INTERACTION, DISLOCATIONS, DÉFAUTS PONCTUELSINTERNAL FRICTION IN TUNGSTEN CONTAINING CARBON

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INTERACTION, DISLOCATIONS, DÉFAUTS

PONCTUELSINTERNAL FRICTION IN TUNGSTEN CONTAINING CARBON

R. Gray, Z. Szkopiak

To cite this version:

R. Gray, Z. Szkopiak. INTERACTION, DISLOCATIONS, DÉFAUTS PONCTUELSINTERNAL

FRICTION IN TUNGSTEN CONTAINING CARBON. Journal de Physique Colloques, 1971, 32

(C2), pp.C2-163-C2-167. �10.1051/jphyscol:1971237�. �jpa-00214563�

IN JERA C TION, D/SL OCA TIONS, D EFA U TS PONC TUEL S

INTERNAL FRICTION IN TUNGSTEN CONTAINING CARBON

R. J. GRAY and Z. C. SZKOPIAK

Department of Metallurgy and Materials Technology, University of Surrey Guildford, Surrey, England

R6sum6.

Le frottement interieur du tungstkne recuit et dBformB a ete Btudie de la temperature ambiante a 950 OC,

environ 1 cycle par seconde. Le pic de Snoek du carbone est observB a 410 OC, et un autre pic dans un domaine entre 550 et 600

Ce dernier pic nBcessite la presence combinke du carbone et de dislocations, et n'est pas un pic de relaxation. I1 est supposB dil au chargement de la relaxation des dislocations en fonction de la tempkature, cause par un rearrangement irrever- sible du carbone pendant le recouvrement. Puis des atomes de carbone provenant de carbures ou de precipites vont ancrer les dislocations. L'knergie &activation du phenomirne d'ancrage est de 56 f 4 kcal.mole-1.

Abstract.

Internal friction in annealed and deformed tungsten has been investigated from room temperature to 950

at a frequency of 1 Hz. The carbon Snoek peak has been observed at a temperature of 410 OC, and another peak at temperatures between 550 OC and 600 OC. The latter peak required the combined presence of carbon and dislocations, and is not a relaxation peak.

It has been accounted for in terms of the change in the temperature-dependent dislocation damping caused by an irreversible rearrangement of carbon during recovery. Subsequently, carbon atoms originating from carbon clusters or carbide precipitates pin dislocations. The activation energy of the pinning process has been determined to be 56 f 4 kcal. mole-1.

1. Introduction.

Considerable use has been made of the well-known Snoek peaks in BCC metals in order to obtain quantitative information concerning the behaviour of atoms forming interstitial solid solutions with these metals. However, the major successes have been limited to iron and the group Va nfetals, in which interstitial solubilities are appre- ciable, and the Snoek peaks are stable in the tempera- ture ranges (at low frequencies) in which they occur.

Tungsten typifies the group V1 a metals, in which under equilibrium conditions the solid solubility of interstitials is less than 1 wt. p p m at temperatures below 1 000 OC. Nevertheless, the existence, at about 400 OC (1 Hz), of a Snoek peak due to carbon in tung- sten has been reported [l, 21. The activation energy of the relaxation process was determined to be 45 kcal.mo1e-l [ l ] and 47

4 kcal-mole-' [2].

The carbon Snoek peak in tungsten was found to anneal away during the measurements on heating [l], indicating that as soon as the carbon atoms become mobile during heating they form clusters or precipi- tates, and are effectively removed from the solid solution. This behaviour of carbon was also investi- gated by resistivity measurements following a series of isochronal anneals of carbon doped and quenched tungsten specimens [3]. This study showed that clus- tering of carbon atoms was complete in 20 mn at 450°C. The binding energy of a carbon atom to a cluster was found to be in the range from 6 to

14 k ~ a l . m o l e - ~ . A value of 14 kcal.mole-l is obtai- ned by recalculating the binding energy using the mean value of 46 kcal.mole-l for the activation energy of carbon diffusion, based on the Snoek peak investigations [l, 21.

Another study of interest [4] involved the examina- tion of dislocation damping at 50 kHz in cold-worked single crystals of tungsten. An interstitial impurity, thought to be carbon, diffused to dislocations during annealing with an activation energy of 47 + ^{5 kcal.}

mole-'. This value agrees well with estimates of the activation energy for the diffusion of carbon obtained from studies of the Snoek peak [l, 21.

Interstitial impurities are also known to be respon- sible for the Koster peak observed in cold-worked BCC metals after annealing treatments permitting the impurities to migrate to dislocations. It is gene- rally believed that the peak is due to relaxations invol- ving impurities at dislocation lines in the form of clusters or precipitates, rather than atmospheres [5-81. Schnitzel [l] reported a peak occurring at about 600 OC in the internal friction curve of a single crystal of tungsten cold-worked by 5 %, which he thought was a cold work (Koster) peak. A peak occurring at this temperature was also reported by Aleksandrov [g].

111

this case, the treatment involved quenching tung- sten specimens under load, and a vacancy relaxation process was suggested as the operating mechanism.

However, it seems likely that such a treatment could

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971237

C2-164 R.

GRAY AND 2. C. SZKOPIAK introduce dislocations into the metal, and the peak

could, therefore, be due to the Koster mechanism.

The object of the present study was to examine more closely the cold-work peak, which was reported in the literature, in order to obtain further informa- tion on the interaction of interstitial atoms with dislo- cations in a system in which interstitial solubilities are known to be extremely low.

2. Material and experimental procedure. - The material used was commercial purity tungsten wire 0.76 mm in diameter. Carbon doping of the wire specimens (45 cm long) was carried out in a direct resistance furnace at 960 OC and at a pressure of 35 torr.

The doped specimens were then recrystallised in vacuo (2

10-5 torr) at 2 200OC for 30 mn. At this tem- perature the solubility of carbon in tungsten is about 100 ppm [10]. At the end of the recrystallisation treatment the specimens were rapidly cooled by inter- rupting the heating current.

In order to produce specimens of lower carbon content, the as-received wire was recrystallised in vacuo or in an oxygen atmosphere of 0.5 torr. The latter treatment is known to be effective in removing carbon from tungsten [ll]. The carbon contents of the treated specimens are given in Table I.

Carbon contents of specimens

Specimen type Treatment Wt. p.p.m.

carbon

- - -

A Carbon doped 30

B Vacuum annealed 15

C Oxygen annealed Not detectable The specimens were then plastically deformed in tension to a measured amount at 400OC.

Internal friction measurements were-carried out in a K& type torsion pendulum [l21 over the temperature range from 200 to 950 OC at a constant heating rate of 10 OC min-

except for specimens used for isother- mal measurements. In this case the initial heating was carried out at 25 OC min-l. The temperature during the subsequent isothermal measurements was control- led to f 2 OC. The logarithmic decrement was calcu- lated from measurements of the decay in amplitude of free oscillations. All measurements were made a t a frequency of 1 Hz, and in the region of amplitude independent damping except where otherwise stated.

3. Results.

3.1 ANNEALED MATERIALS. - Typi- cal internal friction curves, obtained on heating specimens of materials A and B from 200 to 950 OC are shown in figure I. It was observed that whereas the curve exhibited by material A was reproducible between specimens, that exhibited by material B showed irreproducible peaks and a variable level of damping over the whole temperature range. A close

Temperature 'C

FIG. l .

Internal Friction curves of Annealed Tungsten measured on Heating.

examination of the reproducible curve (material A) showed that a peak of height 5

1OP4 was present at 410 OC, which was also observed on rapid cooling from 430OC, but with a reduced height. This peak was termed peak X.

3.2 DEFORMED MATERIALS.

Figure 2 shows the internal friction obtained on heating specimens of

FIG. 2.

Effect of Carbon Content on Internal Friction Curves.

materials A and C after 5.6 % deformation. These measurements were reproducible, as was the case with all measurements on deformed specimens. Conside- ring the curve for material A, a small peak is still visible in the region of 410 OC and a much larger one (peak Y) appears at 580 OC. The overall level ofdam- ping is much higher than in the same material before deformation (Fig. 1). In the curve for material C (Fig. 2) there are two peaks present, one at 150° and the other at 340 OC. These peaks are absent in the curves (Fig. 2 and 3) of tungsten containing carbon and therefore are not considered further in this paper.

The effect of deformation, up to 5.6 % plastic strain, on the internal friction of material A is shown in figure 3. The effect is that both the background damping and the peak Y increase with increasing degree of deformation. The small peak X also appears to increase slightly, particularly after higher strains.

As a result of the heating cycle to 950 OC the peaks X

and Y are completely removed and the background

INTERNAL FRICTION IN TUNGSTEN CONTAINING CARBON

FIG.

-Effect of Deformation on the Internal Friction of Carbon Doped Material (A).

damping considerably reduced (Fig. 3). 0-n rapid cooling from a temperature just above the peak (620 OC) there was no indication of the presence of the peak Y. The large difference between the heating and cooling internal friction curves is due to the annealing away of the damping during heating. The kinetics of the decay of damping was investigated by heating deformed specimens at the highest rate (25 OC min-l) to temperatures in the region of the peak Y, and taking isothermal measurements during periods of up to one week (Fig. 4 and 5).

140k 8 I I I I I

Speomens type (Y ^Annealtng Temperatures OC

5

*

-

*

r

.

_-

O - O -

~

-

-oz0

-*-*-

0 50 100 150 200 250 300 350

FIG. 4.

Decay of Damping During Isothermal Annealing.

140 ^{1 I I I I I}

Spec~menr type '"C" Anneallns Zmpentures *C

5 6 % Detormataon

*

In figure 6 are shown two internal friction curves measured at different frequencies. From the figure it is apparent that the curve obtained at the higher frequency (2.23 Hz) has been shifted to higher temperatures as compared with the curve measured at the lower fre- quency (0.47 NZ). The temperatures of the peaks X and Y have been shifted by about 270 and less than 5 OC, respectively, as a result of the frequency change.

4. Discussion.

4.1 THE SNOEK PEAK (X).

The marked difference in the internal friction curves of carbon doped (material A) and undoped speci- mens (material B) in the recrystallised state (Fig. l),

160

-

Fa.... rho* freqvencies

140

- ^.,,

120

-

0 100 200 300 400 500 600 700 800 900

Temperat". C

FIG.

Effect of Frequency on Internal Friction Curves.

and the lack of reproducibility of the curve for the undoped specimens is an indication that practically all the damping in undoped tungsten is due to disloca- tions. Damping due to dislocations is often very sensi- tive to handling 1131 and might be expected to decrease considerably in the presence of atoms (in this case carbon) which are effective in pinning dislocations.

With dislocations pinned, the small peak X is no longer masked and is shown to have the following characte- ristics.

a) The peak occurs at a temperature close to the temperatures of the peaks reported by other workers in carbon doped tungsten [l, 21,

b) The height of the peak increases with treatments increasing the concentration of carbon in free solid solution [l, 21.

c) The peak is observed on cooling as well as hea- ting (Schnitzel [l] and present work).

d ) The temperature at which the peak occurs chan- ges with the frequency of oscillation (Fig. 6). The temperature shift of the peak of 27 OC caused by a frequency change from 0.47 to 2.23 Hz is in raesona- ble agreement with 33 OC calculated from the previously reported activation energies of the peak [l, 21. The discrepancy of 6 OC between these temperature shifts is due to the annealing away of the peak during its measurement.

The peak X is therefore the Snoek peak due to car- bon in free solid solution with tungsten.

FIG.

Decay of Damping During Isothermal Annealing.

4.2 THE COLD WORK PEAK (Y).

The peak Y

observed after deformation in carbon doped tungsten

C2-166 R.

GRAY AND Z. C . SZKOPIAK (Fig. 2) appears to be similar to the cold-work peak

reported by Schnitzel [l]. It is only observed in the presence, in the material, of both carbon (Fig. 2) and dislocations (Fig. 3) and occurs at a temperature above that of the carbon Snoek peak. These are the charac- teristics of the well known Koster peak observed in other BCC metals. However, as the peak is not obser- ved on rapid cooling from a temperature just above the peak temperature, and since the peak does not shift significantly with frequency (Fig. 6), it appears that it is not a relaxation peak.

If the peak Y is not due to a relaxation process, it may be caused by an irreversible internal rearrange- ment occurring during heating and which is responsible for the large decrease in damping observed on coo- ling. The steadily increasing damping observed on heating from 100° to 500 OC is due to the motion of dislocations under the oscillating stress, as disloca- tion damping in other metals is known to increase with temperature [13]. When a temperature of about 550OC is reached (i. e. near the peak temperature) the process of rearrangement commences and the damping decreases with further increase in tempera- ture. At a temperature of about 700 OC, the process is completed, and the dislocation damping due to the new more stable dislocation structure again increases with temperature. This description explains satisfac- torily the absence of the peak during cooling and the insignificant frequency dependence of the peak tempe- rature. This model has been used to describe a peak in cold-worked iron containing carbon [14].

The rearrangement process in iron was thought to be dislocation pinning by carbon atoms, and the peak temperature coincided with the temperature of the Snoek peak. In tungsten, the rearrangement process causing the change in damping and hence the peak Y may be the same, since carbon is known to cause strain ageing at 650 OC [15]. The fact that the peak temperature is nearly 200 OC higher than that of the Snoek peak can be explained by the instability of the tungsten-carbon solid solution. Clustering or precipi- tation of carbon atoms from solid solution with tungs- ten occurs very rapidly at 450 OC, as shown by the present and previous internal friction studies [l, 21, and by the results of Krautz [3]. This effectively immo- bilises the carbon until the temperature is high enough for thermal energy to overcome the combined energy of activation for carbon diffusion and the energy of binding of carbon in the cluster. The suggested mecha- nism for the peak can now be examined in detail using the results obtained from the isothermal studies.

4.3 ISOTHERMAL RECOVERY

DAMPING.

In view of the above discussion, pointing to the fact that pinning of free dislocations is occurring in the tempe- rature region of the peak Y, isothermal decay of the damping measured in this study was analysed in terms of the kinetics of migration of interstitial atoms to dislocations due to Cottrell and Bilby [16]. According

to this law, the number of carbon atoms (Nt) which arrive at unit length of dislocation in a time ( t ) is given by

where No is the initial concentration of carbon, A the carbon atom misfit parameter, D the diffusion coefficient of carbon, and T the absolute temperature.

The applicability of equation (1) has been demonstra- ted by a series of strain ageing tests carried out on material A of the present investigation [17]. It is therefore necessary to relate internal friction (6) to N,. As shown in figure 4 the damping decay data obeys equation (1) over significant periods of annealing times. In plotting figure 4 it was assumed that 6 varies with N, according t o the equation

where 6, is the value of internal friction after time t , and 6, and K are constants. Combining (1) and (2)

where K' is constant for a given temperature and dislo- cation density. Thus the straight line portions of the curves of figure 4 represent the stage of dislocation pinning by carbon atoms.

The times required for a given drop in damping at different temperatures in the linear regions of figure 4 fitted an equation of the Arrhenius type. Using this equation an activation energy of 56 f 4 kcal . mole-

was obtained for the pinning process. The difference between this value and the value of 47 kcal.mole-l obtained by Carpenter and Baker [4] for dislocation pinning by carbon can be explained by the much higher sensitivity of the technique which these authors used.

The material of Carpenter and Baker contained about 1 p. p. m. carbon, in which the tendency of carbon to cluster or precipitate was much lower. Consequently most of the pinning of dislocations was brought about by carbon atoms diffusing directly from free solid solution.

Figure 4 shows that at each annealing temperature an initial rapid decrease in damping precedes the linear region in which equation (3) applies. In order to iden- tify the process responsible for this initial damping decay, isothermal measurements were also carried out on material C over the same temperature range as used for material A (Fig. 4). These results are plotted in figure 5 also against

From the figure it is appa- rent that the internal friction initially decreases in the same way as in figure 4, and then tends to an assymp- totic value. There is no straight line portion of the curve, and the assymptotic values are only slightly temperature dependent. Since the carbon content of these specimens was undetectable (Table I), the decrease in internal friction is unlikely to be due to the migra- tion of carbon to dislocations.

A recovery process involving dislocation motion

INTERNAL FRICTION IN TUNGSTEN CONTAINING CARBON C2- 167 is known to occur at these temperatures in cold-worked

tungsten [15, 181. It was found that the present isother- mal results gave a good fit, up to 90 % recovery, into the equation

where R is the normalised extent of recovery after time t , and B and n are constants ; n has a value of about 0.5. This empirical equation was shown to give a good description of the recovery of internal friction in cold-worked iron [19]. The isothermal inter- nal friction measurements in carbon doped specimens (material A) were also tested in equation (4), but gave a satisfactory fit up to about 30 % recovery only.

Stephens and Form [l51 studying strain ageing in tungsten containing carbon showed that recovery preceded dislocation pinning by carbon. This was confirmed by similar tests carried out on material A of the present work [17].

The isothermal decrease of internal friction shown in figure 4 can now be interpreted as follows. During the isothermal annealing of deformed tungsten containing carbon, dislocation recovery precedes the pinning of dislocations by carbon. The two stages are represented by the rapid initial drop and subsequent straight line portions of the curves, respectively, at each annealing temperature. The deviation from linea- rity in t2I3 shown at long times is due to over-strain ageing effects.

The highest temperature at which the peak Y was observed is about 580 OC. Even at this temperature about two hours elapse before carbon commences to migrate to dislocations according to equation (1).

Since the peak Y was measured using a heating rate of 10 OC min-l, it is apparent that the irreversible process causing the peak can not initially be the Cot- trell-Bilby type of pinning of dislocations by carbon.

The peak already occurs while rapid dislocation reco- very is still taking place. The exact manner in which carbon causes the peak cannot therefore be ascertai- ned, but the process appears to involve the modifica- tion of the rate of recovery of cold worked tungsten at the temperature at which carbon atoms become mobile.

5. Conclusions.

a) The presence of the Snoek peak has been confirmed in the internal friction curve of tungsten containing carbon.

b) Tungsten exhibits extensive dislocation damping even after small amounts of cold-work.

c) The dislocation damping recovers during heating, and is decreased considerably by the presence of car- bon a t the dislocations.

d ) The

cold-work peak

observed between 5500 and 600 0C in carbon-doped, cold-worked tungsten is not a relaxation peak.

It is due to a change in the rate of recovery of tem- perature dependent dislocation damping as carbon atoms become mobile during the heating cycle.

e) The activation energy of the dislocation pinning process due to carbon atoms is 56 f 4 kcal. mole-' when the source of carbon is clusters or precipitates.

Acknowledgements. - This work was carried out under a Ministry of Defence Extra-Mural Contract.

The Ministry's permission to publish the results is gratefully acknowledged.

The authors wish to thank Mr. A. J. Nicol-Smith of R. A. R. D. E., Fort Halstead, and Professor M. B.

Waldron, Head of the Department of Metallurgy and Materials Technology, University of Surrey, for their continued interest in and support of this work. The technical assistance of Mr. M. R. Francis is also acknowledged.

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