High temperature deformation of aluminum single crystals

HIGH

TEMPERATURE

DEFORMATION S. HOWE,?

OF ALUMINUM

B. LIEBMANN,$

SINGLE

CRYSTALS*

and K. LOCKE5

The temperature and strain rate dependence of work hardening in aluminium crystals has been investigated with special attention to the high temperature range. Single crystals of high purity aluminum have been grown and extended at various temperatures and strain rates. It has been found that above 650°K the yield point drops rapidly with temperature and the easy glide region of the &rem-strain curve lengthens. These results show that the mechanism of work hardening at high ~mperature is quite diflerent from that at low temperatures, and the differences are unexplained by current theories. DEFORMATION

A

HAUTE

TEMPERATURE

DES

MONOCRISTAUX

D’ALUMINIUM

Les auteurs ont Btudie la man&e dont varie la loi d’eorouissage des monocristaux d’aluminium en fonction de la temperature et de la vitesse de deformation, en apportant une attention particuliere aux temperatures elevees. Ils ont prepare des monocristaux d’aluminium de haute purete et ils les ont soumis a traction 9. differentes temperatures et a differentes vitesses de deformation. 11s ont observe qu’au dela de 550”K, le yield point tombe rapidement avec la temperature et que la region de glissement aisb de la courbe tension-d6formation s’titend-Ces resultats montrent qua le mecanisme de l’bcrouissage it haute temperature est tout a fait different de ce qu’il eat a basse temperature. Lea differences observees ne sont pas expliquees par les theories courantes. DIE

~RFOR~U~~

VON EINKRISTALLEN HOHEN ~MPERATUR~~

AUS

ALUMI~~UM

BE1

Die Abh~ngigkeit der Verfestigung von Alum~ni~ristallen von der Temperatur und der Verformungsgeschwindigkeit wurde untersucht unter besonderer Berticksichtigung des Bereichs der hohen Temperaturen. Einkristalle aus Aluminium von hoher Reinheit wnrden hergestellt und bei verschiedenen Temperaturen mit verschiedenen Verformungsgesehwindigkeiten gedehnt. Es wurde gefunden, da13oberhalb von 550°K die FlieDspannung rasch abfallt und der Easy-Glide. Bereich der Verfestigungskurve langer wird. Diese Befunde zeigen, da6 der Verfestigungsmechanismus bei hoher Temperatur verschieden ist von dem bei tiefen Temperaturen; die Unterschiede lassen sich durch die tiblichen Theorien nicht erklaren.

1. INTRODUCTION

Recently there have been published numerous papers on the stress-strain behavior of single crystals of face-centered cubic metals at low temperatures up to room temperature. As a result of these investigations and of corresponding theoretical works the mechanism controlling plastic deformation in these metals in this temperature range is understood to a rather large extent. (1) However, there are literally no useful measurements of work hardening at higher temperatures, especially approaching the melting point. Since the controlling processes in this higher temperature range are quite different from those in the low temperature range it was considered important to extend the measurements into this region. In the present paper, stress-strain curves of high * This research was supported by the U.S. Navy through the office of Naval Research under contract No. NONR-562 (12). Received July 11, 1960. t Submitted in partial fulfillment of the requirements for the degree of Master of Science at Brown University, Providences, RI. $ Now with Degussa, Hanau, Germany. EjNow at the Institut fiir Allgemeine Metallknnde und Metallphysik, Tschnische Hochschule, Aachen, Germany. ACTA-~ETALLURGICA,

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purity aluminum single crystals have been taken at different strain rates in a ~m~rature range between liquid nitrogen temperature and the melting point. Aluminum was chosen since its stress-strain behavior at room temperature and at low temperatures is well known.(2-6) For comparison some curves have been taken on aluminum single crystals of technical purity. 2. EXPERIMENTAL

PROCEDURE

The stress-strain behavior of single crystals depend as much on their orientation relative to the axis of tension as on temperature and strain rate. Thus, in order to investigate the in~uence of temperature and strain rate, one must provide a su~cient number of single crystal samples of exactly the same orientation so that this parameter will be constant. To overcome this difficulty, long single crystals (12 ft long) of high purity aluminum (99.99 per cent Al) have been produced by the strain-anneal method.(7) By cutting these wire shaped crystals (diameter 1.5 mm) a sufficient number of single crystals of exactly the same orientation was made available. After cutting the crystals (using an oxyacetylene 625

626

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FIG. 1.

torch

METALLURGICA,

Phantom

VOL.

view of oven with crystal

to prevent deformation of the ends of the

sample), they are prepared to be placed in specially designed grips in the tensile tester. These grips must be small enough to fit into the furnace, and must not deform the ends of the crystal (so that nucleation and recrystallization will not occur at the high temperatures used). The problem was solved by melting small beads on the ends of the crystals and placing them in a slotted holder. The tensile tester used in the experiments is an Instron prototype table model tensile machine. * * During the first experiments a periodic oscillation of fairly large amplitude with a period of about 1 min was After a long superimposed upon the stress-strain curve. search for the origin of the effect it was finally traced to a modulated vibration originating in the drive system of the tester. Therefore, the motor and gear box were removed from the tensile tester, mounted some distance away and coupled to the cross-head by a long chain. This completely eliminated the oscillation.

9,

1961

in grips (arrow).

A furnace with a range up to 700°C was built to fit the machine (Fig. 1) so experiments could be performed at various temperatures up to the melting point of aluminum. The furnace contains a long silver tube lining to preserve a constant temperature along the sample. A Dewar flask was used for experiments at temperatures down to liquid nitrogen. The machine only draws a load-extension curve which must be replotted to show the resolved shear stress-strain in the acting slip system. The structure of the deformed crystals is further investigated by the Guinier-Tennevin(*) X-ray method to determine the type of deformation that has occurred and whether or not it occurred homogeneously. Slip lines were also studied microscopically. 3. EXPERIMENTAL

RESULTS

In general, high purity face-centred cubic metals show hardening curves that exhibit three parts called

HOWE,

LIEBMANN

AND LOCKE:

HIGH

TEMPERATURE

DEFORMATION

627

I

I

I.1600°C Shear strain,

%

FIG. 2. Flow stress VS. strain at various tempemtures.

stages I, II and III, which may or may not be distinct.(i) Stage I is the “easy glide” region characterized by a small coefficient of work hardening (slope of stress-strain curve). It is most pronounced for crystals with an orientation in the middle of the orientation triangle. Much of the hardening takes place in stage II, which is charac~rized by a constant slope. Stage III begins at higher strains and shows a decreasing coefficient of hardening. As the temperature increases, stage II becomes less and less pronounced. Since in the present paper the effect of temperature and stain rate on the stress-strain curves was the main object of investigation, the orientation of the crystals was not varied; only crystals whose axes were within 4” of each other were used. The orien~tion was chosen to be near the center of the orientation triangle in order to obtain stress-strain curves showing all three stages. It is also an advantage of the center orientation that the effect of slight angular differences between crystals is minimized. The temperature dependence of the stress-strain curve, the influence of the strain rate and the temperature dependence of the yield point were studied. The temperature was varied from 77 to 9OO*K and the strain rate from 10m3set-l to 10h5see-“. In Figs. 2, 3 and 4, stress-strain curves are plotted for various temperatures and extension speeds. If these plots are examined, it will be seen that the “easy glide” region (stage I) slightly decreases with increasing temperature at least up to 27°C and almost disappears

Einitial N IO-J MC-1.

in the room temperature curves. At 200°C and above, however, the whole character of the stress-strain curves changes and an ever increasing “easy glide” region appears with increasing temperature. If the curves taken with various strain rates at 600% are compared, one finds that at the slowest speed of extension (low5 see-l) no hardening is observed. At the medium speed ( IO4 see-l) some hardening occurs after a rather large strain, and at high speed (10-a se+) greater hardening occurs even earlier. This indicates that some thermally-activated strain-rate dependent mechanism is operating. While in Figs. 2, 3 and 4 crystals with exactly the same orientation were used at the same speed, in Fig. 5 crystals of identical orientation were extended at the same temperature in order to study the strain-rate dependence. It is seen that at 27°C the easy glide region is independent of the strain rate, while at 300 and 600°C there appears a slight rate dependence. Stage III is quite rate dependent indicating thermally activated processes. Figure 6 shows the temperature dependence of the yield point. Two curves are shown; one was corrected by dividing the critical resolved shear stress by the shear modulus G. G was determined by assuming that at 300°K, G = 25.5 x lo5 g/mms, and applying a correction factor in order to consider the variation of the shear modulus with temperature.(9) The uncorrected curve was calculated by dividing me by G at 77’K. One can recognize a drop in yield point in the

628

ACTA

METALLURGICA,

VOL.

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1961

500 E! I ‘, 28

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FIG. 3. Flow stress vs. strain at various temperatures.

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,

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FIG. 4. Flow stress vs. strain at various temperatures.

temperature range between 100 and 250°K and a sharp second drop above 550°K. Some stress-strain curves of technically pure (99.8 per cent Al) crystals are included in Fig. 7 to give a comparison of the difference between the deformation of high purity and technical purity aluminum crystals. While at 600% the shapes of the curves are similar,

I

.&initialN lo+

set-I.

there are differences at room temperature to be expected from other work.(lOJ1) Although stage I is completely suppressed, stages II and III are well developed. It is known that a flat increase of the hardening curves is always connected with a very non-uniform type of deformation. Fig. 8 is an enlarged photograph

HOWE,

LIEBMANN

AND

LtTCKE:

HIGH

TEMPERATURE

DEFORMATION

629

125

Shear

strain,

%

FIG. 5. Flow stress vs. strain at various temperatures

and strain rates.

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600

Temperature,

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700

600

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900

1000

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FIG, 6. Variation of yield point vs. temperature. k = 2 x 10m4set-1. of a crystal deformed at 600°C. It shows widely spaced, rather large slip bands, indicating that a large amount of slip hasoccurred

only at afew placesin

while the regions between them remained much more perfect. 4. DISCUSSION From the results given in the previous section, two

the crystal. This is supported by X-ray photographs according to the method of Guinier-Tennevin. Severe

features are most interesting:

lattice bending has been found only at the slip bands,

the yield point with temperature

the second decrease of and the lengthening

630

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5

IO

METALLURGICA,

15

20 Shear

strain,

VOL.

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1961

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I

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Pm. 7. Flow stress vs. strrcin,technical purity Al crystal.

of stage I with increasing temperature, both of which occur at temperatures above room temperature. While the results at low temperatures do not contradict the current theory of work hardening formulated mainly by SeegeG it seems that the results above room temperature cannot be accounted for by this theory. According to this theory,(l) in stage I of the hardening curve slip occurs in only one slip system and the distance over which the dislocations move is only limited by crystal boundaries and similar obstacles. During stage II slip occurs to a small extent also in other slip systems and, as a consequence of this, Lomer-Cottrell dislocations are formed. These sessile dislocations constitute obstacles for dislocations motion so that other dislocations pile up against the Lomer-Cottrell barriers. In stage III, finally, the stress is high enough to cause dislocations to escape

from the piled-up groups with the aid of thermally activated cross slip. The temperature dependence and strain-rate dependence of the hardening curves as described in this paper indicate the presence of a thermally activated process in stage III also at temperatures above room temperature. However the increase of the length of the easy glide region with temperature at high temperatures is in contrast to the general behavior and is not explained by the above theory. It seems questionable whether the division of the stress-strain curve into the three stages is still reasonable at elevated temperatures. There is reason to believe that at high temperatures the mechanism of hardening is quite different. This is supported by X-ray photographs taken in this laboratory after deformation at 600°C which show unusually rough polygonization not apparent after deformation at room

FIG. 8. Crystal deformed at 600°C.

HOWE,

LIEBMANN

AND

LUCKE:

HIGH

temperature. Therefore it can probably be assumed that the idea of dislocation pile-up loses its significance at these temperatures and other processes such as climbing of dislocations (Weertman type of creepo2)) or motion of vacancies (Herring-Nabarro type of creep (is)) take over. According to Seeger’s theory,(l) the critical shear stress of cubic face-centered metals is given by two contributions TV= 76 + 7,. The first contribution, rc, arises from the elastic interactions of the moving dislocations with the other dislocations. The other contribution, rc, is the stress needed to make the dislocations cut through a forest of dislocations intersecting the glide plane more or less perpendicularly. The process of cutting through the forest is thermally activated and it is assumed that the activation energy decreases linearly with the acting stress. As a consequence of this, TVshould decrease linearly with temperature until it reaches zero. At temperatures higher than this (a value below room temperature in the case of aluminum), the only contribution to ry should be from r6, which varies with temperature only as the shear modulus. Such a bend in the yield point temperature curve has been observed in aluminum by Cottrell and Stokeso4). It appears at 170°K in agreement with the Seeger theory. The end of the first drop in yield point in Fig. 6 can probably be identified with this bend. This is also indicated by the fact that at room temperature the yield point is independent of strain rate (Fig. 5) showing the absence of thermally activated processes. However, then no explanation can be provided for the drop above 550°K on the basis of this theory and additional assumptions must be made. In the following some of the possible reasons for the second drop only are listed: (1) It is assumed that the motion of dislocations is restrained by interaction with foreign atoms and that this restraining force disappears at the temperature of the second drop of the yield noint. I

TEMPERATURE

DEFORMATION

631

(2) It is assumed that the motion of dislocations is restrained because of the presence of jogs and that this restraining force disappears at the temperature of the second drop. (3) It is assumed that at temperatures above the second drop the deformation due to dislocation motion is superimposed by a Herring-Nabarro type of creep in which, however, vacancies do not migrate between the different external surfaces of the crystal but between the different small angle boundaries as proposed by Friedel(l@. Further experiments to test the possible reasons for the discrepancies are in preparation and a more thorough discussion will be given after compIetion of the experiments. ACKNOWLEDGMENTS

The authors would like to thank Professor R. True11 for his encouragement and A. Gardner, B. Green, M. Howe, E. Leach, N. Pitula and H. Yoshida for their assistance. REE’ERENCES 1. Survey articles on this subject are given by A. SEE~IZR in Dislocation and Mechanical Properties of Crustal (Ed. by J. C. FISHER, W. G. JOHNSTON,R. THOMSONand T. VREELAND)p. 243. Wiley, New York (1957). Further in Handbuch der Physik Band VII/B. Springer, Berlin (1957). 2. H. LANGE and K. L~~cKE, 2. Metallk. 44, 183 and 514 (1953). 3. K. L~~CKE and W. STAUBWASSER, iVrctwwiss.41,60 (1954); W. STAUBWASSER, Acta Met. 7, 43 (1959). 4. R. DAVIS, R. FLEISCHER,J. LIVINQSTON and B. CHALMERS, J. Metals N.Y. 9. 136 (1957). 5. T. S. NOZZLE snh I. S. KOI&LER, J. Appl. Phys. 28, 53 (1957); A. SOSINand J. S. KOEELER, Phws. Rev. 101.97 (1956). 6. R. BERNER, 2. Naturf. 15,689 (1960). 7. B. LIEBNIANN,K. L~~CKEand G. MASING, 2. Met&k. 47, 57 (1956). 8. A. GUINIER and J. TENNEVIN, Acta Cryst., Canab. 2, 133 (1949). 9. T. S. Kg, Phy8. Rev. 71,533 (1947); P. M. SUTTON,Phys. Rev. 91, 616 (1953). 10. F. HAESZNER and D. SCHREIBER,2. MetaUk. 48. 263 (1957). 11. J. DIERL, 2. MetaUk. 47, 331 (1956). 12. J. WEERTMAN,J. AppZ. Phys. 26, 1213 (1955). 13. C. HERRING,J. Appl. Phys. 21, 437 (1950). 14. A. H. COTTRELL and R. J. STOKES,Proc. Roy. Sot. A2s3, 17 (1955). 15. J. FRIEDEL,personal communication.