A study of the plastic deformation of copper single crystals

A STUDY OF THE PLASTIC DEFORMATION OF COPPER SINGLE CRYSTALS* C. R. CUPPt and B. CHALMERSj Single crystals of copper having uniform rectangular cross-sections, and of known orientations, were tested in axial tension usin a “soft” tensile machine in which the applied load was inde ndent of the resulting strain. During ta e course of stepwise loading of each specimen, a delay was tpe ound to occur between the beginning of the addition of each small stress increment and the resumption of plastic strain. The length of the delay time, in the order of a few seconds, was found to depend to some extent on the length of the waiting period, prior to the addition of a stress increment, during which time the load on the specimen is constant. The effect may be considered as a type of yield point phenomenon. Other results of this work indicated an effect of dissolved hydro en on the mechanical properties of the specimens, and a transition point in the stress-strain curves o f the specimens during the early stages of plastic strain.

UNE

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DE LA DI~F~RMATI~N

PLA~TIQUE

DE MONOCRISTAUX

DE CUIVRE

Des monocristaux de cuivre de section rectangulaire, uniforme, et dont l’orientation etait connue, furent soumis B une extension axiale dans un appareil de traction permettant d’appli uer une charge independamment de la deformation resultante. Lors de l’application etagee d’une c7-large B chaque echantillon., on a constate qu’il y avait un delai entre le commencement de l’addition de chaque petit accrorssement de charge et la reprise de la deformation plastique. 11 fut constate que la dur6e du dClai (de l’ordre de quelques secondes) dependait, dans une certaine mesure, de la dur& de la &riode d’attente qui prC&dait l’addition d’un accroissement de tension et pendant laquelle la charge sur l’eprouvette restait constante. Cet effet peut &re consider6 comme un ph6nomene de limite d’ecoulement. D’autres resultats de cette recherche indiquent un effet de l’hydrogene dissous dans le metal sur les proprieds mecaniques des Cprouvettes et un point de transition dans les courbes tension-deformation des Cprouvettes en question, pendant les premiers stades de la deformation plastique. EINE

UNTERSUCHUNG

DER PLASTISCHEN KUPFEREINKRISTALLEN

VERFORMUNG

VON

Kupfereinkristalle mit gleichfijrmigem rechteckigem Querschnitt und mit vorbestimmten Orientierungen wurden unter einachsigem Zug untersucht; es wurde eine “weiche” Zugmaschine benutzt, bei der die angelegte Last von der resultierenden Dehnung unabhangig war. Wenn man die einzelnen Proben schrittweise belastete, zeigte sich eine zeitliche Verzijgerung zwischen dem Anlegen der zultzlichen Busseren Spannung und dem Wiederbeginn der plastischen Verformung. Die Lange dieser zeitlichen Verzogerung, die von der Grijssenordnung einiger Sekunden war, hing zu einem gewissen Grade davon ab, wie lange man bis zum nachsten Belastungsschritt wartete, d.h. die Probe unter konstanter Belastung hielt. Man kann diesen Effekt als eine Art Fliesspunktserscheinung betrachten. Andere Ergebnisse dieser Untersuchung deuten auf einen Einfluss des gel&ten Wasserstoffes auf die mechanischen Eigenschaften der Proben hi?; ausserdem zeigte sich ein UmkehrEtu;nm den Spannungs-Dehnungskurven in den ersten Stadren der plastrschen Verformung der

Introduction A number of investigators have observed and studied the delay time which may occur between the application (or increase) of a stress, and the observation of the resulting strain. Such observations are closely associated with the existence of yield phenomena. The present paper describes a delay effect that has been observed in single crystals of copper; it appears to be distinct from any of the effects described previously. The delay phenomena reported in the literature are the following: Clark and Wood [l] made a series of rapid-load tests, using stresses exceeding the room-temperature static-elastic limit, on a 0.19 per cent carbon *Received February 10, 1954. tResearch Dept., The Internatiqnal Nickel Co. of Canada, Ltd., Copper Cliff, Ontario, Canada: SDivision of Applied Science, Harvard University, Cambridge, Massachusetts. ACTA

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annealed steel for which the static stress-strain curve exhibits a definite yield point, and on other steels which do not exhibit definite, yield ‘points. It was concluded that a definite time delay in the initiation of plastic deformation is associated only with materials for which the static stress-strain curve exhibits a definite yield point. In later work, Wood and Clark [2] studied the influence of temperature on this time delay. In order to compare the results of rapid load tests with more conventional test results, static tests were made on 0.17 per cent carbon steel at temperatures of - 6O“C, 23’C, 65’C, and 121°C. Stepwise loading was used, allowing approximately two minutes to elapse between points. It was noted that the static stress-strain relationships obtained at 65°C and 121“C show clearly the phenomenon of strain ageing. At these temperatures appreciable strain ageing evidently takes place in the approximately two-minute interval between successive load increments. Dming the

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performance of these tests, it was noted that “in several instances, the secondary yield points exhibit a definite delay time for the resumption of plastic deformation.” Except that these tests were on polycrystalline alloy specimens, and the plastic strain somewhat higher, the effect described in the quotation above is similar to that studied in the present work. In another study, Wood and Clark [3] investigated the effect of the presence and nearabsence of carbon and nitrogen upon the delayedyield phenomenon in steel. The delay was found to occur in steel which had been wet-hydrogen treated to remove the static upper yield point. They concluded that in order to remove completely the effects of carbon and nitrogen upon the mechanism of yielding, the concentrations of those elements would have to be reduced to considerably lower values than were present in the wet-hydrogen treated material. Gensamer and Mehl [4] tested single crystals and polycrystals of iron by dead-weight loading in increments of between 70 g/mm2 and 140 g/mm2 and plotting strain-versus-time curves after each increment of stress. The load increments were added at intervals varying from six hours to five days. In all cases for stresses above the yield point, there was an initial delay time before flow began; the rate of extension then reached a maximum and finally decreased to zero. When the next increment of stress was added, the same behaviour was observed. A valid comparison of these particular observations with others cannot be made since the strain sensitivity was not indicated, and the purification of the specimens reduced the carbon content only “to the limit for detection under the microscope,” which may be a relatively high interstitial impurity content which would affect the plastic properties of the material. McReynolds [5], while studying stepped stressstrain curves of pure (99.996% Al) polycrystalline aluminium, apparently observed a phenomenon which is similar to that studied in the present work. This was not mentioned in the text but it may be seen in Figure 2 of McReynold’s paper that, after holding the stress constant for 15 minutes and then increasing the stress, the strain did not increase to any marked degree until a fairly large stress increment had been made. The presence of a yield point in body-centered cubic and close-packed hexagonal metals containing small quantities of interstitial solute elements is well known. This, and the absence of well-established yield points in face-centered cubic metals

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have been discussed recently by Smallman et al. [6] who observed yield points at liquid-air temperatures in single crystals of commercially pure aluminium and in binary alloys of superpure aluminium containing copper, zinc and hydrogen. In all cases, ageing treatments at elevated temperatures were needed to induce the yield points. Under similar conditions superpure (greater than 99.99’% Al) aluminium crystals gave no yield phenomenon. The purpose of this paper is to present evidence of a yield phenomenon in single crystals of copper, some observations on the effect of hydrogen on the mechanical properties of the crystals, and some observations on a transition in the stress-strain curve of copper crystals.

Experimental

Procedure

Specimens were prepared from copper supplied by Messrs. Johnson, Matthey and Co., Ltd. who reported the major impurities to be silver (0.0003%-0.0005%), nickel (0.0003%), and lead (<0.0004%) with faintly detectable amounts of gallium and calcium. The single crystals were grown in a machined graphite boat which was fitted with a suitable cover and heated in argon in a furnace which has been described by Gow and Chalmers [7]. The crystals were usually grown in pairs originating from the same nucleus so that two crystals of the same crystallographic orientation could be compared after different thermal treatments. The crystals were separated by electrolytic cutting in order to prevent strains introduced into the crystal by mechanical working. Each crystal was approximately 53-6 in. long, 4 in. wide, and 3/16 in. thick. The crystallographic orientation of each specimen was determined from Laue back-reflection patterns by means of Greninger’s technique [S]. The specimens were each annealed for periods of time ranging from two to six days (the majority for six days) in vacuum ( < 5 X 10-6mm Hg), purified hydrogen, or argon. In all cases, the annealing temperature was in the range 975”1ooo”c. An optical extensometer was carefully clamped in position on a specimen, and the specimen then mounted in the balanced “soft” tensile testing machine. Descriptions of the extensometer and the testing machine are to be found elsewhere [9]. A slowly increasing tensile load was applied to the specimen untip the elastic limit had been reached. It was’ possible to record a few stress-strain

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measurements prior to the onset of plastic deformation. These strain measurements, however, can be accepted only as approximations. Once the elastic limit of the specimen had been exceeded, small amounts of load were added to the specimen at recorded time intervals. The increment of stress in the specimen at each loading was in the order of 10-20 g/mm2. After the addition of a load increment to the specimen, the total load and the specimen’s elongation were measured and recorded. At the end of a desired time interval, hereafter called the age&g t&e (usually in the order of minutes), during which the specimen remained under a constant load, the elongation was again recorded in some cases, and in all cases another load increment was added to the specimen. The time interval, hereafter called the delay time (in the order of seconds), between the beginning of the addition of a load increment and an increase of plastic extension was carefully measured and recorded. In order to eliminate the possibility that a spurious delay time was introduced by the machine or by the method of observation, it became necessary to examine the procedure critically. For this purpose, motion pictures were used to record the behaviour of the light beam reflected from the optical extensometer on the specimen. The delay time was recorded on film by photographing the reflected light beam and, in the same field, a small electric light which indicated the time required for the addition of a load increment. To show that the delay time could not be due to the equipment or procedure, similar photographs were made when the extensometer was mounted on the system shown in Figure 1. The steel ring shown was made of black oil-tempered spring St&l and was designed so that a given load increment on the spring, mounted in place of a specimen, would cause the same amount of extension as that occurring (on an average) in the copper crystals due to the same load increments. Thus the distance between the gauge marks on the brass dummy bars shown increased the same amount as on a specimen under an equal load. However, the ring remained elastic, while the copper specimen had deformed plastically. The specimen extensions were recorded to the nearest micron (strain = 2 X 10-6cm/cm on a 5 cm gauge length) ; the stresses were recorded to the nearest g/mm2 in the range O-300 g/mm2, the sensitivity of the measuring system decreasing somewhat above that.

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Steel test spring with brass dummy bars.

Observations As has already been stated, a marked delay was found to occur between the beginning of the addition of a load increment and the observed onset of continued plastic strain. This delay was measured by using a stopwatch and visual observations, and was confirmed by photographing the elongation of the crystal specimens as indicated by the light beam from the optical extensometer. The rate of loading during the addition of a stress increment was also measured, and from this information, and the delay time recorded during each stress increase, some portions of the stressstrain curves of typical crystals have been developed in detail, and are shown in Figures 2-5. The figures located under each constant-stress portion of the curves indicate the ageing time in minutes during which the specimen was held at the indicated stress level. Usually a sequence of three or four measurements was recorded, with a shorter ageing time for each subsequent step of the sequence. In most cases it may be seen that the rise in stress, prior to an increase in plastic strain, is dependent on the length of the ageing time at which the specimen had been held before the load was increased. The curved portions of the stressstrain curves are quite arbitrary since no attempt was made to determine the exact strain value at the time of completion of a load addition. However, the curved sections show reasonably well the behaviour of the specimens. It may be seen that there are two distinct types of “steps” on the stressstrain curve. The most common type has a rounded

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Portion of stress-strain curve for crystal 11A.

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Portion of stress-strain curve for crystal 11B.

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Portion of stress-strain curve for crystal 15.

to the horizontal increase in strain at a constant stress. This results from the delay time being equal to, or longer than, the time required for the addition of a load increment. Figure 6 shows a number of curves of delay times plotted against the waiting period prior to each delay measurement. The curves are numbered as sequences, with each succeeding set of measurements being made on the crystal at higher stress level. It may be seen that the delay times increased with the ageing period. The shortest waiting period is shown as one-half minute, This minimum ageing time was chosen since both visual and photographic records indicated that an elapsed time of between 10 and 30 seconds was required for the rate of strain of the crystals to become imperceptible. When the copper crystals were ~~~ed~a~el~ subjected to a higher load, there was no delay time and, therefore, no yield point. It was mentioned that it took from 10 to 30 seconds after the completion of a load addition before the rate of strain became too slow for detection. Therefore, an immediate reloading simply increased the already perceptible rate of strain. In testing the steel spring system described earlier, it was found that the delays, following ageing periods of the same order as those used for

x IO4

Portion of stress-strain curve for crystal 12B.

corner resulting from the fact that plastic strain was detected prior to the completion of a load increment, addition. The other type of step has a sharp transition from the vertical rise in the stress

FIGURE_ 6.

crystal 1LB.

Ageing-time versus delay-time curves for

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the copper, were too short to be readily measured by visual observations. Photographic records indicated that the delays were less than one-half second so that, for the crystal specimens, any delay above one-half second was entirely due to the behaviour of the copper, and could not be due to inertia or friction in the testing equipment. Also, unlike the behaviour of the metal crystals, perceptible deflection of the steel spring ceased within one-quarter second after loading had stopped. The stress-strain curves for some typical specimens of particular interest are shown below in Figures 7-11 and the specimens’ orientations are shown in Figure 12. The long dashes to zero stress on some of these diagrams indicate the course of the stress-strain curve during unloading, and the shorter dashes show the curve during reloading to the same stress. The solid circles on the curve for crystal No. 15 indicate that the measurements

PLASTIC

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STRAIN

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FIGURE 10.

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Stress-strain curves for crystals 11A and 11B.

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S&es-strain curves for crystals 7A and 7B.

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Stress-strain curve for crystal 14.

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FIGURE 12.

Crystaflographic orientation of specimens.

were obtained while the base of the specimen was packed in solid carbon dioxide. All curves are drawn through the stress-strain conditions at the end of the ageing periods, and do not show the steps which are given, in detail, elsewhere. The crystals 7A and 7B (Figure 7) are of the same orientation but were annealed in vacua for 72 hours and 50 hours respectivefy. The critical resolved shear stress was approximately the same for each crystaf, but the rate of work-h~ening for crystal 7B was considerably higher than that for 7A. Crystals 11A and 11B (Figure 8) are of the same orientation and were annealed, prior to testing, for 146 hours. Crystal 11A was annealed 41 hours in hydrogen, and 105 hours in vacua, while 11B was in vacua the entire time. In this case the criticaf resolved shear stress was exactly the same for each crystaI, whiIe the rate of work-hardening was the same for each in the first part of the plastic region of the stress-strain curve, and greater in the second part of the curve (which started at a lower strain) for crystal 1lA. In all cases where identical crystals were annealed for equal times in different atmospheres, the specimen annealed in hydrogen had a higher rate of work-hardening and, in two instances, a slightly higher critical resolved shear stress. Each of crystals 14,15 and 16 (Figures Q-11) has two definite rates of work-hardening in the plastic region of the stress-strain curves. Table I shows the region of easy glide and the path (in degrees) which the pole of the specimen axis traverses during classical single slip. TABLE I Crystal number Region of easy glide (cm/cm X lol> Single slip path (degrees)

Summary

15 75 12

14 55 7

16 20 1

and Discussion

A type of yield phenomenon has been observed

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in single crystals of “superpure” copper tested at room temperature. A new feature of the present results is that the yielding has been found to occur in a face-centered cubic material with less than 0.002 per cent. substitutional impurities present. It has been found that ageing for a few minutes in situ at 26°C and under the maximum load to which the specimen had been subjected up to the time of ageing, is effective in producing yielding. Since a “soft” tensile machine was used, it was impossible to obtain a fall in load at the beginning of plastic deformation. However, the sudden yielding and subsequent rapid deformation was indicative of the presence of a yield point which could be obtained by suitable ageing treatment, and which was absent if ageing was not allowed. It is interesting to note that the stress-strain curves shown in Figures 2-5 resemble the stepped stress-straincurves found for various alloys [ 10; 111. However, the stepped curves for the afioys were obtained by loading the specimens at a steady and quite rapid rate, while the present curves result from di~ontinuous and sfow loading. In other work on alloys [12], discontinuous, but rapid, loading was used. The dislocation theory mechanism proposed by Cottrell to explain strain-ageing effects and yield phenomena accounts for the behaviour which has been observed here. It has already been pointed out [6; 121 that a substitutional solute should be able to cause a yield point which would be expected to be weaker than the well-known yield point in the iron-carbon system. This is in agreement with the present observations. The consistent effect of developing a higher rate of work-hardening and/or a higher critical resolved shear stress by annealing one of two identical crystals in hydrogen would suggest that this atom in solution affects the slip mechanism. However, the effects of minor crystalline substructures should be determined before it is definitely concluded that the hydrogen alone is responsible for the effect. Lticke and Lange [13] have shown that crystals of aluminium stretched in tension show easy glide, provided they are pure and have orientations which avoid double slip. Figure 13 shows their results on two crystals of pure aluminium, one of which, A, deformed initially by single slip and showed a region of easy glide in which hardening was very small, while the other, B, deformed by multiple slip and began hardening immediately. Curve B is similar to some resuIts obtained here, but curve A does not indicate the sharpIy defined region of

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more rapid work-hardening which has been found for copper crystals. The two regions of easy glide and more difficult glide may be seen in all the stress-strain curves obtained with the single crystals of copper. A similar transition point in the stress-strain curve has been observed in polycrystalline aluminium-base alloys [16], in high-

FIGURE 13. Stress-strain curves crystals (after Liicke and Lange).

of

pure aluminium

purity aluminium single crystals (17; IS), and in copper crystals [19]. Masing and Rdelsieper [ 141 have shown that the region of easy glide in aluminium became smaller the nearer the initial orientation was to one giving multiple slip, and this has been confirmed here as shown in Table I. It should however, be noted that the increase in the rate of work-hardening took place long before multiple slip would normally be expected to operate.

Acknowledgement The authors wish to thank the National Conference of Canadian Universities and the International Nickel Company of Canada, Limited, who

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provided a fellowship for this research. They also thank Dr. C. Elbaum for his valuable assistance in this work, and Dr. L. M. Pidgeon who provided facilities for this work in the Department of Metallurgical Engineering at the University of Toronto.

References 1. CLARK, D. S. and WOOD, D. S. Proc. A.S.T.M. 49 (1949) 717. 2. WOOD, D. S. and CLARK,D. S. Trans. A.S.M. 43 (1951) 571. 3. WOOD, D. S. and CLARK,D. S. Trans. A.S.M. 44 (1952) 726. 4. GENSAMER,M. and MEHL, R. F. Trans. A.I.M.E. 158 (1944) 267. 5. MCREYNOLDS, A. W. Trans. A.I.M.E. 185 (1949) 32. 6. SMULXAN, R. E., WILLIAMSON,G. K., and ARDLEY,G. Acta Met. 1 (1953) 126. 7. Gow, K. V. and CHALMERS,B. Brit. J. Appl. Physics 2 (1951) 300-303. 8. GRENINGER,A. B. Trans. A.I.M.E. 117 (1935) 61. 9. CLARK,R. and CUPP, C. R. To be published. 10. KRUPNIK, N. and FORD, H. J. Inst. Metals 81 (1953) 601. 11. EBORALL, R., LACK, M., and PHILLIPS, V. A. Bull. Inst. Metals 1 (1952) 58. 12. PHILLIPS,V. A., SWAIN, A. J., and EBORALL,R. J. Inst. Metals 81 (1953) 625. 13. LOCKE, K. and LANGE, H. Z. Metallkunde 43 (1952) 55. 14. MASING, G. and RAFFELSIEPER,J. Z. Metallkunde 41 (1950) 65. J. N. Trans. A.I.M.E. 5 15. BECKER,J. J. and HOBSTETTER, (1953) 1231. 16. JAOUL, B. and CRUSSARD, C. Rev. M&t. 47 (1950) 589. Rev. Univ. Mines (Congres A. I. Lg., 17. CRUSSARD,C. Section Metallurgic physique 1947), 41. 18. JAOUL, B. and CRUSSARD,C. J. Inst. Metals 80 (1953) 690. 19. DALTON,A. L. and HON~YCOXBB,R. W. K. Unpublished work.