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Creep at high temperatures in Ni-Fe alloys
CREEP
AT
HIGH C.
A.
TEMPERATURES
PAMPILLOT
and
A.
IN N&Fe ALLOYS* E. VIDOZt
The creep behaviour of N&Fe 8nd Ni-20 8t. % Fe 8110~s has been investigated in the temperature renge between, approximately, 530” to 720°C. For the c&se of the Ni-20 at. % Fe 8110~ the experiment81 8ctiv8tion enthalpy for creep w8s found to be, within the experiment81 error, in 8greement with the available dsta for diffiion of Fe in Ni-Fe alloys. For the stoichiometric composition N&Fe it is suggested that the diffusion of Ni is the controlling f8ctor. It is proposed that dielocetion climbing is the rate controlling process for creep in the Ni-20 at. % Fe alloy and that gliding of dislocations through 8 short range ordered structure is controlling the creep rate in the Ni-25 at. ‘A Fe 8110~. Several other experimental results em discussed. FLUAGE
A HAUTE
TEMPERATURE
DANS
LES ALLIAGES
Ni-Fe
Les auteurs ant 8tudiB le comportement au fluege d’alliages N&Fe et Ni-20 % at.Fe, dans un domaine de tempbretures s’6tandant approximativement de 530 8 720°C. Dens 1’8lliege Ni-20 % at.Fe, l’enthalpie d’activation trouvbe exp&imentalement pour le fluege est en eocord, dsns les limites des erreurs exp&imentales, 8vec les donnbes publibes sur la diffusion de Fe dens les alliages Ni-Fe. Dans le c8a de la composition stoechiom&rique Ni,Fe, lea auteurs suggbrent que le ph&om&ne est gouvernb par la diffusion de nickel. 11est vreisembleble que 18 vitesse de fluage eat contr616e per le grimpege des dislocations dans l’alliage Ni-20 % at.Fe, et per le glissement de8 dislocations 8. travere une structure ordonnbe B petite distance dans l’alliage Ni-25 % at.Fe. Les auteurs discutent Bgalement divers autres &ultats exphrimentaux. HOCHTEMPERATURKRIECHEN
IN Ni-Fe-LEGIERUNGEN
DW Kriechverhelten von N&Fe und Ni-20 at.- % Fe-Legierungen wurde im Temperaturbereich von etwa 530°C bis 720°C untereucht. Bei der Ni-20 et.-% Fe-Legierung war die experimentell gefundene Aktivienmgsenthelpie fiir das Kriechen innerh8lb der Fehlergrenzen in Vbereinstimmung mit den zur Verfiigung stehenden Daten fiir die Diffusion von Fe in Ni-Fe-Legierungen. Bei der stochiometrischen Zus8mm ensetzung N&Fe ist vermutlich die Diffusion von Nickel die kontrollierende GrCiBe. Es wird vorgeschlagen, da3 das Klettern von Versetzungen der geschwindigkeitsbestimmende ProzeB fiir das Kriechen in der Ni-20 8t.- % Fe-Legierung ist, und da0 das Gleiten von Versetzungen in einer Nahordnungs-struktur die Kriechgeschwindigkeit der Ni-25 et.- % Fe-Legienmg bestimmt. Verschiedee andere experimentelle Ergebnisse werden diskutiert.
1. INTRODUCTION
Previous investigstions(1*2) have shown that Ni-Fe alloys exhibit an order-disorder transformation in the composition range between approximately 20 to 30 at.% Fe. A superlattice similar to that of ordered CusAu (Ll,) was observed below the critical temperature of ordering (Tcw 503°C). It was found that annealing treatments of approximately 70 hr at 470°C are sufilcient to develop long range order in the stoichiometric alloy,(3*4) meanwhile the Ni-20 at.% Fe alloy does not present long range order even for very long times of annealing.@) The creep properties of Ni,-Fe were investigated by Suzuki and Yamamoto(5) and later by Davies(@ by measuring the steady state creep rate. Davies reported some discrepancies between his results and the ones of Suzuki and Yamamoto. After an analysis of the results, he stated that apparently Suzuki and * Received May 31, 1965. t Divisi6n Fisica de Metales Centro Atimico Beriloche (C.N.E.A.) Instituto de Fisica “Dr. J. A. Balseiro” (Universided Nat. de Cuyo) S.C. de Bariloche (R.N.) Argentina. ACTA METALLURGICA,
VOL. 14, MARCH 1966
313
Yamamoto have measured the creep rates in some kind of transient stage which obviously mislead their interpretations. With these results in mind, we decided to fully investigate the creep behavior of the Ni-Fe alloys, using one composition inside the ordered regions and another outside it. The results shown in the present work are part of a more extensive investigation of the creep and plastic properties of ordered alloys. 2. EXPERIMENTAL
METHODS
The nickel-iron alloys used in this investigation were made by sintering metal powders of high purity. The compositions selected were 75125 and 80120 at.% Ni-Fe (in the following these alloys are referred as 1 and 2 respectively). Chemical analysis showed that the alloys were within 0.1% of the desired compositions . A typical analysis shows the following impurity content: ca 0.0001%, cu 0.0001%, Mg 0.0001%, Si < O.OOOl%, Na < 0.0001%. Creep specimens were cut from cold rolled strips of the
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In order to obtain a constant stress, small amounts of load were removed after appropriate strains, with the assumptions of a linear relationship between change in cross-section and strain and uniform strain along the section (this is justified because final strains were always smaller than 5%). 3. EXPERIMENTAL
RESULTS
Creep is known to be a thermally activated process. If it is assumed that only one mechanism is rate controlling one can write for the creep rate:‘7-g) 6 = ye-“/kT
sped men
-lb 9dPS
1 0
FIQ. 1. System
J
/
for me&swing creep elongations.
alloys. They were electropolished and then recrystallized in a vacuum furnace at 850°C and quenched by removing the furnace and cooling the quartz tube container with water. Grain boundaries were easily observed under the light microscope due to thermal etching produced during the recrystallization treatment. It was found that the average grain diameter was 0.04 mm in alloy 1 and 0.07 mm in alloy 2. Specimens were deformed in a creep testing machine. The heating was provided by a standard electric furnace which was controlled by an Ether Transitrol temperature controller. The temperature of the tests were measured by means of a thermocouple in contact with the specimens. Temperature fluctuations were less than 1.5”C and the temperature gradient over all the specimen length was found to be less than 3°C. Creep deformations were measured at the upper end of the specimen grips using a transducer, which was held by a stainless steel reference rod which was mechanically connected to the lower specimen grip. This system, which is shown schematically in Fig. 1 minimizes the effect of differential thermal expansion which might be produced by the temperature changes. Creep strains, whrch were measured by the transducer, were recorded by a Leeds and Northrup Speedomax X-t recorder. The minimum observable creep rate was 5 X IO-’ se&.
(1)
where v is a frequency factor, H the activation enthalpy of the rate controlling mechanism, k the Boltzman constant and T the absolute tests temperature. Generally H and v are temperature and stress dependent. In order to understand the atomistic model which is rate controlling it is essential to obtain the values of H and v and their dependence on temperature and stress. From equation (l), the activation enthalpy is easily obtained :cg)
(2) where the shear stress r and the internal structure st. are held constant. Since the distribution of grains orientations was random the acting shear stress is assumed to be $a. The first term on the right hand side of equation (2), can be obtained experimentally by abruptly changing the test temperature and it is often named, the apparent activation enthalpy (H*) t9). The second term is usually neglected,(‘ps) since it is thought to be only a small fraction of the first term, or accounted for, through the temperature dependence of the elastic constants since the frequency factor v depends on them.‘lO-12, Hence, the apparent activation enthalpy is given by: In 6J.6, ln VI/V2 -H-k (3) H* = - k l/T, - l/T, l/T, - l/T2 where .6r,and g2, vr and v2, are respectively the creep rates and frequency factors before and after the abrupt change in temperature from TX to T,. In our experiments rapid changes required less than 9 minutes, the average temperature difference was about &15”C!. The test temperature was changed in general several times during a given test. In this way several values of H* were calculated for each temperature change. As H* was found to be independent of strain (within the experimental error), a mean value
PAMPILLO
m60-
AND
VIDOZ:
CREEP
IN
Ni-Fe
f
ALLOYS
rrloy 1
6040-
FIG. 2. Apparent activation enthalpy for creep as a function of temperature for alloys 1 and 2.
1ogizrithm
of stress, (Kg/m/d)
FIG. 3. Strrm dependence of the areep rate. Double logarithmic plot for alloy 1.
315
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I
I
2
I,5 log~rj~~~ FIG. 4.
VOL.
of stress.
14,
1966
I
2,; IKg./mm+)
Stress dependence of the creeprate. Double logarithmic alloy 2. (points for X = 874°K are not shown.)
of it was calculated using the values obtained at each temperature change. The average temperature for each set of values was defined as 4(Tl + T,). The apparent activation enthalpies obtained in this way are shown in Fig. 2 as a function of temperature. The errors shown are the mean deviations from the average value of H*. For alloy 2 a peak is present in the H* versrs T curve at approxima~ly 904°K. For alloy 1 the value of H* increases as the test temperature decreases and the critical temperature of ordering (T, N 773’K) is approached. It was expected that the stress dependence of H* should be more sensitively determined from the dependence-of the stress on the creep rate. It was found that at temperatures higher than &?O”K, H* was independent of stress for both alloys, with the exception of alloy 2 at temperatures of 900°K where the peak in H* exists. Figures 3 and 4 show the plots
plot for
of In 6 versus In c for alloy 1 and 2 respectively, at several test temperatures. Each set of points which de6nes a line, was obtained with one specimen by changing abruptly the stress by different amounts in a random manner. With this method, creep rates at different stresses and strains can be compared, because a constant structure is assured. The relation between creep rate and stress can be represented in the form, d N 8 where e is the tensile stress and a is a constant which is obtained from the slopes of curves in Figs. 3 and 4. The values of a were calculated by using a least square analysis for each set of experimental points. When the stress exceeds a certain value the power law between creep rate and stress breaks down. Figure 5 shows, for both alloys, the values obtained for the exponent ct as a function of temperature. The errors indicated, give the limiting values of Q. The
PAMPILLO
AND
VIDOZ:
CREEP
IN Ni-Fe
ALLOYS
317
.i
_I I -\ 0 alloy 2
\ - y\
-
_
0 alloy
\ \ i\ \
’ \ ’
\
/-
-f-V/ ‘\ \ \ ‘+-i : ’
’\
I
800
I
I 850
+A ‘L+_+
I 900
I
Temperature FIG. 5.
I
I 950
PKI
Stress exponent a BSa function of temperature for alloy 1 and 2.
curve for alloy 1 does not show any significant variaof a with temperatures above -820°K. This result is an indication that H* is independent of the stress. For the alloy 2, a increases in the temperature range in which the H* versus temperature plot, shows a peak, which suggests that there is a stress dependence of H*. Also, alloy 2 shows an abrupt change in the value of a near 843’K. It is interesting, and perhaps significant, to point out that 843°K is the magnetic Curie temperature for this alloy. However, the Curie temperature for alloy 1 is approximately 880°K and no appreciable change on the exponent a was found near this temperature. It should be pointed out, that no change in H* was found at the Curie temperature in either alloy used, contrary to what has been suggested in the literature.(lO) At temperatures below 820’K the exponent a rises rapidly, which suggests that H* may depend strongly on stress. A similar observation was detected by Davies(ls) in N&Fe (alloy 1). Metallographic observations show the possibility of grain boundary sliding. As the stress exponent a was tion
1
I’ I\ I\
found to be independent of the grain size it wa,s concluded that the creep rate was controlled by an intragranular mechanism, in agreement with the results of Garofalo(l3) in austenitic iron base alloys. It is important to point out the large differences in the magnitude of a for the two alloys. In alloy 1 we obtain a = 3.5 and in alloy 2 a = 5.0. 4. DISCUSSION
Creep at high temperatures, i.e. above about one half of the absolute melting temperature, is known to be diffusion controlled for a great, variety of materials.(8-14) At temperatures near the melting point and very low stresses, stress-directed diffusion of vacancies, has been proposed as the rate controlling mechanism. At lower temperatures and higher stresses, the motion of dislocations which is controlled here by diffusion is considered aa the controlling process. In this latter case two different dislocation motion mechanisms might be rate controlling: climbing or gliding. Both cases have been treated theoretically by Weertmadl”la) and the results of his analysis are taken as a basis of the following discussion.
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Briefly, Wee&man assumed that dislocations which glide in the slip planes interact with an energy barrier and are stopped. Then, pileups of dislocations are formed and the combined back stress cancels the effect of the applied stress. If this situation occurs and enough vacancies flow towards, the leading dislocations of the pileups may climb over the obstacles, thereby lowering the back stresses and additional dislocation’s glide. However, if dislocations have more difficulties for gliding than for climbing, the former mechanism will be the one which controls the creep rate which is the bases of Weertman’s glide controlled theory of creep.06) Hence, two mechanisms take place continuously during creep, in this temperature range, the slower one being rate-controlling. The results of Weertman’s analysis where the climbing mechanism is rate controlling gives for the creep rate the following relation :(15) 2 = Aa3 sinh (BcG’~/~T)D
(4)
where A and B are constants, o the applied stress, D the self-diffusion coefficient for pure metal (or D = DADB/(DArnB + DBma) for an alloy, in which case Da and DB are the chemical diffusion coefficients of the components and mmg,mB their mole fraction@)) and k and T are, as usual, the Boltzman constant and absolute temperature respectively. In the case in which cG’~B/~T < 1, equation (3) reduces to :
When gliding is rate controlling, the creep rate is given by (16) : . 0.359 s=---(6) A’$ where p is the shear modulus, u the applied stress and A’ the proportionality constant between the dislocations velocity v and the force acting upon them, F(F = ab = A’v). This result is obtained by considering a dragging force imposing a viscous movement upon the dislocations. The constant A’ can be evaluated for each particular model (7*11*12*i7*1E) and is in general related to the inverse of the diffusion coefficient. The temperature range in which the present investigation was performed, is sufficiently high to assume that creep was controlled by a diffusion mechanism in harmony with the mass of experimental evidence(7-s) supporting similar conclusions for creep in other metals and alloys.
VOL.
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Neiman and Shiniaev(lg) determined the activation energies for the diffusion of Fe in NiFe alloys. For the compositions used in alloy 1 and 2 these authors observed values of 56 and 53 kcal/mole respectively. The H* values obtained in the present investigation are lower for both alloys (1 ‘and 2) than the values given by Neiman and Shiniaev. In order to compare values, the H* at the highest temperatures were selected, in order to minimize the contribution to the second term of equation (2) resulting from effects due to the approach to Tc.(17) Figure 2 shows the dependence on the temperature of the H* for both alloys. Alloy 2 has a very constant H* of 48 kcal/mole, independent of temperature. This value differs with the results of Fe diffusion given by Neiman and Shiniaevo9) by 5 kcal/mole. If we take into account the contribution of the frequency dependent term of equation (2), which is given mainly by the temperature dependence of the elastic constants,(10s12)this difference is increased to 7 kcal/mole (for the shear modulus, the value given for pure Ni was used(l As the experimental error for the creep measurements reported here amounts to 4 kcal/mole, and for the diffusion measurements errors must be at least 3 kcal/mole (there is no mention of experimental errors in Ref. 19), the difference between the activation energy for Fe diffusion and our H* for creep can be assumed to be within the experimental errors of the measurements. Hence, we concluded that creep in alloys 2, in the range of temperature investigated, is controlled by the diffusion of Fe in the alloy. However, for alloy 1 the difference between the H* shown in Fig. 2 and the values for the diffusion of Feds) is undoubtedly greater than can be accounted for by the experimental errors. Hence, we believe that, in alloy 1, the Fe diffusion rate is not rate controlling. There exists the possibility that the diffusion rate of Ni is the controlling factor in this latter case. Although the activation energy for the self-diffusion of Ni is very high (~64 kcal/mole), it is known that alloying elements can and often do decrease significantly this value.? Unfortunately, to our knowledge, no data is available for the diffusion of Ni in Ni/Fe alloys. The difference between the stress exponent a for alloy 1 and 2 shown in Fig. 5, suggest that different rate controlling mechanisms are acting in each of these alloys. f Au decreases the activation energy for the diffusion of Ni from 64 kcal/mole (self diffusion) to 43 kcal/mole in an alloy of Ni-25 at. % Au’*“‘. An investigation to obtain the activation energy of Ni diffusion in NiFe alloy is in progress in the laboratories of Metallurgy of the C.N.E.A. (Buenos Aires).
PAMPILLO
AND VIDOZ:
Alloy 2 has a value of a equal to 5 which is in close agreement with the value proposed in Weertman’s climb-controlled model.05) Moreover, it is a value very similar to the stress exponent for a great number of metals, in which climbing seems to be rate controlling, as shown by Sherby.(lO) Alloy 1 has a value of a equal to 3.5 which is near to the value shown in equation 6, for the viscous gliding model proposed by Weertman.(16) So, it seems likely that in this latter case, the existence of S.R.O. imposes a restriction to dislocation gliding, which produces the viscous drag on dislocation glide during creep in alloy 1. In such circumstances, gliding dislocations have to cut, during movement, bonds between unlike atoms (right bonds). This process requires an extra amount of energy, which must be supplied by the applied stress, if thermal activation is not taken into account. Then, the stress necessary to move a dislocation, without the assistance of the thermal fluctuations, is given by ci = y/b,t2n where y is the energy per unit area of the slip plane necessary for the creation of wrong bonds, (A.P.B. energy) and b is, as usual, the Burgers vector. If the applied stress is smaller than this critical value (ci), the dislocations can not move, unless thermal activation helps to create disorder (wrong pairs of atoms). (17) It should be emphasized that in order to create disorder by the thermally activated movement of atoms it is irrelevant which kind of atoms move. So, it is concluded that the fastest diffusing kind of atoms is the one that will become rate controlling for the gliding process, i.e. generally the one with the lowest activation energy for diffusion. It has been pointed out already that Fe diffusion is not likely to be the rate controlling process for creep in alloy 1 and that probably diffusion of Ni might explain the experimental H* for creep. If this were the case the activation energy for the diffusion of Ni in Ni-25 at.% F e would have to be between 40 and 48 kcal/mole, which are the calculated limit values for H* for alloy 1. It is interesting to note that in alloy 2, in which the rate of climb seems to be the controlling mechanism, the diffusion coefficients enter into the corresponding creep equation (equation 5) through a weighted average of them, i.e. 1/D = m,lDa + mg/Dg where D, and D, are the chemical diffusion coefficients of species A and B and mA, mB their mole fractions. Then, if the coefficients _D, and D, are very different, due to the differences in their activations energies, for instance D, > D, and if md and mg have comparable values, as in the case we are
CREEP
IN
Ni-Fe
ALLOYS
319
investigating, it is apparent that is D - l/mBjDB. Hence, the apparent creep activation energy when the climbing process is rate controlling should be equal to the activation energy of diffusion for the slowest diffusion species. However, it could be argued that, if in alloy 1, the gliding process is controlled by the fastest diffusing kind of atom, and climbing of dislocations by the slowest ones, then the latter mechanism could be the rate controlling one because it would become the slowest process. However, a rough calculation shows that under the above mentioned circumstances, gliding is rate controlling, unless the ratio of the diffusion coefficients between the fastest and the slowest species is greater than approximately 103. The increase in H* for alloy 1 (Fig. 2) as the ordering temperature is approached, can be related to the contribution to H* associated with the change in local order, in the way mentioned in the paper of Lawley et aZ.(l’) For the case of alloy 2, in which climbing is assumed to be rate controlling, H* is nearly independent of temperature. With the assumption that the gliding process is rate controlling in alloy 1, let us calculate, using equation (5) and the data of Fig. 3, the values for y and E (the interaction energy which is given by 2E,,)). The constant A’ in E = &(E,, + ‘BB equation 6 was estimated for the case of a S.R.O. structure by Lawley et uZ.07) They obtained A’ = yblD, where D was suggested by these authors to be the diffusion coefficients of the fastest component. Hence the creep rate is given by: . 0.35usD e=iuayb
(7)
Using equation (7) a rough estimation of the energy y can be made. Taking D ‘V 2 x lo-l4 cm2 set-l which is calculated with the Do for the Fe diffusion and with 48 kcal/mole as the activation energy which is the upper limit estimated for the diffusion of Ni in alloy 1; ,u N 7.5 x loll dy cm-2 ; b = 2.5 x 1O-s cm; 6 = 4,5 x 10-S seg-’ and c = 8 x lo* dy cm-2 (~8 kg/mm2) it is found for y = 53 ergs cm-2 according to equation (7). Lawley et aZ.u7)have found for Fe-19.4 at.% Al, that y = 46 erg cm-2 by using Flinn’s formula(n*ss) in which the S.R.O. parameter (tcJ is related to the interaction energy E and y. A value of E fi 0.07 eV for alloy 1, was obtained using the calculated value for y. In Flinn’s paper(s2) the value for E for CuaAu was found to be E N -0.028 eV. The higher value for E in N&Fe found in the present calculations as compared with the value for C~,AU(~~)is in agreement with the
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METALLURQICA,
prediction of the order disorder theories which relates E to the critical ordering temperature Tc through the equation E = (k * T,)/4. The calculated values for y and E seems to be quite reasonable if we consider the uncertainties in the values of various parameters used in the calculations (principally D,,). For alloy 2, it is possible to calculate the density of dislocation sources (M) by the use of equation (5) and the data of Fig. 4. Ifwetakea = 5 x 108dycm-2(~5kgmm-2); a=75 x lo-’ set-l; T = 923”K, H = 53 kcal/mole;(ls) D, = 10d2 cm2 sec-l(19) the dislocation source density is estimated as 5 x 1012cm-s. The dislocation density p is related to M in the relationship p314= 1.9 .M1/2 proposed by Weertman. (12) From this expression p ‘u 7.5 x lo* cm-2, which is a very reasonable value. It can be concluded from the above discussion that, in the range of temperature investigated, the operative rate controlling mechanisms for creep are different for alloy 1 and 2. The gliding rate is the rate controlling process in alloy 1 and the climbing rate is the one in alloy 2. Three further experimental observations remain to be discussed: (i) the breakaway from the power law observed for both alloys in Figs. 3 and 4, which is also evident as a rapid increase of stress exponent with decreasing temperature as shown in Fig. 5. (ii) the increase in the H* accompanied by a change in the stress exponent a which was found for alloy 2 at approximately 904“K (see Figs. 2 and 5). (iii) the abrupt change of the stress exponents a for alloy 2 found at the ferromagnetic Curie temperature (see Fig. 5). These three observations are discussed in order : (i) The breakaway of the power law shows the following features: for alloy 2 (see Fig. 4) the breakaway stress does not seem to depend as strongly on temperature as alloy 1. Table 1 gives the estimated values of the breakaway stresses for both alloys at different temperatures. TABLE 1 Alloy 1
Alloy 2
Temp. OK
870
840
822
850
840
(kg/mm’)
12,3
14,9
16;3
12,3
12,‘7
Ni (pure) 822
independent 12,7 7
After exceeding the breakaway stress, alloy 2 showed a dynamic recovery. This effect is shown in Fig. 6 where the experimental points from Fig. 4 for 822’K are plotted separately. Figure 6 includes some other data which are not shown in Fig. 4. The numbers which are adjacent to the experimental points shown in Fig. 6, indicate the
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sequence in which they were obtained. Experimental points plotted as crosses (a and b) were determined during the very first part of the creep curve when the steady state structure was not yet reached. Steady state creep was reached by point 1. It is shown that the points for which recovery effect exist, i.e. points 16, 17 and 18 fall on a curve that passes through the point obtained at the very beginning of the test (point a). For the points 16, 17 and 18, no trace of tertiary creep was detected. The breakaway stress seems to be more dependent on temperature in alloy 1 than in alloy 2. The dynamical recovery effect observed for alloy 2 was less pronounced in alloy 1. Breakaway is-not uncommon in various pure metals and alloys. w The breakaway stress for pure Ni(26) is only 30% less than the breakaway stresses for the two Ni alloys studied here (see Table 1). The correct theory must apply to creep when it is controlled by climb, as well as by viscous gliding, if the deduction made here concerning the rate controlling mechanism for the stoichiometric alloy is correct. Either the density of moving dislocations or their average glide velocity must increase with increasing stress more rapidly than at lower stress levels, once the breakaway stress has been exceeded. Obviously, many alternate possibilities might be suggested that could account for the breakaway from the power law by changing the dislocation density or velocity. However, the experimental evidence and available theories, are not adequate to determine whether, for example, cross-slip or dislocation multiplication in some form, or changes of the pile-up dislocation arrays, or changes of the average vacancy density (as suggested by Weertman (12)), is more likely to be correct. The broad peak in H* found for alloy 2 around 904°K seems to be most likely explained by a change in the rate-controlling process. The cause of the peak and the constant flow stress in a range of temperature is unknown. Borsch et uZ.(ss)ascribed a similar sharp peak in the creep activation energy vs temperature curve in an aluminum-rich magnesium alloy to the drag on gliding dislocations which was caused by a Cottrell atmosphere. At the temperature of the peak, they observed that the creep rate essentially vanished, even when the creep stresses approached the fracture stress. The dislocation velocity for such a process should be given by the Einstein
PAMPILLO
VIDOZ:
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CREEP I
IN
I
Ni-Fe
I
ALLOYS
321
I
l5
alloy2 822.K
I z2
I
z3
logarithm Fxa. 6. Stress
relationship:
v = g
I 2,4
I
25
I
2,6
of stress
I 27
I 50
(Kg/m&
dependenceof the creep rate for T = 82P’K showing the bre8kaway effect.
F where F = obl is the
driving force, D the solute diffusion coefficient, kT, as usual, the Boltzman constant and absolute temperature, 1 the average distance between impurity atoms along the dislocation line and b the Burgers vector. Since, here, the peak in the activation energy value was coincident with a peak in the value of the stress exponent (see Fig. 5) rather than a decrease of that to one predicted by the Einstein relationship, Cottrell dragging does not seem to describe the character of the peaks in a simple way. The strengthening effect is shown still in another way in Fig. 7, where the flow stress for a given creep rate is shown as a function of temperature (the data in Fig. 7 were obtained from Figs. 3 and 4). Figure 7 shows that the flow stress remain constant over the temperature range of the peaks
in Figs. 2 and 5 for alloy 2, whereas no such plateau is present for the alloy 1. (iii) The abrupt drop in the stress exponent shown in Fig. 5 for alloy 2 at the Curie temperature is believed to be associated with a microcreep mechanism acting at temperatures lower than the Curie point. For temperatures above this one, it has already been concluded that climbing was rate controlling in alloy 2. It has been previously poposed that stress induced S.R.O. occurs in NiFe alloys(s7) annealed under stress, also it has been suggestedo7) that magnetic annealing in N&Fe contributes in a similar way to the atomic distribution. It seems possible then, that below the Curie temperature, S.R.O. forms in alloy 2 which results in a change in the creep rate controlling mechanism from climbing to gliding of dislocations through a viscous S.R.O. structure. In alloy 1 the same effect is not observed since,
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Temperature
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(OKI
Fro. 7. Flow stress versus temperature for alloys 1 and 2.
perhaps, even above the Curie point the degree of S.R.O. is sufficient to make viscous gliding rate controlling. ACKNOWLEDGMENTS
Support by the Army Research Office of U.S.A. (Grant No. DA-ARO-092-63-12) of the program in which this work was done is gratefully acknowledged. The authors would like to thank to Dr. Gunther Schoeck for invaluable discussions and to Drs. W. Green and H. Paxton for comments on the manuscript. Thanks are also due to Mr. R. Luzzi for his experimental assistance at the beginning of the investigation. REFERENCES and E. YATES, Proc. Roy. Sot. B 66,221 1. R. K. WAK~LIN (1953). 2. B. G. LYASCHCHENCO,D. F. LITVIN, J. M. PUZEI and Yu. G. ABOY, Ksist&ogra$ya 2, 64 (1967). 3. A. E. Vmoz. D. LAZAXEVIC and R. W. CAEN. Acta Met. ii, 17 (1963j. 4. R. G. DAVIES and N. STOLOFF,Acta Me-t. 11, 1347 (1963). 6. T. SVZIJKIand M. Y.wumoro, J. Phya. Sot. Japan 14,463 (1969). 6. R. G. DAVIES, Trans. Am. In&. Min. Met&l. Engrs 227, 227 (1963). . ,
7. G. SCHOECK,Mechanical Behavior of Material8 at Elevated Temperature-9 (1961). J. DORN, Creep and Recovery, Am. Sot. Metal8 (1956). Z: G. SHOECK, Phys. Stat. Sol. (1965). 10. 0. SHERBY, Acta Met. 10, 136 (1962). 11. C. M. SELLARS, A. G. QUAERELL, J. Inst. Metals 90, 329 119621. 12. j. W~ERTMAN, Trans. Am. Inst. Min. Metall. Engrs 218, 207 --- f 196icI\. 13. F. GAROFALO, Trans. Am. Inst. Min. Metall. Engrs a80, 1460 (1964). 14. J. DORN, PhyW oapeets of Creep, p. 4. University of California UCRL, 10698 (1963). 16. J. WEERTXAN, J. Appl. Phys. 28, 362 (1957). 16. J. WEERTMAN. J. AZ&. Phva. !XL 1185 (1967). 17. A. LAWLEY, j. A. FILL a;d R.-W. &HN, ‘Trans. Am. Inst. Min. Met&Z. Engr8 218, 168 (1960). 18. J. WEERT~N, Ice and Snow, p. 28. M.I.T. Press (1963). 19. M. MEIM!AN,IA. SHINIAEV, Dobl Akad. Nauk SSSR 102, s69 (1955). 20. J. E. REYNOLDS, B. L. AVERBACH, M. COIIEN, Acta Met. 6. 29 119571. -z ~~~ 21. A. H. COTTRELL,Relation of Properties to Microstructure, p. 161. ASM (1963). 22. P. A. FLINN, Phye. Rev. 104, 360 (1956). 23. P. A. FLINN, Acta Met. 6, 631 (1958). 24. D. MCLEAN, K. F. HALE, The stress sensitivity of creep. In& of Metals, London, Special Report No. 70 (1961). 26. J. WEERTYAN, P. SIXAHINIAN, Trans. Am. Inst. Min. Met&. Engw 206, 1223 (1966). 26. N. R. BORSCH, L. A. SEEPARD, J. E. DORN, University of California, Mineral Research Lab. Report, Series 103, 6 (1968). 27. R. VERQNE C.R. Acad. Sci. Paris 247, 197 (1968). \----I-
\----I
AT
HIGH C.
A.
TEMPERATURES
PAMPILLOT
and
A.
IN N&Fe ALLOYS* E. VIDOZt
The creep behaviour of N&Fe 8nd Ni-20 8t. % Fe 8110~s has been investigated in the temperature renge between, approximately, 530” to 720°C. For the c&se of the Ni-20 at. % Fe 8110~ the experiment81 8ctiv8tion enthalpy for creep w8s found to be, within the experiment81 error, in 8greement with the available dsta for diffiion of Fe in Ni-Fe alloys. For the stoichiometric composition N&Fe it is suggested that the diffusion of Ni is the controlling f8ctor. It is proposed that dielocetion climbing is the rate controlling process for creep in the Ni-20 at. % Fe alloy and that gliding of dislocations through 8 short range ordered structure is controlling the creep rate in the Ni-25 at. ‘A Fe 8110~. Several other experimental results em discussed. FLUAGE
A HAUTE
TEMPERATURE
DANS
LES ALLIAGES
Ni-Fe
Les auteurs ant 8tudiB le comportement au fluege d’alliages N&Fe et Ni-20 % at.Fe, dans un domaine de tempbretures s’6tandant approximativement de 530 8 720°C. Dens 1’8lliege Ni-20 % at.Fe, l’enthalpie d’activation trouvbe exp&imentalement pour le fluege est en eocord, dsns les limites des erreurs exp&imentales, 8vec les donnbes publibes sur la diffusion de Fe dens les alliages Ni-Fe. Dans le c8a de la composition stoechiom&rique Ni,Fe, lea auteurs suggbrent que le ph&om&ne est gouvernb par la diffusion de nickel. 11est vreisembleble que 18 vitesse de fluage eat contr616e per le grimpege des dislocations dans l’alliage Ni-20 % at.Fe, et per le glissement de8 dislocations 8. travere une structure ordonnbe B petite distance dans l’alliage Ni-25 % at.Fe. Les auteurs discutent Bgalement divers autres &ultats exphrimentaux. HOCHTEMPERATURKRIECHEN
IN Ni-Fe-LEGIERUNGEN
DW Kriechverhelten von N&Fe und Ni-20 at.- % Fe-Legierungen wurde im Temperaturbereich von etwa 530°C bis 720°C untereucht. Bei der Ni-20 et.-% Fe-Legierung war die experimentell gefundene Aktivienmgsenthelpie fiir das Kriechen innerh8lb der Fehlergrenzen in Vbereinstimmung mit den zur Verfiigung stehenden Daten fiir die Diffusion von Fe in Ni-Fe-Legierungen. Bei der stochiometrischen Zus8mm ensetzung N&Fe ist vermutlich die Diffusion von Nickel die kontrollierende GrCiBe. Es wird vorgeschlagen, da3 das Klettern von Versetzungen der geschwindigkeitsbestimmende ProzeB fiir das Kriechen in der Ni-20 8t.- % Fe-Legierung ist, und da0 das Gleiten von Versetzungen in einer Nahordnungs-struktur die Kriechgeschwindigkeit der Ni-25 et.- % Fe-Legienmg bestimmt. Verschiedee andere experimentelle Ergebnisse werden diskutiert.
1. INTRODUCTION
Previous investigstions(1*2) have shown that Ni-Fe alloys exhibit an order-disorder transformation in the composition range between approximately 20 to 30 at.% Fe. A superlattice similar to that of ordered CusAu (Ll,) was observed below the critical temperature of ordering (Tcw 503°C). It was found that annealing treatments of approximately 70 hr at 470°C are sufilcient to develop long range order in the stoichiometric alloy,(3*4) meanwhile the Ni-20 at.% Fe alloy does not present long range order even for very long times of annealing.@) The creep properties of Ni,-Fe were investigated by Suzuki and Yamamoto(5) and later by Davies(@ by measuring the steady state creep rate. Davies reported some discrepancies between his results and the ones of Suzuki and Yamamoto. After an analysis of the results, he stated that apparently Suzuki and * Received May 31, 1965. t Divisi6n Fisica de Metales Centro Atimico Beriloche (C.N.E.A.) Instituto de Fisica “Dr. J. A. Balseiro” (Universided Nat. de Cuyo) S.C. de Bariloche (R.N.) Argentina. ACTA METALLURGICA,
VOL. 14, MARCH 1966
313
Yamamoto have measured the creep rates in some kind of transient stage which obviously mislead their interpretations. With these results in mind, we decided to fully investigate the creep behavior of the Ni-Fe alloys, using one composition inside the ordered regions and another outside it. The results shown in the present work are part of a more extensive investigation of the creep and plastic properties of ordered alloys. 2. EXPERIMENTAL
METHODS
The nickel-iron alloys used in this investigation were made by sintering metal powders of high purity. The compositions selected were 75125 and 80120 at.% Ni-Fe (in the following these alloys are referred as 1 and 2 respectively). Chemical analysis showed that the alloys were within 0.1% of the desired compositions . A typical analysis shows the following impurity content: ca 0.0001%, cu 0.0001%, Mg 0.0001%, Si < O.OOOl%, Na < 0.0001%. Creep specimens were cut from cold rolled strips of the
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314
METALLURGICA,
VOL.
14. 1966
In order to obtain a constant stress, small amounts of load were removed after appropriate strains, with the assumptions of a linear relationship between change in cross-section and strain and uniform strain along the section (this is justified because final strains were always smaller than 5%). 3. EXPERIMENTAL
RESULTS
Creep is known to be a thermally activated process. If it is assumed that only one mechanism is rate controlling one can write for the creep rate:‘7-g) 6 = ye-“/kT
sped men
-lb 9dPS
1 0
FIQ. 1. System
J
/
for me&swing creep elongations.
alloys. They were electropolished and then recrystallized in a vacuum furnace at 850°C and quenched by removing the furnace and cooling the quartz tube container with water. Grain boundaries were easily observed under the light microscope due to thermal etching produced during the recrystallization treatment. It was found that the average grain diameter was 0.04 mm in alloy 1 and 0.07 mm in alloy 2. Specimens were deformed in a creep testing machine. The heating was provided by a standard electric furnace which was controlled by an Ether Transitrol temperature controller. The temperature of the tests were measured by means of a thermocouple in contact with the specimens. Temperature fluctuations were less than 1.5”C and the temperature gradient over all the specimen length was found to be less than 3°C. Creep deformations were measured at the upper end of the specimen grips using a transducer, which was held by a stainless steel reference rod which was mechanically connected to the lower specimen grip. This system, which is shown schematically in Fig. 1 minimizes the effect of differential thermal expansion which might be produced by the temperature changes. Creep strains, whrch were measured by the transducer, were recorded by a Leeds and Northrup Speedomax X-t recorder. The minimum observable creep rate was 5 X IO-’ se&.
(1)
where v is a frequency factor, H the activation enthalpy of the rate controlling mechanism, k the Boltzman constant and T the absolute tests temperature. Generally H and v are temperature and stress dependent. In order to understand the atomistic model which is rate controlling it is essential to obtain the values of H and v and their dependence on temperature and stress. From equation (l), the activation enthalpy is easily obtained :cg)
(2) where the shear stress r and the internal structure st. are held constant. Since the distribution of grains orientations was random the acting shear stress is assumed to be $a. The first term on the right hand side of equation (2), can be obtained experimentally by abruptly changing the test temperature and it is often named, the apparent activation enthalpy (H*) t9). The second term is usually neglected,(‘ps) since it is thought to be only a small fraction of the first term, or accounted for, through the temperature dependence of the elastic constants since the frequency factor v depends on them.‘lO-12, Hence, the apparent activation enthalpy is given by: In 6J.6, ln VI/V2 -H-k (3) H* = - k l/T, - l/T, l/T, - l/T2 where .6r,and g2, vr and v2, are respectively the creep rates and frequency factors before and after the abrupt change in temperature from TX to T,. In our experiments rapid changes required less than 9 minutes, the average temperature difference was about &15”C!. The test temperature was changed in general several times during a given test. In this way several values of H* were calculated for each temperature change. As H* was found to be independent of strain (within the experimental error), a mean value
PAMPILLO
m60-
AND
VIDOZ:
CREEP
IN
Ni-Fe
f
ALLOYS
rrloy 1
6040-
FIG. 2. Apparent activation enthalpy for creep as a function of temperature for alloys 1 and 2.
1ogizrithm
of stress, (Kg/m/d)
FIG. 3. Strrm dependence of the areep rate. Double logarithmic plot for alloy 1.
315
ACTA
316
METALLURCICA,
I
I
2
I,5 log~rj~~~ FIG. 4.
VOL.
of stress.
14,
1966
I
2,; IKg./mm+)
Stress dependence of the creeprate. Double logarithmic alloy 2. (points for X = 874°K are not shown.)
of it was calculated using the values obtained at each temperature change. The average temperature for each set of values was defined as 4(Tl + T,). The apparent activation enthalpies obtained in this way are shown in Fig. 2 as a function of temperature. The errors shown are the mean deviations from the average value of H*. For alloy 2 a peak is present in the H* versrs T curve at approxima~ly 904°K. For alloy 1 the value of H* increases as the test temperature decreases and the critical temperature of ordering (T, N 773’K) is approached. It was expected that the stress dependence of H* should be more sensitively determined from the dependence-of the stress on the creep rate. It was found that at temperatures higher than &?O”K, H* was independent of stress for both alloys, with the exception of alloy 2 at temperatures of 900°K where the peak in H* exists. Figures 3 and 4 show the plots
plot for
of In 6 versus In c for alloy 1 and 2 respectively, at several test temperatures. Each set of points which de6nes a line, was obtained with one specimen by changing abruptly the stress by different amounts in a random manner. With this method, creep rates at different stresses and strains can be compared, because a constant structure is assured. The relation between creep rate and stress can be represented in the form, d N 8 where e is the tensile stress and a is a constant which is obtained from the slopes of curves in Figs. 3 and 4. The values of a were calculated by using a least square analysis for each set of experimental points. When the stress exceeds a certain value the power law between creep rate and stress breaks down. Figure 5 shows, for both alloys, the values obtained for the exponent ct as a function of temperature. The errors indicated, give the limiting values of Q. The
PAMPILLO
AND
VIDOZ:
CREEP
IN Ni-Fe
ALLOYS
317
.i
_I I -\ 0 alloy 2
\ - y\
-
_
0 alloy
\ \ i\ \
’ \ ’
\
/-
-f-V/ ‘\ \ \ ‘+-i : ’
’\
I
800
I
I 850
+A ‘L+_+
I 900
I
Temperature FIG. 5.
I
I 950
PKI
Stress exponent a BSa function of temperature for alloy 1 and 2.
curve for alloy 1 does not show any significant variaof a with temperatures above -820°K. This result is an indication that H* is independent of the stress. For the alloy 2, a increases in the temperature range in which the H* versus temperature plot, shows a peak, which suggests that there is a stress dependence of H*. Also, alloy 2 shows an abrupt change in the value of a near 843’K. It is interesting, and perhaps significant, to point out that 843°K is the magnetic Curie temperature for this alloy. However, the Curie temperature for alloy 1 is approximately 880°K and no appreciable change on the exponent a was found near this temperature. It should be pointed out, that no change in H* was found at the Curie temperature in either alloy used, contrary to what has been suggested in the literature.(lO) At temperatures below 820’K the exponent a rises rapidly, which suggests that H* may depend strongly on stress. A similar observation was detected by Davies(ls) in N&Fe (alloy 1). Metallographic observations show the possibility of grain boundary sliding. As the stress exponent a was tion
1
I’ I\ I\
found to be independent of the grain size it wa,s concluded that the creep rate was controlled by an intragranular mechanism, in agreement with the results of Garofalo(l3) in austenitic iron base alloys. It is important to point out the large differences in the magnitude of a for the two alloys. In alloy 1 we obtain a = 3.5 and in alloy 2 a = 5.0. 4. DISCUSSION
Creep at high temperatures, i.e. above about one half of the absolute melting temperature, is known to be diffusion controlled for a great, variety of materials.(8-14) At temperatures near the melting point and very low stresses, stress-directed diffusion of vacancies, has been proposed as the rate controlling mechanism. At lower temperatures and higher stresses, the motion of dislocations which is controlled here by diffusion is considered aa the controlling process. In this latter case two different dislocation motion mechanisms might be rate controlling: climbing or gliding. Both cases have been treated theoretically by Weertmadl”la) and the results of his analysis are taken as a basis of the following discussion.
318
ACTA
METALLURGICA,
Briefly, Wee&man assumed that dislocations which glide in the slip planes interact with an energy barrier and are stopped. Then, pileups of dislocations are formed and the combined back stress cancels the effect of the applied stress. If this situation occurs and enough vacancies flow towards, the leading dislocations of the pileups may climb over the obstacles, thereby lowering the back stresses and additional dislocation’s glide. However, if dislocations have more difficulties for gliding than for climbing, the former mechanism will be the one which controls the creep rate which is the bases of Weertman’s glide controlled theory of creep.06) Hence, two mechanisms take place continuously during creep, in this temperature range, the slower one being rate-controlling. The results of Weertman’s analysis where the climbing mechanism is rate controlling gives for the creep rate the following relation :(15) 2 = Aa3 sinh (BcG’~/~T)D
(4)
where A and B are constants, o the applied stress, D the self-diffusion coefficient for pure metal (or D = DADB/(DArnB + DBma) for an alloy, in which case Da and DB are the chemical diffusion coefficients of the components and mmg,mB their mole fraction@)) and k and T are, as usual, the Boltzman constant and absolute temperature respectively. In the case in which cG’~B/~T < 1, equation (3) reduces to :
When gliding is rate controlling, the creep rate is given by (16) : . 0.359 s=---(6) A’$ where p is the shear modulus, u the applied stress and A’ the proportionality constant between the dislocations velocity v and the force acting upon them, F(F = ab = A’v). This result is obtained by considering a dragging force imposing a viscous movement upon the dislocations. The constant A’ can be evaluated for each particular model (7*11*12*i7*1E) and is in general related to the inverse of the diffusion coefficient. The temperature range in which the present investigation was performed, is sufficiently high to assume that creep was controlled by a diffusion mechanism in harmony with the mass of experimental evidence(7-s) supporting similar conclusions for creep in other metals and alloys.
VOL.
14,
1966
Neiman and Shiniaev(lg) determined the activation energies for the diffusion of Fe in NiFe alloys. For the compositions used in alloy 1 and 2 these authors observed values of 56 and 53 kcal/mole respectively. The H* values obtained in the present investigation are lower for both alloys (1 ‘and 2) than the values given by Neiman and Shiniaev. In order to compare values, the H* at the highest temperatures were selected, in order to minimize the contribution to the second term of equation (2) resulting from effects due to the approach to Tc.(17) Figure 2 shows the dependence on the temperature of the H* for both alloys. Alloy 2 has a very constant H* of 48 kcal/mole, independent of temperature. This value differs with the results of Fe diffusion given by Neiman and Shiniaevo9) by 5 kcal/mole. If we take into account the contribution of the frequency dependent term of equation (2), which is given mainly by the temperature dependence of the elastic constants,(10s12)this difference is increased to 7 kcal/mole (for the shear modulus, the value given for pure Ni was used(l As the experimental error for the creep measurements reported here amounts to 4 kcal/mole, and for the diffusion measurements errors must be at least 3 kcal/mole (there is no mention of experimental errors in Ref. 19), the difference between the activation energy for Fe diffusion and our H* for creep can be assumed to be within the experimental errors of the measurements. Hence, we concluded that creep in alloys 2, in the range of temperature investigated, is controlled by the diffusion of Fe in the alloy. However, for alloy 1 the difference between the H* shown in Fig. 2 and the values for the diffusion of Feds) is undoubtedly greater than can be accounted for by the experimental errors. Hence, we believe that, in alloy 1, the Fe diffusion rate is not rate controlling. There exists the possibility that the diffusion rate of Ni is the controlling factor in this latter case. Although the activation energy for the self-diffusion of Ni is very high (~64 kcal/mole), it is known that alloying elements can and often do decrease significantly this value.? Unfortunately, to our knowledge, no data is available for the diffusion of Ni in Ni/Fe alloys. The difference between the stress exponent a for alloy 1 and 2 shown in Fig. 5, suggest that different rate controlling mechanisms are acting in each of these alloys. f Au decreases the activation energy for the diffusion of Ni from 64 kcal/mole (self diffusion) to 43 kcal/mole in an alloy of Ni-25 at. % Au’*“‘. An investigation to obtain the activation energy of Ni diffusion in NiFe alloy is in progress in the laboratories of Metallurgy of the C.N.E.A. (Buenos Aires).
PAMPILLO
AND VIDOZ:
Alloy 2 has a value of a equal to 5 which is in close agreement with the value proposed in Weertman’s climb-controlled model.05) Moreover, it is a value very similar to the stress exponent for a great number of metals, in which climbing seems to be rate controlling, as shown by Sherby.(lO) Alloy 1 has a value of a equal to 3.5 which is near to the value shown in equation 6, for the viscous gliding model proposed by Weertman.(16) So, it seems likely that in this latter case, the existence of S.R.O. imposes a restriction to dislocation gliding, which produces the viscous drag on dislocation glide during creep in alloy 1. In such circumstances, gliding dislocations have to cut, during movement, bonds between unlike atoms (right bonds). This process requires an extra amount of energy, which must be supplied by the applied stress, if thermal activation is not taken into account. Then, the stress necessary to move a dislocation, without the assistance of the thermal fluctuations, is given by ci = y/b,t2n where y is the energy per unit area of the slip plane necessary for the creation of wrong bonds, (A.P.B. energy) and b is, as usual, the Burgers vector. If the applied stress is smaller than this critical value (ci), the dislocations can not move, unless thermal activation helps to create disorder (wrong pairs of atoms). (17) It should be emphasized that in order to create disorder by the thermally activated movement of atoms it is irrelevant which kind of atoms move. So, it is concluded that the fastest diffusing kind of atoms is the one that will become rate controlling for the gliding process, i.e. generally the one with the lowest activation energy for diffusion. It has been pointed out already that Fe diffusion is not likely to be the rate controlling process for creep in alloy 1 and that probably diffusion of Ni might explain the experimental H* for creep. If this were the case the activation energy for the diffusion of Ni in Ni-25 at.% F e would have to be between 40 and 48 kcal/mole, which are the calculated limit values for H* for alloy 1. It is interesting to note that in alloy 2, in which the rate of climb seems to be the controlling mechanism, the diffusion coefficients enter into the corresponding creep equation (equation 5) through a weighted average of them, i.e. 1/D = m,lDa + mg/Dg where D, and D, are the chemical diffusion coefficients of species A and B and mA, mB their mole fractions. Then, if the coefficients _D, and D, are very different, due to the differences in their activations energies, for instance D, > D, and if md and mg have comparable values, as in the case we are
CREEP
IN
Ni-Fe
ALLOYS
319
investigating, it is apparent that is D - l/mBjDB. Hence, the apparent creep activation energy when the climbing process is rate controlling should be equal to the activation energy of diffusion for the slowest diffusion species. However, it could be argued that, if in alloy 1, the gliding process is controlled by the fastest diffusing kind of atom, and climbing of dislocations by the slowest ones, then the latter mechanism could be the rate controlling one because it would become the slowest process. However, a rough calculation shows that under the above mentioned circumstances, gliding is rate controlling, unless the ratio of the diffusion coefficients between the fastest and the slowest species is greater than approximately 103. The increase in H* for alloy 1 (Fig. 2) as the ordering temperature is approached, can be related to the contribution to H* associated with the change in local order, in the way mentioned in the paper of Lawley et aZ.(l’) For the case of alloy 2, in which climbing is assumed to be rate controlling, H* is nearly independent of temperature. With the assumption that the gliding process is rate controlling in alloy 1, let us calculate, using equation (5) and the data of Fig. 3, the values for y and E (the interaction energy which is given by 2E,,)). The constant A’ in E = &(E,, + ‘BB equation 6 was estimated for the case of a S.R.O. structure by Lawley et uZ.07) They obtained A’ = yblD, where D was suggested by these authors to be the diffusion coefficients of the fastest component. Hence the creep rate is given by: . 0.35usD e=iuayb
(7)
Using equation (7) a rough estimation of the energy y can be made. Taking D ‘V 2 x lo-l4 cm2 set-l which is calculated with the Do for the Fe diffusion and with 48 kcal/mole as the activation energy which is the upper limit estimated for the diffusion of Ni in alloy 1; ,u N 7.5 x loll dy cm-2 ; b = 2.5 x 1O-s cm; 6 = 4,5 x 10-S seg-’ and c = 8 x lo* dy cm-2 (~8 kg/mm2) it is found for y = 53 ergs cm-2 according to equation (7). Lawley et aZ.u7)have found for Fe-19.4 at.% Al, that y = 46 erg cm-2 by using Flinn’s formula(n*ss) in which the S.R.O. parameter (tcJ is related to the interaction energy E and y. A value of E fi 0.07 eV for alloy 1, was obtained using the calculated value for y. In Flinn’s paper(s2) the value for E for CuaAu was found to be E N -0.028 eV. The higher value for E in N&Fe found in the present calculations as compared with the value for C~,AU(~~)is in agreement with the
ACTA
320
METALLURQICA,
prediction of the order disorder theories which relates E to the critical ordering temperature Tc through the equation E = (k * T,)/4. The calculated values for y and E seems to be quite reasonable if we consider the uncertainties in the values of various parameters used in the calculations (principally D,,). For alloy 2, it is possible to calculate the density of dislocation sources (M) by the use of equation (5) and the data of Fig. 4. Ifwetakea = 5 x 108dycm-2(~5kgmm-2); a=75 x lo-’ set-l; T = 923”K, H = 53 kcal/mole;(ls) D, = 10d2 cm2 sec-l(19) the dislocation source density is estimated as 5 x 1012cm-s. The dislocation density p is related to M in the relationship p314= 1.9 .M1/2 proposed by Weertman. (12) From this expression p ‘u 7.5 x lo* cm-2, which is a very reasonable value. It can be concluded from the above discussion that, in the range of temperature investigated, the operative rate controlling mechanisms for creep are different for alloy 1 and 2. The gliding rate is the rate controlling process in alloy 1 and the climbing rate is the one in alloy 2. Three further experimental observations remain to be discussed: (i) the breakaway from the power law observed for both alloys in Figs. 3 and 4, which is also evident as a rapid increase of stress exponent with decreasing temperature as shown in Fig. 5. (ii) the increase in the H* accompanied by a change in the stress exponent a which was found for alloy 2 at approximately 904“K (see Figs. 2 and 5). (iii) the abrupt change of the stress exponents a for alloy 2 found at the ferromagnetic Curie temperature (see Fig. 5). These three observations are discussed in order : (i) The breakaway of the power law shows the following features: for alloy 2 (see Fig. 4) the breakaway stress does not seem to depend as strongly on temperature as alloy 1. Table 1 gives the estimated values of the breakaway stresses for both alloys at different temperatures. TABLE 1 Alloy 1
Alloy 2
Temp. OK
870
840
822
850
840
(kg/mm’)
12,3
14,9
16;3
12,3
12,‘7
Ni (pure) 822
independent 12,7 7
After exceeding the breakaway stress, alloy 2 showed a dynamic recovery. This effect is shown in Fig. 6 where the experimental points from Fig. 4 for 822’K are plotted separately. Figure 6 includes some other data which are not shown in Fig. 4. The numbers which are adjacent to the experimental points shown in Fig. 6, indicate the
VOL.
14, 1966
sequence in which they were obtained. Experimental points plotted as crosses (a and b) were determined during the very first part of the creep curve when the steady state structure was not yet reached. Steady state creep was reached by point 1. It is shown that the points for which recovery effect exist, i.e. points 16, 17 and 18 fall on a curve that passes through the point obtained at the very beginning of the test (point a). For the points 16, 17 and 18, no trace of tertiary creep was detected. The breakaway stress seems to be more dependent on temperature in alloy 1 than in alloy 2. The dynamical recovery effect observed for alloy 2 was less pronounced in alloy 1. Breakaway is-not uncommon in various pure metals and alloys. w The breakaway stress for pure Ni(26) is only 30% less than the breakaway stresses for the two Ni alloys studied here (see Table 1). The correct theory must apply to creep when it is controlled by climb, as well as by viscous gliding, if the deduction made here concerning the rate controlling mechanism for the stoichiometric alloy is correct. Either the density of moving dislocations or their average glide velocity must increase with increasing stress more rapidly than at lower stress levels, once the breakaway stress has been exceeded. Obviously, many alternate possibilities might be suggested that could account for the breakaway from the power law by changing the dislocation density or velocity. However, the experimental evidence and available theories, are not adequate to determine whether, for example, cross-slip or dislocation multiplication in some form, or changes of the pile-up dislocation arrays, or changes of the average vacancy density (as suggested by Weertman (12)), is more likely to be correct. The broad peak in H* found for alloy 2 around 904°K seems to be most likely explained by a change in the rate-controlling process. The cause of the peak and the constant flow stress in a range of temperature is unknown. Borsch et uZ.(ss)ascribed a similar sharp peak in the creep activation energy vs temperature curve in an aluminum-rich magnesium alloy to the drag on gliding dislocations which was caused by a Cottrell atmosphere. At the temperature of the peak, they observed that the creep rate essentially vanished, even when the creep stresses approached the fracture stress. The dislocation velocity for such a process should be given by the Einstein
PAMPILLO
VIDOZ:
AND
I
I
I
CREEP I
IN
I
Ni-Fe
I
ALLOYS
321
I
l5
alloy2 822.K
I z2
I
z3
logarithm Fxa. 6. Stress
relationship:
v = g
I 2,4
I
25
I
2,6
of stress
I 27
I 50
(Kg/m&
dependenceof the creep rate for T = 82P’K showing the bre8kaway effect.
F where F = obl is the
driving force, D the solute diffusion coefficient, kT, as usual, the Boltzman constant and absolute temperature, 1 the average distance between impurity atoms along the dislocation line and b the Burgers vector. Since, here, the peak in the activation energy value was coincident with a peak in the value of the stress exponent (see Fig. 5) rather than a decrease of that to one predicted by the Einstein relationship, Cottrell dragging does not seem to describe the character of the peaks in a simple way. The strengthening effect is shown still in another way in Fig. 7, where the flow stress for a given creep rate is shown as a function of temperature (the data in Fig. 7 were obtained from Figs. 3 and 4). Figure 7 shows that the flow stress remain constant over the temperature range of the peaks
in Figs. 2 and 5 for alloy 2, whereas no such plateau is present for the alloy 1. (iii) The abrupt drop in the stress exponent shown in Fig. 5 for alloy 2 at the Curie temperature is believed to be associated with a microcreep mechanism acting at temperatures lower than the Curie point. For temperatures above this one, it has already been concluded that climbing was rate controlling in alloy 2. It has been previously poposed that stress induced S.R.O. occurs in NiFe alloys(s7) annealed under stress, also it has been suggestedo7) that magnetic annealing in N&Fe contributes in a similar way to the atomic distribution. It seems possible then, that below the Curie temperature, S.R.O. forms in alloy 2 which results in a change in the creep rate controlling mechanism from climbing to gliding of dislocations through a viscous S.R.O. structure. In alloy 1 the same effect is not observed since,
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Fro. 7. Flow stress versus temperature for alloys 1 and 2.
perhaps, even above the Curie point the degree of S.R.O. is sufficient to make viscous gliding rate controlling. ACKNOWLEDGMENTS
Support by the Army Research Office of U.S.A. (Grant No. DA-ARO-092-63-12) of the program in which this work was done is gratefully acknowledged. The authors would like to thank to Dr. Gunther Schoeck for invaluable discussions and to Drs. W. Green and H. Paxton for comments on the manuscript. Thanks are also due to Mr. R. Luzzi for his experimental assistance at the beginning of the investigation. REFERENCES and E. YATES, Proc. Roy. Sot. B 66,221 1. R. K. WAK~LIN (1953). 2. B. G. LYASCHCHENCO,D. F. LITVIN, J. M. PUZEI and Yu. G. ABOY, Ksist&ogra$ya 2, 64 (1967). 3. A. E. Vmoz. D. LAZAXEVIC and R. W. CAEN. Acta Met. ii, 17 (1963j. 4. R. G. DAVIES and N. STOLOFF,Acta Me-t. 11, 1347 (1963). 6. T. SVZIJKIand M. Y.wumoro, J. Phya. Sot. Japan 14,463 (1969). 6. R. G. DAVIES, Trans. Am. In&. Min. Met&l. Engrs 227, 227 (1963). . ,
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