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Abstract--CMSX-2 single crystal specimens were submitted to tensile creep tests along <001> between 923 K (650°C) and 1223 K (950°C). The secondary creep rate values are analysed in terms of a Dorn creep law. Three temperature domains have to be considered for the values of the apparent parameters in the creep law. Between 973 K (700°C) and 1073 K (800°C), the Dorn formalism is no longer valid, since it leads to negative apparent values of the thermal activation energy. From the apparent parameters, a model of the evolution of friction stress with temperature and applied stress is established and effective parameters are determined. The effective parameters are then discussed in terms of deformation mechanisms, taking into account TEM observations of deformed specimens: the anomalous behaviour was thus attributed to the effect of the reinforcing 7' phase. Maps of active deformation mechanisms are sketched for small strains with reduced coarsening of precipitates. R6samr--Des 6chantillons monocristallins de CMSX-2 ont 6t6 soumis fi des essais de fluage en traction selon <001 > entre 923 K (650°C) et 1223 K (950°C). Les valeurs des vitesses de fluage quasi-stationnaire sont analysres en termes de loi de Dorn. On distingue trois domaines de temprrature pour les valeurs des paramrtres apparents de la loi de Dorn. Entre 973 K (700°C) et 1073 K (800°C), le formalisme de Dorn ne s'applique pas, car il conduirait 5. des valeurs nrgatives de l'6nergie d'activation thermique. A partir des paramdtres apparents, l'rvolution de la contrainte de friction en fonction de la temprrature et de la contrainte appliqure est modrlisre, et les paramdtres effectifs sont d&erminrs. L'examen par Microscopic Electronique en Transmission des microstructures fludes a permis d'apporter une signification physique aux diffrrents paramdtres de la loi et d'attribuer l'anomalie de comportement du superalliage ~i l'effet de la phase renforqante 7 '- Une cartographie des mrcanismes participant fi la drformation entre 923 K (650°C) et 1223 K (950°C) a alors 6t6 esquissde pour de faibles taux de d6formation prrcrdant toute coalescence prononcre des prrcipitrs. Zusammenfassung--Dehnungskriechversuche einkristalliner CMSX-2 Proben wurden in <001) Orientierung im Bereich 923 K (650°C) ~< 1223 K (950°C) durchgefiihrt. Sekund ire Kriechgeschwindigkeiten werden mit dem Dorn'schen Gesetz analysiert. Wir unterscheiden drei Temperaturbereiche ffir die im Dorn'schen Gesetz auftauchenden Messparameter. Zwischen 973 K (700°C) und 1073 K (800°C) ist dieses Gesetz von Dorn nicht giiltig, well es zu negativen thermischen Aktivationsenergien fiihrt. Aus den Messparametern wird die Ver inderung der Kriechgspannung in Abh ingigkeit der Temperatur und der angelegten Spannung modellhaft beschrieben und die wirklichen Parameter werden berechnet. Die elektronenmikroskopische Untersuchung der Microstruktur nach Kriechen erm6glichte eine physikalische Erkl~rung f ir jeden Parameter des Gesetzes. Die Superlegierungsunregelm issigkeit 1 isst sich dann mit der )" Verst~irkungsphase erkl iren. Eine Schema der beteiligten Verspannungsmechanismen zwischen 923 K (650°C) und 1223 K (950°C) ist dann f ir kleine Dehnungen und mit weniger Niederschlagskoaleszenz ermittelt worden.
Fig. 1. Evolution of the secondary creep strain rate ~ of the CMSX-2 superalloy (single crystal samples). The stress axis is  and all the applied stress values in MPa correspond to the numbers reported in the diagram of the figure. Stars indicate the secondary creep rate values obtained from specimen crept only by a single applied stress. Detail: the zone of anomalous behaviour of the CMSX-2 superalloy is enlarged.
In this relation a a n d T are the experimental imposed p a r a m e t e r s (stress a n d temperature), A is a c o n s t a n t which depends o n the material structural properties, R the universal gas constant. Finally n, a n d Qa are respectively the a p p a r e n t stress e x p o n e n t a n d the a p p a r e n t activation energy. The values of these p a r a m e t e r s are generally related to the activated d e f o r m a t i o n m e c h a n i s m s which control the creep process. The experimental secondary creep rate values displayed o n the A r r h e n i u s plot (Fig. 1), show t h a t a single constitutive e q u a t i o n with a single set of activation p a r a m e t e r s (A, Qa a n d na) will n o t describe the secondary creep o f the C M S X - 2 superalloy, in the whole t e m p e r a t u r e range. A similar conclusion m a y be deduced when plotting log i vs log a, from which the value o f the stress e x p o n e n t n, is usually determined. Three d o m a i n s m u s t be distinguished with respect to the temperature. These are: the "lower t e m p e r a t u r e d o m a i n " below 973 K (700°C); the " u p per t e m p e r a t u r e d o m a i n " a b o v e 1073 K (800°C); a n d the " h a r d e n i n g peak t e m p e r a t u r e d o m a i n " between the other two domains. Several a u t h o r s have already noticed these three t e m p e r a t u r e domains, when considering d y n a m i c tensile tests on other superalloys (see for example [11-13]). T a k i n g these t e m p e r a t u r e intervals into account, the a p p a r e n t activation energies Qa a n d the a p p a r e n t stress e x p o n e n t p a r a m e t e r na m a y be deduced from a linear regression analysis of the secondary creep rate values, in a D o r n relationship. • In the "lower t e m p e r a t u r e d o m a i n " , the stress e x p o n e n t is 22 + 5 a n d the a p p a r e n t activation energy is 725 _+ 50 k J- m o l - 1. • In the " h a r d e n i n g peak t e m p e r a t u r e d o m a i n " , the stress e x p o n e n t decreases from 22-I-5 to 3.5 +__0.5. T h e n the a p p a r e n t activation energy shows a dependence on the applied stress. It becomes negative between 973 K (700°C) a n d 1023 K (750°C). • In the " u p p e r t e m p e r a t u r e d o m a i n " , the stress e x p o n e n t is 3.5 ___0.5 a n d the a p p a r e n t activation energy is 270 + 40 k J- m o l - 1 W i t h these values, a new A r r h e n i u s d i a g r a m (Fig. 2) is constructed. This d i a g r a m underlines the specific a n o m a l o u s creep b e h a v i o u r o f the material.
Table 1. Threshold stress values obtained during the creep experiments, by the stress dip method (Ref. ) Maximum Secondary Lower and upper limits Threshold stress to Temperature applied stress creep rate of the threshold stress applied stress ratio T(K) (°C) aa.i (MPa) ~"(h -n) ~rs low (MPa) a s up (MPa) as/a a 922 (649) 955 6.01 x 10 4 746 806 (0.78-0.85) n073(800) 685 (*) 305 (?-0.44) 1080 (807) 711 1.75 × 10 -3 456 (.9-0.64) 1125 (852) 502 2.77 × 10 - 3 231 255 (0.464).51) 1148 (875) 430 3.14 x 10 -3 148 179 (0.34-0.42) 1221 (948) 281 3.30 × 10-3 88 117 (0.31~).42) Thick numbers correspond to experiments under vacuum and the asterisk to a tertiary state crept sample.
", , \,',',~\'~'" - \ \ \ ~e~o "
Fig. 3. Evolution of the ratio between the friction stress a F and the applied stress a0 as a function of temperature for creep and stress relaxation experiments performed on the CMSX-2 superalloy.
Fig. 4. Diagram illustrating the dependence of the different parameters which define the friction stress with respect to the temperature 0. a is the proportional coefficient to the applied stress and a c the critical stress.
Considering relations (7) and (8), it may be noted that at any constant experimental temperature, two limiting cases may be encountered: • if the critical stress O-~ is zero, then O-F= ~tr~ (9) and na = n~ (lO); and • if ~t remains constant in a temperature domain, then Q~ = Qa (11).
• In the " u p p e r temperature domain", the proportionality of the friction stress to applied stress is straightforward and n a = no . Then, tr~ = 0 and the term ~ represents the proportionality constant. It decreases from 0.6 at 1073 K (800°C) to 0.4 at 1223 K (950°C) and remains constant at higher temperatures.
Fig. 5. Arrhenius plot of the CMSX-2 creep behaviour in terms of effective parameters. The numbers correspond to effective stresses, full dots to experiments in ambient atmosphere and white dots to experiments under vacuum.
Fig. 7. Microstructure showing the characteristic dislocation substructure developed when reaching 1.3% strain under the secondary creep regime activated at I073 K (800°C) under 725 MPa. The diffraction vector is 200. The letters F and S correspond to stacking faults and a (110) superdislocations respectively. Interfacials networks are visible on the left part of the picture.
285 kJ m o l - 1 [56-58]. This value supports our microstructural observations and previous conclusions: diffusion in the matrix corridors activates the cooperative climb of dislocations which controls the global secondary creep of the superalloy in this temperature range, as deduced from the value of the parameter ct. Concerning the lower temperature domain, the value of the effective activation energy deduced from experiments remained much higher: 5 0 9 _ 30 k J m o l -~. As shown from our microstructural observations, secondary creep in this domain is related to dislocation slip across the V' precipitates, at least for the range of creep rates we explored. This activation energy value may be compared to the value of 424 kJ mo1-1 reported for creep of pure Ni3A1 by Hemker and Nix  or to the value of 447 kJ m o l - l reported by Leverant and Duhl on Ni3(A1,Mo) . 4.2.3. Creep mechanisms: Taking into account the microstructural observations and the comparison of our creep parameter values (~, trc, n~ and Qe) with references to literature, we propose to explain the creep behaviour of the CMSX-2 superalloy in terms of mechanisms. In the "lower temperature domain", dislocations propagate through the alloy by Orowan bowing into the matrix corridors and by shearing the ~,' precipitates. As mentioned above, the term go can be assimilated with the Orowan stress and when aa is larger than ¢rc, a significant density of matrix dislocations are provided. Trapped in the precipitate interfaces with their elongated shape along a (110) direction and a short heading screw segment, these dislocations are characteristic of their forced propagation between the precipitates according to the Orowan bowing process. This mechanism represents the main contribution to the hardening of the alloy. However, in this "lower temperature domain", the creep kinetics is controlled by the shearing of V' precipitates. Indeed, creep rates were only detected when shearing of precipitates with stalking faults or superdislocations was observed. The high effective activation energy value we determined is similar to the energy value deduced for creep of pure or alloyed Ni3A1. A possible reason for such a high value is the need for recombining of interfacial dislocations from the matrix to generate the superpartials which will shear the V' precipitate creating the observed extrinsic and intrinsic stacking faults. The high activation energy value could also be attributed to the very special hardening mechanisms of the ~' phase, which causes the yield strength anomaly. Many investigations are devoted to this question and various theoretical models have been proposed (not possible to review here). Let us simply quote the recent TEM Fig. 8. (a, b) Typical microstructures developed during a in situ observations published by Courbon et al.  secondary creep regime at 1223 K (950°C) and with a stress about the kinetics of shearing of V' precipitates by of 280 MPa, when reaching a 1.9% global strain, m are ~(112) super-Shockley dislocations in the temperamatrix dislocations, i interfacial networks and S superdislocations in the precipitates. The diffraction vectors are indi- ture range of interest here. These authors insist on the viscous character of the dislocation motion, which cated in the micrographs.
may be attributed to the core structure of these super-Shockley defects, and which may be an argument in favor of a high thermal activation energy value. The fact that hardening mechanisms of the 7 ' phase may be responsible for these high activation energy values is in agreement with the anomalous creep behaviour of our superalloy between 973 K (700°C) and 1073 K (800°C), which corresponds to the temperature domain of the yield strength anomaly of the 7 ' phase . So, the "hardening peak temperature domain" is characterised by shearing of ~ ' precipitates still acting as the controlling mechanism, but with the transition in the nature of mobile dislocations in this phase which generates the yield strength anomaly. Thus this domain is basically no different from the low temperature one as far as deformation processes are concerned. However it should be distinguished since the thermal activation classical model cannot be applied because of the anomalous behaviour of the reinforcing phase. Moreover, when increasing the temperature, mechanisms for recombining interfacial dislocations to induce precipitate shearing become progressively easier, because of elastic energy decreasing and increasing of diffusion activity. So, propagation of dislocations through the material by Orowan bowing tends to disappear in favour of shearing the precipitates. As previously observed by other workers [2,63-65], from 1073 K (800°C), shearing by superdislocations appears and progressively replaces shearing with stalking faults, which practically disappears at temperatures higher than 1173 K (900°C). For instance, only straight a (110) superdislocations can be seen in precipitates in Fig. 8. However, in the "upper temperature domain", according to the activation energy value similar to the nickel self diffusion energy, the controlling mechanism seems to be rather a climb process. Now, concerning precipitates overcoming by climb, McLean recently reviewed the various possible dislocation motion mechanisms in alloys with a high precipitate volume fraction . He suggests that the most likely mechanism to occur is a cooperative climb of dislocations around groups of precipitates leading to a threshold creep stress proportional to the applied stress, which is consistent with our measurements in the high temperature domain, as well as with our observations of elongated matrix dislocations along (110). The numerical calculation of the proportionality coefficient in the case of superalloys provides an estimated value around 0.4, which is precisely the limiting value for our coefficient ~ in the high temperature range (Fig. 4). Since the value of ~ is always less than unity, whatever the applied stress, the subsequent threshold stress a~ = ~t~a will never be higher, and the material should always creep at a detectable rate, possibly very small. It will only stop creeping if the applied stress is subsequently reduced to a value below the threshold t~v built up by the larger first applied stress.
So, in the "upper temperature domain", as long as the precipitate oriented coalescence is still uncompleted, the controlling mechanism may be the cooperative climb process. However we may recall that under the effect of high temperature but very low applied stress, creep may sometimes become negative (for instance at 955°C, 80 MPa), even without clear modification of the observed microstructure. This unexpected behaviour was sometimes attributed to the volume contraction due to the partial dissolving of 7 ' precipitates [6, 67], but no obvious contraction effect could be detected during dilatometric tests on the same alloy up to 1573 K (1300°C) . Another possible origin for this anomalous effect may be the cubic to tetragonal transformation which is undergone by the 7 ' phase at elevated temperatures [69, 70]. In their paper, Bonnet and Ati suggest that this phase transformation interacts strongly with the oriented coalescence of the 7 ' precipitates under stress at high temperatures. The larger cell parameter c might indeed be arranged either parallel or perpendicular to the applied stress according to the tensile or compressive direction of this stress. But when the stress is very small, three variants in the direction of the c axis might appear with almost equal probability and result in an overall reduction of specimen length. The phase transformation would then provide the driving force for this length reduction against the applied stress. If this is true, this anomalous behaviour should be limited to the case of tensile creep, and never be observed in compression or torsion creep, which seems to be the case . Using both the information deduced from TEM observations and numerical treatment, maps may be drawn (Fig. 9) for different creep rate values i indicating an approximate distribution of the activated mechanisms according to the temperature. For example, for an average value of the deformation rate (around 10 -3 or 10 4h l), in the lower temperature range, dislocations overcome precipitates by Orowan bowing or by shearing them. Above 1073 K (800°C), the controlling mechanism is the cooperative climb process while the precipitates are mostly sheared by superdislocations. As in the "lower temperature domain", for the "hardening peak temperature domain", the kinetics of deformation are controlled by the shearing of the precipitate, which may be the cause of the anomalous creep behaviour of the superalloy. For much smaller deformation rates (such as I 0 6 h - ~) - - a n d consequently smaller applied stresses--the thermally activated mechanisms will take the control of kinetics even at lower temperatures (see Fig. 9). Inversely, at very large deformation rates (higher than 10 2h 1) and applied stresses, stress sensitive mechanisms such as Orowan by-passing of precipitates and shearing should dominate the deformation kinetics up to higher temperatures such as 1173 K (900°C) or 1223 K (950°C) (see Fig. 9).
logarithmic creep for very small stress values. A negative activation energy arises for deforming conditions in the hardening peak domain. When considering periods of secondary creep rate, one may distinguish three well defined temperature domains. We chose to describe this secondary creep rate in terms of a modified Dorn law involving a friction stress term. The value of this friction stress as well as the stress sensitivity exponent and the thermal activation energy have been determined from consistent experimental results of the present creep tests and previous stress relaxation tests on the same alloy. This modelling leads to physically acceptable values of the creep parameters on the high temperature (over 1073 K, 800°C) and low temperature (below 973 K, 700°C) domains, but the anomalous behaviour of the superalloy between 973K (700°C) and 1073K (800°C) cannot be described through this classical scheme. Microstructural TEM observations of specimens after creep tests provided information about the controlling deformation mechanisms corresponding to the various deformation regimes. Indications coming from the numerical treatment and from the observations are consistent and may be summarised on maps like Fig. 9.
ROUAULT-ROGEZ et al.: CREEP OF Ni BASE SINGLE CRYSTALS The modified D o r n equation we used to represent the tensile creep behaviour of the alloy, although rather simple due to being valid in a restricted stress and temperature domain, has helped to bring to light a number of important physical phenomena, such as the existence and the variations of the internal friction stress. It allowed us to determine various temperature domains where the controlling deformation mechanisms are different, which was confirmed by T E M observations. It has been shown in a previous work  that the same modified D o r n equation may be used to work out the stress relaxation law for this alloy. When this is done with the values of parameters ct, trc, ne, Qo determined from the present work, all experimental previous stress relaxation curves can be modelised within a 6.6% maximum discrepancy in the "lower temperature d o m a i n " and 32% in the "upper temperature domain". Then it may be concluded that our proposed model for behaviour and hypotheses on deformation mechanisms are valid for a wide range of loading conditions on these CMSX-2 single crystals. Acknowledgements--Authors are grateful to Professor M. McLean from Imperial College (London) for very helpful discussions. The superalloy crystals were provided by S.N.E.C.M.A. and financial support by the Groupement Scientifique "Microstructure et Propri&rs des Superalliages Monocristallins" of the French Centre National de la Recherche Scientifique.
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Report "High temperature tensile creep of CMSX-2 Nickel base superalloy single crystals"

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