High temperature tensile creep of CMSX-2 Nickel base superalloy single crystals

High temperature tensile creep of CMSX-2 Nickel base superalloy single crystals

Acta metall, mater. Vol. 42, No. 9, pp. 3137-3148, 1994 ~ Pergamon 0956-7151(94)E0093-V Copyright © 1994 Elsevier Science Ltd Printed in Great Bri...

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Acta metall, mater. Vol. 42, No. 9, pp. 3137-3148, 1994




Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0956-7151/94 $7.00 + 0.00


H. ROUAULT-ROGEZ,M. DUPEUXand M. IGNAT Laboratoire de Thermodynamique et Physico-Chimie MrtaUurgiques, ENSEEG, BP 75, 38402 St Martin d'Hrres, France (Received 14 January 1994)

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 Between 973 K (700°C) and 1073 K (800°C), the Dorn formalism is no longer valid, since it leads to negative apparent values of the thermal activation energy.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) ~
1. INTRODUCTION A l t h o u g h superalloys in general a n d single crystals in particular are in widespread commercial use, there is incomplete u n d e r s t a n d i n g o f the m e c h a n i s m s leading to their attractive properties. F o r example, there has been considerable a t t e n t i o n given to aspects of the s h o r t term strength o f these materials, such as the a n o m a l o u s t e m p e r a t u r e dependence o f the yield strength, b u t there has been no parallel p h e n o m e n o n reported in the relation to their creep performance. However, m a n y models o f creep d e f o r m a t i o n relate the creep b e h a v i o u r to a stress normalised with

respect to the yield stress. The absence o f any reported t e m p e r a t u r e a n o m a l y in creep p e r f o r m a n c e m a y simply be due to the fact t h a t n o sufficiently detailed study has been undertaken. The purpose o f the present p a p e r is to report the results o f a comprehensive study of secondary creep rates as functions of stress a n d t e m p e r a t u r e with some particularly detailed m e a s u r e m e n t s at small stress/temperature intervals in the t e m p e r a t u r e range where the yield a n o m a l y has been reported. The creep m e a s u r e m e n t s have been c o m p l e m e n t e d by the use of stress transient testing to establish a n d measure the presence of threshold stresses associated with creep in




the various testing conditions and by TEM studies to provide evidence of the microstructural phenomena which cause these different threshold stresses. Finally, a model of creep deformation based on previous threshold stress concepts is proposed to account for the newly identified temperature anomalies of creep. 2. EXPERIMENTAL APPROACH

Tensile creep experiments were performed on CMSX-2 nickel base superalloy single crystals. The characteristics of this type of superalloy have already been presented [1]. Its microstructure after a standard O N E R A heat treatment [2] can be described by small cubic precipitates (0.4 # m size) of the Ni3A1 LI2 y ' phase (70% by volume). This phase is embedded in a nickel rich f.c.c, y matrix. The CMSX-2 tensile creep specimens we used were fiat with a 3 x 1 mm 2 cross section and a 20mm gauge length [1]. They are cut so that their tensile axis is along a (001) direction and their average plane is parallel to a {100} plane. They are tested on a M A I R creep machine, with specially designed extensometers adapted for the specimen tips and allowing the elongation during the creep test to be directly followed. Twelve specimens were tested to thoroughly analyse the secondary creep rate. The creep temperatures ranged from 923 K (650°C) to 1223 K (950°C); The initial applied stress interval was taken correspondingly between 750 and 950 MPa for the lowest temperature, and 150 to 300 MPa for the highest temperature. Under these stress conditions, typical creep curves were obtained with the magnitude of the secondary creep rates between 10 _5 and 10-2h -1 at all temperatures. It is well known, especially for superalloys, that the secondary creep stage is not a true steady state but is rather characterized by a temporary minimum strain rate [3]. Our criteria for assuming that the secondary creep regime was reached was to obtain a constant strain rate for a minimal duration, which was chosen to be equal to 5 h for the highest temperatures and stresses. In order to obtain a maximum number of secondary creep rate values, each test was performed so as to include initial increasing temperature steps of 5-15°C after reaching a secondary creep rate and then decreasing stress drops with the aim of measuring the stress sensitivity exponent and detecting the threshold stress of the materials, according to a well established procedure [4]. The secondary creep rates were measured at total creep strains below the level at which tertiary creep is significant (1-2% [5]), before strong oriented coarsening of precipitates. However, because of the decreasing stress drops, secondary creep rates could be measured for strain levels as high as 5%. In conclusion, this experimental procedure is assumed to maintain the creep in a secondary regime,

with a well defined and stable creep microstructure in the material and without a prevalent damaging process which could activate the tertiary creep [5]. Moreover, the secondary creep rate values obtained from increasing temperature or decreasing stress drops were consistent with secondary creep rate magnitudes measured on dedicated specimens crept with a single value of stress. These last samples were used for microstructural TEM observations. Maintained under load, each sample was air quenched during the secondary creep to preserve its internal microstructure, before the preparation of thin foils. A few exploratory tests were conducted at 1223 K (950°C) and very low stresses (71 and 83MPa). Under such conditions, small but detectable negative creep rates have been measured (~ = - 1.34 x 10 -5 and - 1.14 x 10 -5 h -1 respectively). This unexpected behaviour has already been observed by other workers [6]. An attempt will be made to interpret it in the final part of this paper, taking into account all our test results. 3. EXPERIMENTAL RESULTS The secondary creep rates obtained during our experiments are displayed on the Arrhenius plot of Fig. 1. The experimental creep values show reasonably good correlation with straight lines for isostress values on two separate temperature intervals: from 923 K (650°C) to 973 K (700°C) and 1073 K (800°C) to 1223 K (950°C). However, between these two temperature intervals, an anomalous creep behaviour has been observed. For example, under 650 MPa, starting from 973 K (700°C), secondary creep rate values decrease with increasing temperature (see details on Fig. 1). As far as we know, this anomalous behaviour, which was repeatedly observed for different values of applied stress, has never been reported in literature. The stress dip procedure also allowed us to determine values for a threshold creep stress [4]. The values we obtained are reported in Table 1. The ratio of the threshold stress to the applied stress appears to be temperature dependent. Such a threshold creep stress has been reported for other superalloys [3, 7-10]. Taking into account this creep behaviour, we chose to analyse the microstructure of deformed specimens at 923 K (650°C), 953 K (680°C), 1073 K (800°C) and 1223 K (950°C), which were found to have similar values of secondary creep rate. The observed microstructure will be commented on to support our further discussion on mechanisms. 4. INTERPRETATION OF THE DATA 4.1. The creep constitutive laws 4.1.1. Creep rates mapping: Creep results are often represented by Norton or Dorn type constitutive laws [5]. A general representation of the creep rate according to these constitutive laws is given by the relation






o(oc) 10-2 j*










650 , 9


10"4(K-1 ) T / ~101

,~ , 11

Fig. 1. Evolution of the secondary creep strain rate ~ of the CMSX-2 superalloy (single crystal samples). The stress axis is [100] 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. [6]) 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.





the same microstructural effect: a structural stress barrier to the activation of deformation mechanisms. We shall call "friction stress" the mentioned effect. The results of the secondary creep in terms of stress and temperature can now be remodeled by a modified law, including the effective stress term 0"e= o ' a - O.F with O'F as the friction stress. The new Dorn law relation involves effective terms for the Don activation energy Qe and stress exponent n¢

T 900



I •




t t L




~', I ~ I



' ' \\'' ,








e =


I .",5 I -'

Y ', \ \ \,


", , \,',',~\'~'" - \ \ \ ~e~o "


ln-5L •v I



\ \~"\\~,/ \ ~'1"~3,\ . ,I ~ v,\,,


/ i




'.1, I ~,tt,i

10 -4



(o.a - - O.F)


exp ~



The form of such equations has been extensively discussed [5, 20, 24, 29]. Mathematical relations have abbeen isenc, established by Li [30] and Saxl and Kroupa [31] to deduce the effective parameters from the apparent ones O'a - - O.F

\ \ \ g '~ \ \ \800 \ \ \


ne=nao.a( 1 _(OO'F

,-, \ \


\ ~~I' ~~~'-, I







Qe = Qa + RT 2na


\ aT ,a


\ 0o'a/r/



Fig. 2. Arrhenius plot modelling the creep behaviour of the CMSX-2 superalloy, from the values of the calculated activation parameters. Dashed lines correspond to an extrapolated behaviour. ( corresponds to the secondary creep rate, and the reported numbers to applied stresses. However, the values of the activation parameters (such as we deduced in the "low temperature domain") are high as it is commonly the case for other superalloys [7,10,14-22] and two-phase alloys [23-25]. Subsequent physical interpretation remains difficult. A solution to this problem has already been developed for two-phase alloys [20, 24] and structurally anisotropic materials like composites [26]. It consists of an introduction of a complementary parameter in the constitutive equation: the internal or friction stress [27]. The measured strain rate is then considered as activated by an effective stress. This effective stress corresponds to the difference between the applied stress and the internal or friction stress of the material. 4.1.2. Modified constitutive law: In the case of CMSX-2 superalloy, stress relaxation experiments were performed in a previous work [1, 28]. When comparing a similar imposed experimental temperature, the threshold creep stress values and those of asymptotic relaxation stress show the same dependence. Their ratios to the initially applied stress are equivalent (Fig. 3). Consequently, we shall assume, in the following, that the stress relaxation asymptotic stress and the creep threshold stress both represent

To describe the secondary creep behaviour of the CMSX-2 superalloy, we also have to make two other basic assumptions, concerning on the one hand the value of the effective stress exponent no and on the other hand the dependence of the friction stress with applied stress and temperature. Taking into account reported values of ne between 3 and 5 for other superalloys [9, 32-35], considering our experimental value of na in the "upper temperature domain" and the experimental results of our O'E ~0 1.O



I croq~

0.8 -














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.

ROUAULT-ROGEZ et al.: CREEP OF Ni BASE SINGLE CRYSTALS previous stress relaxation experiments [1], an average value of 3.5 for the effective stress exponent is selected. We will show that all further analysis o f the experimental data are consistent with this value. Concerning the global relation of the friction stress aF with the applied stress O-a, a general linear form is applied O-v= ~o-a + ac

i = ~ [(1 - ~)o-a - O-~]"oexp - ~

-- ~)O" a -- O'c]


aa(1 - ~ )

and an effective activation energy __

Qe = Oa + RT:n~

.0- a +

o~ O-a"(l - - a )






el'c) 0



' 750



' 850


. ' 950

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.


with an effective stress exponent [(l



where ~ is a proportional coefficient and a~ a critical stress. Such a general expression for a friction stress has already been used successfully by Carry and Strudel [10, 35]. The values of both ~ and a~ are, of course, dependent on the temperature. (a) Phenomenologieal equations. Including the derivation of the friction stress term with respect to the experimental parameters: applied stress and temperature, the modified D o r n equation (2) may then be written

n e = n,





• In the "lower temperature domain", the values of a and O-care different and depend on the creep temperature. At 923 K (650°C), the critical stress O-c is equal to 330 MPa. • Between 973 K (700°C) to 1073 K (800°C), we interpolate the values of a and ac from the above. With the above mentioned values of ~t and O-c, the new activation diagram of Fig. 5 may be drawn in terms of effective stress. The slope of the iso-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).

(b) Values of effective parameters. The mathematical technique developed for the determination of the parameters ct and O-~ from our experiments has been described in detail elsewhere [36]. It is based on the treatment of the experimental value of av from both the creep tests and the stress relaxation tests. At each test temperature, when several values for a F were available in an interval of O-~, a numerical optimisation procedure was introduced to calculate the values of (~t,a~) which gave the best fit to experimental values. Using our second basic assumption (n~ = 3.5), the calculated values of ~ and tr~ and their dependence on temperature are reported on Fig. 4. These are:






1 0 -2

t (hl)

e ('c)

zoo... \250 10 .3

10 . 4


10 "6

• In the " u p p e r temperature domain", the proportionality of the friction stress to applied stress is straightforward and n a = no [37]. 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.






(K'3 t




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.



curves leads to a value of the effective activation energy Qe, but Qe may also be directly calculated from relation (8) together with the information of Fig. 4. However, by both methods, only a negative value of Qe could be deduced between 973 K (700°C) and 1073 K (800°C). This clearly means that a Dorn creep equation cannot adequately describe creep of the superalloy in the "hardening peak" temperature domain, and that a gap has to be introduced in the modeled Arrhenius plot. The graphically (Fig. 5) determined effective activation energy value is 509 + 30 kJ/mol in the "lower temperature domain" and decreases to 230 + 40 kJ/mol in the "upper temperature domain". In similar temperature ranges, applying relation (8), we obtain: 494 ___20 kJ/mol for the lower temperatures and 247 + 55 kJ/mol in the upper temperature domain. These consistent values will be used to build up the constitutive equation for the description of the creep behaviour of the alloy. Since this equation is not valid in the intermediate temperature domain, a more sophisticated model for thermal activation would be necessary to describe creep behaviour under these conditions (see for instance [38]). (c) Creep model validity. All the creep rates corresponding to our experimental values of tra and T have been recalculated on the basis of equation (2) using the values of the parameters deduced from the previous treatment, together with: • in the "lower temperature domain", Qe=509kJ/mol and A = 4 . 6 7 0 × 102°Kh-I MPa -35 (determined graphically from a log ~ vs log ~re plot); and • in the "upper temperature domain", Q~ = 240 kJ/mol and A = 1.204 x 103 K h - l MPa-3.5. With these data, the maximum relative deviation between calculated and observed values was 48.5% in the lower temperature range and only 1 5 o in the upper. This was satisfactory when considering the 3 orders of magnitude variation in ~. We will now discuss the physical bases for the model associated to our constitutive law, taking into account our microstructural observations. 4.2. Discussion 4.2.1. Contributions to the friction stress: ottra, ~ . Many published analyses concerning a friction stress parameter (called internal, threshold or asymptotic stress) refer directly to a stress barrier which inhibits the deformation of the material. This barrier is generally related to a precise controlling deformation mechanism activated under the given stress and temperature [5]. Several attempts have been made in superaUoys to associate the experimental value of the internal stress to the Orowan stress for bowing of dislocations around reinforcing precipitates. The observed deformation mechanism actually seems to be highly dependent on microstructural parameters such

as precipitate shape and volume fraction [39-43]. It has also been proposed to define the threshold stress as the sum of a term related to the properties of the precipitates and a term due to the contribution of the matrix hardening by a solid solution effect [44-46]. This second term is proportional to the applied stress and the definition is formally equivalent to equation (5) which we used to define the friction stress. The critical stress term ac in equation (5) then represents an intrinsic resistance property of the superalloy to deformation, mainly due to its initial microstructure, after a standard O N E R A heat treatment and without any previous external mechanical loading. It corresponds to the limiting stress in order to create and propagate dislocations over a long distance. For example, at 923 K (650°C) under an applied stress of 115 MPa (below tr¢ equal to 330 MPa) no secondary strain rate was detected after 24 h creep and our TEM observations of the corresponding specimen showed only a few dislocations. But under 432 MPa (over trc), even if the creep rate remained undetectable after 36 h, the deformation seemed to be localised in narrow bands with dislocation substructure developed only in the matrix corridors between the y ' precipitates. These dislocations with ~ ( l l 0 ) r Burgers vectors have an elongated shape with edge character along a (110) direction, and a short heading screw segment. So under the effect of the applied stress, the dislocation lines are forced by Orowan bowing into the matrix corridors and their heading screw segment will propagate along these corridors by cross-slip as analysed in detail elsewhere [47]. In the lower temperature domain, the order of magnitude of the critical stress as estimated from experiments and its evolution with temperature are actually in agreement with the estimated value of Orowan stress for dislocation loops to propagate on { 111 } planes into the matrix corridors; this can be estimated to be between 100 and 400 MPa according to the dislocation screw or edge character [10]. Finally, in the "lower temperature domain", the critical stress a~ can be assimilated to the Orowan stress. When increasing the creep temperature to 1073 K (800°C) or 1223 K (950°C), a well developed dislocation substructure was always observed whatever the applied stress value. For instance, at 1228 K (955°C) after 30 h under 80 MPa, dense dislocation networks appear surrounding the directional coarsened precipitates (Fig. 6), even without any detectable secondary creep rate. Over 1073 K (800°C), the critical stress term can be taken as negligible (Fig. 4). Thus we may consider that the temperature elevation completely erases the barrier effect represented by the term a¢ because the creep kinetics become controlled by high temperature mechanisms which are less sensitive to the precipitate structure. Now we try to understand the physical significance of the term ctaa. Taking into account the microstructural observations, we shall assume that this term is


Fig. 6. Characteristic dislocation microstructure which is developed after 30 h creep at 1228 K (995°C) under 80 MPa with a non detectable secondary creep rate. i and j are interfacial dislocation networks having +~[10T] and ___~[110]Burgers vectors; S and S' correspond to superdislocations with a [10T] and a [101] Burgers vectors, t is a (001) superdislocation, gliding on a (010) cubic plane, m is an ~[101] matrix dislocation and n a recombination of several partial dislocations outcoming from the matrix, with a superdislocation in the precipitate. The diffraction vector is 200. the back stress induced by the dislocation substructure. This term will only appear for applied stresses over a c. In this case, a dislocation substructure develops and internal stress fields become greater: for example, the dislocations which moved in matrix corridors and are then trapped at interfaces exert their repelling stress fields on the incident dislocations thus balancing the applied stress and preventing any further dislocation motion. The term cara acts as a strain hardening term directly dependent on the applied stress level through the density of previously emitted dislocations. But this strain hardening reaches its limit when the local stress becomes high enough for the obstacles to be overcome. Thus, at low or intermediate temperature, the secondary creep rate was detected only when the applied stress was sufficiently high to induce the shearing of the 7 ' precipitates. For instance, at 953 K (680°C) under 940 MPa (over a F equal to 785 MPa), after 2 0 h creep the sample reached 5.4% strain through a well defined stationary creep behaviour. Dislocation microstructures were dense in the matrix corridors and interactions of the dislocations with the precipitates were observed: resulting aligned (110) screw segments on the interfaces, then typical fringe contrasts in the 7 ' phase, showing that ~ (112) superpartials sheared the precipitates leaving the subsequent stacking fault. Other microstructural observations, based on the same type of material showed a similar transition among matrix slip and the onset of precipitate shearing [2, 48-50]. So according to this interpretation three cases may be distinguished at low and intermediate temperatures depending on the values of o-a and a F = aaa + ac. All of them are supported by our observations and measurements, and consistent with other published observations [2, 51-53]: AMM 42/9--P


(i) For a a > a F, creep will be easily detected. But it stops if the applied stress is later reduced below the subsequent threshold aF = Ctaa + ac. In this first case, after a transient regime, a constant flow of dislocations is possible through the material with shearing of precipitates, with stacking faults at low and moderate temperatures, progressively switching to perfect superdislocations at higher temperatures. Indeed, for example at 1073 K (800°C), with an applied stress of 725 MPa (greater than aF), a microstructure corresponding to secondary creep behaviour showed that the 7 ' precipitates were sheared by 3 (112) superpartials and also by a ( l l 0 ) superdislocations. Interfacial networks were developed from the observed (110) segments aligned against the precipitates (Fig. 7). The occurrence of precipitates shearing is consistent with the fact that the value of the hardening coefficient ~ increases on Fig. 4 between 1023 K (750°C) and 1073 K (800°C) when the phase 7 ' becomes more difficult to shear due to anomalous hardening. This could be the reason why the mechanical behaviour of the superalloy presents a temperature anomaly similar to the bulk 7 ' phase. (ii) For ~o-a + o-c > a a ~> O-c,a progressive hardening of the alloy will take place until the generated friction stress balances the applied one, all the matrix corridors and precipitate interfaces becoming progressively saturated with trapped dislocations. In this case a logarithmic creep behaviour will be detected or, on a long time basis (which was not explored in the present study) at very low rate creep with pure by-passing of precipitates by climb mechanisms. (iii) For tr~ < trc, the few dislocations initially present in the specimen cannot propagate and multiply throughout the alloy by Orowan bowing. Only incubatory creep can be observed for periods longer than 100 h. These three cases can easily be transposed to the high temperature situation when trc is negligible

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 [59] or to the value of 447 kJ m o l - l reported by Leverant and Duhl on Ni3(A1,Mo) [60]. 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. [61] 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.

(or similarly to very long term creep at moderate temperature, when thermal effects may progressively relax the stress barrier with very slow kinetics leading to a creep rate far below the lowest values we observed). In such cases, the critical term ac can be taken as negligible, because of diffusion effects which help relaxing interfacial dislocation walls and building up the regular networks which were already detectable in a few places on Figs 6 and 7. At 1228 K (955°C) under 280 MPa, after 5 h creep, recombination of the interfaciai ~(110) dislocations formed square or hexagonal networks on the directional coarsened precipitate interfaces clearly seen in Fig. 8. These stable networks are very likely to relax the interfacial misfit and the associated stresses [54, 55]. Then it will be possible for moving dislocations to overcome precipitates either by shearing, or more probably by climb. 4.2.2. The effective activation parameters: The physical meaning of the effective stress exponent value ne = 3.5 (chosen on the basis of further experimental results) is limited to the general fact that such value is representative of volume deformation processes. On the high temperature domain, we deduced an effective activation energy value Q e = 2 4 0 _ 60 kJ mol-l. This is similar to the nickel self diffusion energy which is reported to be between 265 and



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 [62]. 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 [66]. 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) [68]. 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 [6]. 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).






100 %

100% < 10-5

100 % 10-4 < [ < 10"2


I ~

~ " " - T (°C)

~00 00 >> I0 -2 ~, ~ (h -1) Fig. 9. Schematic representation of the domains which correspond to activated deformation mechanisms during creep at undetectable or very low rates (g = 10-6 h-t), secondary creep (10 -4 h-I < g < 10-3 h-t) and creep at high rates (~ > 10-2 h-~). Again, we must insist on the fact that our exploration of the superalloy creep behaviour was limited to the case of reduced total plastic strains, before strong oriented coarsening of precipitates. It has been established that the shearing of the coarsened microstructure indicates the onset of the long lasting tertiary creep of superalloys [71], while we tried to operate our tests only in the domain of secondary creep. Summarising, for the superalloy, these main bartiers to deformation will be the resistance to shearing of the 7 ' particles in the "lower temperature domain"; in the "hardening peak domain" they will be associated to the observed cubic cross slip blocking the dislocation movement during sheafing of ? ' precipitates; and finally at the higher temperatures they will correspond to the resistance to cooperative climbing of matrix dislocations around precipitates. 5. CONCLUSIONS Our series of tensile creep tests on the CMSX-2 nickel based superaUoy using a wide range of temperatures and applied stresses have demonstrated several types of secondary creep responses. The behaviour of the superalloy may show negative creep or

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 [37] 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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