Microyielding in tantalum single crystals—II. High-amplitude damping

MICROYIELDING IN TANTALUM SINGLE CRYSTALS-II. HIGH-AMPLITUDE DAMPING. &I. J. COWLING*

and D. J. BACON

Department of Metallurgy and Materials Science. Thz Universitl;. P.O. BOX 1-J:. Liverpool L69 3BX, England (Receired 12 ,-lpril 1976; in rrcisrdfornl

9 .l’ocrrnher 1976)

Abstract-The damping at high amplitudes and low frequencies in tantalum single crystals of three purity levels has been determined from uniaxial compression tests at temperatures in the range 77-300 K. Specimens were tested in the as-annealed or 77 K-prestained states. The results have an amplitude- and temperature-dependence which can be related to previous studies of internal friction and to the microflow parameters of the same specimens. It is concluded that at total strain amplitudes s5 x IO-‘, non-screw dislocation motion is controlled by double-kink nucleation on 71' segments. which is the 2’ mechanism. and the motion of dislocations close to the screw orientation is controlled by kink migration, which is the 1 mechanism. Screw dislocation segments can move by double-ink nucleation at room temperature and this is the 7 mechanism. At higher amplitudes. dislocations moving by these mechanisms can overcome the barriers provided by interstitial impurity atoms. RCsum&-On a ktudib I’amortissement aus fortes amplitudes et aux basses frequences dans des monocristaux de tantale de trois puretis difftrentes par des essais de compression uniaviale ~~des tempiratures comprises entre 77 et 300 K. Les essais t-taient effect&s sur des &hantillons recuits ou bien pr2d8orml-s $ 77 K. La variation des rt?sultats en fonction de ~‘amplitude et de Ia temperature peut &re r&i&e h des etudes anterieures de frottement intPrieur et aux param&res de la microd~formation dcs mPmes &chantillons. On en conclut que pour une amplitude de la deformation totale infirieure i 5 x 10-j. le mouvement des dislocations non vis est contr26 par la germination de doubles crans sur Its segments ?I 71’ (mecanisme I’) et le mouvement des dislocations proches de I’orientation vis est contrale par la migration des crans (mCcanisme 2). Des segments de dislocation vis peuvent se d&placer par germination de doubles crans h I’ambiante; c’est le mecanisme 7. Auu fortes amplitudes. ies dislocations se deplacant par ces micanismes peuvent franchir les barritres que constituent les atomes d’impurstts interstitielles. Zusammenfassung--An Tantaleinkristallen dreier Reinheitsgrade wurde die Dlmpfung bei goDen Amplituden und niedrigen Frequenzen aus einachsialen Druckversuchen im Temperaturbereich van 77 bis 300 K bestimmt. Die Proben wurden untersucht im gegliihten und bei 77 K vorverformten Zustand. Die Ergebnisse zeigen eine Amplituden- und Temprraturabhlngigkeit, die in Beziehung mit friiheren Untersuchungen der inneren Reibung und mit MikrofiieOparametern derselben Proben stehen. Es wird geschlossen. dal3 bei Gesamtdehnamp~ituden van s 5 x 10-j die Bewegung der Nicht-Schraubenvers~tzungen durch die Bildung von Doppelkinken an 7I’-Segmenten (~‘-Mechanismus}. diejenige der Versetzungen nahe der Schraubenorientierung durch die Kinkbewegungen kontrolliert (z-Mechanismus) ist. Schraubenversetzungen kGnnen bei Raumtemperatur durch die Bildung von Doppelkinken gleiten (y-Mechanismus). Bei hijheren Amplituden k8nnen die sich iiber diese Llechanismen bewegenden Versetzungen Barrieren iiberwinden, die von interstitiellen Verunreinigungsatomen gebildet werden.

1. IiVTR&XKTIO~ We have briefly reviewed in a previous paper [l]. hereinafter referred to as I, the information obtained from monotonic tests on the microyielding of the b.c.c. transition metals. The evidence, some of which is contradictory. and our own results obtained from compression tests leave several issues unresolved. These are: (a) when non-screw dislocation motion is the sole contribution to plastic flow in the pure metal. is double-kink nucleation or kink migration parallel to the Burgers vector the rate-controlling process’?: * Now at: Department of ltlechanical Engineering. The L%iversity of Glasgow, Glasgow G 12 SQQ. Scotland. 6 It now seems that the 1’ relaxation is not the same as the d process. which appears to have a lower activation energy [II].

(b) in xhat ways do interstitial solutes affect this motion‘?: and (c) is screw dislocation motion in the microflow region the correct interpretation of the evidence that different mechanisms are rate-controlling at different temperatures in certain prestrained specimens? It seems unlikely that these questions can be answered from further study of the microyield parameters such as those reported in I. and a different approach is probably required. It was remarked in I that in parallel with the numerous microyielding experiments which have been carried out. several investigators have studied internal friction associated with dislocations in b.c.c. metals. (For reviews see [W&I.) This work has enabled four main relaxation peaks to be identified, namely x’ (or ci).: r. p and 7. and the ranges of their activation

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0. I eV for zi [5], 0.25 eV for r,O.4 eV for fi and 1.0 eV for 7 [2]. The forms of these peaks in the b.c.c. metals have been examined in a variety of specimen conditions, and the results, which are not always clear-cut, can be surnmarised as follows. The peaks are reduced in height and moved to lower temperatures by anneals carried out a few hundred “C [Z-4]. The x’ and c(peaks are reduced by an increase in the interstitial-impurity concentration [S, 61, whereas the fl peak may require the presence of interstitial hydrogen [7]. Moderate prestrains at room temperature increase the r .and /I peak heights and shift the peak temperature [2,4], and prestraining at 77 K enhances the z’ peak [S] and is reported to enhance the a peak more than the fi [2,8] and vice versa [6,9]. The damping shows a strong amplitude-dependence at strain amplitudes near 1O-6-1O-5, and it saturates at amplitudes above approximately 5 x 1O-4 [2]. As the strain amplitude is increased from below to above these levels, the peaks are increased in height and there is a tendency for the peak temperatures to be lowered, indicating a dependence of activation energy on stress. The y peak in particular becomes large and broad as the amplitude is increased [Z]. In the light of this experimental evidence, numerous interpretations of the mechanisms associated with the peaks have been presented. The z’ peak has been assigned to double-kink nucleation on non-screw dislocations [lo] and the migration of kinks on screw dislocations [5]. The x relaxation has been ascribed to thermally-activated breakaway of dislocations from pinning points [63, double-kink nucleation on nonscrew dislocations [5,9], the migration of kinks on screws [lo], thermal depinning of trapped kinks El I] and the hydrogen cold-work peak [123. The /? peak has been identified with point-defect complexes [13], double-kink relaxation on screws [9,14-J, interaction of dislocations with hydrogen interstitials [lo] and the stress-induced relaxation of twin boundaries [lS]. Seeger and Sestik [lo] have interpreted the 7 process as arising from double-kink nucleation on screw dislocations. This information should be of use for understanding the results of the microflow tests reviewed in I. At the higher strain amplitudes, such as those reported by Chambers [2], the dislocations move over distances comparable to those observed in microstrain tests, and the basic mechanisms involved should be the same. We have therefore tried to relate our microflow results to the possible internal friction mechanisms by carrying out low-frequency loadunload cycles during the uniaxial microflow tests; the total strain amplitudes involved were therefore 15 x lO-‘j. The ratio of the energy dissipated per cycle to the maximum energy stored is a direct measure of the damping, and the way in which this varies with amplitude, temperature and strain rate for the specimen conditions described in I have been determined. The results are presented in Section 3, and then discussed with reference to I in Section 4.

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2. EXPERIMEXI.&L

PROCEDURE

The specimens (x = 25’ only) and testing apparatus employed were as described in Section 2 of I, and the load-unload cycles were carried out at stress levels between 6, and G,~, by the procedure outlined in Section 3 of I. (a, and cmyr were defined in I as the stress required to produce a plastic strain of 5 x lo-’ and a permanent plastic strain of lO-6 respectively.) The area of the load-unload loop obtained on the recorder chart gives the energy dissipated during the cycle AW. and the area under the loading curve gives the maximum energy stored during the cycle W These quantities were determined for the many loops analysed by weighing pieces cut from the chart paper and converting to area by using a calibration piece of the same paper. The damping, A W/ W, was measured as a function of amplitude o,/E for each test condition, where cr,,, is the maximum axial stress per cycle and E is the Young’s modulus of the specimen for the given crystal orientation and temperature. (The single-crystal elastic constants used for E are those given by Armstrong and Mordike [16-J) It was only possible to vary the frequency at a given amplitude by a factor of about 25--typically 0.02-0.5 Hz-and the damping AW/W in all specimens was approximately independent of frequency within these limits. Variations which were observed fell within the experimental error. Consequently, all tests on a given specimen at different amplitudes or temperatures were carried out at a constant total strain rate rather than constant frequency. Although most tests were restricted to the three temperatures 77, 203 and 295K, the damping at constant amplitudes was measured as a function of temperature in a few cases by avowing cyclic tests as the specimen was allowed to warm up stowly from 77 or 203-295 K. 3. RESULTS In most cases, the damping AW/W was found to decrease initially with increasing amplitude and to become amplitude-independent as the maximum stress rr,,,approached G,,_. In a minority of specimen conditions, the damping increased with increasing G, at the highest stresses, or was independent of 6, over the whole range 6, < pi, c CT,_. Results for 2 = 25” crystals of the three purity levels in the annealed or 1% 77 K-prestrained states are shown in Figs. l(a-f). Each data point shown is the average of at least three experimental values. It can be seen that the damping levels tend to be high and span a broad range from -1% to -25%. The trends in the data of Fig. 1 are not well-defined, but those which are discernible can be summarized as follows, In the annealed condition (Figs, la-c) the effect of a decrease in the interstitial content is small at 77 K but it tends to increase ACVW at 203 and 295K. The damping increases strongly with amplitude at these temperatures as G, approaches G,,, in the UHV case. There appear to

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”

(b)

Fig. I. The variation of the damping capacity AW/W with stress amplitude urn. normalized with respect to Young’s modulus E, for the various specimen conditions considered.

is small at 77 K but it tends to increase energy measured in the common b.c.c. metals are 0.01-0.1 eV, 0.1-0.3eV, 0.4-0.6eV and 0.8-1.5eV respectively; the activation energies for tantalum are be no simple trends in the prestrained state. The effect of the prestrain on the damping of the 2zp material is slight. and it strongly reduces the damping at 203 K and 295 K in the UHV crystal. The effect in the 4 zp material is to reduce AWjW at 77 K and increase it at 295 K. The apparent complexity of these results can perhaps best be understood by noting that the damping vs temperature spectra of the b.c.c. metals exhibit a series of peaks at constant amplitude and, as discussed in Section 1, the peaks are shifted in temperature and changed in height by changes in the interstitial content and by cold-work. Thus, a comparison of the AW/W values obtained at one temperature can be complicated by these effects. To investigate this further, the damping was measured at two amplitudes at 15’-20’ intervals over the range 77-295 K for the annealed 4 zp specimen and over the range 203-295 K

content

for the 1% 77 K-prestrained 2 zp, 4 zp and G-W crystals. The resulting data are shown in Fig. 2. and. in addition to showing the expected amplitude-dependence, they explain some of the effects of purity and prestrain seen in Fig. 1. The annealed 4 zp specimen (Fig. 2a) exhibits two broad damping peaks centred about 100 K and 230 K. The 230 K peak is still present after the 1:; prestrain at 77K (Figs. 2b and c). and tends to move to lower temperatures with increasing purity. The most striking effect of the prestrain occurs in the 4zp material where it produces a large increase in the damping above about 270K. It appears that another damping peak is present above 295 K, and this explains the apparently anomalous results for 295 K in Fig. l(e). 4. DISCUSSION

From the activation energies and frequency factors determined for tantalum by Chambers [Z] and Knoblauch er al. [S]. the Eeaks associated with the Y’. r. fi and 7 processes should occur at approximately

!Y 4aterial:2zp

4zp UHL I ’ rnA. ,3i‘restrained ! F-O.64

x10-4

.l-

.l -

I-

T(OK)

200

301 T?K) (b>

%m---Yz T@) (cl

Fig. 2. The variation of the damping capacity AW/W with temperature T for (a) the annealed -tzp specimen at two amplitudes and (b) and (c) the 77K-prestrained specimens at two amplitudes.

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60 K. 110 K. 190 K and 470 K respectively for the frequencies used in this investigation. These temperatures are those for low strain amplitudes. and they tend to change. and in some cases merge. at high amplitudes [2]. Thus, although the 100 K peak shown in Fig. 2(a) may be associated with the x relaxation, this assignment is an uncertain one. It is also difficult to assign the broad 230 K peak in the annealed specimen (Fig. 2a) with one of the low-amplitude processes. although the p relaxation would appear to be the most likely candidate. It is clear, however, that 77 K is in the vicinity of the z’ and x peaks. and 295 K is on the low-temperature side of the 7 peak. At each test temperature. the damping depends more strongly on amplitude (Fig. 1) than would normally be expected for processes involving dislocation motion controlled by kink migration or nucleation in the pure crystal. Strong amplitude dependence is a feature of damping associated with the breakaway of dislocations from fixed pinning points. and, within the usual range of amplitudes, manifests itself by the damping increasing strongly with increasing amplitude. At very high amplitudes. however. the damping should decrease since the number of unpinning events per cycle should be independent of amplitude. This is predicted theoretically tvhether the unpinning is thermally activated [17] or not [lS]. A test for this kind of damping is to construct a Granato-Liicke plot; this should yield a straight line, for the theory predicts that the logarithm of the product of damping and stress amplitude should be proportional to the inverse of the amplitude. Granato-Lilcke plots for the 2zp data of Fig. 1 at 295 and 77K are shown in Fig. 3; plots for the 4zp and UHV data are similar in form. In most cases the data tend to fit straight lines rather well. particularly at the lower amplitudes where AWjW decreases most strongly. The slopes of the plots should be proportional to the dislocationsolute binding energy and the inverse of the mean spacing of the pinning points [17, IS] ; they should therefore decrease with increasing temperature and decreasing impurity concentration c. The gradients of

O.C+

I 1.0

05

0;’ Fig. 3. Granato-Liicke

plots for the 2 zp specimens at 77 and 295 K.

IN TANTALUM

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the plots tend to follow these trends. These plots could therefore be taken as evidence that the damp ing at all temperatures and amplitudes in the range CJ,< ~~ < G,,,_ is associated with dislocation breakaway from interstitial-impurity atoms, but this conclusion is in one respect at variance with the results of paper I. It was concluded there that breakaway does not occur at 17~.and. if this were so. the damping should increase with amplitude at amplitudes just above a,; this was not observed here. It is possible, however, that other damping mechanisms occur at amplitudes close to u, and prior to breakaway which mask this effect. particularly since there was a large stress bias (=OS x a,) in our experiment. Chambers et nl. [2, 191 studied the internal friction of tantalum specimens with a range of impurity levels at high strain amplitudes (10-5-10-3) in a torsion pendulum, and in some respects our results are not unlike the ones they obtained. For example, they found (Fig. 25 [Z] and Fig. 24 [ 191) that the amplitude-dependent damping decreased with increasing amplitude at high strains. They obtained (Fig. 24 [Z]) GranatoLiicke plots for specimens intermediate in purity between our 4 zp and UHV crystals which are fitted by straight lines at strain amplitudes above about 4 x IO-‘, which suggests a change of mechanism at this amplitude. They also found (p. 155 [2]) that the amplitude-dependent damping is closely coupled to the amplitude-independent relaxation process observed at lower amplitudes. for it shows damping maxima near the temperatures of the z and 7 peaks which are shifted in temperature by a frequency change in much the same way as the peaks themselves. These observations are important. for they confirm the interpretation that the damping observed here is related to the mechanisms discussed in Section 1, and they admit the following model for the explanation of our results. The damping at all amplitudes arises from the nucleation and,/or migration of kinks. The energy barrier associated with these mechanisms is increased by the presence of impurity atoms, and these larger barriers are only overcome. and thereby contribute to the damping. at amplitudes cr, > G,. This interpretation is supported by (a) the results of paper I, (b) the straight-line fits to the Granato-Liicke plots of most of the data obtained here. (c) the correlation between the present results and the observations of Chambers et a!. [Z, 191, and (d) the majority view discussed in Section 1 that the 1’: z. and 7 relaxations are due to intrinsic lattice mechanisms. Perhaps the best way in principle of identifying the basic mechanisms involved would be to compare the values of activation energy AH measured in uniaxial tests at oe with those reported for the internal friction peaks [2.5]. It was noted in I, however. that measurement of AH is beset with difficulty and. as revealed by the large r* values and curvature of AH vs T plots, changes in dislocation density and/or mechanism create uncertainty in the meaning of the values

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obtained. Nevertheless. if the probable values of AH at zero effective stress. which is the state appropriate to an activation energy obtained from an internal friction peak. are estimated from the data of I, the values for small strains are found to be approximately 0.1. 0.3 and 0.9 eV (? jO", in each case) for the annealed state and the 77 K-prestrained state at low (77-203 K) and high (N-295 K) temperatures respectively. These values are close to the activation energies for the x’. 1 and ;‘ mechanisms, respectively. and thus if some reliance can be placed upon the trends of the AH v-alues reported in I. they indicate that these mechanisms have been controlling at the lowest strains in the tests performed here. The view that the 7 mechanism is occurring at 295 K in the prestrained state is reinforced by the ACV W vs T data of Figs. 2(b) and (c). where the damping for the 1 zp crystal. which shows the largest AH values, increases strongly as T approaches 295 K. It is probable that this is the beginning of the 7 peak. for Chambers (Fig. 29 [ 11) sho\ved it to be discernible above about 250 K at 1 Hz at high strain amplitudes. In view of the evidence discussed here and in I. we conclude that the following mechanisms were controlling dislocation motion in the tests reported. At were stress amplitudes SG,. non-screw dislocations mobile in the annealsd state. and their motion was controlled by double-kink nucleation on the (I I I) segments at 71’ to their Burgers vector. This process is the r’ mechanism observed in conventional internal friction experiments. (Computer simulation experiments[20] indicate that the Peierls stress of the 71’ (11 I) dislocation is larger than that of other nonscrew dislocations. and we assume that kink migration on this dislocation is a lower-energy process than double-kink nucleation.) In the 77 K-prestrained state, dislocations close to the screw orientation were observed to move by the migration of kinks in a direction parallel to their Burgers vector. This has a higher activation energy and is the z mechanism. As the temperature is raised to 29j K, screw dislocation segments are able to move by double-kink nucleation at the stress levels used here. and this is the mechanism of the ;’ relaxation peak. These various mechanisms are modified by the presence of interstitial impurity atoms and are made more difficult by them. Thus, dislocations are only able to overcome the barriers provided by the interstitials at applied stress levels between ce and G,).,. It is noted that although various aspects of our results can be accounted for in other ways. the scheme outlined above appears to provide the best overall explanation of the effects discussed. The interpretation of the relaxation peaks agrees with that of Seeger and Sestik [ IO]. and as far as the 3’ and x mechanisms are concerned. is the reverse of that of Knoblauch et al. [YJ. It is not in agreement with the thermal impinning model of the 7 relaxation proposed by Korenko rr ai. [l I]. We ha\-e no indication as to the mechanism of the p relaxation and cannot be certain

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that the peak observed at 230 K is relatsd to that process. It is clear that the unambiguous interpretation of all these relaxations requires still further esperiments to determine the damping and activation parameters over a wide range of amplitudes in specimens with well-characterized substructures.

.-lckno~vlrngrrnenrs-The investigation was supported by a grant from the Science Research Council. which is also acknowledged by one of us (h1.J.C.) for the award of an S.R.C. Studentship.

REFERESCES I. M. J. Cowling and D. J. Bacon, .-lcrci .\I
.iDDED

IN PROOF

Seeger and Wiithrich [21] have recently given an extensive review of the dislocation mechanisms involved in plastic flow of the b.c.c. metals. and have discussed their relation to microplasticity and internal friction. W‘hilst noting that considerable uncertainty exists concerning the interpretation of the damping peaks, and that additional experiments are required. these authors conclude that the mechanisms responsible for the r’ and x peaks are the reverse 01 those suggested here.