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Plastic deformation of aluminium bicrystals having ∑7 and ∑21 coincidence tilt boundaries
PLASTIC DEFORMATION OF ALUMINIUM BICRYSTALS HAVING 27 AND C21 COINCIDENCE TILT BOUNDARIES S MIURA,’ K. HAMASHIMAZ andK. T. AUST3 ‘Department of Engineering Science. Faculty of Engineering Kyoto University, Kyoto, Japan 2Department of Mechanical Engineering. Faculty of Engineering. Doshisha University. Kyoto, Japan and 3Department of Metallurgy and Materials Science, University of Toronto, Toronto, Ontario, Canada (Received 26 February 1980)
Abstract-Three types of isoaxial summetrical bicrystals and their component single crystals were tested in tension to clarify the effect of the grain boundary on plastic properties. The (11 I) oriented bicrystal was deformed by the mode similar to that of the (111) oriented single crystal. Fine multiple slip which appeared from the early stage of plastic deformation was suppressed at the boundary. It was found that the flow stress of this bicrystal was almost equal to that of the component single crysml and. the effect of grain boundary on the flow stress did not appear. Two bicrystals having the Z7 and X21 coincidence tilt boundary were deformed by single slip at the early stage of plastic deformation. The flow stress of each bicrystal was increased by the presence of the boundary. The boundary strength rapidly increased from the yield point to 0.5% strain by the interaction between primary slip and additional stip in the vicinity of the boundary; onfy a shght increase was observed from about l.O-S.Op/bstrain. The effect of the grain boundary on the flow stress of the bicrystal is prominent by introducing multiple slip near the grain boundary in the stage I region of the component single crystal but not prominent in the stage I1 region. The effect of the grain boundary on the flow stress is negligible after multiple slip takes place away from the boundary in the adjoining grains. RcUm&Nous avons deform& en traction trois types de bicristaux isoaxiaux symetriques et les monocristaux qui les constituent afin de pr&iser i’influena du joint de grains sur les propriettes plastiques. Le bicristal (I 11) a subi fe mime mode de deformation que Ie monocristal (Ill}. Le fin glissement multiple, qui apparait dts its premiers stades de la d~fo~ation, ftait supprime au joint. La contrainte d’&ouiement de cc bicristal ttait pratiquement igale a celle du monocristal composant et le joint de grains ne modifiait apparemmcnt pas la limite tlastique. Nous avons dCformi en glissement simple deux bicristaux prisentant dcs joints de torsion de comcidence 17 et Z21 et nous avons en ttudie les premiers stades de la deformation plastique. La contrainte d’&oulement des deux bicristaux Ctait augmentC par la presence du joint. La resistance m&anique du joint augmentait rapidement de la limite elastique a une dtformation de 05% du fait dune interaction entrc le glissemeat primaire et des glissements secondaires au voisinage du joint; on n’observait msuite qu’une faibie augmentation pour une deformation comprise entre 14% environ. Le joint de grains influe notablem~t sur la contrainte ~~coulement du bicristal en intr~ui~t du glissement multiple au voisinage du joint dans le stade I des monocristal composant, mais cette influence est faible darts le stade Il. L’influence du joint de grains sur la contraiate d’Ccoulemmt deviant t&&eable lorsque le glissement multiple se dtveloppe loin du joint darts Ies grains adjaccnts. Zmms~Ea wurden drei isoaxial symmetrische Bikristalle und deren Komponenten-Einkristalle im Zugversuch verformt, urn den Eingug der Korngrenze auf die plastischm Eingmschaften zu untersuchen. Der (111 )-orientierte Bikristall wurde in einer iihnlichm Art wie der (1 ll)-orientierte Einkristall verformt. Die feine Vielfachgleitung, die von Anfang der plastischen Verformung an at&rat, war an der Korugrenze unt~~~ckt. Es ergab sicb, dal3 die ~ie~s~nung dieses Bikristalies nabezu gleich der des Korn~n~t~-Eink~s~ll~ war; die FlieBs~ung war durch die Komgrenze nicht beeinBu&. Zwei Bikristalle mit 2% und ZZl-Koiruidenz-Kippgretuen verformten sich zu Anfang in Einfachgleirung. Die FlieBspatmung eines jeden Bikristalles war durch die Korngrettze erhaht. Die Komgmnzfestigkeit erhbhtc sich rasch zwischen FlicBpunkt und O,S% Dehnung wegen der Wechselwirkung zwischen prim&rer und zut&zBcher Gleitung in der N&be der Grenze; zwischcn 1,0 und S,Oo/,Dehnung wurde ein nur schwacher Ansticg beobachtet. Der BinfluB tier Komgrenze auf die FlieBspatmung des Bikristalles ist deutlich im Bereich I des Komponenten-EinkristaJks dadurcb, &al3 Vielfachgleittmg in der Nilhe der Komgrenze auftritt; im Bereich II ist der EinfluB unbedeutcnd. Der EinfluD der Komgrenze wird v~~~ig~, wenn Vielf~~tung in den angenzcnden K~mem--entfemt von der Komgrenze-auftritt.
1. INTRODUCTION It is well known that the deformation mode and mechanical properties of polycrystalline materials are influenced by the grain boundary. This result arises
from the interaction of neighbouring grains across the grain boundary. To clarify the effect of the grain boundary, investigations have been performed by
many workers using bicrystal specimens of aluminum
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[l-lo], B-Brass [ll J, and Fe-% [12]. Changes in the yield stress and flow stress due to the existence of the grain boundary, effects of crystal orientation and misorientation of the bicrystal on the flow stress, and slip systems at the boundary, were studied in detail. As a result of these studies, it was determined that the effect of grain boundaries on the flow stress is caused chiefly by the back stress of piled-up dislocations, the multiple slip due to compatibility at the boundary and the stress concentration of piled-up dislocations in the neighbouring grain. The importance of the coincidence boundary model in the interpretation of grain boundary structures is indicated in many studies, e.g., Refs [ 13-221. It is considered that the coincidence boundary has smaller boundary-energy than the random boundary due to the regularity of atomic configuration in the coincidence boundary. However, the effect of the coincidence boundary on the plastic deformation of a bicrystal has not been studied, except for the work on the E7 twist boundary in aluminum by Inoko et al. [23], and on the ES tilt boundary in aluminum by Miura and Saeki [24]. Moreover, the bicrystals, which are deformed by multiple slip from the beginning of plastic deformation, are considered to be relevant to the polycrystal in plastic deformation. (Such bicrystals are described as bicrystals having multiple-slip-orientation in this paper.). Davis et al. [3] compared the flow stress of bicrystals having multiple-slip-orientation with those of their component single crystals; however, their detailed deformation modes were not known. In the present investigation, three types of isoaxial symmetric bicrystals were tested in tension. The bicrystal having a (111) tensile orientation and a 27 coincidence tilt boundary. was examined to clarify the interaction of the grain boundary and multiple slip. Two bicrystals, which are deformed by single slip at an early stage of plastic deformation, having a E7 and Z21 coincidence tilt boundary were also examined to clarify the effect of the grain boundary on flow stress and the occurrence of additional slip in the vicinity of the grain boundary.
2 EXPERIMENTAL
PROCEDURE
The material used in this experiment was 99.99% pure ahmrinum. Single crystals having the desired orientation, were prepared as seed crystals. TWO seed crystals, each 6 mm in diameter and 60 mm in length were positioned in a graphite mould so that both seed crystals were symmetrically rotated around their central axis by a desired misorientation. Bicrystals of 2 x 17 x 250 mm* in size were grown from these seeds by the Bridgman method in a vacuum of 10m6mm Hg. Specimens having a gauge dimension of 2 x 5 x 15 mm3 were obtained from the bicrystals by spark cutting. The specimens were annealed at 823 K for 3 hrs and then electrolytically
polished. All specimens had a grain boundary in the central section and parallel to the tensile direction in subsequent tensile testing. In Fig. l(a)+). the orientations of these isoaxial bicrystal specimens are shown. In this paper. the bicrystal specimens shown in Fig. l(a)-(c). are termed (111)-X7 bicrystal. Stage I-27 bicrystal and Stage I-E21 bicrystal, respectively. The component single crystals of the (111)~17 bicrystal have a [ 11l] tensile orientation and are deformed by triple slip from the beginning of plastic deformation. The component single crystals of the Stage I-E7 and Stage I-Z21 bicrystals are deformed by single slip at an early stage of plastic deformation, i.e. they have Stage I region. (Such a bicrystal is described as a single-slip-oriented bicrystal in this paper). Furthermore, the boundaries of (111)~27 bicrystal or Stage I-Z7 bicrystal and Stage I-E21 bicrystal are E7 and X21 tilt coincidence boundaries (38.2” and 21.8” around (111) axis respectively). The geometrical position of the (111) coincidence plane in these bicrystals, is illustrated in Fig. Z(a)-(c). The accuracy with which the misorientations and boundary plane of the bicrystals could be controlled was within f0.5” and f 1” respectively. Tensile tests were carried out at a strain rate of 4 x 10m5 s-i at 293 f 2 K. Slip line observation was made at each stage of deformation.
3. EXPERIMENTAL
RESULTS
3.1. Plasric deformation of (111 )-X7 bicrystal The stress-strain curves of the (Ill)-17 bicrystal and its component single crystal are shown in Fig. 3. The two curves show a similar behaviour, namely. their flow stress increases rapidly due to interaction of multiple slip at the initial stage of plastic deformation. subsequently increases gradually with decreasing work hardening rate until failure of the specimen. It is found that the flow stress of this bicrystal is almost equal to that of the component single crystal from the yield point to the final strain. These results are in accord with conclusion of Davis et al. [3]:- the flow stress of bicrystals having various multiple slip orientations is almost qua1 to that of the component single crystal at Stage II. It is found that the deformation mode of this bicrystal is similar to that of its component single crystal, by surface observation. When the deformation has started, fine multiple slip takes place almost homogeneously in the whole region of the specimen. as shown in Fig 4. This multiple slip becomes finer and denser with increasing deformation, but the clustered slip or cross slip is not observed until failure. This fine multiple slip occurs due to the frequent interruption of slip, caused by obstacles such as sessile dislocations. The deformation mechanism is similar to that of a (111) oriented single crystal, as reported previously [25].
MIURA. HAMASHIMA
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ii0
loi Y
101
Y
B-groin
A-grain SurfOCe
X
Normol 10 top
Y
Normal to side surface
2
Tensile axis
A-qoin
(cl
Fig. 1. Orientation of bicrystals. termed (a) (111 )X7 (b) Stage I-X7 (c) Stage I521
3.2. Plastic deformation of single-slip-oriented bicrystols 3.2.1. Flow stress. The critical resolved shear stress of Stage I-Z7 bicrystal, Stage 1421 bicrystal, (1 11)27 bicrystal and their component single crystals are given in Table 1. It is found that the critical resolved shear stress of the bicrystal is equal to that of its component single crystal. It is evident that the deformation mechanism of the bicrystal is not influenced
by the presence of the grain boundary at this stage of deformation. Generally, it is believed that piled-up dislocations against a grain boundary complicate the deformation mechanism or deformation mode in the vicinity of the grain boundary at macroscopic plastic deformation. However, at elastic deformation or instantly after yield, it is considered that the deformation property of a bicrystal is influenced very little by
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MIURA, HAMASHIMA AND AUST: III - I;7
PLASTIC DEFORMATION OF BICRYSTAU stage I -x21
Stage I- 27
hatching
plone
is
(I
II)
coincidence
pIOne
Fig. 2. Schematic illustration of the (11If coincidence plane in the three tyPes of bicrystals studied.
the presence of a grain boundary owing to elastic isotropy in the case of isoaxial symmetric bicrystals used in this study. The stress-strain curves of the Stage I-E7 bicrystal and its com~nent single crystal are shown in Fig. 5. It is found that the flow stress of the bicrystal is slightly larger than that of its component single crystal in the entire stage of deformation. The stressstrain curve of the bicrystal inclines steeper than that of its component single crystal from the yield point to 0.3% strain, and has inflection points at 0.3% strain and 2.00/, strain. In Fig. 6, stress-strain curves of Stage I-Z21 bicrystal and its component single crystal are shown. The tendency of these curves is similar to the case of the Stage I-X7 series. Namely, a difference of work hardening rate is found from the yield point to 0.6% strain, and inflection points are found at 0.6% strain and 3.0% strain. 3.2.2. Slip line observation. When the plastic deformation of Stage 1-X7 bicrystal proceeds, primary slip: (111) [lOi] is observed immediately after yielding, and conjugate slip is observed after a plastic strain of 0.4-0.50,, In the vicinity of the grain boundary, additiona slip corresponding to the trace of (lil), which is considered to be induced by the primary slip
20
v
-mtxystor ----Compamnt
of the neighbouring grain, appears in the initial stage of deformation. Furthermore, additional slip corresponding to the trace of (111) is also observed at the larger strain region. Figure 7 shows the top surface of this biaystal specimen stretched by 5.6% strain. It is found that the primary slip: (117) [loll and the conjugate slip: (Iii) [IlO] are activated in both grains and the additional slip corresponding to (171) or (111) is introduced in the vicinity of the grain boundary. In the-case of the Stage IS21 bicrystal, the primary slip: (111) [lOI] appears imm~iately after yielding, but the conjugate slip or additional slip is rarely observed on the surface throughout plastic deformation. Figure 8 is a photograph taken on the top surface of this bicrystal stretched by 5.1% strain. Only primary slip and kink bands normal to primary slip, are found. 4. DISCUSSION 4.1. The crystal having multiple slip orientation and the grain boundary The fine multiple slip, taking place during plastic defor~tion of the (11 I)Z7 bicrystal, is suppressed by the grain boundary and cannot pass through the boundary (Fig. 4). Furthermore, it is considered that
houinQ
m
n
gmln beundory
uyll0l
I
Fig. 3. Stress-strain curves of a
bicrystal and the component single crystal.
MIURA. HAMASHIMA
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PLASTIC DEFORMATION
OF BICRYSTALS
.-c
0, CT
4
.-c u
b
cl,
1595
cs c ._
s! iij
I
EE
5
MIURA.
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Crystal
AND
HAMASHIMA
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shear stress of bicrystals and single crystals (MN mZ) Stage-127
Stage I-E.21
1.13
Bicrqstal Component single cr~stai
1.13 I.23
I .O’
(111)27 1.09
where z is the stress concentration factor. and 7 is the shear stress through the boundary which is associated with a slip system i in crystal A which has a slip plane normal pi and a slip direction 8,. In the above equation, (ei’ej~$i’$j)
Livingston and Chalmers [4] and Hauser and Chalmers [6] have shown that the additional .shear stress 5 on a slip system j in a neighbouring grain B, which has ej as its slip plane normal and gj as its slip direction. can be expressed by
-
OF BICRYSTALS
1.09
this multiple slip induces very little. if any. additional slip in the neighbouring grain beyond the grain boundary. After the plastic deformation starts, triple slip is jmmedjatel~ activated in the crystal having the (Ill> tensile orientation. In such a crystal, the slip lines become short and fine due to mutual interaction, and they cannot pass through the boundary and are suppressed by the grain boundary. However, it is not only the grain boundary that interrupts the fine multiple slip. The multiple slip is interrupted much more frequently by obstacles such as sessile dislocations formed by slip interaction; as a result the effect of the grain boundary on the flow stress of the (111) oriented bicrystal is minimized. Previously, Miura and Saeki [24] reported that the grain boundary had no apparent effect on the flow stress of (100) oriented bicrystals. It is concluded that the presence of the grain boundary has very little effect on the flow stress of a bicrystal having a multiple slip orientation.
7 =
DEFORMATION
r:(ri’uj)(gi’$j)
+
(ei’$j)(ej*$i))Ti
(1)
single
(ei’$,XCJj’$i)
=
6ij
(2)
is called the transmission factor. They also reported good agreement between their experimental result and their prediction of additional slip being due to the value of Ni,. The larger the .hIij value of the slip system j. the easier slip of slip system j is induced by slip of slip system i. The total shear stress 7, on the stip system j will be the sum of 7 and the applied shear stress on this system, that is Tc =
Tj
+
YjVij’ti
(3)
Considering the case of the isoaxial bicrystal the primary slip system of both grains is denoted as i. and the slip system of the neighbouring grain respective to i, is taken as j, and putting the Schmidt factors of the i and j systems as mp and m respectively. then equation (3) will be given by 75,= Ti(~~~Z~+ X’N,j)
(4)
Saeki and Miura [lo] found that equation (3) was suitable to predict the slip systemj induced by the slip system i considering the values of Nij and m, t71P As the bicrystals used in this investigation are isoaxiaf symmetric bicrystals, it is considered that the com~nents of plastic strain in both grains are compatible at the grain boundary plane. The additional slip, shown in Fig. 7 (5.60/, strain), is the one which appeared at 0.4-0.5~0 strain and becomes more distinct after a larger amount of deformation. It is evident that this additional slip is activated immediately
~Bicrysfal ho&q 821 grain bolndory --- Componentsingle crystal
Blcrystol hovlng 27 grain boundary
---Component
+
crystal
-I
z
I
Strain
r (%)
Fig. 5. Stress-strain curves of a Stage I-X.7 bicrystal and the component single crystal.
0
I
2
Strotn
3
c (%f
Fig. 6. Stress-strain curves of a Stage I-El bicrystal and the component single crystal.
MIURA. HAMASHIS4A
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Table 2. iy, values against each slip system in the B-grain due to (I 11) [IOI] slip system in the A-grain for (a) Stage I-27 bicrystal (b) Stage f-K?1 bicrystal (a) Slip plane
Slip direction
tgg (111) :%I;
(ITI) (iii)
;z; f%:
wt1
;t::j (1i-l) :%;
)?I %
.Ki, i: (I ti, [lOi]
0.211
0.920 0.118 0.713 0.528 0.854 0.330 0.538 0.435
0.485 0.299 0.018 0.204
;z 0:037 0.42 I
0.361 0.307 0.671 0.293 0.898 0.607 0.709 0.239 0.588 0.511 0.430 0.066
m 0.446 0.057 0.346 0.256 0.414 0.160 0.261
(b) Slip plane
Slip direction
nr m 0.420 0.135 0.282 0.182 0.354 0.153 0.210 0.262 0.493 0.144 0.024 0.119
n’P
0.852 0.274 0.572 0.369 0.700 0.310 0.426 0.531
zij i:(1II)[lOlJ
0.544 0.210 0.633 0.013 0.633 0.636 0.549 0.018 0.570 0.521 0.580 0.004
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m!m, = 0.700). Therefore,
slip of (171) [ 1 lo] must be induced by the primary- slip of the neighbouring grain at the vicinity of the grain boundary. However, additional slip on (171) is hardly observed as shown in Fig. 8. since the [I 101 direction in the Stage I-Z21 bicrystal is nearly parallel to the top surface [Fig. l(c)]. Furthermore. as the :Ylj value for primary slip of the ne~~hbol!ring grain in the Stage I-E?1 bicrystal is generally lower than that in the Stage I-17 bicrystal. it is considered that the frequency of occur-
rence of additional slip in the Stage I-X21 bicrystal is lower than that in the Stage I-27 bicrystal. However. most careful observations with higher magnification of Stage I-E21 bicrystal show the additional slip traces not only on (lil) but also on (Ill) in the vicinity of boundary as shown in Fig. 9. On the basis of Table 2(b), the slip system of additional slip on (111) is considered to be (Ill) ClOT]. having relatively large values of Nij and rn,$, (h’,, = 0.544, m/mp = 0.852). 4.3. Tire boundary strength ar?d the deformation mode
In the isoaxial symmetrical bicrystal. the macroscopic compatibility of the strain component is satisCl 101 fied in three directions at the grain boundary piane. Therefore, Livingston and Chalmers [47 concluded (Iii) EfZ$ that the ffow stress of the isoaxial symmetrical bilOit1 crystal was not affected by the presence of the grain (1 Ii) [bll$ boundary, since an increase of flow stress due to the 1.ooo [loll occurrence of additional slip at the vicinity of the 0.292 Ellol (II-I) grain boundary did not appear. 0.049 Eziij 0.241 However, in this study additional slip is observed at the vicinity of the grain boundary in the Stage I-Z7 bicrystal, which was an isoaxial symmetrical bicrystal. after yield. Therefore, the slip system of the additional The flow stress of this bicrystal is slightly larger than slip can be predicted with use of the Nij and m/mp that of its component single crystal (Fig. 5). As a values. result, it is apparent that the deformation mode of an The values of rn~rn~and Nij for each slip system in isoaxial symmetrical bicrystal can be influenced by the B-grain, due to primary slip system: (117) [liO] in the presence of a grain boundary. The relations between strain and the boundary the A-grain, are shown for Stages I-Z7 bicrystal and Stage I-Z21 bicrystal in Table 2(a) and (b) respectstrength for the Stage I-27 and Stage I-Z21 bicrystals ively. Since these bicrystals are of the isoaxial sym- are shown in Fig. 10. In Fig. 10. the boundary metric type, the value of Nij for the slip system in the strength is the difference in flow stress at the same B-grain due to the slip system in the A-grain, is equal strain between the bicrystal and its component single to that for the slip system in the A-grain due to the crystal. It is evident that the boundary strength inslip system in the B-grain, in each case. creases rapidly in the initial stage of plastic deformaIn Table l(a), it is evident that the slip system in the tion. from the yield point to 0.3q; strain for the Stage B-grain, which has a maximum value of Ni, and a I-17 bicrystal and from the yield point to 0.67; strain large value of m/m,, is (lil) [i lo] (Nij = 0,898. for the Stage I-X21 bicrystal. In the initial strain m/mp = 0.854). As can be seen in Fig. 7. slip on (lil) region, the component single crystals are deformed is induced by the activation of primary slip in the only by primary slip, while in the bicrystals additional Stage I-27 bicrystal. As the result. it is considered that slip induced by piled-up dislocations of primary slip the slip system of this induced slip is (lil) [1 IO]. of the neighbouring grain is active in addition to Similarly, it is considered that the slip system of ad- primary slip. Therefore, it is considered that this rapid ditional slip on (111) shown in Fig. 7 is (111) [IiO], increase of boundary strength arises from the interhaving relatively large values of iv,, and m/mp action between additional slip and primary slip in the 0.671, m/m, = 0.713). vicinity of the grain boundary. In Table 2(b), it is found that the slip system (lil) Fujita er al. [93. using non-isoaxial bicrystals, found [110-j in the B-grain has the maximum value of lvij that at strains less than 0.19; additional slip appeared and a relatively large value of m/m, (Nij = 0.663, and interaction of primary slip and additional slip cq
(111)
(Nij
=
p.~l
1600
ii
W
MIURA. HAMASHIMA
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PLASTIC DEFORMATION
OF BICRYSTALS
MIURA. HAMASHIMA
m
0
I
2
Normal
4
3
Strom
l
AND
5
AUST:
6
7
P/d
Fig. 10. Relation between grain boundary strength strain in Stage I-17 and Stage I-t21 bicrystals. occurred. It is concluded primary slip and additional
PLASTIC DEFORMATION
boundary do influence plasticity. However, in the present study the angles between the Burgers vector. a/2. [loll, on the primary plane (1 Ii) and the line of intersection of boundary plane and primary slip plane were 52” for Stage I-17 and 47’ for Stage I-Z21 crystals, the Burgers vector of a grain boundary dislocation which is formed when a dislocation passes through the boundary will be almost the same. Therefore, the effect of atomic structure of these two bicrystals could not be known in this experiment.
and
that the interaction of slip occurs immediately
after yield in both isoaxial and non-isoaxial bicrystals. The earlier increase of grain boundary strength of the Stage I-Z.7 bicrystal than that of the Stage I-221 bicrystal is consistent with the larger value of maximum Nij in the Stage I-17 bicrystal. From about 1.0% strain to 5.0% strain, the boundary strength of both bicrystals increases slightly. In this strain region, the flow stress of the component single crystal increased rapidly due to the appearance of secondary slip. On the other hand, the low stress of the bicrystal is greatly affected by the interaction between primary slip and secondary slip in each grain of the bicrystal. It is considered that the effect on the flow stress of the bicrystal caused by the interaction of secondary slip and primary slip is much greater than that due to the interaction of additional slip. Therefore, the boundary strength is only slightly increased at this stage of the deformation. At a later stage of deformation (from about 5% strain), the boundary strength of both bicrystals begins to increase again. At this stage, cross slip can occur in the crystal, corresponding to Stage III of the component single crystal. Since the obstacles formed in the crystal can be evaded by double cross slip, the work-hardening-rate of the crystal decreases greatly. In the bicrystal, the deformation mode is more complex due to the additional slip in the vicinity of the grain boundary, and many obstacles formed in the vicinity of the grain boundary cannot be evaded by simple cross slip. Therefore, it is considered that the boundary strength of both bicrystals is increased by the effect of these obstacles. The boundary strength of Stage I-Z7 bicrystal and Stage I-E21 bicrystal is important in the Stage I region of their component single crystals, and is absent in the Stage II region of their component single crystals. It is concluded that the effect of the coincidence grain boundary on flow is largely due to multiple slip introduced in the vicinity of the grain boundary, and is obscured by the appearance of multiple slip in the respective grains. This mechanism is similar to that of the non-isoaxial bicrystal reported by Saeki and Miura [lo]. It is thought that dislocation processes in the
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5. SUMMARY The effects of the grain boundary on the plastic properties of a (111) oriented aluminum symmetric bicrystal having the 27 tilt coincidence boundary. a single-slip-oriented symmetric bicrystal having the X7 tilt coincidence boundary and a single-slip-oriented symmetric bicrystal having the X21 coincidence boundary were studied. It is found that the (111) oriented bicrystal deforms by the mode similar to that of (111) oriented aluminum single crystals. Fine, multiple slip which appears in the entire stage of deformation is suppressed at the boundary, and no effect of the grain boundary on flow stress is observed. In the single-slip-oriented bicrystal having a X7 tilt coincidence boundary. additional slip is observed near the grain boundary and the slip system of the additional slip agrees well with the slip system predicted by the transmission factor Nij and the ratio of Schmid factors. The boundary strength of bicrystals having a X7 tilt coincidence boundary and having a Z21 tilt coincidence boundary, increases rapidly due to the occurrence of additional slip until the appearance of secondary slip in the respective grains. After secondary slip appears, the boundary strength increases slightly and subsequently increases more rapidly at a strain region corresponding to Stage III of the component single crystal. Acknowledgemenrs-The authors wish to thank the Sumitomo Light Metal Industries Ltd. Japan, for the supply of materials. Thanks are due to Dr Y. Saeki of the Nagoya Institute of Technology, Nagoya. Japan for valuable advice and discussion. We acknowledge with gratitude the financial support by the Light Metals Educational Foundation. Japan.
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218, 245 (1960).
6. J. J. Hauser and B. Chalmers. Acra
meroll.
9. 802
(1961).
7. T. Inoko, K. Akizono and G. Mima, .!. Japan Metal
36, 373. 380 (1972).
Insr
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8. 0. lzumi and T. Takasugi, 2. Mere//k. 6S, 542 (1974). 9. H. Fuji@ K. Toyoda and Y. Kanetsuki, Trans. JIM 16, 151 (1975). 10. Y. Saeki and S. Miura, Mechanical Behavior of Marerials. (hoc. 1974 Symp. of Mech. Behavior of Materials, Kyoto, 1974). The Society of Materials Science, Japan), Vol. II, p. 11 (1974). 11. Y. Chuang and H. Margolin, Merafl. Trans. 4, 1905 (1973). 12. R. E. Hook and J. P. Hirth, Acta meroll. IS, 535, 1099 (1967). 13. D. G. Brandon, B. Ralph, S. Raneanathan and M. S. Wald, Acra metall. 12, 813 (1967). 14. D. G. Brandon. Acta metall. 14, 1479 (1966). 15. G. H. Bishop and B. Chalmers. Scripra metal/. 2, 133 (1966).
OF BICRYSTALS
16. M. J. Bain, H. Gleiter and B. Chalmers, J. appl. Phps. 42, 2639 (1971). 17. Y. lshida and M. Mclean, Phil. Mag. 27, 1125 (1973). 18. T. Schober and R. W. Balluffi, Phil. Mag. 21, 109 (1970). 19. G. Hasson and C. Goux, Scripra metal). 5,889 (1971). 20, P. Chaudhari and J. W. Matthews, J. appl. Pkys. 42, 3063 (1971). 21. R. C. Pond and D. A. Smith, Can. Met. Quart. 13, 39 (1971). 22. G. Hermann. G. Baro and H. Gleiter. Acra metal/. 24, 353 (1976). 23. T. Inoko, H. Yamazi, K. Akizono and G. Mima, Nip von Kink.
Gakk 39. 467 (1975).
24. s. Miura and Y. Saeki, kcra herall. 26,93 (1978). 25. S. Miura and K. Hamashima, J. Sot. mater Sci. Japan 27, 1146 (1978).
Abstract-Three types of isoaxial summetrical bicrystals and their component single crystals were tested in tension to clarify the effect of the grain boundary on plastic properties. The (11 I) oriented bicrystal was deformed by the mode similar to that of the (111) oriented single crystal. Fine multiple slip which appeared from the early stage of plastic deformation was suppressed at the boundary. It was found that the flow stress of this bicrystal was almost equal to that of the component single crysml and. the effect of grain boundary on the flow stress did not appear. Two bicrystals having the Z7 and X21 coincidence tilt boundary were deformed by single slip at the early stage of plastic deformation. The flow stress of each bicrystal was increased by the presence of the boundary. The boundary strength rapidly increased from the yield point to 0.5% strain by the interaction between primary slip and additional stip in the vicinity of the boundary; onfy a shght increase was observed from about l.O-S.Op/bstrain. The effect of the grain boundary on the flow stress of the bicrystal is prominent by introducing multiple slip near the grain boundary in the stage I region of the component single crystal but not prominent in the stage I1 region. The effect of the grain boundary on the flow stress is negligible after multiple slip takes place away from the boundary in the adjoining grains. RcUm&Nous avons deform& en traction trois types de bicristaux isoaxiaux symetriques et les monocristaux qui les constituent afin de pr&iser i’influena du joint de grains sur les propriettes plastiques. Le bicristal (I 11) a subi fe mime mode de deformation que Ie monocristal (Ill}. Le fin glissement multiple, qui apparait dts its premiers stades de la d~fo~ation, ftait supprime au joint. La contrainte d’&ouiement de cc bicristal ttait pratiquement igale a celle du monocristal composant et le joint de grains ne modifiait apparemmcnt pas la limite tlastique. Nous avons dCformi en glissement simple deux bicristaux prisentant dcs joints de torsion de comcidence 17 et Z21 et nous avons en ttudie les premiers stades de la deformation plastique. La contrainte d’&oulement des deux bicristaux Ctait augmentC par la presence du joint. La resistance m&anique du joint augmentait rapidement de la limite elastique a une dtformation de 05% du fait dune interaction entrc le glissemeat primaire et des glissements secondaires au voisinage du joint; on n’observait msuite qu’une faibie augmentation pour une deformation comprise entre 14% environ. Le joint de grains influe notablem~t sur la contrainte ~~coulement du bicristal en intr~ui~t du glissement multiple au voisinage du joint dans le stade I des monocristal composant, mais cette influence est faible darts le stade Il. L’influence du joint de grains sur la contraiate d’Ccoulemmt deviant t&&eable lorsque le glissement multiple se dtveloppe loin du joint darts Ies grains adjaccnts. Zmms~Ea wurden drei isoaxial symmetrische Bikristalle und deren Komponenten-Einkristalle im Zugversuch verformt, urn den Eingug der Korngrenze auf die plastischm Eingmschaften zu untersuchen. Der (111 )-orientierte Bikristall wurde in einer iihnlichm Art wie der (1 ll)-orientierte Einkristall verformt. Die feine Vielfachgleitung, die von Anfang der plastischen Verformung an at&rat, war an der Korugrenze unt~~~ckt. Es ergab sicb, dal3 die ~ie~s~nung dieses Bikristalies nabezu gleich der des Korn~n~t~-Eink~s~ll~ war; die FlieBs~ung war durch die Komgrenze nicht beeinBu&. Zwei Bikristalle mit 2% und ZZl-Koiruidenz-Kippgretuen verformten sich zu Anfang in Einfachgleirung. Die FlieBspatmung eines jeden Bikristalles war durch die Korngrettze erhaht. Die Komgmnzfestigkeit erhbhtc sich rasch zwischen FlicBpunkt und O,S% Dehnung wegen der Wechselwirkung zwischen prim&rer und zut&zBcher Gleitung in der N&be der Grenze; zwischcn 1,0 und S,Oo/,Dehnung wurde ein nur schwacher Ansticg beobachtet. Der BinfluB tier Komgrenze auf die FlieBspatmung des Bikristalles ist deutlich im Bereich I des Komponenten-EinkristaJks dadurcb, &al3 Vielfachgleittmg in der Nilhe der Komgrenze auftritt; im Bereich II ist der EinfluB unbedeutcnd. Der EinfluD der Komgrenze wird v~~~ig~, wenn Vielf~~tung in den angenzcnden K~mem--entfemt von der Komgrenze-auftritt.
1. INTRODUCTION It is well known that the deformation mode and mechanical properties of polycrystalline materials are influenced by the grain boundary. This result arises
from the interaction of neighbouring grains across the grain boundary. To clarify the effect of the grain boundary, investigations have been performed by
many workers using bicrystal specimens of aluminum
1591
1592
MIURA, HAMASHIMA
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PLASTIC DEFORMATION OF BICRYSTALS
[l-lo], B-Brass [ll J, and Fe-% [12]. Changes in the yield stress and flow stress due to the existence of the grain boundary, effects of crystal orientation and misorientation of the bicrystal on the flow stress, and slip systems at the boundary, were studied in detail. As a result of these studies, it was determined that the effect of grain boundaries on the flow stress is caused chiefly by the back stress of piled-up dislocations, the multiple slip due to compatibility at the boundary and the stress concentration of piled-up dislocations in the neighbouring grain. The importance of the coincidence boundary model in the interpretation of grain boundary structures is indicated in many studies, e.g., Refs [ 13-221. It is considered that the coincidence boundary has smaller boundary-energy than the random boundary due to the regularity of atomic configuration in the coincidence boundary. However, the effect of the coincidence boundary on the plastic deformation of a bicrystal has not been studied, except for the work on the E7 twist boundary in aluminum by Inoko et al. [23], and on the ES tilt boundary in aluminum by Miura and Saeki [24]. Moreover, the bicrystals, which are deformed by multiple slip from the beginning of plastic deformation, are considered to be relevant to the polycrystal in plastic deformation. (Such bicrystals are described as bicrystals having multiple-slip-orientation in this paper.). Davis et al. [3] compared the flow stress of bicrystals having multiple-slip-orientation with those of their component single crystals; however, their detailed deformation modes were not known. In the present investigation, three types of isoaxial symmetric bicrystals were tested in tension. The bicrystal having a (111) tensile orientation and a 27 coincidence tilt boundary. was examined to clarify the interaction of the grain boundary and multiple slip. Two bicrystals, which are deformed by single slip at an early stage of plastic deformation, having a E7 and Z21 coincidence tilt boundary were also examined to clarify the effect of the grain boundary on flow stress and the occurrence of additional slip in the vicinity of the grain boundary.
2 EXPERIMENTAL
PROCEDURE
The material used in this experiment was 99.99% pure ahmrinum. Single crystals having the desired orientation, were prepared as seed crystals. TWO seed crystals, each 6 mm in diameter and 60 mm in length were positioned in a graphite mould so that both seed crystals were symmetrically rotated around their central axis by a desired misorientation. Bicrystals of 2 x 17 x 250 mm* in size were grown from these seeds by the Bridgman method in a vacuum of 10m6mm Hg. Specimens having a gauge dimension of 2 x 5 x 15 mm3 were obtained from the bicrystals by spark cutting. The specimens were annealed at 823 K for 3 hrs and then electrolytically
polished. All specimens had a grain boundary in the central section and parallel to the tensile direction in subsequent tensile testing. In Fig. l(a)+). the orientations of these isoaxial bicrystal specimens are shown. In this paper. the bicrystal specimens shown in Fig. l(a)-(c). are termed (111)-X7 bicrystal. Stage I-27 bicrystal and Stage I-E21 bicrystal, respectively. The component single crystals of the (111)~17 bicrystal have a [ 11l] tensile orientation and are deformed by triple slip from the beginning of plastic deformation. The component single crystals of the Stage I-E7 and Stage I-Z21 bicrystals are deformed by single slip at an early stage of plastic deformation, i.e. they have Stage I region. (Such a bicrystal is described as a single-slip-oriented bicrystal in this paper). Furthermore, the boundaries of (111)~27 bicrystal or Stage I-Z7 bicrystal and Stage I-E21 bicrystal are E7 and X21 tilt coincidence boundaries (38.2” and 21.8” around (111) axis respectively). The geometrical position of the (111) coincidence plane in these bicrystals, is illustrated in Fig. Z(a)-(c). The accuracy with which the misorientations and boundary plane of the bicrystals could be controlled was within f0.5” and f 1” respectively. Tensile tests were carried out at a strain rate of 4 x 10m5 s-i at 293 f 2 K. Slip line observation was made at each stage of deformation.
3. EXPERIMENTAL
RESULTS
3.1. Plasric deformation of (111 )-X7 bicrystal The stress-strain curves of the (Ill)-17 bicrystal and its component single crystal are shown in Fig. 3. The two curves show a similar behaviour, namely. their flow stress increases rapidly due to interaction of multiple slip at the initial stage of plastic deformation. subsequently increases gradually with decreasing work hardening rate until failure of the specimen. It is found that the flow stress of this bicrystal is almost equal to that of the component single crystal from the yield point to the final strain. These results are in accord with conclusion of Davis et al. [3]:- the flow stress of bicrystals having various multiple slip orientations is almost qua1 to that of the component single crystal at Stage II. It is found that the deformation mode of this bicrystal is similar to that of its component single crystal, by surface observation. When the deformation has started, fine multiple slip takes place almost homogeneously in the whole region of the specimen. as shown in Fig 4. This multiple slip becomes finer and denser with increasing deformation, but the clustered slip or cross slip is not observed until failure. This fine multiple slip occurs due to the frequent interruption of slip, caused by obstacles such as sessile dislocations. The deformation mechanism is similar to that of a (111) oriented single crystal, as reported previously [25].
MIURA. HAMASHIMA
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PLASTIC DEFORMATION
OF BICRYSTALS
1593
ii0
loi Y
101
Y
B-groin
A-grain SurfOCe
X
Normol 10 top
Y
Normal to side surface
2
Tensile axis
A-qoin
(cl
Fig. 1. Orientation of bicrystals. termed (a) (111 )X7 (b) Stage I-X7 (c) Stage I521
3.2. Plastic deformation of single-slip-oriented bicrystols 3.2.1. Flow stress. The critical resolved shear stress of Stage I-Z7 bicrystal, Stage 1421 bicrystal, (1 11)27 bicrystal and their component single crystals are given in Table 1. It is found that the critical resolved shear stress of the bicrystal is equal to that of its component single crystal. It is evident that the deformation mechanism of the bicrystal is not influenced
by the presence of the grain boundary at this stage of deformation. Generally, it is believed that piled-up dislocations against a grain boundary complicate the deformation mechanism or deformation mode in the vicinity of the grain boundary at macroscopic plastic deformation. However, at elastic deformation or instantly after yield, it is considered that the deformation property of a bicrystal is influenced very little by
1594
MIURA, HAMASHIMA AND AUST: III - I;7
PLASTIC DEFORMATION OF BICRYSTAU stage I -x21
Stage I- 27
hatching
plone
is
(I
II)
coincidence
pIOne
Fig. 2. Schematic illustration of the (11If coincidence plane in the three tyPes of bicrystals studied.
the presence of a grain boundary owing to elastic isotropy in the case of isoaxial symmetric bicrystals used in this study. The stress-strain curves of the Stage I-E7 bicrystal and its com~nent single crystal are shown in Fig. 5. It is found that the flow stress of the bicrystal is slightly larger than that of its component single crystal in the entire stage of deformation. The stressstrain curve of the bicrystal inclines steeper than that of its component single crystal from the yield point to 0.3% strain, and has inflection points at 0.3% strain and 2.00/, strain. In Fig. 6, stress-strain curves of Stage I-Z21 bicrystal and its component single crystal are shown. The tendency of these curves is similar to the case of the Stage I-X7 series. Namely, a difference of work hardening rate is found from the yield point to 0.6% strain, and inflection points are found at 0.6% strain and 3.0% strain. 3.2.2. Slip line observation. When the plastic deformation of Stage 1-X7 bicrystal proceeds, primary slip: (111) [lOi] is observed immediately after yielding, and conjugate slip is observed after a plastic strain of 0.4-0.50,, In the vicinity of the grain boundary, additiona slip corresponding to the trace of (lil), which is considered to be induced by the primary slip
20
v
-mtxystor ----Compamnt
of the neighbouring grain, appears in the initial stage of deformation. Furthermore, additional slip corresponding to the trace of (111) is also observed at the larger strain region. Figure 7 shows the top surface of this biaystal specimen stretched by 5.6% strain. It is found that the primary slip: (117) [loll and the conjugate slip: (Iii) [IlO] are activated in both grains and the additional slip corresponding to (171) or (111) is introduced in the vicinity of the grain boundary. In the-case of the Stage IS21 bicrystal, the primary slip: (111) [lOI] appears imm~iately after yielding, but the conjugate slip or additional slip is rarely observed on the surface throughout plastic deformation. Figure 8 is a photograph taken on the top surface of this bicrystal stretched by 5.1% strain. Only primary slip and kink bands normal to primary slip, are found. 4. DISCUSSION 4.1. The crystal having multiple slip orientation and the grain boundary The fine multiple slip, taking place during plastic defor~tion of the (11 I)Z7 bicrystal, is suppressed by the grain boundary and cannot pass through the boundary (Fig. 4). Furthermore, it is considered that
houinQ
m
n
gmln beundory
uyll0l
I
Fig. 3. Stress-strain curves of a
bicrystal and the component single crystal.
MIURA. HAMASHIMA
AND
AUST:
PLASTIC DEFORMATION
OF BICRYSTALS
.-c
0, CT
4
.-c u
b
cl,
1595
cs c ._
s! iij
I
EE
5
MIURA.
1596 Table I. Critical
Crystal
AND
HAMASHIMA
AUST:
PLASTIC
shear stress of bicrystals and single crystals (MN mZ) Stage-127
Stage I-E.21
1.13
Bicrqstal Component single cr~stai
1.13 I.23
I .O’
(111)27 1.09
where z is the stress concentration factor. and 7 is the shear stress through the boundary which is associated with a slip system i in crystal A which has a slip plane normal pi and a slip direction 8,. In the above equation, (ei’ej~$i’$j)
Livingston and Chalmers [4] and Hauser and Chalmers [6] have shown that the additional .shear stress 5 on a slip system j in a neighbouring grain B, which has ej as its slip plane normal and gj as its slip direction. can be expressed by
-
OF BICRYSTALS
1.09
this multiple slip induces very little. if any. additional slip in the neighbouring grain beyond the grain boundary. After the plastic deformation starts, triple slip is jmmedjatel~ activated in the crystal having the (Ill> tensile orientation. In such a crystal, the slip lines become short and fine due to mutual interaction, and they cannot pass through the boundary and are suppressed by the grain boundary. However, it is not only the grain boundary that interrupts the fine multiple slip. The multiple slip is interrupted much more frequently by obstacles such as sessile dislocations formed by slip interaction; as a result the effect of the grain boundary on the flow stress of the (111) oriented bicrystal is minimized. Previously, Miura and Saeki [24] reported that the grain boundary had no apparent effect on the flow stress of (100) oriented bicrystals. It is concluded that the presence of the grain boundary has very little effect on the flow stress of a bicrystal having a multiple slip orientation.
7 =
DEFORMATION
r:(ri’uj)(gi’$j)
+
(ei’$j)(ej*$i))Ti
(1)
single
(ei’$,XCJj’$i)
=
6ij
(2)
is called the transmission factor. They also reported good agreement between their experimental result and their prediction of additional slip being due to the value of Ni,. The larger the .hIij value of the slip system j. the easier slip of slip system j is induced by slip of slip system i. The total shear stress 7, on the stip system j will be the sum of 7 and the applied shear stress on this system, that is Tc =
Tj
+
YjVij’ti
(3)
Considering the case of the isoaxial bicrystal the primary slip system of both grains is denoted as i. and the slip system of the neighbouring grain respective to i, is taken as j, and putting the Schmidt factors of the i and j systems as mp and m respectively. then equation (3) will be given by 75,= Ti(~~~Z~+ X’N,j)
(4)
Saeki and Miura [lo] found that equation (3) was suitable to predict the slip systemj induced by the slip system i considering the values of Nij and m, t71P As the bicrystals used in this investigation are isoaxiaf symmetric bicrystals, it is considered that the com~nents of plastic strain in both grains are compatible at the grain boundary plane. The additional slip, shown in Fig. 7 (5.60/, strain), is the one which appeared at 0.4-0.5~0 strain and becomes more distinct after a larger amount of deformation. It is evident that this additional slip is activated immediately
~Bicrysfal ho&q 821 grain bolndory --- Componentsingle crystal
Blcrystol hovlng 27 grain boundary
---Component
+
crystal
-I
z
I
Strain
r (%)
Fig. 5. Stress-strain curves of a Stage I-X.7 bicrystal and the component single crystal.
0
I
2
Strotn
3
c (%f
Fig. 6. Stress-strain curves of a Stage I-El bicrystal and the component single crystal.
MIURA. HAMASHIS4A
AXI>
AUST:
PLASTIC DEFORMATION
OF BJCRYSTALS
1597
1598
MIURA. HAMASHIMA
N
ASD
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PLASTIC
DEFORMATION
OF BICRYSTALS
MIURA, HAMASHIMA
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PLASTIC DEFORMATION
Table 2. iy, values against each slip system in the B-grain due to (I 11) [IOI] slip system in the A-grain for (a) Stage I-27 bicrystal (b) Stage f-K?1 bicrystal (a) Slip plane
Slip direction
tgg (111) :%I;
(ITI) (iii)
;z; f%:
wt1
;t::j (1i-l) :%;
)?I %
.Ki, i: (I ti, [lOi]
0.211
0.920 0.118 0.713 0.528 0.854 0.330 0.538 0.435
0.485 0.299 0.018 0.204
;z 0:037 0.42 I
0.361 0.307 0.671 0.293 0.898 0.607 0.709 0.239 0.588 0.511 0.430 0.066
m 0.446 0.057 0.346 0.256 0.414 0.160 0.261
(b) Slip plane
Slip direction
nr m 0.420 0.135 0.282 0.182 0.354 0.153 0.210 0.262 0.493 0.144 0.024 0.119
n’P
0.852 0.274 0.572 0.369 0.700 0.310 0.426 0.531
zij i:(1II)[lOlJ
0.544 0.210 0.633 0.013 0.633 0.636 0.549 0.018 0.570 0.521 0.580 0.004
OF BICRYSTALS
1599
m!m, = 0.700). Therefore,
slip of (171) [ 1 lo] must be induced by the primary- slip of the neighbouring grain at the vicinity of the grain boundary. However, additional slip on (171) is hardly observed as shown in Fig. 8. since the [I 101 direction in the Stage I-Z21 bicrystal is nearly parallel to the top surface [Fig. l(c)]. Furthermore. as the :Ylj value for primary slip of the ne~~hbol!ring grain in the Stage I-E?1 bicrystal is generally lower than that in the Stage I-17 bicrystal. it is considered that the frequency of occur-
rence of additional slip in the Stage I-X21 bicrystal is lower than that in the Stage I-27 bicrystal. However. most careful observations with higher magnification of Stage I-E21 bicrystal show the additional slip traces not only on (lil) but also on (Ill) in the vicinity of boundary as shown in Fig. 9. On the basis of Table 2(b), the slip system of additional slip on (111) is considered to be (Ill) ClOT]. having relatively large values of Nij and rn,$, (h’,, = 0.544, m/mp = 0.852). 4.3. Tire boundary strength ar?d the deformation mode
In the isoaxial symmetrical bicrystal. the macroscopic compatibility of the strain component is satisCl 101 fied in three directions at the grain boundary piane. Therefore, Livingston and Chalmers [47 concluded (Iii) EfZ$ that the ffow stress of the isoaxial symmetrical bilOit1 crystal was not affected by the presence of the grain (1 Ii) [bll$ boundary, since an increase of flow stress due to the 1.ooo [loll occurrence of additional slip at the vicinity of the 0.292 Ellol (II-I) grain boundary did not appear. 0.049 Eziij 0.241 However, in this study additional slip is observed at the vicinity of the grain boundary in the Stage I-Z7 bicrystal, which was an isoaxial symmetrical bicrystal. after yield. Therefore, the slip system of the additional The flow stress of this bicrystal is slightly larger than slip can be predicted with use of the Nij and m/mp that of its component single crystal (Fig. 5). As a values. result, it is apparent that the deformation mode of an The values of rn~rn~and Nij for each slip system in isoaxial symmetrical bicrystal can be influenced by the B-grain, due to primary slip system: (117) [liO] in the presence of a grain boundary. The relations between strain and the boundary the A-grain, are shown for Stages I-Z7 bicrystal and Stage I-Z21 bicrystal in Table 2(a) and (b) respectstrength for the Stage I-27 and Stage I-Z21 bicrystals ively. Since these bicrystals are of the isoaxial sym- are shown in Fig. 10. In Fig. 10. the boundary metric type, the value of Nij for the slip system in the strength is the difference in flow stress at the same B-grain due to the slip system in the A-grain, is equal strain between the bicrystal and its component single to that for the slip system in the A-grain due to the crystal. It is evident that the boundary strength inslip system in the B-grain, in each case. creases rapidly in the initial stage of plastic deformaIn Table l(a), it is evident that the slip system in the tion. from the yield point to 0.3q; strain for the Stage B-grain, which has a maximum value of Ni, and a I-17 bicrystal and from the yield point to 0.67; strain large value of m/m,, is (lil) [i lo] (Nij = 0,898. for the Stage I-X21 bicrystal. In the initial strain m/mp = 0.854). As can be seen in Fig. 7. slip on (lil) region, the component single crystals are deformed is induced by the activation of primary slip in the only by primary slip, while in the bicrystals additional Stage I-27 bicrystal. As the result. it is considered that slip induced by piled-up dislocations of primary slip the slip system of this induced slip is (lil) [1 IO]. of the neighbouring grain is active in addition to Similarly, it is considered that the slip system of ad- primary slip. Therefore, it is considered that this rapid ditional slip on (111) shown in Fig. 7 is (111) [IiO], increase of boundary strength arises from the interhaving relatively large values of iv,, and m/mp action between additional slip and primary slip in the 0.671, m/m, = 0.713). vicinity of the grain boundary. In Table 2(b), it is found that the slip system (lil) Fujita er al. [93. using non-isoaxial bicrystals, found [110-j in the B-grain has the maximum value of lvij that at strains less than 0.19; additional slip appeared and a relatively large value of m/m, (Nij = 0.663, and interaction of primary slip and additional slip cq
(111)
(Nij
=
p.~l
1600
ii
W
MIURA. HAMASHIMA
ASD
AUST:
PLASTIC DEFORMATION
OF BICRYSTALS
MIURA. HAMASHIMA
m
0
I
2
Normal
4
3
Strom
l
AND
5
AUST:
6
7
P/d
Fig. 10. Relation between grain boundary strength strain in Stage I-17 and Stage I-t21 bicrystals. occurred. It is concluded primary slip and additional
PLASTIC DEFORMATION
boundary do influence plasticity. However, in the present study the angles between the Burgers vector. a/2. [loll, on the primary plane (1 Ii) and the line of intersection of boundary plane and primary slip plane were 52” for Stage I-17 and 47’ for Stage I-Z21 crystals, the Burgers vector of a grain boundary dislocation which is formed when a dislocation passes through the boundary will be almost the same. Therefore, the effect of atomic structure of these two bicrystals could not be known in this experiment.
and
that the interaction of slip occurs immediately
after yield in both isoaxial and non-isoaxial bicrystals. The earlier increase of grain boundary strength of the Stage I-Z.7 bicrystal than that of the Stage I-221 bicrystal is consistent with the larger value of maximum Nij in the Stage I-17 bicrystal. From about 1.0% strain to 5.0% strain, the boundary strength of both bicrystals increases slightly. In this strain region, the flow stress of the component single crystal increased rapidly due to the appearance of secondary slip. On the other hand, the low stress of the bicrystal is greatly affected by the interaction between primary slip and secondary slip in each grain of the bicrystal. It is considered that the effect on the flow stress of the bicrystal caused by the interaction of secondary slip and primary slip is much greater than that due to the interaction of additional slip. Therefore, the boundary strength is only slightly increased at this stage of the deformation. At a later stage of deformation (from about 5% strain), the boundary strength of both bicrystals begins to increase again. At this stage, cross slip can occur in the crystal, corresponding to Stage III of the component single crystal. Since the obstacles formed in the crystal can be evaded by double cross slip, the work-hardening-rate of the crystal decreases greatly. In the bicrystal, the deformation mode is more complex due to the additional slip in the vicinity of the grain boundary, and many obstacles formed in the vicinity of the grain boundary cannot be evaded by simple cross slip. Therefore, it is considered that the boundary strength of both bicrystals is increased by the effect of these obstacles. The boundary strength of Stage I-Z7 bicrystal and Stage I-E21 bicrystal is important in the Stage I region of their component single crystals, and is absent in the Stage II region of their component single crystals. It is concluded that the effect of the coincidence grain boundary on flow is largely due to multiple slip introduced in the vicinity of the grain boundary, and is obscured by the appearance of multiple slip in the respective grains. This mechanism is similar to that of the non-isoaxial bicrystal reported by Saeki and Miura [lo]. It is thought that dislocation processes in the
1601
OF BKRYSTALS
5. SUMMARY The effects of the grain boundary on the plastic properties of a (111) oriented aluminum symmetric bicrystal having the 27 tilt coincidence boundary. a single-slip-oriented symmetric bicrystal having the X7 tilt coincidence boundary and a single-slip-oriented symmetric bicrystal having the X21 coincidence boundary were studied. It is found that the (111) oriented bicrystal deforms by the mode similar to that of (111) oriented aluminum single crystals. Fine, multiple slip which appears in the entire stage of deformation is suppressed at the boundary, and no effect of the grain boundary on flow stress is observed. In the single-slip-oriented bicrystal having a X7 tilt coincidence boundary. additional slip is observed near the grain boundary and the slip system of the additional slip agrees well with the slip system predicted by the transmission factor Nij and the ratio of Schmid factors. The boundary strength of bicrystals having a X7 tilt coincidence boundary and having a Z21 tilt coincidence boundary, increases rapidly due to the occurrence of additional slip until the appearance of secondary slip in the respective grains. After secondary slip appears, the boundary strength increases slightly and subsequently increases more rapidly at a strain region corresponding to Stage III of the component single crystal. Acknowledgemenrs-The authors wish to thank the Sumitomo Light Metal Industries Ltd. Japan, for the supply of materials. Thanks are due to Dr Y. Saeki of the Nagoya Institute of Technology, Nagoya. Japan for valuable advice and discussion. We acknowledge with gratitude the financial support by the Light Metals Educational Foundation. Japan.
REFERENCES 1. R. Clark and B. Chalmers, Acta metall. 2. 80 (1954). 2. K. T. Aust and N. K. Chen. Acra metal/. 2, 632 (1954). 3. R. S. Davies, R. L. Fleischer, J. D. Livingston and B. Chalmers. Trans. merall. Sot. A.I.M.E. 209, 136 (1957). 4. J. D. Livingston and B. Chalmers. Acfa merall. 5, 322 (1957). 5. R. L. Fleischer and B. A. Backofen. 7rarrs meroll. Sot. A.I.M.E.
218, 245 (1960).
6. J. J. Hauser and B. Chalmers. Acra
meroll.
9. 802
(1961).
7. T. Inoko, K. Akizono and G. Mima, .!. Japan Metal
36, 373. 380 (1972).
Insr
1602
MIURA. ~AMASHIMA
AND
AUST:
PLASTIC D~FORMATlO~
8. 0. lzumi and T. Takasugi, 2. Mere//k. 6S, 542 (1974). 9. H. Fuji@ K. Toyoda and Y. Kanetsuki, Trans. JIM 16, 151 (1975). 10. Y. Saeki and S. Miura, Mechanical Behavior of Marerials. (hoc. 1974 Symp. of Mech. Behavior of Materials, Kyoto, 1974). The Society of Materials Science, Japan), Vol. II, p. 11 (1974). 11. Y. Chuang and H. Margolin, Merafl. Trans. 4, 1905 (1973). 12. R. E. Hook and J. P. Hirth, Acta meroll. IS, 535, 1099 (1967). 13. D. G. Brandon, B. Ralph, S. Raneanathan and M. S. Wald, Acra metall. 12, 813 (1967). 14. D. G. Brandon. Acta metall. 14, 1479 (1966). 15. G. H. Bishop and B. Chalmers. Scripra metal/. 2, 133 (1966).
OF BICRYSTALS
16. M. J. Bain, H. Gleiter and B. Chalmers, J. appl. Phps. 42, 2639 (1971). 17. Y. lshida and M. Mclean, Phil. Mag. 27, 1125 (1973). 18. T. Schober and R. W. Balluffi, Phil. Mag. 21, 109 (1970). 19. G. Hasson and C. Goux, Scripra metal). 5,889 (1971). 20, P. Chaudhari and J. W. Matthews, J. appl. Pkys. 42, 3063 (1971). 21. R. C. Pond and D. A. Smith, Can. Met. Quart. 13, 39 (1971). 22. G. Hermann. G. Baro and H. Gleiter. Acra metal/. 24, 353 (1976). 23. T. Inoko, H. Yamazi, K. Akizono and G. Mima, Nip von Kink.
Gakk 39. 467 (1975).
24. s. Miura and Y. Saeki, kcra herall. 26,93 (1978). 25. S. Miura and K. Hamashima, J. Sot. mater Sci. Japan 27, 1146 (1978).