b) are carried out under constant stress. The presence of an initial internal stress alters the effective stress, ðr rk Þ, differently in tension and compression. The highly nonlinear dependence of strain rate on the effective stress, manifested as a large asymmetry in the initial creep rates, is clearly visible in Fig. 12. In the compression test, recovery processes
ðB:9Þ
where Dc is the cavitation damage and is permanently set to zero in a compression creep test; ef is the rupture strain and for IN100 alloy at 704 C it varies with stress as %ef ¼ 17:15 0:015r ðMPaÞ:
ðB:10Þ
Illustrative calculations are presented here, using this unimodal model to represent the behaviour of the trimodal alloy under consideration. The semi-empirical parameter set used in the calculations is listed in Table 3. For a given volume fraction the evolution of particle spacing can be determined from the Ostwald ripening rate constant; kOswald . Four sets of calculations have been carried out to illustrate the following: 1. Geometrical effect of constant load creep testing in tension and compression. 2. Effect of the presence of internal stress on the tension–compression asymmetry. 3. Effect of the magnitude of initial internal stress. 4. Effect of microstructural weakening alone due to prior ageing.
Fig. 11. A comparison of the model predictions for constant load and constant stress tests in tension and in compression.
Table 3 The model parameters used for the present illustrative calculations e_ 00 Qj=v C h0 H E 704 C kOswald QD A
1.8 106 s1 310 kJ/mol 20 30,000 MPa 0.4 175,000 MPa 1 1030 m3 /s 280 kJ/mol 16,035 MPa1
Fig. 12. The asymmetric influence of internal stress in tension and compression, as predicted by the present creep model. Clearly, the creep strain rates in compression are much higher than in tension.
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lower the internal stress thereby lowering the magnitude of effective stress. This leads to lower creep rates and the shape of the creep curve is similar to that of primary creep. The effect of recovery is quite the opposite in a tension test and there is a continuous increase in the creep rate.
Fig. 13. Variation of the compressive creep response with the initial magnitude of the internal stress.
The initial magnitude of internal stress has a large influence on initial creep rates, as shown in Fig. 13. Higher magnitude of initial internal stress leads to higher compressive creep rates. The recovery rates are also higher in these cases and a steady state value of the internal stress is soon reached. Beyond this point, the creep strain rates are independent of the initial magnitude of the internal stress and all three creep curves are parallel to each other. Even when no internal stresses are present, pre-aging has two direct consequences. As mentioned earlier, coarsening of the strengthening precipitate lowers r0 , thereby leading to higher strain rates. However, the rate of increase of particle radius varies inversely with the square of the particle radius. Hence, prior thermal ageing will reduce the initial creep strength, but the subsequent rate of weakening during creep will be lower than that of the unaged material. When the creep life far exceeds the pre-ageing time, the pre-ageing will have little effect on the creep rupture life. However, the reduction in life will be more severe at higher stresses and short-term tests. The model predictions presented in Fig. 14 are in agreement with this qualitative analysis. The effect of microstructural weakening has been simulated for two different pre-ageing conditions at test stresses of 400 and 738 MPa. The reduction in life is more severe for high stress/short-term creep test at 738 MPa.
References
Fig. 14. Effect of microstructural weakening due to particle ageing on the tensile creep response at 704 C: (a) 400 MPa, (b) 738 MPa.
[1] Sondhi SK, Dyson BF, McLean M. In: Gupta NK, editor. Proceedings of the 8th International Symposium on Plasticity and Impact Mechanics. Delhi: Phoenix Publishing House; 2003. p. 59. [2] Metcalfe E, Nath B, Wickens A. Mater Sci Eng 1967;67:157. [3] Marucco A, Nath B. J Mater Sci 1988;23:2107. [4] Timmins R, Greenwood GW, Dyson BF. Scr Metall 1986;20:67. [5] Stoloff NS. In: Sims CT, Hagel WC, editors. The superalloys. New York: Wiley; 1972. p. 98. [6] Reppich B. Z Metallkd 1994;85:28. [7] Reppich B. Z Metallkd 1984;75:193. [8] Volkl R, Glatzel U, Feller-Kniepmeier M. Scr Mater 1998;38:893. [9] Muller L, Link T, Feller-Kniepmeier M. Scr Metall Mater 1992;26:1297. [10] Sieborger D, Brehm H, Wunderlich F, Moller D, Glatzel U. Z Metallkd 2001;18:52. [11] Mallet O et al. Int J Fatigue 1995;17:129. [12] White CH. In: Betteridge W, Heslop J, editors. The nimonic alloys. Edward Arnold (Publishers) Limited; 1974. p. 63. [13] Ardell AJ. Acta Metall 1968;16:511. [14] Stevens RA, Flewitt PEJ. Mater Sci Eng 1979;37:237. [15] Ashby MF. Philos Mag 1970;14:399. [16] Dyson BF. In: Mishra RS, Earthman JC, Raj SV, editors. Proceedings of Creep Deformation: Fundamentals and Applications. Warrendale, PA: TMS; 2002. p. 309. [17] Derby B, Ashby MF. Acta Metall 1987;35:1349. [18] Ashby MF, Dyson BF. In: Valluri, et al., editors. Advances in fracture research. Oxford: Pergamon Press; 1984. p. 3.
Tension–compression creep asymmetry in a turbine disc superalloy: roles of internal stress and thermal ageing S.K. Sondhi 1, B.F. Dyson, M. McLean
*
Department of Materials, Imperial College London, Exhibition Road London SW7 2AZ, UK Received 27 August 2003; received in revised form 29 November 2003; accepted 12 December 2003
Abstract The tension and compression creep behaviour of an as-received and pre-aged IN100 disc alloy have been characterised in order to validate a previous hypothesis that the unusual response of low and even negative initial creep rates in tension was caused by the presence of an internal stress field within the alloy. Absolute values of initial creep rates in compression were found to be much greater than in tension and this asymmetric creep response is conclusive proof of the presence of an internal compressive stress field in the alloy matrix. The asymmetry was virtually removed by pre-ageing prior to creep and this is attributed to the decay of the internal stress. These features have been simulated using a microstructure-based creep model incorporating an evolving internal stress field. The model also simulates the additional (and complicating) reduction in general creep strength that is thought to be due to coarsening and dissolution of the smallest particles of the tri-modal c0 distribution in the alloy. The net consequence of these two competing thermal processes is that the short-term creep response is dominated by the initial magnitude of the internal stress field whereas coarsening and dissolution of the smallest c0 particles determines the long-term behaviour. 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nickel alloys; Creep; Internal stress; Tension–compression asymmetry
1. Introduction Although the nickel-base superalloy IN100 was originally developed for use in the cast form to produce turbine blades, it is now also used for making turbine discs by a powder metallurgical route. Since these two engine components experience very different operating conditions, the microstructures required to optimise their engineering performance differ considerably. Turbine blades, manufactured by investment casting a high carbon (0.18 wt%) version of this alloy, are heat-treated to give a large grain size for maximum creep resistance. A low carbon (0.07 wt%) variant, produced as powder by gas atomisation is forged into turbine discs. The discs are solution heat-treated below the c0 solvus temperature to *
Corresponding author. Tel.: +44-2075946812; fax: +442075843194. E-mail address: [email protected] (M. McLean). 1 Now at: National Metallurgical Laboratory, Jamshedpur 831007, India.
obtain a fine grain size and heat-treated to produce a fine c0 distribution required for high yield strength and long fatigue life. At present, turbine discs operate at temperatures where creep deformation is insignificant. However, the operating temperatures of turbine discs are expected to rise to levels where creep deformation, and, in particular its interaction with low cycle fatigue, can no longer be ignored. The present study addresses this projected application by: (a) characterising the creep behaviour of the IN100 disc alloy at temperatures around 700 C, and (b) modifying an existing quantitative microstructurespecific model to simulate the creep behaviour. A preliminary study of uniaxial tensile creep of this alloy had revealed an atypical creep curve shape at 704 C [1] compared to blade alloys at higher temperatures. The creep strain rates were extremely low for prolonged periods, taking more than half of the rupture life to accumulate 0.5% strain. Indeed, at the lowest test stress of 400 MPa the initial creep rates were negative for 100 h while loaded in tension. The material also shrank when aged at 704 C with no applied stress.
1359-6454/$30.00 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2003.12.017
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Various mechanisms have been proposed for negative creep observed in nickel-base superalloys. In a few superalloys the nickel/chromium matrix undergoes an ordering transformation leading to a decrease in the lattice parameter [2,3], the associated volumetric change manifesting itself as a linear shrinkage of a test piece. However, such ordering transformations are restricted to temperatures below 600 C whereas the present alloy exhibits shrinkage at 704 C. Negative creep has also been attributed to a decrease in c0 volume fraction with increasing temperature [4]. However, this can only occur in a superalloy with large positive misfit (ac0 > ac ) heated well above its final ageing temperature. IN100 does not have the prerequisite large positive misfit [5] and exhibits negative creep below the final ageing temperature of 732 C. Reppich [6,7] investigated negative creep in a number of superalloys, attributing it to solid-state phase transformations involving carbides; the associated volumetric changes can cause shrinkage. However, they do not interact with the creep process, so that the strains due to phase transformations and creep can simply be added [7]. Since the maximum shrinkage observed by Reppich was 0.1% over hundreds of hours, its addition to the creep strain has little effect on the overall shape of the creep curve. This contrasts with our recent work [1] where the initial tensile creep rates in IN100 were highly suppressed. None of these previous explanations can explain the low and negative creep strains observed in IN100. It was proposed that these results are consistent with a compressive internal stress in the matrix of this two-phase alloy [1], with compensating tensile stresses within the particles. A possible source of such an internal stress field is a volumetric mismatch between matrix and coherent precipitate particles. The objective of the work presented below was to extend the characterisation of tensile creep behaviour previously reported [1] and to carry out a series of diagnostic tests to confirm or disprove the existence of the internal stress field that was proposed. A compressive internal stress within the matrix should result in an asymmetrical creep response – suppressing creep in tension but enhancing creep in compression. A comparison of the creep responses in tensile and compressive loading therefore constitutes an unambiguous test of the presence of an internal stress field. Furthermore, tension and compression creep tests have also been performed on pre-aged material, since any thermally induced attenuation of an internal stress field should reduce this asymmetry. A microstructure-based creep model, modified to include the effects of an evolving internal stress, is used to simulate the shapes of creep curves in both the
as-received and pre-aged material under tension and compression.
2. Experimental procedure 2.1. Alloy composition and heat treatment The nominal chemical composition of the low carbon variant of IN100 is given in Table 1. The material was supplied by Pratt & Whitney, USA, in the form of rods, 11 mm in diameter and 130 mm in length, machined from a commercially heat-treated turbine disc. The commercial heat treatment was designed to obtain a fine grain size, so the material was solution heat-treated below the c0 solvus temperature at 1143 C for 2 h followed by an oil-quench. It was subsequently aged at 982 C for 1 h and 732 C for 8 h. Because of the sub-solvus heat treatment, some of the primary c0 remains un-dissolved and inhibits grain growth. This, coupled with the subsequent two-stage ageing, results in a tri-modal distribution of c0 particles. Material subject to this heat treatment will subsequently be described as being in the as-received condition. 2.2. Microstructural characterisation The microstructure was characterised using scanning electron microscopy. To observe the precipitate dispersion, specimens were electro-polished using a solution containing 45% butanol, 45% acetic acid and 10% perchloric acid. The electro-polishing was carried out at 25 V for 25 s. Subsequently, the samples were electroetched using the same solution but at a lower voltage of 5 V for 2–3 s. For grain size measurement the samples were etched for 1 min using a solution of 5.5 g of CuSO4 in 100 ml of hydrochloric acid and 100 ml of ethanol. 2.3. Creep and yield tests Creep and yield tests in tension were carried out in accordance with the British Standard BS 4 A4 Part 1 which specifies the test procedures as well as the testpiece specifications for both tests. Section 1 of this standard deals with the yield test whereas Section 3 provides relevant details for the creep test. In all cases, cylindrical testpieces were used. Compression yield tests were carried out in accordance with British Standard BS EN 24506. No British Standard is available for compression creep testing and an in-house method was used. Cylindrical specimens with a height to diameter ratio of
Table 1 Chemical composition of the present IN100 disc alloy (in wt%) Al
B
C
Co
Cr
Fe
Mo
Si
Ti
V
W
Zr
Ni
5
.02
.07
18
12
.09
3.1
.03
4.3
.75
.02
.07
Rest
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1.5 and minimum diameter 5.5 mm were used. For the creep and yield tests in tension, strain was measured by linear transducers attached to extensometers that were clamped to the ridges on the testpiece. In the case of compression tests, the extensometer was attached to the plates that are compressing the testpiece, adjacent to the specimen. The yield tests were carried at a constant strain rate of 1 103 per second.
3. Results 3.1. Microstructural examination The typical microstructure of the as-received material in Fig. 1(a) clearly shows a significant amount of pri-
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mary c0 at the grain boundaries. The diameter of the primary c0 varies from 1 to 2 lm and the average grain size is 5 lm. Fig. 1(b), at a higher magnification, reveals two further distinct populations of the c0 precipitate. The secondary c0 particles have diameters of 150–250 nm, whilst the smallest tertiary c0 particles are 10–20 nm in size. The distribution of the secondary and the tertiary c0 was found to be relatively uniform in all the samples examined. Fig. 1(c) shows the microstructure of this alloy after 1000 h of ageing at 704 C. The tertiary c0 particles have significantly increased in size, and their number density has clearly reduced; the size of the larger precipitate is almost unaffected. 3.2. Creep test results at 704 C – as-received material Creep tests were carried out on the as-received material in both tension and compression. Tensile creep curves, at all five stress levels between 400 and 738 MPa, have the same unusual shape and these are presented in Fig. 2(a) in a normalised form for ease of comparison.
Fig. 1. Typical microstructure of IN100 disc alloy (a) and (b) as received at two different magnifications and (c) after 600 h at 704 C at the same magnification as (b).
Fig. 2. (a) Normalised creep curves for IN100 disc alloy at 704 C. The test stress varies from 400 to 738 MPa. (b) Initial stages of the creep curve at 400 MPa.
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There is no evidence of primary creep. In all cases, the initial creep rates are extremely low and there is a long period of apparent inactivity. This is followed by a steep rise in creep rates leading to rupture. The initial creep rates are smaller at lower applied stresses and are negative at the lowest test stress of 400 MPa considered. The initial part of the 400 MPa creep curve, magnified in Fig. 2(b), shows a negative strain rates that extends for the first 100 h developing a maximum negative strain is 0.01%. To gain a better understanding of this unusual phenomenon, dimensional changes were monitored in a creep testpiece at 704 C, in the absence of any applied stress. The results, in Fig. 3, show a continuous shrinkage for more than some 500 h. The maximum magnitude of shrinkage in the absence of an applied stress is 0.1%; approximately 10 times the extent of negative creep observed when tested at 400 MPa. Compression creep tests were carried out at the two extreme stress levels of 400 and 738 MPa. The compression creep curves are presented along with the corresponding tensile data in Fig. 4. The compression creep curves have been inverted for ease of comparison. It is important to recall that all the creep tests were carried out under constant load, rather than constant stress. For a constant load test in tension, the cross-sectional area decreases with increasing axial strain, leading to progressively increasing stresses and strain rates. This geometrical effect is quite the opposite in a constant load compression test and would decrease creep rates. In reality, initial creep strain rates in compression are much higher than in tension, at both stress levels considered. There is an initial rapid accumulation of strain in compression, followed by a decrease to a minimum strain rate. In the later stages, tensile creep curves show a rapid acceleration in strain rates while the compressive creep rates undergo only slight increases over long periods. Thus, there is a large asymmetry in the creep
Fig. 4. Tension and compression creep curves for the as-received material at 704 C: (a) 400 MPa, (b) 738 MPa. The compression creep curves have been inverted for ease of comparison.
behaviour of this alloy in both the initial and final stages of lifetime. 3.3. Creep test results at 704 C – after ageing
Fig. 3. Shrinkage profile during thermal ageing at 704 C, in absence of any externally applied stress.
Cylindrical blanks were aged for 600 h at 704 C in air and then air-cooled prior to testpiece manufacture. Creep testing in tension was at 400 and 738 MPa. The tensile creep curves of the aged material are presented in Fig. 5, along with the corresponding test results for the as-received material. The aged material exhibits consistently higher creep rates throughout the tests and this leads to shorter rupture lives. At the lower test stress of 400 MPa, the rupture life of the aged material is approximately 27% less than that of the as-received alloy. The loss of rupture life is more severe at the higher test stress of 738 MPa, with the lifetime being reduced after ageing to less than one-third of that of the as-received alloy. The aged material was also creep tested in compression at 704 C at 738 MPa. The data are presented in
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Fig. 5. Effect of thermal ageing on the tensile creep response at 704 C: (a) 400 MPa, (b) 738 MPa.
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Fig. 7. (a) Tension and compression creep response of the IN100 disc alloy at 704 C and 738 MPa; in the as-received condition and after thermal ageing for 600 h at the test temperature. (b) Initial stages of the same.
aged material are 3–4 times higher than in the asreceived material. The tension and compression creep curves for the asreceived and pre-aged material are compared in Fig. 7(a) with the initial stages of the same curves presented in Fig. 7(b). Clearly, the initial creep rates of the pre-aged materials are similar in tension and compression. The large asymmetry in the initial creep rates, that was present in the as-received material, has been almost completely removed by thermal ageing. In contrast, the asymmetry in the later stages of the creep curve is present in the as-received as well as the pre-aged material. Fig. 6. Effect of thermal ageing on the compressive creep response at 704 C and 738 MPa.
Fig. 6, along with the corresponding test results for the as-received material. In the initial stages, the aged material exhibits lower initial strain rates than the asreceived material. However, there is a cross-over of the two creep curves and the long-term creep rates of the
4. Discussion 4.1. Tension–compression asymmetry in creep It is clear from Fig. 4 that the compressive creep response of the as-received material is quite different from that observed in tension. The initial creep rates in
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compression are much greater than in tension, in spite of the fact that geometrical changes in constant load conditions would decrease the stress in compression and increase the stress in tension leading to the opposite effect. The asymmetry cannot therefore be a testing artefact and must be a consequence of an anisotropic material response. The asymmetric initial creep rates in tension and compression are qualitatively consistent with the presence of volumetric changes due to carbide transformations as proposed by Reppich [7]. However, this hypothesis has three quantitative implications: (a) Measured displacements in a tensile creep testpiece will always be a linear sum of the intrinsic creep displacements and the uniaxial component of volumetric shrinkage associated with any microstructural transformation, such as carbide formation or c0 precipitation. (b) The uniaxial component of volumetric shrinkage can be measured independently by an isothermal ageing test in the absence of an applied stress. (c) Any difference between the displacements measured during compressive and tensile creep tests will simply be twice the current amount of linear shrinkage. However, in the experiments on IN100 described above, the difference between the tensile and compressive creep strains is far greater than twice the observed shrinkage obtained without stress. Consequently, the two phenomena (creep and shrinkage) cannot be independent processes. Rather, creep is being significantly influenced by the mechanism causing of the shrinkage. In other words, there must therefore be a coupling between the mechanism attenuating the volume mismatch and the creep mechanism which is not a simple summation of the dimensional changes. The asymmetric initial creep rates shown in Fig. 4 are also consistent with the presence of the internal stress field hypothesised in our preliminary work in tension [1]. To be consistent with the tension–compression data in Fig. 4, such a field would require the stress within the matrix to be compressive with a compensating tensile stress within the particles. So, a compressive internal stress within the matrix opposes an applied tensile stress but reinforces an applied compressive stress – provided of course that the rate controlling creep process is occurring within the matrix, not in the particles. Regardless of the detailed creep mechanism, or the functional form of the creep rate equation, creep rates in compression will be greater than in tension when there is a compressive internal stress. The reverse is true when the internal stress field is reversed. 4.2. Possible origin of internal stress It has not been possible in the present work to identify the exact origin of the internal stress field in this alloy. However, there is a body of literature on their
possible presence in nickel-based superalloys. Although it has been reported that the difference in lattice parameters of the c matrix and coherent c0 precipitate can be accommodated by a tetragonal distortion of the softer face centred cubic matrix [8], it is more likely that the volume misfit on precipitation will be relatively symmetric and hydrostatic on the scale of the particles. When the lattice parameter of the particle is smaller than that of the matrix, this distortion leads to a compressive internal stress within the matrix. Consequently, the particles are in tension and the relative magnitudes of misfit stresses will be determined by the extent of lattice mismatch and their respective volume fractions. Lattice parameter mismatch has previously been linked to compressive internal stress within the matrix phases of SRR99 and CMSX4 [8–10]. Although there have been no similar measurements on IN100, it is speculated that such lattice parameter (i.e. volume) mismatch leads to the internal stress fields deduced in the present study. As discussed in Section 1, the complex heat treatment of this disc alloy results in a tri-modal c0 distribution, the smallest particles of which are precipitated at 732 C. Whether or not all the particles contribute equally to the internal stress field is unknown but clearly the lower the temperature of precipitation, the less chance there will be for recovery processes to attenuate its magnitude. Such an internal stress should have a wavelength similar to the inter-particle spacing with highest magnitudes being near the matrix–particle interface. The internal stress is generated by a combination of volume misfit and coherency constraints between the particle and matrix lattices. In our analysis it is implicitly assumed that the initially coherent particles quickly become semi-coherent, so allowing attenuation of the volume mismatch by stress-directed diffusion of vacancies between the particle/matrix interfaces and grain boundaries. 4.3. Magnitude of the internal stress It is useful to estimate the magnitude of the internal stress field more directly. Room temperature yield data for the IN100 alloy are presented in Appendix A for constant strain rate tests in both tension and compression. Fig. 10 shows that there is a large asymmetry in the yield response with the 0.02% yield in compression occurring approximately 340 MPa below that in tension, which means that the mean compressive internal stress within the matrix at room temperature is of the order of 170 MPa. Available literature [9,10] indicates that the lattice mismatch in superalloys remains almost unchanged between room temperature and 700–800 C, and becomes more negative as the temperature is further increased. Therefore, the internal stress at 704 C is expected to be close to its room temperature value of 170 MPa but will increase at higher temperatures.
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One could also try to estimate the magnitude of internal stress at 704 C from dimensional changes during thermal ageing in the absence of an applied stress. Although there is no externally applied stress, the presence of an internal stress can induce stress-directed diffusion. This mass transport leads to a relaxation of the internal stress due to volumetric mismatch, manifesting itself in the form of testpiece shrinkage. Assuming the rate of decrease of internal stress is proportional to the magnitude of the internal stress, consistent with a diffusioncontrolled relaxation mechanism, a classical exponential decay is observed (Fig. 3). Within the elastic limits, the initial magnitude of internal stress will be given by 1 E e1 sh ; where E is YoungÕs modulus and esh the shrinkage at infinite time. The maximum accumulated shrinkage without applied stress was slightly less than 0.1%. Using an elastic modulus value of 175 GPa [11] at 704 C, the shrinkage data suggest a value of 160 MPa for the compressive internal stress, which is very close to the value obtained from the room temperature yield data analysis. Because of the progressive decay of the driving force for stress relaxation, it is unlikely that the full shrinkage has been achieved. Consequently, 160 MPa will be a lower limit of the true internal stress. Alternatively, an Eshelby-type analysis could be attempted to estimate the stresses generated by the particle/matrix volume misfit. This is complicated by the high volume fraction and tri-modal distribution of the particles. A full stress analysis accounting for the overlap of stress fields is beyond the scope of this study. 4.4. Effect of thermal ageing Fig. 3 also shows that the relief of internal stress is almost complete after 600 h of thermal ageing at 704 C. Accordingly, this particular pre-ageing treatment was selected for investigating the creep response in the absence of an internal stress. Comparison of the tensile creep curves of as-received and pre-aged materials in Fig. 5 showed the tensile creep rates to be consistently much higher after ageing, leading to a reduction in creep life. The loss of tensile creep life is most severe at the higher test stress. This decrease in lifetime could possibly be due to the loss of internal stress; however, coarsening of the tertiary c0 particles during thermal ageing may also be a contributory factor. Available experimental data on the coarsening kinetics in these superalloys [12,13] indicate that there should be little change in the size of primary and secondary c0 precipitate during the present ageing treatment. However, the size of the tertiary c0 will increase by 70–80% during pre-ageing. There may even be a decrease in the volume fraction of the smallest c0 , similar to the observations made by Steven and Flewitt [14] for the IN738 superalloy. These predictions are consistent with the experimental observations made in the present study (Fig. 1(c)). Hence
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significant coarsening and dissolution of the smallest c0 precipitate during the ageing may influence the creep strength of this superalloy. Diagnostic compression creep testing on the same batch of pre-aged material, shown in Fig. 6, was designed to clarify the relative roles of microstructural weakening and loss of internal stress. Any loss of compressive internal stress in the matrix due to ageing lowers the effective applied stress when tested in compression, leading to lower strain rates, but increases the effective stress in tension to give higher strain rates. Thus relaxation of the internal stress should decrease, or even eliminate, the tension–compression creep asymmetry. This kinematic behaviour of an internal-stress field contrasts with the isotropic consequences of coarsening of strengthening particles, which will affect creep response in tension and compression in the same way. The compression creep data in Fig. 6 are in accord with this prediction: the initial creep rates of pre-aged material are indeed lower than in the as-received material. The overall result of the tension and compression tests – that pre-ageing elevates the initial creep rates in tension but lowers them in compression is, to us, unambiguous proof of the presence of the internal stress field in the as-received alloy. However, the long-term creep rates of the pre-aged material are higher than those of the as-received material in compression as well as in tension. Therefore, the influence of the internal stress alone is limited to the initial stages of creep and the long-term creep response is governed by the inherent strength of the material. This agrees with the work of Ashby [15] on the non-homogeneous plastic deformation of two-phase alloys, which suggests that internal stress fields influence mechanical behaviour only up to 1–2% strain. We conclude therefore that microstructural weakening is indeed taking place in parallel with the attenuation of the internal stress field. It is also worth noting that initial creep rates of the pre-aged material are very similar in tension and compression (Fig. 7). The later divergence in the creep rates of the pre-aged material is due to: (a) geometrical effects of constant load tests, and (b) cavitation damage being operative in tension but not in compression. The tensile and compressive yield stresses after ageing are also very close, although they are higher than at room temperature (Table 2). Clearly, the asymmetry in creep and yield, as observed in the unaged material, is removed after thermal ageing. The tertiary c0 particles are in the size range where resistance to particle cutting increases with increasing particle size. Since there is significant increase during ageing in the size of the tertiary particles, but not the primary and secondary, this should lead to the observed increase in yield stress. This contrasts with the creep behaviour where creep deformation is predominantly confined to the matrix. However, the effects of heat treatment on both yield stress
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and creep behaviour indicate that a combination of the attenuation of internal stress and a change in the tertiary particle size, modifying the creep and yield stress, accounts for the observed behaviour. 4.5. Illustrative calculations using a constitutive creep model The quantitative implications of the competing and interacting phenomena identified by the present set of diagnostic tests are important in developing a constitutive creep model. A physically based approach, developed at Imperial College for engineering alloys with unimodal particle strengthening, has been modified to incorporate the effect of internal stresses in an alloy with a tri-modal particle distribution. The details of this model can be found elsewhere [16]; it is, however, summarised in Appendix B, with appropriate modifications, along with some relevant example calculations using a set of semi-empirical model parameters. Illustrative calculations in Appendix B clearly show that a compressive internal stress within the matrix leads to higher strain rates in compression than in tension (Fig. 12). Calculations also show the changes in creep response due to: (a) changing magnitude of internal stress, and (b) microstructural weakening due to particle coarsening (Figs. 13 and 14). The model has been used to simulate a number of the experimental results. 1. Dimensional changes in this material due to thermal ageing. The specimen shrinkage during thermal aging at 704 C in the absence of an applied stress (Fig. 3) has been simulated as a zero-applied stress creep test on a material that has a compressive internal stress of 160 MPa. The model predictions are presented in Fig. 8 along with the experimental data. Experimental data and the predicted fit show excellent agreement.
Fig. 8. A comparison of the model predictions for shrinkage during thermal ageing, using the present creep model, with the experimental data.
2. A comparison of the compressive creep curves, before and after ageing. Fig. 6 showed a cross-over in the two strain trajectories in the early stages of the creep curves. The creep response of the as-received material was calculated using the parameter set presented in Table 3 with an initial internal stress of 160 MPa. The thermal ageing was assumed to remove this internal stress and weaken the material by way of lowering the value of r0 . Accordingly, the creep response of the preaged material has been modelled using the same parameter set except that: (a) there was no internal stress at the beginning of the test, and (b) r0 was lowered from 70 to 65 MPa to simulate the coarsening of the tertiary c0 . The model predictions for the pre-aged and the unaged materials are presented in Fig. 9(a) and show similar trends as the experimental data, Fig. 6. The pre-aged material has lower initial creep rates but higher longterm creep rates and a cross-over in strain trajectory which occurs at a similar time scale as observed in the
Fig. 9. Model predictions of creep response; before and after thermal ageing. (a) The initial stages of compressive creep curves showing the experimentally observed cross-over, and (b) complete creep curves in tension and compression.
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experimental data. The illustrative calculations in Appendix B show that the cross-over of the compression creep curves can not be explained by considering the decay of internal stress or the microstructural weakening in isolation. It is therefore concluded that the thermal ageing treatment used in the present study, does indeed cause a microstructural weakening of the material as well as relieving the compressive internal stress. 3. Tension–compression asymmetry. Example calculations presented in Appendix B clearly show how the tension–compression asymmetry in the initial stages can result from the presence of an internal stress. There is also an asymmetry in the later stages of the creep curves, with the creep rates in tension undergoing a large increase while the compressive creep rates are almost constant. This asymmetry is present in the as-received as well as the pre-aged material. The complete creep curves under tension and compression, at 704 C and 738 MPa were presented in Fig. 7(a) and these creep curves have been modelled by taking into account the effect of cavitation damage that is present in tension but not in compression. The incorporation of cavitation damage in the present model is presented in Appendix B. The model predictions, presented in Fig. 9(b), and the experimental data show good quantitative agreement.
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Acknowledgements The work described in this paper was carried out as apart of DARPA Accelerated Insertion of Materials programme in conjunction with Pratt & Whitney and GE Aircraft Engines. The creep and tensile testing was carried out in the accredited testing laboratory of Incotest. The authors are particularly grateful to Dr. Hector Basoalto and Mr. Reza Sharghi-Moshtaghin for advice and information on modelling and microstructural characterisation, respectively. Appendix A A.1. Yield tests in tension and compression Room temperature yield tests were carried out in both tension and compression to estimate the magnitude of the internal stress field. The alloy was tested in two conditions: (a) as-received, and (b) aged for 600 h at 704 C. The stress–strain curves are shown in Fig. 10 with the compression test strains being inverted for ease of comparison. All data have been converted to true stress versus true strain to remove any geometrically induced asymmetry. The 0.02% yield stress values for all conditions are listed in Table 2.
5. Conclusions 1. A commercially heat-treated IN100 disc alloy exhibits a large tension–compression asymmetry, having greater creep resistance in tension than in compression. 2. Comparison of tensile and compressive creep of asreceived and pre-aged IN100 is consistent with plastic deformation being largely confined to the matrix where there is a a compressive internal stress. This accounts for the tension–compression asymmetry and the unusual tensile creep response. It is speculated that the internal stress field originates from a volumetric mismatch between c and c0 . 3. The large tension–compression creep asymmetry present in the as-received material can be relieved by thermal ageing; it is proposed that this is due to relief of the initial internal stress. 4. The complicated tension and compression creep response in as-received and pre-aged alloy has been simulated by using a simple constitutive equationset which linearly superimposes volumetric- and shear-induced internal stresses. 5. Only the short-term creep performance depends on the presence of the internal stress field; long-term behaviour is determined by the coarsening rate of the smallest c0 particles.
Fig. 10. Yield test data for IN100 disc alloy in tension and compression; in the as-received and pre-aged conditions.
Table 2 0.02% Yield stress data for IN100 disc alloy
0.02% YS (MPa)
As received
Pre-aged
Tension
Compression
Tension
Compression
1130
790
1140
1180
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Appendix B B.1. Computer simulations of creep behaviour The creep test data presented above demonstrate unambiguously that there must be a compressive internal stress within the c matrix. Although its origins have only been surmised, it is possible to simulate its impact on creep behaviour in tension and compression by extending a microstructure-based creep model that has been developed at Imperial College for unimodal precipitation-strengthened alloys [16]. Within this model, the uniaxial creep rate e_ creep is expressed as r rk _ecreep ¼ e_ 00 exp½Qj=v =RT sinh ; ðB:1Þ r0 where e_ 00 is a variable rate parameter that depends upon particle volume fraction and mobile dislocation density; Qj=v is the combined activation energy for diffusion and thermal jog formation; r is the applied stress; rk an internal stress; T is the absolute temperature; and r0 is a normalising stress that is dependent upon particle dispersion and varies inversely with the inter-particle spacing. There are four key features of the model: 1. The magnitude of e_ 00 is independent of the state of particle dispersion and depends only upon its volume fraction, which is usually a function only of temperature. 2. The mobile dislocation density, q, embedded within e_ 00 is not a constant during creep but increases progressively as strain accumulates, thereby weakening the material. 3. r0 is inversely proportional to inter-particle spacing and therefore to the average size of the particles for a given volume fraction. The microstructural weakening of the alloy due to thermally induced particle coarsening manifests itself in the reduction of r0 . Its presence within the argument of the sinh function ensures that there is a large and stress dependent, but scalar (stress-state independent), increase in creep rate with time. 4. The magnitude of rk is a measure of the straininduced stress redistribution between matrix and particles because of the requirement to maintain compatibility of strain between the inelastically deforming matrix and elastically deforming particles. Two situations can be envisaged at the start of creep: • In a well-annealed alloy rk ¼ 0 at t ¼ 0 and the subsequent build-up of rk with creep strain will oppose the applied stress (i.e. the effective stress in the matrix becomes lower than the applied stress) resulting in a reduction in creep rate. This is the underlying mechanism of primary creep in this creep model. • If the alloy had been pre-strained in tension, then rk > 0 at t ¼ 0 and the initial creep rate is lower. Because the internal stress fields are kinematic in nature, a build-up of rk during creep in compression will
have the opposite sign to that generated in tension. The initial creep rate on tensile reloading will now be greater than was the case when the internal stress was initially zero. This is important in appreciating the significance of the tension–compression tests performed in the present work. Since changes always occur in both q and rk during creep (as they are both strain-induced) and changes may occur in inter-particle spacing k (and therefore r0 ) due to particle coarsening, it is vital to know their evolution kinetics. These may be written as [16] q_ ¼ C e_ creep ; h rk i r_ k ¼ h0 1 e_ creep ; rH k3 k30 ¼ kt:
ðB:2Þ ðB:3Þ ðB:4Þ
The relationship of the individual model parameters to the microstructural features is described elsewhere [16]. This creep model has been extended to accommodate the presence of an initial internal stress in the following way. The internal stress due to a volumetric mismatch has been approximated as an initial non-zero value of rk . Furthermore, this is assumed to be directly additive to the internal stress build-up due to stress transfer during creep. Eq. (B.3) represents only the generation and dynamic recovery of internal stress and ignores the normally small contributions of thermal recovery. However, one does need to consider the thermal recovery of internal stress when the creep strain rate, the driving force for dynamic recovery, is extremely low. Thermal recovery of strain-compatibility-induced internal stresses in particle-strengthened alloys has been discussed and quantified by Ashby and Derby [17] and we adopt the same approach. While the transport path for the straincompatibility-induced internal stresses is of the order of particle size; the path for volume-difference-induced internal stresses should be related to the nearest vacancy source/sinks such as grain boundaries. Eq. (B.3) may therefore be modified to accommodate the thermal recovery of internal stresses: h rk i r_ k ¼ h0 1 ðB:5Þ e_ creep E_ethermal ; rH e_ thermal ¼ A exp½QD =RT rk ;
ðB:6Þ
E is YoungÕs modulus, ethermal is the dimensional change associated with thermal recovery of internal stresses, and QD is the activation energy associated with selfdiffusion. The pre-exponent A should be similar to the term observed by Ashby and Derby [17] and varies as 1=d 2 where d is the grain size. It may be noted that the rate of thermal recovery has presently been taken to be same for both types of internal stresses; the individual kinetics may, however, be quite different.
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The dimensional change associated with the thermal recovery of internal stress, ethermal , is normally small compared to the total creep strain and therefore can be neglected. However, when the creep rates are very low and internal stresses are present in the material, e_ thermal , can no longer be ignored. Evolution of the overall dimensional change may be written as e_ total ¼ e_ creep þ e_ thermal :
ðB:7Þ
It may appear at first glance that the two terms in Eq. (B.7) are independent of each other. That is not the case, however, as the evolution of internal stress has a strong and direct influence on the creep strain rate by way of changing the effective applied stress. The tension–compression creep data for this alloy also suggest the presence of creep cavitation as a microstructural damage. This will elevate the strain rates in a tensile creep test but will not operate in compression. This can be simulated following the approach of Ashby and Dyson [18] in the following way: r rk 0 e_ creep ¼ e_ 0 exp½Qj=v =RT sinh ; ðB:8Þ r0 ð1 Dc Þ 1 D_ c ¼ e_ creep ; 3ef
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When there is no initial internal stress and the tests are carried out under constant stress, the model predictions are identical for tension and compression; the effect of cavitation damage has been ignored. For the constant load tests, the initial creep rates are identical in tension and compression. However, the accumulation of strain increases the stress in tension while lowering it in compression and leads to diverging creep rates in the later stages. These creep curves are presented in Fig. 11. To illustrate the individual influence of internal stress and particle coarsening, all of the following calculations in this section: (a) ignore the cavitation damage, and (b) are carried out under constant stress. The presence of an initial internal stress alters the effective stress, ðr rk Þ, differently in tension and compression. The highly nonlinear dependence of strain rate on the effective stress, manifested as a large asymmetry in the initial creep rates, is clearly visible in Fig. 12. In the compression test, recovery processes
ðB:9Þ
where Dc is the cavitation damage and is permanently set to zero in a compression creep test; ef is the rupture strain and for IN100 alloy at 704 C it varies with stress as %ef ¼ 17:15 0:015r ðMPaÞ:
ðB:10Þ
Illustrative calculations are presented here, using this unimodal model to represent the behaviour of the trimodal alloy under consideration. The semi-empirical parameter set used in the calculations is listed in Table 3. For a given volume fraction the evolution of particle spacing can be determined from the Ostwald ripening rate constant; kOswald . Four sets of calculations have been carried out to illustrate the following: 1. Geometrical effect of constant load creep testing in tension and compression. 2. Effect of the presence of internal stress on the tension–compression asymmetry. 3. Effect of the magnitude of initial internal stress. 4. Effect of microstructural weakening alone due to prior ageing.
Fig. 11. A comparison of the model predictions for constant load and constant stress tests in tension and in compression.
Table 3 The model parameters used for the present illustrative calculations e_ 00 Qj=v C h0 H E 704 C kOswald QD A
1.8 106 s1 310 kJ/mol 20 30,000 MPa 0.4 175,000 MPa 1 1030 m3 /s 280 kJ/mol 16,035 MPa1
Fig. 12. The asymmetric influence of internal stress in tension and compression, as predicted by the present creep model. Clearly, the creep strain rates in compression are much higher than in tension.
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lower the internal stress thereby lowering the magnitude of effective stress. This leads to lower creep rates and the shape of the creep curve is similar to that of primary creep. The effect of recovery is quite the opposite in a tension test and there is a continuous increase in the creep rate.
Fig. 13. Variation of the compressive creep response with the initial magnitude of the internal stress.
The initial magnitude of internal stress has a large influence on initial creep rates, as shown in Fig. 13. Higher magnitude of initial internal stress leads to higher compressive creep rates. The recovery rates are also higher in these cases and a steady state value of the internal stress is soon reached. Beyond this point, the creep strain rates are independent of the initial magnitude of the internal stress and all three creep curves are parallel to each other. Even when no internal stresses are present, pre-aging has two direct consequences. As mentioned earlier, coarsening of the strengthening precipitate lowers r0 , thereby leading to higher strain rates. However, the rate of increase of particle radius varies inversely with the square of the particle radius. Hence, prior thermal ageing will reduce the initial creep strength, but the subsequent rate of weakening during creep will be lower than that of the unaged material. When the creep life far exceeds the pre-ageing time, the pre-ageing will have little effect on the creep rupture life. However, the reduction in life will be more severe at higher stresses and short-term tests. The model predictions presented in Fig. 14 are in agreement with this qualitative analysis. The effect of microstructural weakening has been simulated for two different pre-ageing conditions at test stresses of 400 and 738 MPa. The reduction in life is more severe for high stress/short-term creep test at 738 MPa.
References
Fig. 14. Effect of microstructural weakening due to particle ageing on the tensile creep response at 704 C: (a) 400 MPa, (b) 738 MPa.
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