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Cyclic stress–strain response of the ODS nickel-base, superalloy PM 1000 under variable amplitude loading at high temperatures
Materials Science and Engineering A281 (2000) 37 – 44 www.elsevier.com/locate/msea
Cyclic stress–strain response of the ODS nickel-base, superalloy PM 1000 under variable amplitude loading at high temperatures M. Heilmaier a,*, H.J. Maier b, A. Jung c, M. Nganbe a, F.E.H. Mu¨ller d, H.-J. Christ c b
a Institut fu¨r Festko¨rper- und Werkstofforschung Dresden, D-01171 Dresden, Germany Lehrstuhl fu¨r Werkstoffkunde, FB 10, Uni6ersita¨t Paderborn, D-33095 Paderborn, Germany c Institut fu¨r Werkstofftechnik, Uni6ersita¨t Siegen, D-57068 Siegen, Germany d Plansee GmbH Lechbruck, D-86983 Lechbruck, Germany
Received 21 May 1999; received in revised form 1 November 1999
Abstract The cyclic stress–strain behaviour of the recently developed oxide dispersion-strengthened nickel-base alloy PM 1000 was studied under constant and variable amplitude loading conditions. Single-step tests with a constant total strain amplitude as well as incremental step tests covering the same amplitude range have been carried out at 1123 and 1273 K. The interaction of the dislocations with the fine, homogeneously distributed oxide dispersoids was found to suppress the formation of dislocation cell structures. Rather, networks with dislocations frequently pinned at the particle/matrix interface have been observed by transmission electron microscopy. However, wavy dislocation slip still contributes to the stress – strain response. Despite the similarity of the resulting microstructures, the cyclic stress – strain curve obtained from constant amplitude tests deviates slightly from the one observed in incremental step tests. While non-Masing behaviour was found for constant amplitude testing, the strong influence of the dispersoids on dislocation mobility in combination with the constancy of dislocation arrangement yields Masing behaviour for the incremental step tests. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Nickel-base superalloy; Low-cycle fatigue; Oxide dispersion strengthening; Cyclic stress – strain response; Incremental step test; Masing behaviour; Microstructure
1. Introduction Components used in high-temperature applications commonly experience a combination of hot gas corrosion, creep and fatigue loading. Oxide dispersion strengthened (ODS) nickel-base superalloys have been shown to be promising candidate materials to best fulfil these multiple challenges, especially for hot and severely stressed components in aircraft and stationary gas turbines. Considerable progress has been achieved in the understanding of the basic creep mechanisms, with respect to involving in particular the interaction of dislocations with precipitated and dispersoid particles (for a recent review see [1,2]). However, systematic studies of the fatigue behaviour of ODS nickel-base superalloys are still missing. Besides their technical * Corresponding author. Tel.: +49-351-4659-721; fax: +49-3514659-320. E-mail address: [email protected] (M. Heilmaier)
importance, these materials represent ideal model systems for studying the influence of particles on fatigue behaviour at high temperatures without concomitant changes in particle microstructure, as a result of the excellent thermal stability of the dispersoids [3]. Thus, those mechanisms observed in precipitation-strengthened materials which lead to cyclic hardening or softening in cyclic straining, as a consequence of a change in the state of precipitation, should not be active in ODS nickel-base superalloys [4–6]. One method initially proposed to facilitate the determination of the cyclic stress–strain (CSS) curve is the incremental step test (IST) [7,8]. In the IST the strain amplitude is increased linearly with time up to a maximum in the first half of a so-called ‘strain block’. The strain amplitude is then decreased linearly during the second half of the strain block. The complete block is repeatedly applied until a stabilised stress–strain response is obtained, thus the CSS curve is obtained
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using only one specimen. Experiments performed at room temperature consistently indicate that the CSS curve obtained from an incremental step test matches its counterpart determined from constant amplitude tests only under specific microstructural conditions. In the case of planar-slip materials (such as a-brass [9,10]) or in materials with a strong influence of second-phase particles the CSS curve was found to be independent of the testing mode applied [6,11]. In both types of materials almost identical microstructures were observed after constant and variable amplitude loading. On the other hand, if wavy dislocation slip prevails, the microstructural state that develops is highly dependent on the cyclic loading conditions. Consequently, for wavy dislocation slip materials such as single-phase copper [12], nickel [13] and nickel – chromium solid solutions [14] the CSS curves obtained from the IST and constant amplitude tests, respectively, are reported to differ largely [11]. The objective of the present study is to correlate microstructural observations with the high-temperature stress–strain response of the recently developed ODS nickel-base superalloy PM 1000 (trademark of Plansee GmbH Lechbruck, Germany). The matrix of this material should favour wavy dislocation slip and therefore different CSS curves are expected from ISTs and constant amplitude tests. However, the dislocation/particle interaction in ODS alloys is currently considered to be the major strengthening mechanism under creep conditions [1,3,15]. If dislocation/particle interactions dominate not only creep, but also cyclic deformation behaviour as well then similar CSS curves are expected from ISTs and constant amplitude tests.
2. Experimental PM 1000 is essentially a nickel-base solid solution with 20 wt.% chromium and some minor additions of
Al and Ti. In order to increase the high-temperature strength Y2O3 dispersoids (0.6 wt.%) are added. The material tested was produced by mechanical alloying and supplied in the form of a hot extruded bar with a diameter of 50 mm. A subsequent recrystallisation heat treatment was employed to promote the evolution of a sharp 100-fibre texture, resulting in a microstructure with coarse elongated grains. The average length of the grains was found to be 2.6 mm in longitudinal direction. In the transverse direction grain size was 0.25 mm, yielding a grain aspect ratio (GAR) of about 10. Transmission electron microscopy (TEM) was used to study dislocation arrangements and to quantitatively determine the characteristic microstructural particle parameters. A mean diameter of d= 14 nm, a mean planar centre to centre spacing between particles of L=99 nm, and a volume fraction f=1.0% were evaluated for the Yttria particles. The microstructural parameters obtained for PM 1000 in the present study are almost identical to those reported for MA 754 (trademark of Inco Alloys International, Huntington, USA), which furthermore has a similar chemical composition [3]. For fatigue testing cylindrical specimens with a gauge length of 12.5 mm and a gauge diameter of 6 mm were machined such that the loading axis was parallel to the longitudinal direction. All specimens were electropolished within the gauge length prior to testing. Fully reversed total strain control loading with a triangular wave shape was conducted in air at constant strain rates (o; ) of 10 − 3 and 10 − 5 s − 1, respectively. All tests were carried out under isothermal conditions at temperatures (T) of 1123 or 1273 K. The constant amplitude tests were performed using an electromechanical testing machine (Instron 8562) with total strain amplitudes oa,t in the range from 0.1 to 0.7%. ‘Classical’ incremental step tests were carried out as proposed in [7] by means of a servohydraulic test system (MTS 810). In these tests each strain block consisted of 15 cycles. Within each strain block the total strain amplitude was increased and decreased linearly with time between the set limits of 0.1 and 0.6%, see Fig. 1. Thus, the total test time of one block amounted to approximately 180 and 18 000 s for the strain rates of 10 − 3 and 10 − 5 s − 1, respectively. The strain blocks were repeated until cyclic saturation was established.
3. Results
3.1. Constant amplitude loading
Fig. 1. Example of one block of the incremental step test at o; = 10 − 5 s − 1: total strain as a function of time.
Fig. 2 depicts a representative hysteresis loop obtained from a fatigue test conducted at oa,t =0.6% and T= 1273 K in the form of stress (s) versus total strain (solid line) and plastic strain (dashed line), respectively. As discussed in detail in [16], severe damage, which
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Fig. 2. Stabilised s – o-hysteresis loop with a total strain amplitude of oa,t = 0.6% (solid curve); dashed: s− opl-hysteresis loop. Temperature T =1273 K, strain rate o; = 10 − 3 s − 1.
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processes affect the stress–strain response at high temperatures, therefore the elastic modulus (E) is not reliable when determined from the slope of the unloading part of the hysteresis loop as usually done. Consequently, the dynamic elastic modulus was used, and E was determined to be 101 and 92 GPa for temperatures of 1123 and 1273 K, respectively. Cyclic stress response curves of PM 1000 at o; =10 − 3 −1 s are plotted in Fig. 3a and b for test temperatures of 1123 and 1273 K, respectively. At the lower test temperature of 1123 K the material displayed fairly constant stress amplitudes from the start of the test. In contrast, specimens cycled at the higher test temperature of 1273 K showed continuous cyclic softening. The irregularities observed in the stress response curves are caused by the onset of damage. The higher the total strain amplitude the earlier damage sets in, and in fatigue tests with oa,t = 0.6% or higher an immediate onset of internal damage, i.e. crack formation, was observed [16]. CSS curves are usually determined from stress and strain amplitudes at half-life if the material does not show stabilised deformation behaviour. It is obvious from Fig. 3a and b that the damage induced in the bulk material does affect stress–strain response for a considerably large part of fatigue life. Hence, in order to avoid any superimposed influence from damage the CSS curves had to be calculated using stress–strain behaviour prior to the onset of damage. This was carried out as follows: in cases where a plateau in the stress level of the cyclic hardening/softening curves was observed this plateau value was defined as the actual stress amplitude of cyclic saturation sa,s. In contrast, in cases where continuous softening was present the stress amplitude at half life was chosen for sa,s. It is important to note that the former case applied to most of the single step tests at the lower temperature of 1123 K, while the latter was found to hold for tests at the higher temperature of 1273 K. It is conceivable to use a different criterion for constructing the CSS curves from single step tests, however, this has a negligible influence on the overall trends discussed in the next section.
3.2. Variable amplitude loading Fig. 3. Cyclic hardening/softening curves for different applied total strain amplitudes at o; =10 − 3 s − 1. The open symbols mark the saturated stress amplitude, testing temperature: (a) 1123 K and (b) 1273 K.
affects cyclic stress – strain response, occurs early in fatigue life under these tests conditions. Therefore, the hysteresis loop plotted in Fig. 2 was recorded after 10 cycles in order to show the true cyclic stress–strain response of the material. Plastic strain (opl) was obtained by subtracting the elastic strain (oel) from the measured total strain. Time dependent deformation
Fig. 4a and b shows representative stress–strain responses to the loading scheme of Fig. 1 for ISTs conducted at 1123 and 1273 K, respectively. A state of cyclic saturation was approached rapidly, i.e. no further changes in the stress–strain path were observed after a few strain blocks were applied. Specifically, at the lower strain rate of o; = 10 − 5 s − 1 and T= 1123 K (Fig. 4a) cyclic saturation was attained after only two blocks. For the test conditions shown in Fig. 4b, nine strain blocks were required to establish cyclic saturation. From plots like Fig. 4a and b the CSS curve was
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obtained by connecting the tips of the load-reversal points in tension. Fig. 5 compares the CSS curves obtained from incremental step tests (dashed lines) with the saturation values of the stress amplitude, sa,s, from constant amplitude tests (open and full symbols). Note that the sa,s
values given were calculated from hysteresis loops before damage. Monotonic stress–strain curves are given as solid lines for comparison clearly revealing cyclic softening for all cyclic deformation conditions chosen at the lower temperature of 1123 K. Further, it is appreciable from Fig. 5 that differences exist between CSS curves obtained in constant amplitude tests and ISTs. These differences are more pronounced at the lower temperature (1123 K). The CSS curve of the single-step tests clearly lies above the one from the IST at high plastic strain amplitudes, whereas the reverse is true at low amplitudes. This behaviour is typical of wavy-slip material [11]. While the scatter of the data points at 1123 K is of the order of the size of the symbols in Fig. 5 and, hence, relatively small, the rapid development of damage leads to a somewhat higher scatter of data at the higher temperature (1273 K). As an example the two data points at a total strain amplitude of 0.6% (corresponding to a plastic strain amplitude of : 0.41% in Fig. 5) represent two independent tests carried out under the same testing conditions. Consequently, differences between the single step tests and the IST that appear to be small are only tendentiously detectable, if at all. Hence, from an engineering point of view, it can be concluded that in the present case the IST fulfils its originally proposed purpose [7,8] as a time and material saving method to determine the CSS curve.
3.3. Microstructure
Fig. 4. Stress – strain response for incremental step tests, deformation conditions: (a) 1123 K and o; =10 − 5 s − 1; (b) 1273 K and o; =10 − 3 s − 1. For the sake of clarity only the decreasing half of the strain block is shown.
Fig. 5. Comparison of the cyclic stress–strain curves obtained from incremental step tests (dashed lines) and single-step tests (symbols) with monotonic stress–strain curves (solid lines) at o; = 10 − 3 s − 1.
The TEM micrographs depicted in Fig. 6a–c show typical dislocation microstructures as observed in samples cycled into saturation. It is clearly apparent that the dislocation arrangements formed under cyclic loading conditions are barely affected by the actual loading mode. Similar to results reported from creep tests [2,17], an attractive dislocation-particle interaction (interfacial pinning) was frequently observed. Fatigued specimens typically displayed networks of loosely connected dislocations with a mesh size in the range from 100 to 200 nm (Fig. 6a and b). This mesh size coincides well with the mean planar particle spacing reported in Section 2. In contrast, such dislocation arrangements were absent after monotonic deformation (Fig. 7). Additional TEM investigations on specimens fatigued to failure have proven changes in the dislocation microstructure to be negligible. Thus, from similar TEM micrographs such as Fig. 6a–c and Fig. 7 steadystate dislocation densities r were evaluated for different applied strain rates and strain amplitudes, respectively. With increasing strain amplitude, and thus an increasing value of Ds/2= sa,s the dislocation density was found to vary according to r8s 2 [18]. Fig. 8 summarises these data in a plot of the calculated steadystate dislocation spacing r − 0.5 versus the applied stress
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the data obtained from cyclic deformation seem to be limited to r − 0.5 values above the grey shaded area for the average particle spacing L and, hence, the formation of characteristic dislocation networks is observed as previously demonstrated in Fig. 6a and b. However, no changes in the basic deformation mechanism and in the dislocation arrangements could be detected. Particularly, the evolution of ‘classical’ heterogeneous dislocation structures, consisting of subgrain boundaries or cell walls, during cyclic plastic deformation was not observed. In contrast, in the case of monotonic deformation the limitation of the dislocation density by the particle spacing seems not to be fulfilled. Generally, compared to cyclic deformation one obtains lower r − 0.5 values and vice versa higher dislocation densities, compare the corresponding circles and squares in Fig. 8. Specifically, at o; = 10 − 3 s − l the dislocation spacings for the monotonic deformation (full squares) are even significantly lower than L.
Fig. 7. Bright-field TEM micrograph of a specimen deformed monotonically to 5 pct plastic strain at T= 1123 K and o; = 10 − 3 s − 1.
Fig. 6. TEM micrographs of samples fatigued at 1123 K and o; = 10 − 3 s − l into cyclic saturation. (a) constant amplitude loading at oa,t = 0.7%, bright-field condition; (b) constant amplitude loading at oa,t = 0.5%, bright-field condition; (c) IST, weak-beam condition.
s. As our TEM investigation was limited to only one temperature (1123 K) we have omitted the commonly used normalisation of s by the shear modulus G in Fig. 8. All data follow the well-known inverse stress proportionality, see [19], with kr =1.6 independently on the applied strain rate and loading conditions. Note that
Fig. 8. Inverse stress proportionality of characteristic dislocation spacings after monotonic (squares) and cyclic (circles) deformation at 1123 K. The grey shaded area indicates the average particle spacing L.
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4. Discussion
4.1. Constant amplitude loading As expected, saturated stress amplitudes decreased with reduced strain amplitude and, hence, cyclic life increased (Fig. 3a and b). Moreover, the stress amplitudes are decreased drastically as the temperature was increased from 1123 to 1273 K. This can be rationalised by the decline of dispersion strengthening which is commonly observed during monotonic creep testing of ODS nickel-base alloys [1,2]. Comparison of Fig. 3a and b reveals that despite the drastic decrease in stress amplitude, fatigue life for a given strain amplitude is lower at the higher test temperature. The effect of test temperature on fatigue life can be attributed mainly to the enhanced diffusion-controlled growth of voids on transverse grain boundaries. For further details on fatigue life issues the reader can refer to [16].
4.2. Variable amplitude loading As shown in earlier systematic studies [11,13] materials revealing wavy dislocation slip generally yield significantly different CSS curves in constant amplitude tests and ISTs. This can be rationalised as follows. In constant amplitude tests drastically different dislocation arrangements are formed in fatigue tests with small and large plastic strain amplitudes, respectively. In an IST, however, the dislocation arrangement cannot adapt rapidly enough to follow the continuously varying plastic strain amplitude. Thus, a dislocation arrangement is established which corresponds to some average plastic strain amplitude [11]. At high temperatures nickel – chromium solid solutions were found to exhibit wavy dislocation slip [14]. Further, as test temperatures applied in the present study correspond to roughly 0.67 and 0.76 of the melting point, easy cross-slip in combination with dislocation climb is expected. In this study it was observed that the cyclic loading conditions only slightly affected the CSS curves (Fig. 5). We may thus conclude that, despite the strong interactions between the small incoherent Yttria dispersoids and dislocations, the deformation behaviour is also affected by dislocation / dislocation interactions. Obviously, the formation of complex three-dimensional dislocation structures typical of wavy-slip materials is suppressed. However, dislocation networks are formed showing a mesh size that depends on the stress amplitude.
4.3. Masing beha6iour Masing [20] developed a simple model for describing the cyclic stress–strain behaviour of polycrystals. In the model, the material is treated as a composite of elemen-
tary volumes that are strained in parallel. The deformation behaviour of each element is assumed to be ideally elastic–plastic, and the distribution of elements is chosen in such a way as to represent the actual variations in local yield stress within the microstructure [21]. As seen in Fig. 2 an almost square shaped hysteresis loop is obtained if stress is plotted versus plastic strain. In terms of the Masing model this means that all the elements have quite similar yield levels. This is expected from the observation that dispersoid/dislocation interactions dominate stress–strain response and that the mean particle spacing is within a narrow range. A simple graphical check whether a material exhibits ‘Masing behaviour’ in cyclic loading or not only requires a set of stabilised hysteresis loops obtained at different values of Dopl/2. The hysteresis loops are plotted in relative co-ordinates, i.e. the points of load reversal in compression are shifted into a common origin, and Masing behaviour is fulfilled if the ascending branches of the loops form a common curve (see [22]). Consequently, the term ‘non-Masing behaviour’ is used if deviations from a common curve are observed. An implicit assumption in Masing’s consideration is that no microstructural changes occur during loading. In other words, the same microstructure and deformation mechanisms prevail at all plastic strain amplitudes applied. Following this line of reasoning and keeping in mind the observed microstructural dominance of the dispersoids on the resulting dislocation arrangements, one should expect Masing behaviour for variable amplitude loading conditions. In the case of constant amplitude testing a slight deviation from Masing behaviour is to be expected, since, in addition to the important particle/dislocation interaction an amplitudedependent dislocation arrangement was tendentiously observed, see e.g. Fig. 6a and b. Indeed, this prediction is realised. On the one hand, non-Masing behaviour was observed in constant amplitude tests, compare Fig. 9a and Fig. 10a. The deviations in the ascending branches indicate that different microstructural states form during cycling at different strain amplitudes which is hard to confirm by TEM. On the other hand, Masing behaviour is clearly apparent in Fig. 9b and Fig. 10b, which were obtained from the ISTs. Interestingly, the effect of loading mode on deformation behaviour described above was simultaneously observed for both the test temperatures. The experiments have clearly revealed that a stable particle microstructure, which dominates stress–strain response, is not the only prerequisite for Masing behaviour. Rather, additional effects resulting from dislocation/dislocation interactions need to be taken into account. The differences in dislocation arrangements were too small to be quantitatively determined by TEM, but are clearly apparent if the fatigue data is plotted in relative coordinates.
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of these findings, differences in the CSS curves obtained in different testing modes can be easily understood. However, it should be stated that these differences are small, since the dislocation/particle interactions dominate the cyclic stress–strain response irrespectively of the type of testing. Therefore, from an engineering point of view the incremental step test can be considered to fulfil its originally proposed purpose for ODS nickel-based alloys, that is, to enable a fast and easy determination of the CSS curve.
Acknowledgements This work has been carried out within the framework of the priority programme ‘Microstructure and mechanical behaviour of metallic materials at high temperatures’ of the Deutsche Forschungsgemeinschaft (DFG). Funding from the DFG is gratefully acknowledged. One of the authors (M.H.) would like to thank the Alexander von Humboldt-Stiftung for financial support through the Feodor-Lynen program.
Fig. 9. Cyclic stress – strain response in Masing representation (relative co-ordinates) at 1123 K and o; = 10 − 3 s − l. (a) Single-step tests (non-Masing behaviour); (b) Incremental step test (Masing behaviour).
5. Conclusions and summary In the present work a nickel-base alloy strengthened by a small quantity of incoherent oxide dispersoids (PM 1000) has been subjected to constant and variable amplitude loading at elevated temperatures. Only variable amplitude loading yielded Masing behaviour. Furthermore, the CSS curve obtained from constant amplitude tests deviated slightly from the corresponding curve determined by the incremental step test. This behaviour, which is identical to that observed for wavyslip materials, is surprising when taking the strong dislocation/particle interaction and the stability of the dispersoids into account. As investigated by thorough TEM studies, the dislocation arrangement is slightly affected by the strain amplitude applied in single-step tests. Despite the fact that it is not possible to quantitatively determine this dependence, it manifests itself in non-Masing behaviour found under these testing conditions. In the incremental step test, however, the rapidly changing strain amplitude leads to a microstructure, which is constant in both the particle and dislocation arrangement. Consequently, Masing behaviour was observed. On the basis
Fig. 10. Same as Fig. 9, T=1273 K. (a) Single-step tests (non-Masing behaviour); (b) Incremental step test (Masing behaviour).
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References [1] E. Arzt, Res. Mech. 31 (1991) 399. [2] M. Heilmaier, B. Reppich, in: R.S. Mishra, A.K. Mukherjee, K.L. Murty (Eds.), Creep Behavior of Advanced Materials for the 21st Century, TMS, Warrendale, PA, 1999, p. 267. [3] M. Heilmaier, B. Reppich, Met. Mater. Trans. 27A (1996) 3861. [4] S.J. Brett, R.D. Doherty, Mater. Sci. Eng. 32 (1978) 255. [5] M. Clavel, A. Pineau, Mater. Sci. Eng. 55 (1982) 157. [6] H.-J. Christ, K. Lades, L. Vo¨lkl, H. Mughrabi, in: K.-T. Rie (Ed.), Proc. Conf. LCF-3, Elsevier, London, 1992, p. 100. [7] R.W. Landgraf, in: Achievement of High Fatigue Resistance in Metals and Alloys, ASTM STP 467, American Society for Testing and Materials, Philadelphia, PA, 1970, p. 3. [8] R.W. Landgraf, J. Morrow, T. Endo, J. Mater. JMLSA 4 (1969) 176. [9] P. Lukas, M. Klesnil, Phys. Stat. Sol. 37 (1970) 833. [10] P. Lukas, M. Klesnil, Phys. Stat. Sol. 38 (1971) 247.
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[11] H.-J. Christ, H. Mughrabi, Fatigue Fract. Eng. Mater. Struct. 19 (1996) 335. [12] H. Mughrabi, Acta Met. 31 (1983) 1367. [13] C. Holste, H.-J. Burmeister, Phys. Stat. Sol. (a) 57 (1980) 269. [14] V. Gerold, H.P. Karnthaler, Acta Met. 37 (1989) 2177. [15] J. Ro¨sler, E. Arzt, Acta Met. 38 (1990) 671. [16] F.E.H. Mu¨ller, M. Nganbe, M. Heilmaier, J. Adv. Mater., in press. [17] J.H. Schro¨der, E. Arzt, Scr. Met. 19 (1985) 1129. [18] M. Heilmaier, F.E.H. Mu¨ller, in: K.-T. Rie, P.D. Portella (Eds.), Proc. Conf. LCF-4, Elsevier, Oxford, England, 1998, p. 629. [19] W. Blum, in: R.W. Cahn, P. Haasen, E.J. Kramer (Eds.), Materials Science and Technology, H. Mughrabi (Ed.), vol. 6: Plastic Deformation and Fracture of Materials, VCH-Verlagsgesellschaft, Weinheim, Germany, 1992, pp. 359 – 405. [20] G. Masing, Z. Techn. Physik 6 (1925) 569. [21] R.P. Skelton, H.J. Maier, H.J. Christ, Mater. Sci. Eng. A238 (1997) 377. [22] H. Abdel-Raouf, T.H. Topper, A. Plumtree, Proc. 4th Int. Conf. on Fracture, Pergamon Press, London, 1977, p. 1207.
Cyclic stress–strain response of the ODS nickel-base, superalloy PM 1000 under variable amplitude loading at high temperatures M. Heilmaier a,*, H.J. Maier b, A. Jung c, M. Nganbe a, F.E.H. Mu¨ller d, H.-J. Christ c b
a Institut fu¨r Festko¨rper- und Werkstofforschung Dresden, D-01171 Dresden, Germany Lehrstuhl fu¨r Werkstoffkunde, FB 10, Uni6ersita¨t Paderborn, D-33095 Paderborn, Germany c Institut fu¨r Werkstofftechnik, Uni6ersita¨t Siegen, D-57068 Siegen, Germany d Plansee GmbH Lechbruck, D-86983 Lechbruck, Germany
Received 21 May 1999; received in revised form 1 November 1999
Abstract The cyclic stress–strain behaviour of the recently developed oxide dispersion-strengthened nickel-base alloy PM 1000 was studied under constant and variable amplitude loading conditions. Single-step tests with a constant total strain amplitude as well as incremental step tests covering the same amplitude range have been carried out at 1123 and 1273 K. The interaction of the dislocations with the fine, homogeneously distributed oxide dispersoids was found to suppress the formation of dislocation cell structures. Rather, networks with dislocations frequently pinned at the particle/matrix interface have been observed by transmission electron microscopy. However, wavy dislocation slip still contributes to the stress – strain response. Despite the similarity of the resulting microstructures, the cyclic stress – strain curve obtained from constant amplitude tests deviates slightly from the one observed in incremental step tests. While non-Masing behaviour was found for constant amplitude testing, the strong influence of the dispersoids on dislocation mobility in combination with the constancy of dislocation arrangement yields Masing behaviour for the incremental step tests. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Nickel-base superalloy; Low-cycle fatigue; Oxide dispersion strengthening; Cyclic stress – strain response; Incremental step test; Masing behaviour; Microstructure
1. Introduction Components used in high-temperature applications commonly experience a combination of hot gas corrosion, creep and fatigue loading. Oxide dispersion strengthened (ODS) nickel-base superalloys have been shown to be promising candidate materials to best fulfil these multiple challenges, especially for hot and severely stressed components in aircraft and stationary gas turbines. Considerable progress has been achieved in the understanding of the basic creep mechanisms, with respect to involving in particular the interaction of dislocations with precipitated and dispersoid particles (for a recent review see [1,2]). However, systematic studies of the fatigue behaviour of ODS nickel-base superalloys are still missing. Besides their technical * Corresponding author. Tel.: +49-351-4659-721; fax: +49-3514659-320. E-mail address: [email protected] (M. Heilmaier)
importance, these materials represent ideal model systems for studying the influence of particles on fatigue behaviour at high temperatures without concomitant changes in particle microstructure, as a result of the excellent thermal stability of the dispersoids [3]. Thus, those mechanisms observed in precipitation-strengthened materials which lead to cyclic hardening or softening in cyclic straining, as a consequence of a change in the state of precipitation, should not be active in ODS nickel-base superalloys [4–6]. One method initially proposed to facilitate the determination of the cyclic stress–strain (CSS) curve is the incremental step test (IST) [7,8]. In the IST the strain amplitude is increased linearly with time up to a maximum in the first half of a so-called ‘strain block’. The strain amplitude is then decreased linearly during the second half of the strain block. The complete block is repeatedly applied until a stabilised stress–strain response is obtained, thus the CSS curve is obtained
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using only one specimen. Experiments performed at room temperature consistently indicate that the CSS curve obtained from an incremental step test matches its counterpart determined from constant amplitude tests only under specific microstructural conditions. In the case of planar-slip materials (such as a-brass [9,10]) or in materials with a strong influence of second-phase particles the CSS curve was found to be independent of the testing mode applied [6,11]. In both types of materials almost identical microstructures were observed after constant and variable amplitude loading. On the other hand, if wavy dislocation slip prevails, the microstructural state that develops is highly dependent on the cyclic loading conditions. Consequently, for wavy dislocation slip materials such as single-phase copper [12], nickel [13] and nickel – chromium solid solutions [14] the CSS curves obtained from the IST and constant amplitude tests, respectively, are reported to differ largely [11]. The objective of the present study is to correlate microstructural observations with the high-temperature stress–strain response of the recently developed ODS nickel-base superalloy PM 1000 (trademark of Plansee GmbH Lechbruck, Germany). The matrix of this material should favour wavy dislocation slip and therefore different CSS curves are expected from ISTs and constant amplitude tests. However, the dislocation/particle interaction in ODS alloys is currently considered to be the major strengthening mechanism under creep conditions [1,3,15]. If dislocation/particle interactions dominate not only creep, but also cyclic deformation behaviour as well then similar CSS curves are expected from ISTs and constant amplitude tests.
2. Experimental PM 1000 is essentially a nickel-base solid solution with 20 wt.% chromium and some minor additions of
Al and Ti. In order to increase the high-temperature strength Y2O3 dispersoids (0.6 wt.%) are added. The material tested was produced by mechanical alloying and supplied in the form of a hot extruded bar with a diameter of 50 mm. A subsequent recrystallisation heat treatment was employed to promote the evolution of a sharp 100-fibre texture, resulting in a microstructure with coarse elongated grains. The average length of the grains was found to be 2.6 mm in longitudinal direction. In the transverse direction grain size was 0.25 mm, yielding a grain aspect ratio (GAR) of about 10. Transmission electron microscopy (TEM) was used to study dislocation arrangements and to quantitatively determine the characteristic microstructural particle parameters. A mean diameter of d= 14 nm, a mean planar centre to centre spacing between particles of L=99 nm, and a volume fraction f=1.0% were evaluated for the Yttria particles. The microstructural parameters obtained for PM 1000 in the present study are almost identical to those reported for MA 754 (trademark of Inco Alloys International, Huntington, USA), which furthermore has a similar chemical composition [3]. For fatigue testing cylindrical specimens with a gauge length of 12.5 mm and a gauge diameter of 6 mm were machined such that the loading axis was parallel to the longitudinal direction. All specimens were electropolished within the gauge length prior to testing. Fully reversed total strain control loading with a triangular wave shape was conducted in air at constant strain rates (o; ) of 10 − 3 and 10 − 5 s − 1, respectively. All tests were carried out under isothermal conditions at temperatures (T) of 1123 or 1273 K. The constant amplitude tests were performed using an electromechanical testing machine (Instron 8562) with total strain amplitudes oa,t in the range from 0.1 to 0.7%. ‘Classical’ incremental step tests were carried out as proposed in [7] by means of a servohydraulic test system (MTS 810). In these tests each strain block consisted of 15 cycles. Within each strain block the total strain amplitude was increased and decreased linearly with time between the set limits of 0.1 and 0.6%, see Fig. 1. Thus, the total test time of one block amounted to approximately 180 and 18 000 s for the strain rates of 10 − 3 and 10 − 5 s − 1, respectively. The strain blocks were repeated until cyclic saturation was established.
3. Results
3.1. Constant amplitude loading
Fig. 1. Example of one block of the incremental step test at o; = 10 − 5 s − 1: total strain as a function of time.
Fig. 2 depicts a representative hysteresis loop obtained from a fatigue test conducted at oa,t =0.6% and T= 1273 K in the form of stress (s) versus total strain (solid line) and plastic strain (dashed line), respectively. As discussed in detail in [16], severe damage, which
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Fig. 2. Stabilised s – o-hysteresis loop with a total strain amplitude of oa,t = 0.6% (solid curve); dashed: s− opl-hysteresis loop. Temperature T =1273 K, strain rate o; = 10 − 3 s − 1.
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processes affect the stress–strain response at high temperatures, therefore the elastic modulus (E) is not reliable when determined from the slope of the unloading part of the hysteresis loop as usually done. Consequently, the dynamic elastic modulus was used, and E was determined to be 101 and 92 GPa for temperatures of 1123 and 1273 K, respectively. Cyclic stress response curves of PM 1000 at o; =10 − 3 −1 s are plotted in Fig. 3a and b for test temperatures of 1123 and 1273 K, respectively. At the lower test temperature of 1123 K the material displayed fairly constant stress amplitudes from the start of the test. In contrast, specimens cycled at the higher test temperature of 1273 K showed continuous cyclic softening. The irregularities observed in the stress response curves are caused by the onset of damage. The higher the total strain amplitude the earlier damage sets in, and in fatigue tests with oa,t = 0.6% or higher an immediate onset of internal damage, i.e. crack formation, was observed [16]. CSS curves are usually determined from stress and strain amplitudes at half-life if the material does not show stabilised deformation behaviour. It is obvious from Fig. 3a and b that the damage induced in the bulk material does affect stress–strain response for a considerably large part of fatigue life. Hence, in order to avoid any superimposed influence from damage the CSS curves had to be calculated using stress–strain behaviour prior to the onset of damage. This was carried out as follows: in cases where a plateau in the stress level of the cyclic hardening/softening curves was observed this plateau value was defined as the actual stress amplitude of cyclic saturation sa,s. In contrast, in cases where continuous softening was present the stress amplitude at half life was chosen for sa,s. It is important to note that the former case applied to most of the single step tests at the lower temperature of 1123 K, while the latter was found to hold for tests at the higher temperature of 1273 K. It is conceivable to use a different criterion for constructing the CSS curves from single step tests, however, this has a negligible influence on the overall trends discussed in the next section.
3.2. Variable amplitude loading Fig. 3. Cyclic hardening/softening curves for different applied total strain amplitudes at o; =10 − 3 s − 1. The open symbols mark the saturated stress amplitude, testing temperature: (a) 1123 K and (b) 1273 K.
affects cyclic stress – strain response, occurs early in fatigue life under these tests conditions. Therefore, the hysteresis loop plotted in Fig. 2 was recorded after 10 cycles in order to show the true cyclic stress–strain response of the material. Plastic strain (opl) was obtained by subtracting the elastic strain (oel) from the measured total strain. Time dependent deformation
Fig. 4a and b shows representative stress–strain responses to the loading scheme of Fig. 1 for ISTs conducted at 1123 and 1273 K, respectively. A state of cyclic saturation was approached rapidly, i.e. no further changes in the stress–strain path were observed after a few strain blocks were applied. Specifically, at the lower strain rate of o; = 10 − 5 s − 1 and T= 1123 K (Fig. 4a) cyclic saturation was attained after only two blocks. For the test conditions shown in Fig. 4b, nine strain blocks were required to establish cyclic saturation. From plots like Fig. 4a and b the CSS curve was
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obtained by connecting the tips of the load-reversal points in tension. Fig. 5 compares the CSS curves obtained from incremental step tests (dashed lines) with the saturation values of the stress amplitude, sa,s, from constant amplitude tests (open and full symbols). Note that the sa,s
values given were calculated from hysteresis loops before damage. Monotonic stress–strain curves are given as solid lines for comparison clearly revealing cyclic softening for all cyclic deformation conditions chosen at the lower temperature of 1123 K. Further, it is appreciable from Fig. 5 that differences exist between CSS curves obtained in constant amplitude tests and ISTs. These differences are more pronounced at the lower temperature (1123 K). The CSS curve of the single-step tests clearly lies above the one from the IST at high plastic strain amplitudes, whereas the reverse is true at low amplitudes. This behaviour is typical of wavy-slip material [11]. While the scatter of the data points at 1123 K is of the order of the size of the symbols in Fig. 5 and, hence, relatively small, the rapid development of damage leads to a somewhat higher scatter of data at the higher temperature (1273 K). As an example the two data points at a total strain amplitude of 0.6% (corresponding to a plastic strain amplitude of : 0.41% in Fig. 5) represent two independent tests carried out under the same testing conditions. Consequently, differences between the single step tests and the IST that appear to be small are only tendentiously detectable, if at all. Hence, from an engineering point of view, it can be concluded that in the present case the IST fulfils its originally proposed purpose [7,8] as a time and material saving method to determine the CSS curve.
3.3. Microstructure
Fig. 4. Stress – strain response for incremental step tests, deformation conditions: (a) 1123 K and o; =10 − 5 s − 1; (b) 1273 K and o; =10 − 3 s − 1. For the sake of clarity only the decreasing half of the strain block is shown.
Fig. 5. Comparison of the cyclic stress–strain curves obtained from incremental step tests (dashed lines) and single-step tests (symbols) with monotonic stress–strain curves (solid lines) at o; = 10 − 3 s − 1.
The TEM micrographs depicted in Fig. 6a–c show typical dislocation microstructures as observed in samples cycled into saturation. It is clearly apparent that the dislocation arrangements formed under cyclic loading conditions are barely affected by the actual loading mode. Similar to results reported from creep tests [2,17], an attractive dislocation-particle interaction (interfacial pinning) was frequently observed. Fatigued specimens typically displayed networks of loosely connected dislocations with a mesh size in the range from 100 to 200 nm (Fig. 6a and b). This mesh size coincides well with the mean planar particle spacing reported in Section 2. In contrast, such dislocation arrangements were absent after monotonic deformation (Fig. 7). Additional TEM investigations on specimens fatigued to failure have proven changes in the dislocation microstructure to be negligible. Thus, from similar TEM micrographs such as Fig. 6a–c and Fig. 7 steadystate dislocation densities r were evaluated for different applied strain rates and strain amplitudes, respectively. With increasing strain amplitude, and thus an increasing value of Ds/2= sa,s the dislocation density was found to vary according to r8s 2 [18]. Fig. 8 summarises these data in a plot of the calculated steadystate dislocation spacing r − 0.5 versus the applied stress
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the data obtained from cyclic deformation seem to be limited to r − 0.5 values above the grey shaded area for the average particle spacing L and, hence, the formation of characteristic dislocation networks is observed as previously demonstrated in Fig. 6a and b. However, no changes in the basic deformation mechanism and in the dislocation arrangements could be detected. Particularly, the evolution of ‘classical’ heterogeneous dislocation structures, consisting of subgrain boundaries or cell walls, during cyclic plastic deformation was not observed. In contrast, in the case of monotonic deformation the limitation of the dislocation density by the particle spacing seems not to be fulfilled. Generally, compared to cyclic deformation one obtains lower r − 0.5 values and vice versa higher dislocation densities, compare the corresponding circles and squares in Fig. 8. Specifically, at o; = 10 − 3 s − l the dislocation spacings for the monotonic deformation (full squares) are even significantly lower than L.
Fig. 7. Bright-field TEM micrograph of a specimen deformed monotonically to 5 pct plastic strain at T= 1123 K and o; = 10 − 3 s − 1.
Fig. 6. TEM micrographs of samples fatigued at 1123 K and o; = 10 − 3 s − l into cyclic saturation. (a) constant amplitude loading at oa,t = 0.7%, bright-field condition; (b) constant amplitude loading at oa,t = 0.5%, bright-field condition; (c) IST, weak-beam condition.
s. As our TEM investigation was limited to only one temperature (1123 K) we have omitted the commonly used normalisation of s by the shear modulus G in Fig. 8. All data follow the well-known inverse stress proportionality, see [19], with kr =1.6 independently on the applied strain rate and loading conditions. Note that
Fig. 8. Inverse stress proportionality of characteristic dislocation spacings after monotonic (squares) and cyclic (circles) deformation at 1123 K. The grey shaded area indicates the average particle spacing L.
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4. Discussion
4.1. Constant amplitude loading As expected, saturated stress amplitudes decreased with reduced strain amplitude and, hence, cyclic life increased (Fig. 3a and b). Moreover, the stress amplitudes are decreased drastically as the temperature was increased from 1123 to 1273 K. This can be rationalised by the decline of dispersion strengthening which is commonly observed during monotonic creep testing of ODS nickel-base alloys [1,2]. Comparison of Fig. 3a and b reveals that despite the drastic decrease in stress amplitude, fatigue life for a given strain amplitude is lower at the higher test temperature. The effect of test temperature on fatigue life can be attributed mainly to the enhanced diffusion-controlled growth of voids on transverse grain boundaries. For further details on fatigue life issues the reader can refer to [16].
4.2. Variable amplitude loading As shown in earlier systematic studies [11,13] materials revealing wavy dislocation slip generally yield significantly different CSS curves in constant amplitude tests and ISTs. This can be rationalised as follows. In constant amplitude tests drastically different dislocation arrangements are formed in fatigue tests with small and large plastic strain amplitudes, respectively. In an IST, however, the dislocation arrangement cannot adapt rapidly enough to follow the continuously varying plastic strain amplitude. Thus, a dislocation arrangement is established which corresponds to some average plastic strain amplitude [11]. At high temperatures nickel – chromium solid solutions were found to exhibit wavy dislocation slip [14]. Further, as test temperatures applied in the present study correspond to roughly 0.67 and 0.76 of the melting point, easy cross-slip in combination with dislocation climb is expected. In this study it was observed that the cyclic loading conditions only slightly affected the CSS curves (Fig. 5). We may thus conclude that, despite the strong interactions between the small incoherent Yttria dispersoids and dislocations, the deformation behaviour is also affected by dislocation / dislocation interactions. Obviously, the formation of complex three-dimensional dislocation structures typical of wavy-slip materials is suppressed. However, dislocation networks are formed showing a mesh size that depends on the stress amplitude.
4.3. Masing beha6iour Masing [20] developed a simple model for describing the cyclic stress–strain behaviour of polycrystals. In the model, the material is treated as a composite of elemen-
tary volumes that are strained in parallel. The deformation behaviour of each element is assumed to be ideally elastic–plastic, and the distribution of elements is chosen in such a way as to represent the actual variations in local yield stress within the microstructure [21]. As seen in Fig. 2 an almost square shaped hysteresis loop is obtained if stress is plotted versus plastic strain. In terms of the Masing model this means that all the elements have quite similar yield levels. This is expected from the observation that dispersoid/dislocation interactions dominate stress–strain response and that the mean particle spacing is within a narrow range. A simple graphical check whether a material exhibits ‘Masing behaviour’ in cyclic loading or not only requires a set of stabilised hysteresis loops obtained at different values of Dopl/2. The hysteresis loops are plotted in relative co-ordinates, i.e. the points of load reversal in compression are shifted into a common origin, and Masing behaviour is fulfilled if the ascending branches of the loops form a common curve (see [22]). Consequently, the term ‘non-Masing behaviour’ is used if deviations from a common curve are observed. An implicit assumption in Masing’s consideration is that no microstructural changes occur during loading. In other words, the same microstructure and deformation mechanisms prevail at all plastic strain amplitudes applied. Following this line of reasoning and keeping in mind the observed microstructural dominance of the dispersoids on the resulting dislocation arrangements, one should expect Masing behaviour for variable amplitude loading conditions. In the case of constant amplitude testing a slight deviation from Masing behaviour is to be expected, since, in addition to the important particle/dislocation interaction an amplitudedependent dislocation arrangement was tendentiously observed, see e.g. Fig. 6a and b. Indeed, this prediction is realised. On the one hand, non-Masing behaviour was observed in constant amplitude tests, compare Fig. 9a and Fig. 10a. The deviations in the ascending branches indicate that different microstructural states form during cycling at different strain amplitudes which is hard to confirm by TEM. On the other hand, Masing behaviour is clearly apparent in Fig. 9b and Fig. 10b, which were obtained from the ISTs. Interestingly, the effect of loading mode on deformation behaviour described above was simultaneously observed for both the test temperatures. The experiments have clearly revealed that a stable particle microstructure, which dominates stress–strain response, is not the only prerequisite for Masing behaviour. Rather, additional effects resulting from dislocation/dislocation interactions need to be taken into account. The differences in dislocation arrangements were too small to be quantitatively determined by TEM, but are clearly apparent if the fatigue data is plotted in relative coordinates.
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of these findings, differences in the CSS curves obtained in different testing modes can be easily understood. However, it should be stated that these differences are small, since the dislocation/particle interactions dominate the cyclic stress–strain response irrespectively of the type of testing. Therefore, from an engineering point of view the incremental step test can be considered to fulfil its originally proposed purpose for ODS nickel-based alloys, that is, to enable a fast and easy determination of the CSS curve.
Acknowledgements This work has been carried out within the framework of the priority programme ‘Microstructure and mechanical behaviour of metallic materials at high temperatures’ of the Deutsche Forschungsgemeinschaft (DFG). Funding from the DFG is gratefully acknowledged. One of the authors (M.H.) would like to thank the Alexander von Humboldt-Stiftung for financial support through the Feodor-Lynen program.
Fig. 9. Cyclic stress – strain response in Masing representation (relative co-ordinates) at 1123 K and o; = 10 − 3 s − l. (a) Single-step tests (non-Masing behaviour); (b) Incremental step test (Masing behaviour).
5. Conclusions and summary In the present work a nickel-base alloy strengthened by a small quantity of incoherent oxide dispersoids (PM 1000) has been subjected to constant and variable amplitude loading at elevated temperatures. Only variable amplitude loading yielded Masing behaviour. Furthermore, the CSS curve obtained from constant amplitude tests deviated slightly from the corresponding curve determined by the incremental step test. This behaviour, which is identical to that observed for wavyslip materials, is surprising when taking the strong dislocation/particle interaction and the stability of the dispersoids into account. As investigated by thorough TEM studies, the dislocation arrangement is slightly affected by the strain amplitude applied in single-step tests. Despite the fact that it is not possible to quantitatively determine this dependence, it manifests itself in non-Masing behaviour found under these testing conditions. In the incremental step test, however, the rapidly changing strain amplitude leads to a microstructure, which is constant in both the particle and dislocation arrangement. Consequently, Masing behaviour was observed. On the basis
Fig. 10. Same as Fig. 9, T=1273 K. (a) Single-step tests (non-Masing behaviour); (b) Incremental step test (Masing behaviour).
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