Plastic deformation of copper crystals under alternating tension and compression

PLASTIC

DEFORMATION

OF COPPER CRYSTALS UNDER AND COMPRESSION*

ALTERNATING

TENSION

M. S. PATERSON+ The strain hardening of high purity copper single crystals during cycles of reversed plastic strain has been studied and shown to depend markedly on the orientation of the crystal. Crystals oriented near Cl(H] or [I 1 l] show a high rate of strain hardening, while those in the middle of the stereographic triangle or near [l lo] show a very low rate of strain hardening, i.e., “easy glide”; in crystals oriented near the [lOO]-[ll l] and [lOO].-[llO] boundaries, the rate of strain hardening is low at first and later increases, while in those oriented near the [llO]-[lit] boundary the rate of strain hardening is more uniform. Similar behaviour was shown in tensile tests, but the easy glide was not as extensive. The importance of small diameter and the unimportance of mishandling of the specimens are discussed in connection with the conditions for the occurrence of easy glide. Easy glide is shown to be accompanied by very uniform distribution of slip lines, while in crystals oriented nearer [lli] or [loo] and showing rapid strain hardening the slip lines are strongly clustered and sometimes traces of slip on other systems appear between the clusters of main slip lines. X-ray Laue photographs show no asterisms for any crystals after reversed deformation; however, the crystals of high strain hardening give faint Kossel lines while those showing easy glide do not. An explanation of the observed strain-hardening behaviour in terms of the interaction of dislocations on intersecting planes is proposed. The Bauschinger effect is clearly demonstrated in the copper single crystals. DEFORMATION

PLASTIQUE DES CRISTAUX DE CUIVRE ET COMPRESSION ALTERNEES

EN TRACTION

La consolidation des monocristaux de cuivre de haute pure&5 au conrs des cycles de deformations plastiques alter&es est montree comme dependant nettement de l’orientation du cristai. Les cristaux orient& au voisinage de [lOO] cm [tll] possedent un coefficient de consolidation 6lev6, tandis que celui-ci est faible pour ceux situ& au milieu du triangle stdreographique ou au voisinage de [l lo] (“easy glide”) ; pour ies cristaux au voisinage du coti? [loo]-[ill] et du cot& [loo]-[llO], le coefficient de consolidation est d’abord has, puis croit ensuite, tandis que pour ceux p&s du cot6 [llO]-[Ill], ce coefficient est. plus uniforme. Un comportement analogue a 4th observ6 dans les essais de traction, mais le “easy glide” n’est pas aussi Ctendu. Le role du diametre de l’eprouvette et le peu d’importance de son alignement sont discutes en fonction des conditions d’apparition du “easy glide.” Le “easy glide” est accompagnt d’une r&partition tr?s uniforme des lignes de glissement, tandis que, dans les autres cas, les lignes de glissement sont rassemblees en paquet et ii apparait m&me quelquefois des traces d’un autre systeme de glissement entre les paquets des lignes principales. Les diagrammes de Laue ne presentent pas d’astkrisme apres deformations alter&es, tandis que les cristaux a grand coefficient de consolidation prBsentent de faibles lignes de Kossel, tandis que les autres n’en presentent pas. L’auteur propose une explication de la consolidation par l’intersection des dislocations. L’existence d’un

&et Bauschinger est nettement Ctablie. CBER DIE PLAsTIscHE VERFORMUNG VON KUPFER-KRISTALLEN WECHSELNDE ZUG- UND DRUCKBEANSPRUCHUNG

DURCH

Die Verfestigung von sehr reinen Kupfer-Einkristallen durch eine plastische Verformung bei Wechselbeanspruchung wurde untersucht und dabei festgestellt, dass sie in besonders ausgepr%gt& Weise von der Orientierung der Kristalle abhangig eine -_ ist. Kristalle mit einer Orientieruncr nahe rloO1 und f-1111 _ zeinen u sehr starke ~e~esti~ng, wahrend Kristalle, die mit iher Orientierung in der Mitte des Orie~tierungsdreiecks und nahe [I lo] Iiegen, nur eine geringe Verfestigung zeigen, d.h. sie Zeigen “Leicht-Gleitung” (“easy-glide”). Bei Kristallen, die nahe den Seiten [lOO)-Clli] und [lOO>[llO] des Orientierungsdreiecks liegen, ist die Verfestigung zunachst gering und steigt spater an, wahrend bei Kristallen, die nahe der Dreiecksseite [110] [111] orientiert sind, der Verfestigungsverlauf einheitlich ist. Ein gleiches Verhalten zeigt sich beim Zugversuch, jedoch war dabei das Leicht-Gleiten (easy-glide) nicht so ausgepragt. Im Zusammenhang mit dem Auftreten der Leicht-Gleitung (easy-glide) wird die Bedeutung kleiner Probendurchmesser und cler geringe Eintluss einer weniger sorgflltigen Probenbehandlung diskutiert. Beim Auftreten von I,eicht-Gleitung (easy-glide) sind die Gleitlinien sehr einheitlic~ verteilt, wahrend in Kristailen, die naher bei [ill] oder [t00] orientiert sind, die also eine schnellere Verfestigung zeigen, dieGleitlinien sehr stark zusammengezogen sind und manchmal Gleitspuren auf anderen Systemen zwischen den Anhaufungen der Hauptgleitlinien zeigen. Laue-Aufnahmen z&en bei keinem Kristall nach der Wechselbeanspruchung Asterismus. Es treten jedoch bei den Kristallen mit starker Verfestigung schwache Kossel-Linien auf, die bei den Kristalien, die ein Leicht-Gleiten zeilren ieasv-dide). fehlen. Auf Grund der Wechselbeziehung von Versetzung auf sich scheid;nden dknEbenen wird eine E&&rung fur das beobachteten Verfesti~ngsverhalten vorgeschlagen. Der ~auschinger-Effekt konnte deutlich in den Kupfer-Einkristallen nachgewiesen we&en. Y

* Received January 10, 19.55. t Department of Geophysics, The Australian ACTA

METALLURGICA,

National

VOL. 3, SEPTEMBER

University,

1955

491

Canberra, Australia,

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~~T~LLURGIC~,

I. INTRODUCTION

The study of single crystals under reversed plastic deformation is interesting for several reasons. The strain hardening and the development of the slip pattern can be observed while avoiding the progressive rotation of the crystal orientation, relative to the direction of the stress, that is inevitable in simple tension tests. Observations of the effect of changing the direction of straining should assist the development of dislocation theories of strain hardening, Further, a detailed study of the mechanism of reversed deformation in single crystals is an essential step in understanding the process of fatigue in metals. While fatigue of practical importance occurs under very small strain amplitudes, it should be profitable first to study the grosser processes occurring at larger strain amplitudes. Orowan’s theory of fatigue’ is based on the strainhardening of local “plastic” regions under reversed straining. The present work began, in part, as an attempt to provide such data for copper single crystals at comparatively large strain amplitudes; the only previous measurements of this kind were those made by Held” on tin. However, the dependence of the strain hardening on the orientation of the copper crystals was soon discovered and the work has largely concentrated on this aspect. Contrary to the former belief that the strain hardening of a single crystal can be expressed independently of its orientation by the shear stress-glide curve far its active slip system, an initial region of low strain hardening, or “easy glide,” has been observed for certain orientations in several face-centered cubic metals, viz., Cy-brass,8r4aluminium,5-8 gold9 and silveP~r0. Easy glide has now been observed in tensile tests on copper, very in the presrecently by RosirO, and independently ent work. However, the reversed deformation experiments demonstrate easy glide in copper more spectacularly. II

PREPARATION

OF SPECIMENS

The copper, of 99,999 per cent purity, was supplied by Messrs. Johnson, Matthey and Company. It was cold-drawn to about 1.6 mm diameter and then etched III

FIG.1. The orientations reversed

of the crystals straining tests.

used in the

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to remove any impurities from the dies. The single crystals were grown in tubes of spectrographically pure graphite in a vacuum of about 1c4 mm Hg by the method of Andrade and Roscoe.rr Each crystal was of sufficient length to provide two specimens of the same orientation; the cutting was done by nitric acid on a reciprocating thread. The specimens were finally electropolished in an orthophosphoric acid electrolyte. Their orientation was determined by the back-reflection Laue method. III. E~E~~ENTAL

METHODS

The testing machine is described elsewhere.12 It was designed to ensure that the specimen chucks were strongly constrained to move axially, thereby minimizing external bending or torsion of the specimen, Also, there was negligible hystersis in the machine for cycles of load between tension and compression. The load and extension (or relative movement of the chucks) were measured optically with the aid of mirrors attached to rollers. In addition, a microscope was attached to the machine so that the whole length of the specimen could be traversed and the slip pattern observed during the tests. One of the main di~culties was to develop a method of clamping the specimen firmly without accidentally straining it. Early attempts were made to clamp the ends in V-chucks, after attaching suitable shoulders. Although stress-strain results were obtained in this way which showed the same types of strain hardening as were established in later experiments, there was much scatter since the chucks could not be aligned sufficiently accurately to eliminate distortion of the specimen. However, the following method of “clamping” overcame this difficulty and was used in the experiments described in this paper. A cylindrical steel shoulder was cemented to one end of the specimen with Araldite, the curing being done in a vacuum to avoid oxidizing the electropolished surface of the crystal. This shoulder was clamped in the upper chuck which was of conventional V-groove type, The lower end of the specimen was then dipping into molten “Cornsol” solder* at about 320350°C contained in the lower ‘Lchuck,” which was a hollow block, heated electrically and insulated from the machine by mica washers. On reducing the heating current the solder solidified and firmly gripped the specimen. The load on the specimen was held close to zero during cooling by operating the machine by hand in the direction to compensate for the thermal contraction of the specimen and other heated parts. A stream of nitrogen was directed at the surface of the specimen to prevent oxidation while it was hot. The free length of the crystals was about 7 mm and the diameter 1.5 mm. This length: diameter ratio seemed * 5% Sn, 1.5% Ag, remainder Pb; m.pt. 296°C. Preliminary tests showed negligible creep in this solder under the loads used in the stress-strain tests. “ Comsol” was chosen for its creep properties in preference to solders of lower meIting point, especially Wood’s metal in which creep proved very troublesome.

PilTERSON:

REVERSED

DEFORMATION

OF

493

Cu CRYSTALS

FIGS. 2, (a) and (b). A selection of the results of the reversed straining ICS~S. to be the maximum permissible to avoid buckling in tile reversed straining tests. The testing machine was operated manually in a manner to ensure an approximately constant rate of extension of the specimen, of the order of 1 in. per minute; this could not readily be done by means of a motor drive of constant speed since during elastic straining most of the total deflection occurred in the lortdmeasuring springs, while during ptastic stmining, when the load was changing much less rapidly, most of the dcfleclion was due to extension of the specimen. Xn the reversed straining tests, the complete stress-strain curves for the first three cycles of deformation were plotted by taking load and extension readings at small intervals, the straining being interrupted momentarily ai each reading. Thereafter, only the 1oa.d at the end of each half-q& was recorded. The total strain amylitude was increased during strain hardening so that the plastic strain amplitude was constant throughout the test. In the simple ten&z tests, readings were again taken during momentary interruptions in the straining. However, the amount of creep occurring during these inlerruptions is small and should not appreciably a&cl the stress-slrnin curves.

IV. REVERSED DEFORMATIOM EXF’ERIMENTS

The behavior of high-purity copper crystals in reversed straining was found to be highly dependent on their orientat.ion relative to the specimen axis. The manner in which this is revealed in the strain hardening, the appearance of the sIip lines and Laue X-ray photographs is described in the following sections. Later a comparison will be made with the behaviour of similar copper crystals in simple tensile tests. 1. Measurements

of Strain

Hardening

Vsing the procedure described in Sec. III, reversed straining tests were clone on copper crystals of about twenty five different orientations (Fig. 1); the plastic resolved shear strain amplitude was 0.0083 in all cases. Rleasurements were usually done on two specimens oi the same orientation (see Sec. II), the results from which agreed to within about S-10 per cent except for some orientations in region B (Fig. 31, where greater scatter seemed to be inherent; the curve t-hat was initially lower was taken to be the better result since the specimen giving the higher result may have been previously damaged. A selection of the strain-hardening curves is shown in Figs. Z&a) and Zjb) , The curves are drawn through ihe

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(34

METALLURGICA,

(3b)

FIG. 3. Schematic representation of the orientation dependence of strain hardening in reversed deformation. Curve 1 is typical for orientation region A; curves 3 and 4 represent tr~sitional types in regions B and C, respectively, which become more like curve 2 as the orientation approaches [lOO] or [ill].

final stresses reached in each half-cycle of strain ; the abscissae represent the number of cycles or the equivalent total absolute strain. The very marked dependence on orientation is seen in these results, and is summarized schematically in Fig. 3. For a crystal oriented in the middle or towards the [IIO] corner of the stereographic triangle [region A, Fig. 3 (b)], the strain-hardening curve is very flat [type 1, Fig. 3(a)] and almost independent of orientation except for a tendency to be a little higher for orientations near the [llO] corner. On the other hand, for a crystal the strain-hardenof approximately [ 11 I] orientation, ing curve is very steep (type Z), especially during the first few cycles. From the trend of the results in Fig. Z(b), it appears probable that a crystal of [IOO] orientation would also show a strain-hardening curve of type 2. However, in the absence of measurements on crystals of exact [Ill] and [IOO] orientations, it is not clear whether the strain-hardening curve for [IOO] would be quite as steep as for [Ill]. For all intermediate orientations except those near the alloy-~1111 boundary (region B), the strainhardening curve has two points of inflexion (type 3). The curve is initially of relatively low slope and then

FIG. 4. Slip line pattern in crystal no. 59 in the easy glide region (200X).

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3, 1955

rises more steeply; later it tends to flatten out again. The number of cycles at which it bends upwards is less, and the slope of the steep part greater, for o~entations nearer the [loo]-flli] boundary; the same trend occurs to a lesser extent for orientations near the [lOO][IIO] boundary. Further the minimum slope before the curve bends upwards is greater for orientations nearer the [IOO] corner. For o~entations near the ~110~~111~ boundary (region C), the strain-hardening curve has a similar shape to that of the limiting types 1 and 2, but is of intermediate slope (type 4) ; its steepness is greater for orientations nearer [I 1 I]. A feature of the strain hardening common to all orientations was the development of a slightly higher yield stress in compression than in tension, independently of_whether the first half-cycle was tensile or compressive [Figs. 2(a) and (b)]. This is not thought to be due to a zero drift in the testing machine. Neither does it appear to be due to the development of a buckle in the specimen; when conditions were arranged so that

FIG. 5. Clustered primary slip and faint cross-slip in crystal no. 57 near [111] (200X).

obvious buckling occurred, the discrepancy between tensile and compressive yield stresses was no greater. 2. Microscopic

Observations

The appearance of the slip lines after reversed straining depended markedly on the orientation of the crystals in a way that could be correlated with the strainhardening behaviour. Crystals with a low rate of strain hardening showed very uniformly distributed slip on a single system; crystals of high strain-hardening rate showed clustering of slip lines and, frequently, slip on more than one system. In more detail, the observations were as follows: (a) All crystals with orientations falling within region A and giving strain-hardening curves of type 1 (Fig. 3) showed very uniformly distributed slip on a single system (Fig. 4). No deformation bands of any kind nor any traces of secondary slip were observed. Also, the slip appeared to develop homogeneously over the whole specimen during an experiment.

PATERSON:

REVERSED

DEFORMATION

(b) In crystals with orientations near [ill] or [loo], corresponding to the highest strain hardening, the prominent slip lines were clustered into bands, between which fine slip lines on both the primary system and a second system were faintly visible. Most of the prominent slip clusters appeared during the early cycles of deformation, after which the main changes were in the general intensity of the slip picture. The final appearance for crystal no. 57, near [ill], is shown in Fig. 5. Here the second slip plane was identified as that for cross-slip. For crystal no. 51, near [loo], the secondary traces were either conjugate or cross-slip but the measurements were insufficiently accurate to identify them definitely. Crystal no. 58, which was oriented almost on the [ill]-[loo] boundary but close to [ill], showed two sets of widely separated clusters of prominent slip on different planes, which in some places intersect.ed. These planes were the two on which the maximum resolved shear stress occurred; no cross-slip traces could be identified. The appearance was, therefore, not that of uniformly distributed duplex slip, but rather it suggested independent activity of one or other of the favoured systems in different parts of the crystal (a similar appearance was shown by crystals nos. 54 and 85). It was also particularly noticeable in crystal no. 58 that the boundaries of the clusters of slip were not quite parallel to the slip lines themselves (cf., Lange and Li.icke7); this suggests that cross-slip probably occurs between the coarse slip clusters but was too fine to be observed. (c) For crystals oriented in the intermediate regions B and C (Fig. 3), there was a mild clustering of the slip lines, which was more marked for orientations nearer to the higher strain[111-J or [loo], corresponding hardening curves. The final appearance of the slip in both orientation regions was similar (Fig. 6 is typical). Traces of slip on a second system between the main clusters were often observed when the clustering was more marked. There was some evidence that for crystals oriented in region B the slip was at first uniformly distributed and later took on a clustered appearance as some Iines became more pronounced than others, corresponding to the steeper part of the strain-hardening curves; however, more observations are needed to confirm this. No kink bands or deformation bands of any type except that described above were observed in crystals of any orientation in these experiments.

OF

495

CLI CRYSTALS

Frc. 6. Clustered orientation

slip in crystal no. 77, typical regions R and C (200X).

of

fluorescent copper characteristic radiation excited by the incident white radiation from an X-ray tube with a tungsten target. Normaily, Kossel lines cannot easily be distinguished from the general background radiation in Laue photographs, but Borrmannl* obtained very clear Kossel lines in Laue photographs of copper crystals, the surface of which had been roughened and then etched to remove the more disturbed layers. In t.he present work it was found that fairly clear Kossel lines could also be obtained from copper crystals, of suitable orientation, that had been subjected to reversed straining. This probably indicates that a state of imperfection has been reached in which extinction effects have been substantially reduced but in which there is not yet excessive distortion of the lattice which would cause blurring and consequent loss of contrast of the Kossel lines.

3. X-Ray Observations Laue X-ray photographs were taken after each reversed straining test. No asterism or other marked change in the Laue spots was observed for crystals of any orientation. However, Kossel lines were frequently visible (Fig. 7). Kassel &ws’~ are produced by the diffraction of X-rays originating within a crystal, in this case, the

FIG. 7. KosseI lines in X-ray

Laue X-ray photograph beam parallel

to [llOj.

of crystal

no. 58;

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METALLURGICA,

No Kossel lines were observed in Laue photographs from the crystals before deformation. Also, no Kossel lines were observed after reversed deformation for crystals with orientations within region A (Fig. 3), corresponding to low strain hardening, On the other hand, Kossel lines were clearly visible after reversed deformation for crystals oriented near [ill J and [loo], showing high strain hardening; faint Kossel lines were obtained for the intermediate orientations (regions B and C, Fig. 3). These observations probably mean that the perfection of crystals showing low strain hardening is not greatly disturbed by the reversed straining, whereas the higher strain hardening is accompanied by greater disturbance of the lattice, as would be expected ; in neither case is a large-scale spread of orientation introduced which would give rise to asterisms. 4. Other

Observations

The critical shear stresses for the crystals used in the reversed straining and tensile tests are given in Fig. 8 according to orientation. These are the values of stress at which the stress-strain curve begins to depart rapidly from the elastic line;* values obtained by extrapolating the early linear plastic part of the stress-strain curve to cut the elastic line were about 20 per cent higher. The Schmid lawI appears to hold in region A of the stereographic triangle (Fig. 3), where the critical shear stress is about 45 gm mmM2. However, nearer the [111-J-[lOO] boundary, the critical shear stresses are higher (the same is true if the extrapolated values are considered). Thus the Schmid law is not obeyed over the whole range of orientations. The rn~~~rn~rn sE@e of the resolved shear stress-glide curve in the first half-cycle varies like the critical shear stress, with rather more scatter but a greater range. The greatest value is 30 kg mm-2 for crystal no. 58 oriented near [ill], compared to an average value of about 2.5 kg mm+ for orientations in region A (Fig. 3). Stress-strain measurements for several cycles of reversed strain similar to those applied to the single crys-

FIG. 8. Critical *The

value

shear stresses (in gm mm”) for crystals in strain-hardening experiments.

strain-h~dening

3,

195.5

tals were made on two very,coarse-grained polycrystalline specimens of the same copper (grain size about s-1 mm, obtained by annealing the cold-drawn wire). In each case, the stress-strain curves were rather similar in shape, and the rates of strain hardening of similar magnitude, to those obtained from single crystals oriented near [ill]; the initial yield stresses were rather higher. A ~a~sc~~~g~ e$kEt was clearly shown by all crystals, taking as its criterion a lower yield stress for straining in the reversed direction than the previously applied stress; in most cases, the yield stress for reversal after the first half-cycle of strain (0.0083 glide) was also less than the initial critical shear stress. Figure 9 shows a typical example. However, if the “yield stress” after reversal was determined by extrapolating the linear plastic part of the cycle to cut the previous elastic line, it was usually nearly equal to the stress previously applied in the first direction (this was also true for the coarse-grained polycrystalline copper). In general, the ~aus~hi~ger effect in the single crystals appeared to be of similar magnitude to that in polycrystalline copper. This is further evidence against Heyn stresses (intercrystalline stresses) being the cause of the IJauschinger effect.‘” A pronounced jerkiltess in the rate of deformation during cyclic straining was observed for several crystals near the ClOO] orientation; a slight drop in load would accompany an abrupt change in the strain, Lange and Lucker observed a similar effect in the tensile deformation of aluminium crystals oriented near [loo]. The effect in the copper crystals also occurred to a very slight extent for other orientations, but never for those within region A (Fig. 3) except after previous torsion. However, the most pronounced jerky deformation was shown by crystal no. 86b, oriented near [llO], which had undergone previous torsional strain (see below). Since the stress-strain measurements were not recorded automatically, it was difficult to determine the increment of strain in each jerk but it was probably of an order of magnitude corresponding to a slip of about 1000 A on one plane. eflect of previous torsion. In order to observe the effect that previous slip on planes other than that normally

used

(101 gm mm-l) for crystal no. 58 oriented near inde6nite because of the steepness of its curve.

[111J is somewhat

VOL.

FIG. 9. Stress-strain curves for first cycle of deformation for no. 86a (near [llo]), showing Bauschinger effect.

crystal

PATERSON:

0

10

REVERSED

10 NclPrBI~

so

DEFORMATION

OF

Cu

497

CRYSTALS

10

OP CICZES

FIG. 11. Shear stress-glide FIG. 10. Effect of prior torsion on strain hardening in reversed deformation. Maximum surface shear strain in torsion was 0.02 for crystal no. 7411 and 0.1 for crystal no. Mb.

active in direct stress would have on the rate of strainhardening of crystals oriented in region A (Fig. 3), two specimens were twisted by amounts corresponding to about 0.02 and 0.1 surface shear strain, respectively, and then t.wisted back by the same amounts. This was followed by reversed deformation tests, carried out in the usual way. The results of these are given in Fig. 10. Fol comparison, curves are also given for specimens of the same orientations, cut from the same crystals, but not previously twisted. It is remarkable that the rate of strain hardening is even less after prior torsion than in an undamaged crystal ; there is 110 tendency to strainharden at the high rate that is characteristic of crystals oriented near [ll l] or [loo], which often show signs of slip on more than one plane. The final distribution of slip lines resulting from the reversed straining after prior torsion was very uniform, similar to that normally observed for crystals in this orientation region. However, during the first few cycles, the slip pattern developed first in some parts of the specimen and then spread gradually to all parts. This was accompanied by jerky deformation, especially in crystal no. 86b; once, a jerk was actually observed to coincide with the appearance of a new prominent slip line in a previously unmarked area. V. TENSILE TESTS In order to compare the strain hardening of copper crystals in cyclic straining with that in unidirectional straining, simple tensife tests were carried out for a number of orientations. The method of gripping, the lengths of the specimens and the measuring procedure

curves

from tensile tests.

were identical with those used in the reversed deformation tests. The rigid gripping of the ends of the specimens must lead to very considerable inhomogeneity of strain when the crystal orientation tends to rotate during extension ; however, for small strains the effect on the strain hardening should not be serious. Since these tests were done, an account of similar work on copper has been published by Rosi.‘O While in many respects the two sets of results are similar, it is interesting to compare them and discuss some of the differences, since the method of gripping and the size of the specimens were different. The results for typical orientations are given in Fig. 11 as resolved shear stress-shear strain curves. These were derived from the tensile stress-strain measurements by the usual method of calculationlr; in the two cases (no. 70 after 0.08 glide and no. 84 almost from the beginning) where the calculated orientation reaches the [ loo]-[ 11 l] boundary, Giiler and Sachs’ method’* for duplex slip has been used. As in the reversed deformation tests, there is a pronounced dependence on orientation, mainly due to different behaviour up to strains of about 0.1. For orientations far from the [lOO]-[ill] boundary, there is a region of low strain hardening extending for several per cent strain, after which the rate of strain hardening is much higher. For the orientations close to [lOO], [ill] or the [loo]-[ill] 1’me, the initial region of low strain hardening is shorter (no. 70) or absent (nos. 84 and 87). However, for all orientations, the rate of strain hardening at the larger strains is of similar magnitude. Some of the results are plotted as tensile stress-strain curves in Fig. 12, in which are also included Rosi’s results [lo] for similar orientations. Curve no. 53 is the

ACTA

0

r

O’ol

= PAEJEW

0.01 TcNJlLC

METALLURGICA,

AEJVLZJ

O-03

o-04

0.05

S-&&N

FIG. 12. Comparison of tensile stress-strain curves with those of Rosi’o and Lange and Liicke.?

only one given by Rosi for 99.999 per ‘cent pure copper and should be comparable to curves no. 69 and no. 89 for similar orientations from the present work. However, the region of low strain hardening is of much greater extent in the latter cases than in Rosi’s. The other curves from Rosi’s paper refer to less pure copper (99.98 per cent). While they are rather similar to the present results for orientations near [ill] (nos. 41 and 87) and [.lOO] (nos. 37 and 84), there is again a considerable difference for orientations near [llO] (nos. 34 and 69 or 89). Thus the most striking difference between Rosi’s and the present results lies in the greatly extended region of low strain hardening for orientations near [llO] in the latter. This is at first surprising in view of the fact that Rosi’s specimens were gripped in a manner to minimize the inhomogeneous strain due to lattice rotation whereas in the present work the ends of the specimens were prevented from rotating and the specimens were relatively much shorter. Also, Rosi concludes that higher purity crystals show a shorter region of low strain hardening. However, the explanation may lie in the fact that Rosi’s specimens were of greater diameter (9.5 mm compared to 1.5 mm), In this connection, it may be observed that t,he curve reproduced in Fig. 12 from Lange and Liicke’s measurements7 on high-purity aluminium for an orientation near [llO] was obtained from an electropolished crystal of 1.5 mm diameter and shows a very extensive region of low strain hardening. The distributions of slip lines for the various orientations were similar in most respects to those illustrated by Rosilo and ‘Becker and Hobstetterlg for copper and by Lange and Liicke’ for high-purity aluminium. The

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3, 1955

crystals oriented near [ill J and [lOO] showed strong clustering of the primary slip lines, with slip on other planes (cross-slip or conjugate slip) developed more strongly between the clusters. Crystal no. 70 near the middle of the [loo]--J-cl11 J boundary did not show clustering of the slip to a marked extent, but the slip lines of the two main systems were fairly intimately intermingled. The crystals near [llOJ showed very uniformly distributed slip on one plane. This is in contrast to Rosi’s conclusion that a mild tendency for clustering of the slip lines existed for orientations away from the [lOO]-[ill] boundary. The crystals oriented near Cl101 also showed kink bands, such as illustrated by RosilO and Lange and Liicke.7 These were probably due to the rigid grips, in agreement with Rosi’s observations; their absence in the reversed deformation tests also supports this conclusion. Slip on a second plane sometimes occurred in the kinked regions, as observed in aluminium.7~21 “Bands of secondary slip” (cf. Honeycombem and Rosi”O) were a common feature of deformed crystals of orien~tions away from CllO]. However, no “intimate cross-slip” such as occurs in aluminium*~7~2~~22was observed in any crystals. Luue X-ray photographs taken after the tensile tests showed marked asterism for those crystals which contained kink bands, that is, for orientations near [110-J. The crystals oriented near [MO], [ill] or the [100-J[ill] boundary showed only slight asterism, although the Laue spots were considerably blurred. This confirms the conclusions of Honeycombe,m Lange and Liicke,7 and others that asterism arises from kink bands. The asterisms from the deformed copper crystals often showed a fine structure (cf. Honeycombed) ; however, the specimens had been heated to about 350°C for 15 seconds or so when removing them from the testing machine. Some faint Kossel lines were observed in the Laue photographs. However, they were usually rather broad and, for the orien~tions near [llO], were extremely faint. VI. DISCUSSION The striking contrast between the high rate of strain hardening for crystals oriented near [loo] and [ill] and the initial low rate for crystals nearer [llO] is a feature common to the tensile tests and the cyclic straining tests; that is, in both types of straining, crystals oriented in region A (Fig. 3) show “easy gZide.“s However, whereas in simple tensile straining the region of easy glide ends after a few per cent strain, when the yield stress is still below 0.2 kg mm+, the low rate of strain hardening persists in the reversed straining until the yield stress has been raised to at least 0.8 kg mrnsz. Thus a change to a high rate of strain hardening (the onset of “turbulent hardening,” in Cottrell’s graphic terminologyzs) does not always occur when the applied stress exceeds a critical value. The difference in the two

PATERSON:

REVERSED

DEFORMATION

cases must lie in the development of the internal stresses from stuck dislocations; because of the alternation of slip of opposite senses on neighbor~g active slip planes during reversed straining, the internal stresses in this case probably change sign more frequently in a given distance and so give rise to weaker long-range internal stresses than result for simple tensile straining. The present experiments throw some further light on the cu~d~~~o~zs for the ap~eura~~e of easy glide. These have been given as: suitable crystal orientation, careful handling of the crystals, high-purity material, and absence of an oxide layer.4~5,6~QJ3The present experience with copper confirms the importance of crystal orientation. The copper was also of high purity; however, the role of purity is doubtful in view of Rosi’s results10 and observations on cr-brass.3*4 The presence of an oxide film on the copper does not seem to matter, since all tests were done in air; even when a visible oxide film was allowed to form it did not appear to affect the results. An unexpected conclusion is that mishandling of the specimens, such as accidental bending, does not prevent easy glide. Slight damage usually results in the strainhardening curve in reversed deformation being slightly higher than-but of parallel course to-that for an undamaged specimen. The experiments in which crystals were deliberately distorted in torsion showed that although the yield stress had been considerably raised, the subsequent rate of strain hardening in the reversed straining tests was even lower than in undamaged crystals. (This was in contrast to Paxton and Cottrell’s observations24 that small twists raise the subsequent rate of strain hardening in a tensile test.) However, the high stress-strain curves for polycrystalline specimens suggest that easy glide did not occur in many of the crystals contained in them. From the evidence given in Sec. V a crystal of smaller diameter probably shows more extensive easy glide. This favours Mott’s suggestionz5 that in the region of easy glide most dislocations pass out of the crystal and so do not contribute to the hardening, since in a larger crystal there would be a greater chance of a dislocation meeting an obstacle during its passage through the crystal. If the absence of Kossel lines in the Laue photographs from crystals after easy glide is a reliable indication of higher crystal perfection, this further supports the idea that not many dislocations are trapped in the crystal during easy glide. The most prominent feature accompanying a high rate of strain hardening, whether in cyclic straining or in simple tensile straining, is the clustering of the primary slip lines, and, frequently, the appearance of other slip lines between these clusters, in spite of the orientation being such that slip on only one set of planes would be predicted. This is in contrast to the very regular distribution of the single set of slip lines resulting from easy glide. The idea that the high rate of strain hardening (turbulent hardening) arises from the interaction of dis-

OF

Cu

CRYSTALS

499

locations on intersecting planes26J7r28 is supported by the observation of traces of slip on more than one set of planes. Although it is only on the primary slip planes that the shear stress component is sufficientiy high to cause the movement of large numbers of dislocations (probably due to the catastrophic generation of dislocation loops at Frank-Read sources), the shear stresses effective on some of the other slip planes may also cause the movement of some of the less tightly bound dislocations lying in them; at least, the dislocation segments in these planes will bulge out to some extent and so increase the chance of interaction with dislocations moving in the primary planes. Such an effect will be less for orientations further from the [loo]-[ill] and triangle, [100-j-fllO] b oun d aries of the sterographic that is, for orientations nearer the middle of the [llO][ill] boundary, since here the ratio of the shear stress component on the second most favoured slip plane to that on the primary slip plane is least. This enables one to give a qualitative explanation of some of the features of the dependence of the strain hardening on orientation in region B. Thus by assuming that dislocations in the conjugate plane9 interact with those in the primary planes, one can explain the observation that the upward bend in the strain-hardening curve (type 3) occurs at a lower stress for orientations nearer the ll#]-[Ill] boundary ; as the ratio of the resolved shear stress on the co~ljugate planes to that on the primary planes increases, dislocations on the conjugate planes will be increasingly likely to move (or the dislocation segments to bulge out further) and to int.eract with dislocations moving on the primary planes. The slope of the steeper part of the strain-hardening curve will also be increased due to the greater number of these dislocation interactions as the relative shear stress component on the conjugate planes is increased. A similar explanation of the trend of the strainhardening curves for orientations near the [ lOO]-[ 1lo] boundary is possible in terms of interaction with dislocations in the unpredicted planesi instead of the conjugate planes. The different type of behaviour in region C can now be understood, since no new slip plane is favoured when the [llO]~[lll] boundary is approached; only the slip direction changes when this boundary is crossed. Thus the strain-hardening curves {type 4) do not show an upward bend but remain of similar shape to type 1 for region A. It is interesting to note that increased amounts of cross-slip accompany the increased rate of strain hardening in region C as [ll l] is approached ; this corresponds to the increasing relative shear stress on the cross-slip planes. However, if these slip lines are due to true cross-slip, involving dislocations having the same Burgers vector as the primary slip, they cannot. be associated with hardening resulting from interactions of Lomer-Cottrell type with the dislocations in the primary slip planes. Rather, their presence probably in-

so0

ACTA

METALLURGICA,

dicates the relief of piling up of screw dislocations in the primary planes.26 MotP has already suggested that the intersection of screw dislocations may be the mechanism of hardening in the easy glide region. Thus, if the increased amount of cross-slip is evidence that screw dislocations are playing an increasing role in the deformation, it may be that Mott’s hardening mechanism for easy ghde is still operative in region C but to an increasing degree nearer [ill]. Similarly, in region B the part of the strain-hardening curve (type 3) before the upward bend is probably associated with the same mechanism. Here, also, the slope increases as [loo] is approached and the relative shear stress component in the cross-slip plane is increased. No asterisms were observed in the Laue photographs after any of the reversed straining tests; where strong asterisms resulted in the tensile tests, they could be attributed to kink bands. This again shows that the structural features (especiahy kink bands) that give rise to asterisms are not essential to strain hardeningez6 ACKNOWLEDGMENT

The main part of the design and construction of the apparatus used for the reversed deformation tests was done at the Aeronautical Research Laboratories of the Department of Supply, Melbourne. The author is grateful to the Chief Scientist for the continued use of the apparatus for this work at the Australian National University.

VOL.

3, 1955 REFERENCES

1. 2. 3. 4.

E. Orowan, Proc. Roy. Sot. (Lond.) A171, 79 (1939). H. Held, Z. Metallk. 32, 201 (1940). F. v. Galer and G. Sachs, 2. Phys. 55, 581 (1929). R. Maddin, C. H. Mathewson, and W. R. Hibbard, Trans. A.I.M.E. 175, 86 (1948); 185, 527 (1949). 5. G. Masing and J. Raffelsieper, Z. Metallk. 41, 65 (1950). 6. K. Liicke and H. Lange, Z. Me&&k. 43, 5.5 (1952). 7. H. Lange and K. Liicke, Z. Metaflk. 44, 183 and 514 (1953). 8. G. Masing and H. Weik, Z. Metalik. 45, 417 (1954). 9. E. N. daC. Andrade and C. Henderson, Phif. Trans. Roy. Sot. (Land.) A244, 177 (1951). 10. F. D. Rosi, Trans. A.I.M.E. 200, 1009 (1954); J. Metals (Scot. 1954). 11. J?. k. daC. Andrade and R. Roscoe, Proc. Phys. Sot. (Lond.) 49, 381 (1937). 12. J. Sci. Instrum. In press. 13. R. W. James, The Optical Principles of the Diffraction of X-Rays (London, 1948), pp. 438-452. 14. G. Borrmann, Ann. Phys. 27,669 (1936). 15. E. Schmid and W. Boas. The Plasticitv of Crvstals {Berlin. 1935; Eng. transl., London, 19SO), p. 16.5. * ’ ’ 16. R. L. Woolley, Phil. Mag. 44, 597 (1953). 17. Reference IS, pp. 57 and 105. 18. F. v. GBler and G. Sachs, Z. Phys. 41, 103 (1927). 19. J. J. Becker and J. N. Hobstetter, Trans. A.I.M.E. 197, 1231 (1953); J. Metals (Sept. 1953). 20. R. W. K. Honeycombe, J. Inst. Metals (Land.) SO,45 (1951). 21. R. W. Cahn, J. Inst. Metals (Land.) 79, 129 (19.51). 22. G. J. Ogilvie and W. Boas, Trans. A.I.M.E. 175, 102 (1948). 23. A. H. Cottrell, Dislocations and Plastic Flow in Crystals (Oxford. 1953). DD. 1.57-180. 24. l? W. Paxton’& A. H. Cottrell, Acta Met. 2, 3 (1954). 2.5. N. F. Mott, Phil. Msg. 44. 741 (1953). 26. N. F. Mott; Phil. Mai. 43; 1151‘(1952). 27. P. Haasen and G. Leibfried, 2. Phys. 131, 538 (1952). 28. P. Haasen, Z. Phys. 136, 26 (1953). 29. Terminology of F. D. Rosi and C. H. Mathewson, Trans. A.I.M.E. 188, 11.59 (1950).