mechanical deformation of aluminium bicrystals

MECHANICAL DEFORMATION OF ALUMINIUM BICRYSTALS*

R. CLARI&t and B. CHALMERS3

Aluminium specimens composed of two symmetrically oriented crystals having a common (111) axis were subjected to a tensile test. It was observed that the yield stress and the rate of work hardening increased with the orientation difference between the crystals. In the initial stages of plastic deformation a linear stress-strain region was observed; the length of this region became shorter as the rate of work hardening (i.e., the orientation difference) increased.

LA DfiFORMATION Ml?CANIQUE DE BICRISTAUX D’ALUMINIUM

Des &hantillons d’aluminium consistant en deux cristaux orient& sym&riquement, ayant uu axe (111) commun. furent soumis ?I un essai de traction. I1 a 6th constat aue la limite 6lastioue et la &e&e d’&rou’issage augmentaient en mCme temps que la difference d’orientation entre ies deux cristaux. Une rCgion lineaire de la relation tension-dbformation fut observtie durant Ies premiers stades de la deformation plastique; la longueur de cette region diminuait quand la vitesse d’Pcrouissage (C.-&d., la difft?rence d’orientation) augmentait.

DIE MECHANISCHE VERFORMUNG VON ALUMINIUM BI-KRISTXLLEN

Es wurden Zugversuche an Aluminiumproben, die aus zwei symmetrisch orientierteu Einkristallerl mit gemeinsamer (111) Achse bestanden, unternommen. Es wurde beobachtet, dass die Fliess- spannung und die Verfestigungsgeschwindigkeit mit zunehmendem Unterschied in der kristallographischen Orientierung der Kristalle zunahm. In den Anfangsstadien der plastischen Verformung wurde ein Gebiet mit linearer Spannungs-Verzerrungs Beziehung gefunden. Die Ausdehnung dieses Gebiets nahm mit zunehmender Verfestigungsgeschwindigkeit (d.h. zunehmendem I’nterschied in der kristallographischen Orientierung) ab.

Introduction

It has long been observed during the plastic deformation of polycrystals that there exists a mutual interaction between neighbouring crystals that influences the mode and the extent of the deformation in each crystal concerned [l-7]. Chalmers’ [5] experiments with tin bicrystals, for example, showed that neighbouring crystals have a marked effect in inhibiting slip in each other. The specimens consisted of two crystals identical with respect to the specimen axis (the axis of applied stress) but rotated about this axis with respect to each other. It was observed that the stress necessary to cause an arbitrary amount of plastic deformation increased with the orientation difference.

Boas and Hargreaves [3] have shown that in coarse grained polycrystalline samples, the strain near a boundary may either be greater or less than in the interior of the same crystal depending on the deformation of the neighbouring grain. It is evi- dent that for the metal to remain continuous, the stress system must cause slip on systems that would not be observed in single crystals stressed in a similar manner. Chalmers [8] was of the opinion that this concept should be extended to include families of slip planes and directions never observed in the deformation of single crystals. More recently, an

*Received July 27, 1953. iuniversity of Toronto, Canada. Now at Norton Company,

Chippawa, Ontario. funiversity of Toronto, Canada. Now at Harvard Univer-

sity, Cambridge, Massachusetts.

ACT.4 METALLURGICA, VOL. 2, J.4N. 1954

example of a new slip system becoming active has

been observed by Craig and Chalmers [9]. The) showed that, while the deformation of a zinc single crystal could be accounted for entirely in terms of slip on the basal plane in a (1120) direction, the deformation of a ‘tricrystal’ could not be so described. It was shown that, with boundaries present, slip occurred on an entirely new family of planes, as well as on the basal plane, in the boundary region. The boundary inhibited slip on the normal system sufficiently to allow the application of resolved shear stresses on other slip systems higher than those possible in a single crystal.

Cottrell [lo] suggests that there may be three forces acting on a dislocation as it approaches a boundary, one long range, and two short range forces. The long-range force exists where the elastic constants are different beyond the boundary; as the dislocation approaches the boundary more of its strain field is imposed on the material beyond the boundary, and the energy to deform this is different from that to deform the material on the near side of the boundary. For a free surface, Koehler [I I] showed that this force is inversely proportional to the distance of the dislocation from the surface. It should be remembered, however, that most metal surfaces are coated with oxide (or other metal compound) layers. Even internal boundaries in ‘pure’ metals may differ in composition from the crystals [12]. There is much experimental evidence to show that oxide films make slip more difficult in soft metal crystals 113-181. This implies that such

surfaces generally repel dislocations approaching from inside the crystal. Barrett [19] has demon- strated that a pressure of piled-up dislocations existed in plastically twisted, oxide-coated, zinc crystals. When the oxide layer was iemoved from a freshly twisted crystal, the crystal would spon- taneously twist a little further as the piled-up dislocations were allowed to run out.

A study of the effects of intercrystalline junctions (i.e., the mutual interaction of neighbouring grains) would be quite difficult in ordinary poly?rystalline metals;. However, the problem can be greatly simplified by the use of specimens containing only a few large crystals and by preparing samples con- sisting of two or three crystals of controlled orientation. Such specimens can be produced by using ‘seed’ crystals of the desired orientation. This technique provides a powerful tool of the investigation of the properties and effects of graia -boundaries as functions of the orientation difference existing across a boundary.

In the work to be described, rectangular bars composed of two crystals separated by a longi- tudinal boundary were subjected to a tensile test. The orientations were arranged such that there was a slip plane common to both crystals and inclined at 45 degrees to the specimen axis. A rotation through an angle 4 about the normal to the common slip plane would bring one crystal into coinci- dence with the other.

Experimental

The experimental work consisted of (a) preparing rectangular bars of pure aluminium as single and bicrystals of controlled orientations, and (b) record- ing the stress-strain characteristics of the specimens when subjected to a gradually increasing stress.

The specimens were grown from the melt in an argon atmosphere using a technique described previously [20]. The aluminium was obtained from the Aluminum Company of Canada, and was reported to be 99.99 per cent aluminium. Spectro- graphic analysis showed the presence of small amounts of iron, magnesium, silicon, copper and titanium. Comparison of the original ingot metal with that in specimen form revealed no change in impurity concentration with the exceptions that silver and zinc appeared as new trace impurities in the specimens. Chemical analysis showed the major impurity, iron, to be 0.005 per cent and revealed an acid (HCl) insoluble residue amounting to 0.012 per cent (oxidized). Spectrographic analysis showed the major component of the residue to be titanium,

with smaller amounts of magnesium, silicon, aluminium, copper and iron.

To produce uniform specimens, a machined graphite boat equipped with a cover was used. The boat is illustrated in Figure 1. The specimens (Figure 2) were approximately I .3 cm wide, 0.5 cm

FIGURE 1. Graphite boat used to prepare specimens.

FIGURE 2. Typical specimen showing the direction of boundary and the gauge length markers.

thick, and 14-15 cm long. The metal was melted in a graphite crucible and poured into the boat. The specimens were parted from the excess metal at one end and the seed crystals at the other by means of a fine toothed saw.

Each specimen was etched in a solution of 9 parts HCl, 3 parts HNOS, 2 parts HF, and 5 parts water; this revealed the presence of any stray crystals and showed the direction of the boundary in the bicrystals. The crystal orientations were determined by Greninger’s back-reflection Laue method [21]. The striations [22] occurring caused an orientation distribution of 4 degrees to exist within the crystals.

A 5-cm (approx.) gauge length was marked on each specimen and accurately measured with a travelling microscope. The width and thickness of each specimen were measured with a micrometer, and the average cross-sectional area of their gauge lengths calculated. The specimens were annealed in air for five days at 630°C ~5” and etched im- mediately prior to straining.

The tensile testing machine [23] was, in essence, the type described by Andrade and Chalmers [24]. Water was used as the load; the extension was measured with a single-mirror optical extenso- meter. The ‘stresses’ were calculated on the original specimen area and measured to the nearest gram,/ mm2. Strain was measured to the nearest 2 X 1O-5 cm/cm.

A slip plane, ( 111 } , was fixed at 45 degrees to the specimen axis, the position of maximum resolved

shear stress. Further, a (110) slip direction in the

82 ACTA i~E’~~~LLURGICA, VOL. 2, 1954

slip plane was also fixed at 45 degrees to the specimen axis. This orientation is illustrated in Figure 3. A seed crystal, having the orientation shown in Figure 3, was rotated about the normal to the (111) plane (both clockwise and counterclockwise) to prepare seeds for the single and bicrystal specimens. These rotations were labelled positive and negative respectively and caused the (110) ‘slip directions to rotate in the { 111 f plane;

FIGURE 3. Stereographic projection showing initial orientation + = 0’.

the angle of rotation from the initial position was called 8. The seeds prepared by rotating the initial seed about the (111) axis, were ‘paired’ so that the average values of 8 were equal (f lo), but of oppos- ite sign. Each pair of crystals was used to prepare a bicrystal seed; the difference in orientation between the crystals in these seeds was designated by

b, = 28 degrees.

Observations and Results

Some difficulty was experienced in preparing aluminium crystals sufficiently free of ‘striations’ (22). Figure 4 illustrates an exceptionally large orientation distribution due to striations. The largest pin hole available (l-2 mm diam. spot.) was used to give good coverage to determine the widest orientation difference existing in any one crystal. In general, the spread was found to be 2-4 degrees. The ‘best’ crystals were prepared in a boat with graphite inserts as illustrated in Figure 1. The use of these thin inserts effectively reduces the lateral heat loss, and the ratio of the heat flow across the liquid-solid interface to that through the graphite boat is increased. These conditions favour the

growth of single crystals free from striations and stray crystals. This effect has also been observed by other investigators [25].

Examination of the stress-strain curves obtained from the bicrystal specimens showed that the general form of the curve is as illustrated in

FIGURE 4. by ‘striations.’

Unusually large orientation distribution caused

Figure 5. There is an elastic range CA (approximately) where the stress is proportional to the strain, followed by the plastic region B-C where the stress-strain relation is linear but the slope of the curve is much less. Beyond point C, the proportion- ality between the stress and strain disappears and the curve rises more steeply. When no definite

”

STRAIN -

FIGURE 5. General form of observed stress-strain curve.

yield point is observed (as with these crystals) the normal procedure is to define the yield stress as the stress that causes a stated elongation of the speci-

men, e.g., 0.1 per cent. However, in this case, because of the linearity of the plastic region B-C, the yield stress was defined as that value of stress obtained by extrapolating the line C-B to zero strain. In Figure 5 the yield stress is represented by OA.

FIGURE 6. Plot of yield stress versus difference in orientation &J.

CLARK AND CHALMERS: ALUMINIUM BICRYST.4LS 83

FIGURE 7. Plot of rate of work-hardeningl(ds/de) versus difference in orientation qi.

TABLE I

Specimen 4 Strain at Average

Degrees point C strain cm/cm X lo4 cm/cm X 10’

Single crystals <SO 4A 12 >80 4B 12 80 4c 12 80 80

5A 22 80 5B 22 70 75

6A 6B

7A 60 25 7B 60 25 25

8A

40 >35 40 46 40

74=46 40 40

The experimental results are shown as graphs in Figures 6 and 7. Figure 6 relates the observed yield stresses to the difference in crystal orientation, while Figure 7 relates the slope of the plastic region B-C to the difference in crystal orientations. The approximate strains at which the linear stress- strain regions ended (Point C in Figure 5) are shown in Table I. The presence of the boundary shortened the linear region as the orientation difference between the crystals was increased.

Discussion

As noted before, the specimens were prepared with a ( 111) plane common to both crystals. Before discussing the results described above, it may be useful to consider the relations between the crystals’ axes as they are rotated with respect to each other about the common axis.

The (111) axis of rotation has three-fold rota- tional symmetry with respect to the unit cell of the crystals. Thus, when a crystal is rotated about this axis it reaches an identical position every 120 degrees. The position of maximum difference with respect to the original orientation occurs at a rotation of 60 degrees. Considering the (110) slip directions in the plane of rotation, it can be seen (Figure 8) that they have six-fold symmetry and thus repeat themselves every 60 degrees. There- fore, the maximum possible angular difference from the original and corresponding identical positions is 30 degrees.

The specimens used were composed of a ‘pair’ of crystals rotated about the common (111) axis through the same angle 0, one clockwise (positive) and the other counterclockwise (negative). When both rotations are 30 degrees, the angular difference (4) between the crystals is 60 degrees. We see from the foregoing discussion that the slip directions in the common plane are again codirectional. That is, in terms of the (110) slip directions in the common plane the specimen would appear to be a single crystal. However, considering the general crystal orientations as defined by the (100) axes, the orientation difference between the crystals is the maximum. Figure 8 is a stereographic projection showing the relative positions of the major axes of the two crystals for @I = 60”. It can be seen from the projection that the crystals are twins, i.e., mirror images in the common ( 111) plane. The projection shows the slip directions of the two crystals as being codirectional in the common plane. Utilizing the fact that the crystals are twins, it is nossible to build a model illustrating the rela-

84 ACT:\ iVETALLURG1C.A. VOL. 2, 1954

tive positions of the successive layers of atoms in the two crystals. The ideal face centered cubic struc- ture can be described as an ABCABC . . . . . . . stacking sequence of close-packed { 111) planes, where the B- and C-layers are situated above alternate sets of hollows between the atoms of the

0 - alO> COMMON TO BOTH CRYSTALS

0 - (100) PLANES OF CRYSTAL I 8 = + 30’

n - (IOO) PLANES OF CRYSTAL H 8 = -30’

FIGURE 8. Stereographic projection showing the relative orientation of the crystals when 6 = 60”.

A-layer. In face-centered cubic structures the twinning plane is { 111) and so the relation between twinned crystals may be illustrated by

ABCABCACBACBA Crystal I I Crystal II

Twinning plane.

The crystals in the specimen 4 = 60” are twins and the relation between them is illustrated as follows :

Crystal I A B C A B C A B C A B C crystal -- boundary

Crystal11 ACBACBACBACB

The crystals are looking, as it were, into the same side of the mirror plane. The boundary between the

crystals is a noncoherent twin boundary. It can be

seen that two out of four (1111 planes (the A- layers) are identical; in the intermediate layers,

the close-packed directions are codirectional but

not collinear. The displacement is illustrated in Figure 9.

0 COMhlCf4 PLANE A

x C PLANE CRYSTAL I, B PLANE CRYSTAL II

+ B PLANE CRYSTAL I, C PLANE CRYSTAL II

FIGURE 9. Diagram illustrating the stacking sequence of parallel common ( 111) planes for a bicrystal in which 4 = 60”.

Consideration of Figure 6 shows that the yield stress reached a maximum value of 130 gms/mmz at approximately 4 = 30’ (the maximum slip direction orientation difference) and remained con- stant up to 4 = 60”. There is a notable exception to this at + = 40” Here the yield stress values reach as high as 170 gms/mm *. These values were first considered to be in error since the operation of the slip system considered to be active (Figure 1)

would result in a yield stress curve symmetrical about d = 60”. It was pointed out, however, that a new slip system becomes more favourably oriented for slip (in one crystal only) at approximately + = 4o”.* The original slip system again becomes operative beyond 4 = 60”. It is possible that the operation of a different slip system could cause the large yield stress observed at 4 = 40”.

It is possible that the bicrystal specimens do actually begin yielding at the same stresses as the corresponding single crystals. Dislocations within the crystals far removed from the boundary would be expected to move at the same stress as in the single crystal. It is suggested that the boundary causes the moving dislocations to ‘pile up’ and effect a rapid increase in the stress necessary to (1)

*The authors are indebted to Dr. R. Maddin for this sug- gestion. At q~ = 40” the slip system in both crystals was expected to correspond to x = 45”, X = 48”(sin x cos X = 0.472). However, in the crystal rotated 20” in the counterclockwise direction, a system having x = 42” and X = 44” (sin x cos X = 0.474) is more likely to operate. At least, it could interfere with the initiation of slip.

CLARK AND CHALMERS: ALUMINIUM BICRYSTALS 85

move other dislocations and (2) produce the large number of new dislocations required to cause observable deformation. In this way, it would be possible to reach the stress required to overcome the slip inhibiting effect of the boundary before any observable plastic deformation had occurred. It might well be expected that the inhibiting effect would become less as the position 4 = 60” is approached. Here, the crystals have one out of every three planes common in every sense to both crystals. Examination of Figure 6 shows that while the yield stress of the bicrystals is essentially con- stant from 4 = 30” to 9 = 60”, the yield stress of the single crystals is increasing and reaches a maximum at 8 = 30” (equivalent to 4 = 60”). The differences between the yield stresses of single crystals and the corresponding bicrystals are a measure of the inhibiting effect of the boundary; they are listed in Table II. It can be seen that at $ = 60’ the boundary causes a smaller increase in the yield stress than at 4 = 30”.

TABLE II

Yield Stress gms/mm*

S. Crystals 90 90 92 95

100

Bicrystals

90 118 126 130 130

Difference d gms/mm* Degrees

0 0 28 12

34 22

35 40

30 60

Examination of Figure 7 shows that, as well as inhibiting the initiation of the deformation process, the presence of the boundary increased the rate of strain hardening. In the initial stages of the plastic deformation, the relation between the stress and strain was linear. The slope of this region was greatest at 4 = 60” the position of maximum orientation difference. The difference between the slope

as

0 de for the bicrystals and the single crystals is a

measure of increase in the rate of strain hardening caused by the boundary. These differences are listed in Table III.

Comparison of the increase in yield stress (Table II) with the increase in the rate of work-hardening (Table III) shows that the boundary has a more marked effect in inhibiting the progress of the deformation process than in its initiation. Since no definite yield point was observed (as for example with mild steel) the values used are relative to one

TABLE III

dS

0 z gms/mm*

Difference 4 gms/mm2 Degrees

S. Crystals Bicrystds 0.6 0.6 0.8 1.4 0.9 2.2 1.2 3.4 1.5 4.9 1.4 3.8

0 0 0.6 12 1.1 22

2.2 40 3.4 60 2.4 74 = 46

another and may or may not be of physical signi- ficance with regard to the initiation of the deforma-

ds tion process. The slope de ,

0 however, is an experi-

mental observation not dependent on a definition; it is a direct measure of the mutual interaction effect of the two crystals.

The general stress-strain curve for single crystals of face-centered cubic metals is parabolic in form and shows intense work-hardening. However, such single crystals of high purity oriented for single slip have shown regions of ‘easy’ glide similar to the laminar flow of hexagonal metals [2630]. Masing and Raffelsieper [29] found that the region of ‘easy’ glide in aluminium crystals became smaller as the initial orientation approached one of multiple slip. The initial orientation C$ = 0” is one of single slip. At + = 60” the crystals are oriented for double slip; specimens 74 and 7, (# = 60”) showed the shortest ‘easy’ glide regions. The termination of the ‘easy’ glide has been related to the start of double glide in a-brass [28]. The general conclusion is that when the “laminar flow” breaks up into a more complex process, the work-hardening becomes more intense. Comparison of the single and bicrystal stress-strain curves (Table I) shows that the presence of the boundary made the ‘easy’ glide region shorter as the orientation difference between the crystals increased. This might well be interpreted as evidence of a more complex deformation process in the boundary vicinity, since the termination of laminar flow is associated with multiple slip or inhomo- geneous lattice rotations. Since slip is increasingly inhibited as the orientation difference of the crystals is increased, greater resolved shear stresses can be applied to latent slip systems causing the most favourable of them to become active. The more active slip systems there are, the more complex is the deformation process and, as a result, the greater is the rate of work-hardening.

86 ACTA METALLURGICA, VOL. 2, 1954

From the experimental yield-stress values obtained at 4 = O”, the critical resolved shear stress (6) necessary to cause plastic deformation was calculated to be 45 gms/mm2. Using this value and the relation 6 = p sin x cos X the curve relating the yield stress p to the crystal orientations tias plotted. It can be seen from Figure 6 that the observed and expected yield-stress values agree extremely well.

Acknowledgment

The financial assistance of the Defense Research Board of Canada, and a summer grant from the School of Engineering Research, University of Toronto, are gratefully acknowledged.

The authors wish to thank their colleagues in the Department of Metallurgical Engineering, Univer- sity of Toronto, for their helpful discussion.

1. 2.

3.

4.

5. 6. 7. 8.

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mechanical deformation of aluminium bicrystals

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