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Behavior of dislocations in ALMG single crystals observed by high voltage electron microscopy
BEHAVIOR OF DISLOCATIONS IN Al-Mg SINGLE CRYSTALS OBSERVED BY HIGH VOLTAGE ELECTRON MICROSCOPY TEIZO TABATA,
HIROSHI FUJITA
and YASUHIRO NAKAJIMAt
Research Cneter for Ultra-High Voltage Electron Microscopy, Gsaka University, Yamada-Kami, Suita, Osaka 565. Japan (Received 2 September 1979) Abatraet-41 situ d~o~ation of Al-U.3 wt.% Mg single crystals has been carried out to investigate the behavior of dislocations related to serrated yielding (P-L effect) at room temperature and - 80°C. As the formation of dislocation tanglings proceeds, motion of both edge and screw dislocations is retarded around them. The waiting time of mobile dislocations at the tangles is markedly prolonged at room temperature so that dislocations are piled up against the tangles. These piled-up dislocations make jerky motion in a group when the applied stress increases and form the coarse slip bands rapidly. In this process, screw dislocations make cross slip abruptly in a group and many dislocations are suddenly multiplied. Heterogeneous deformation corresponding to the serrated yielding is emphasized by these sudden bursts of dislocation motion. At -SOT, however, the waiting time of mobile dislocations at the dislocation tan&s becomes similar to that in pure alu~um crystal, so that the motion of both edge and screw dislocations becomes reiativciy homogeneous and smooth through the crystat. Ott the basis of the observations, the origin of the serrated yielding in AI-Mg alloy was discussed. RsNous avons deforme in situ des monocristaux d’Al-O,3%Mg (en poids), afin d%tudier le comportement des dislocations lie aux hachures de la limite Clastique (eget P-L) g la temperature ambiante et H -80°C. Au fur et i mesure de la formation d’echeveaux de dislocations, le deplacement da dislocations coin et vis cat ret&& J..e temps d’attcnte dcs dislocations mobiles sur les &heveaux est nettcment plus grand B la temp&ature ambiante, de sorte que ks dislocations s’y empiknt. Ces d&cations empii&s se d&p¢ en groupe de m&&e saccad& Iorsque la contra&e apptiiute augrnmxte et e&4 fommt ra~tdc~~~&~~tAucoursdcce~~desgroup?Jdtdisioatiansvis peuvent partir soudainement en glissement d&vie et se multiplier rapidement. La d&rmation -gene ot aux hachures de la limite tlastique est accenttree par ces variations brutales dam ie d6placement des d&cations. A -8O“C par contre, le temps d’attente des dislocations mobiles aux Ccheveaux devient comparable a celtti observe dam l’aluminium pur, de sorte que le d&placement des dislocations coin et vis est homogtne et regulier dam tout le cristal. Compte term de ces observations, nous discutons de I’origine des hachures it la limite CIastique dam f’alliage Al-J@. h-g-Einkristaile Al-O.3 Gew.-% Mg wurden bei Raumtemperatur tmd -80°C in s&u verform& urn das Verhalten der Versetzungen beim ruckweisen F’lieBen zu untersuchen. Mit dem wachsenden Aufbau von Versetzungskn&teln wird die Bewegung von Stufen- tmd Schraubenversetzungen um die Ktiuel herum vertigert. Die Wartezeit beweglicher Versetzungen ist an den Kniiueln bei Raumtemperatur merklich verliingert, so dag sich Versetzungen gegen die KnPuel aufstauen. Wenn die angelegte Spsnnung erhaht wird, ftihren diese aufgestauten Versetzungen als Gruppe einc ruckweise Bewegung aus und bilden pliitzlich ein grobes Gleitband Bei diesem Prozess quergleiten die Schraubenversetzungen abrupt in einer Gruppe und viele Versetzungen vervielfachen sich plijtzlich. Die heterogene Verformung, die dem ruckweisen PlieDen entspricht, wird durch diese pl&zlichen Verset2~~~~~~ verstirkt. Bei -80°C dagegen ist die Wartezeit beweglicher Versetzungen an den Ver~~~~~uein iihnlich der in reinem Aluminium. Dadurch wird die Bewegung von St&n- und Schraubenversetzungen reiativ homogen und gleichn&iBig. Ausgehend von den Beobachtungen wird die Ursache fur ruckweises PliDen in Al-Mg-Legierungen diskutiert.
and interstitial
1. XNTRODUCI’ION
The serrated yielding (Portevin-Le Chatelier effect) has been extensively studied in both substitutional t Present address:
Kobe
Steel Industry,
Yamaguchi,
Japan. 795
alloys [l,Zj.
This
phenomenon
has
been generally accompanied by the i~orno~~~ deformation 13-53 and the shape and magnitude of serratious strongly depend on the deformation and specimen conditions such as temperature[6], strain rate [7J, amount of strain [S, 91, number of active slip
TABATA, et ai.: DISLOCATIONS IN Al-Mg SJNGLE CRYgTALS
-I!36
systems [9], existence of grain boundaries [8] and so on. Two of the present authors showed that the serrated yielding results from the enhancement of the heterogeneous deformation by the interaction between mobile dislocations and solute atoms 183. Many theories have been proposed to explain the origin of serrated yielding, or mechanism of interaction between solute atoms and dislocations [NJ-123. They can be roughly classified into two groups. One is based on dynamic strain aging model [lo] and the other is derived from Johnston-Gilman dislocation dynamics [II]. Recently, the static strain aging model [12] has also been proposed. As mentioned above, many experiments have been carried out and many theories have been developed on serrated yielding to explain this phenomenon, but there is as yet no clear consensus as to the details of the mechanism. This is mainly due to the lack of dynamic observation of dislocation behavior related to the serrated yielding. From this point of view, the present experiment has been carried out to observe dankly the behavior of both edge and screw dislocations and their temperature dependence in AI-Mg singie crystals,
2. SPECIMENS AND EXPERIMENTAL PROCEDURES 21 Specimens AM.3 wt%Mg singie crystals were grown by a modified Sridgman method in Ar-10% HZ gas after binding seed crystals in a vacuum of 3 x lo-’ torr. TWO sets of crystals named specimen S and E were grown as shown in Fig. 1. In specimen S, the slip direction [110] (primary Burgers vector) makes an angle of 45” with the top surface of the specimen and projection of sfip direction to the top surface is parallel to the tensile axis, as shown in Fig. l(a). In this specimen, the glide path of edge dislocations decreases with decreasing specimen thickness and the behavior of screw dislocations can be mainly observed by electron microscopy. On the other hand, the Burgers vector of primary slip system in specimen E is parallel to the top surface of specimen so that the glide path of screw dislocations decreases with decreasing specimen thickness while the glide path of edge dislocations is not changed as shown in Fig l(b). The tensile axes of specimens E and S are shown in Fig. 2. Chemical composition of the specimens is shown in Table 1.
Fig 1. Geometry of primary siip system of specimen S (a) and specimen E (b).
Fig 2. Tensile ales of specimens S and E
2.2 Experimental procedures The ~xperimcntaI apparatus, operation procedures and electropolishing techniques of spa5mens for in situ deformation have been drcadydtzcrhd in previousppcrs [13,14]. The specimen was continuously stretched in electron microscope using tensile testing specimen holder drived by motor and strain rate was roughly determined as 5-8 x IO-*//s which is the suitable strain rate for appearance of serrated yielding of ACMg alloys around room temperature. The shape and size of thin specimen used for in situ deformation is shown ~emati~Iy in Fig. 3. The thickness of the local region of specimen where dynamic observation of dislocation behavior was carried out was determined as about 10 q or more by the combination of thickness fringes and width of slip traces. Electron microscope used for in situ experiments is Hitachi HU-2000 type operated at 2 MV. Behavior of dislocation was recorded using h&h sensitive image or&icon television camera and video tape recording system. The ordinary image recording with photoplates WBS also used intermittently. Following special precautions have been taken in order to establish the reliability of the experiments.
Table 1. Chemical composition of specimens. 1 Alloy
Al-O.Jwt%Mg
Magnes iuta Iwt%I 0.33
Impurity
content
(wt%I
CU
Si
Fe
Mn
0.004
0.006
0.007
0.002
TABATA, et al.: DISLOCATIONS IN Al-Mg SINGLE CRYSTALS
797
(1O’6e/crr?+s) using high sensitive image orthicon tube and the dislocation motion was usually recorded from the first several seconds of electron irradiation by VTR system. (iii} There are some ~ssibiliti~ of disappearance of serrated yielding when thin specimen is used for in situ deformation. Therefore, it is necessary to examine whether or not the dislocation behavior observed by in situ ~efo~ation experiments exactly correspond to that in bulk specimen. From this point of view, size effect on the deformation mode and magnitude of serration was investigated in specimens E and S as will be described in the following section.
-_-I-3orm 3. EXPERIMENTAL
RESULTS
Fig. 3. Schematic representation of thin specimen used for in situ deformation. Dynamic observation of dislocation behavior was carried out around the region indicated by a dashed line.
3.1 Thickness e&x% on the stress-strain curve and characteristics of serrations
(if A sudden burst of dislocation motion is considered to be usually observed by in situ experiments even in materials which don’t normally exhibit serrated yield because of the uneven friction in the straining stage mechanism Stretching device for in situ deformation used in the present experiment is so smooth that strain can be applied very continuously to the specimen as reported in the previous paper [ 133, Moreover, the dislocation behavior in pure ahnninum single crystals (99.99% in purity) with the same orientations as those of A:-Mg alloys used in the present experiment was observed using this stretching device and compared with those in Al-Mg alloys. The disiocation motion in pure aluminum was not so discontinuous as those in Al-Mg alloys even at low stress level, e.g. at higher temperatures. Evidence has been given by this pre-experiment that the stretching device used in the present experiment for in situ deformation has not so severe uneven friction which cause a sudden burst of dislocation motion. Therefore, it is concluded that dislocation behavior, which is the origin of serrated yielding of Al-Mg alloys, can be observed substantially by in situ deformation method. {ii) The major difficulty in these experiments arise from radiation damage under illumination of electron beam. From this point of view, the microscope should be operated under the threshold voltage of radiation damage. However, at low accelerating voltage, the maximum observable thickness is limited under the critical one above which the behavior of dislocations is the same to those in bulk specimen. Actually, the jerky collective motion of edge and screw dislocations cannot be observed at thin parts of specimen in the present experiment. Therefore, the accelerating voitage was determined as 2 MV and several kinds of devices were considered to suppress the effect of radiation damage as possible as we can. Namely, specimens were observed at low fluxes of electrons
Figures 4 and 5 show the stress-strain curves of specimens S and E with various kinds of thicknesses together with the comparison of mode and magnitude of serrations in bulk and thin specimens at strains pointed by arrows A and A’, respectively. The stress level and total elongation decrease with decreasing specimen thickness in specimen S as shown in Fig. 4. On the other hand the decrease of stress level in the stress-strain curves of specimens E with decrease of specimen thickness is not so large compared with that of specimen S even when the specimen thi&nem is widely changed, as shown in Fig. 5. The magnitude of serrations in thin specimens used for in situ deformation is generally larger than that of bulk specimens, and the drop occurs more rapidly in thin specimens as recognized in Figs. 4 and 5. The magnitude of serrations increases with increasing strain up to 10% strain in thin specimens and 15% strain in bulk specimens and then decreases to the roughly constant value of magnitude in both type of specimens with various thicknesses as the same manner as described in the previous papers [8,9]. The details of configuration of stip bands appeared on the top surface of thin specimen S used for in situ deformation was observed by optical microscopy and compared with that of bulk specimen to examine the size effect on the slip mode at room temperature, as shown in Figs. 6 and 7. As recognized in Fig. 6, slip bands appear homogeneously all over the gauge parts of thin specimen used for in situ deformation and the slip bands arrangement is very similar to that in bufk specimen. Moreover, detaiis of slip bands arc compared in bulk and thin specimens, as shown in Figs. 7(a) and (b). Configuration of slip bands in both specimens are very similar with each other, as recognized by comparing Figs. 7(a) and (b). On the basis of these investigations, it is concluded that the serrated yielding can be observed in thin specimens and that the dislocation behavior observed by in situ defo~ation can be closely related with the serrated yielding of bulk specimens.
790
TABATA, et al.: DISLOCATIONS IN Al-Mg SINGLE CRYSTALS
STRAIN ck) Fig 4. Re~tions~p between stress-strain curves and thickness of specimens S al room temmture. The magnitude and shape of serrations in bulk and thin specimens at the strains pointed by arrows A and A are also shown in squares A and A’, respectively. The thicknesses of specimens are shown in figure. The average thickness d thin specimen used for in s&udeformation is about 3Oqn.
3.2 Behavior of edge dislocations at room temperature in q&men E Edge dislocations move smoothly at the very eariy stage of deformation. As the deformation proceeds, the dislocation tangles are formed by the interaction among mobile dislocations. Once the dislocation tangles arc formed, edge dislocations are trapped by these obstacles and pile up against the dislocation tangles. These edge dislocations abruptly move in a group through the obstacles according to the increase of applied stress. Namely, once obstacles, such as dii location tangles, for the mobile dislocations are
0
IO
formed in specimen, a sudden burst of edge dislocation motion becomes dominant around them. Figure 8 shows an exampie of a sudden burst of edge dislocation motion around obstacles at the early stage of deformation. In Figs. g(a)-+), edge dislocations l-9 are trapped by the dislocation tangle T and then these piled up edge dislocations overcome colloctively a dislocation tangle T at a time as recognized in Fig. g(d). The c&xtive motion d edge disbc&iw becomes more dominant when well deveioped dislo. cation tangles arc formed with increasing strain as shown in Fig. 9. Edge dislocations 1, 2, 3, 4 etc., pile
20 STRAIN
30
40
(W
Fig. 5. Re~tio~shlp between stress-strain curves and thickness of specimen E at room temperature. The magnitude and shape of serrations in bulk and thin specimens at the strains pointed by arrows A and A’ are also shown in squares A and A’, respctively.
TABATA, et al.: DISLOCATIONS IN Al-Mg SlNGLE CRYSTALS
799
Fig. 6. The arrangements of slip bands on the top surface of thin specimen S used for in situ deformation. Specimen wss deformed to the begirting of fracture (about 20”/, strain) in electron microscope at room temperature. Dynamic observation of dislocation behavior was carried out around the regions indicated by a dashed line.
up against a well developed dislocation tangle T one after another as shown in Figs. 9(a)-(d) and edge dislocations l-10 are finally trap& by a dislocation tangle T as recognized in Fig. 9(e). At the next moment, the piled up edge dislocations abruptly overcome the dislocation tangle T in a group as shown in Fig. 9(f). These sudden bursts of edge dislocation motion at dislocation tangles are intermittently repeated, while the specimen is stretched continuously. 3.3 Behavior of screw disiocatimts at mm in speei~ S
Ts in Fig 1qc). These sudden bursts of screw dislocation motion are also repeated intermittently as in the case of edge dislocations, while the specimen is stretched continuously.
temperature
Figure 10 shows the behavior of screw dislocations around dislocation tangles in specimen S at room temperature. When the dislocation tangles Tr, T2 and TJ are formed, screw dislocations l-6 and l”-9” pile up against these dislocation tangles, as recognized in Figs. 10(a) and (b). These piled up screw dislocations suddenly escape out from the obstacks Tr and T2 with abrupt collective cross-slip as shown by arrows in Fig. lo(c) and following screw dislocations l’-10 pile up again at the dislocation tangles TI and TX as recognized in Fig. lo(c). At the dislocation tangle T3 which may be a relatively weak obstacle, piled up screw dislocations l”-9” in Fig. lo(b) overcome collectively and form the coarse slip bands S as recognized in Fig. lo(c). Other group of screw dislocations 1”‘-4”’ begin to pile up again against the dislocation tangle
Fig. 7. Comparison of slip band configuration at about loO/, strain between bulk specimen (a) and thin specimen (b) used for in situ deformation. The thickness of bulk and thin specimens is 1.1 mm and about 20 m respectively.
TABATA, et ak: DISLOCATIONS IN Al-Mg SINGLE CRYSTALS
Fig. 8. Cokctive motion of edge dislocations at the dislocation tang&s at room tampcfature in specimen E. Thase Photographs are picked up from VTR taken at aorraal speed {30 frames/s) with an interval of about 0.5 s.
Figure 11 shows the successive stages of sudden burst of screw dislocation motion around d&cation tar&es at about 10% strain in specimen !S. Many screw dislocations are trapped by the dislocation tangies Tr, T2 and T3 as shown in Figs. ll(aHf). These screw dislocations suddenly make cross slip at a time as shown by arrows in Figs. 11(b), (c) and (d), and many dislocations are multiplied abruptly as recognized in Figs. 11(c)-@). Coarse slip bands are formed by these processes as shown in Figs. 11(c) and (d). These behavior of screw dislocations are very different from those in pure aluminum single crystals in which pileup and coRective cross-slip of screw dislocations are scarcely observed. 3.4 Behavior of edge and screw dislocations at -&PC Figure 12 shows the successive stages of the motion of edge and screw dislocations in specimen E at -80°C at which the magnitude of serrations is very small compared with that at room temperature. As recognized in Fig. 12, both edge (l&) and screw (ls+ dislocations move continuously and pile-up of dislocation group at the dislocation tangles T1 and T2
is not observed so often as in the deformation at room temperature. Consequently, a sudden burst of dislocation motion is scarcely observed at - 80°C. 4 DWXJSSXON 4.1 Origin of serrated yielding As a function of the nucleation and growth of sIip bands, the macroscopic plastic strain rate (i) can be written as;
& = Is(t)d, + N(t)G
ut
where N(t) is the formation rate of slip band and N(t) = j$~(x)dx. do and G are terms describing the initial displacement and growth of slip band [lS]. Thus the abrupt appearance of slip band with a large displacement would cause a serrated yielding on the stress-strain curve. As shown in Figs. 8,9, 10 and 11, a sudden burst of dislocation motion at such obstacles as dislocation tangles is observed corresponding to the serrated yielding. On the other hand, smooth movement of dislocations is observed homogeneously all over the specimen before the onset of the serrated
TABATk et al.: DISLOCATIONS
IN Al-Me SINGLE CRYSTALS
Fig. 9. Successive stages of colktive motion of edge dislocations at the well devdoped dislocation tanglings at room temperature in specimen E. These photographs are picked up from VTR with an interval of about 0.5 s.
TABATA, et al.: DISLOCATIONS
IN ACMg SINGLE CRYSTALS
Fig. 10. Collective motion of screw dislocations around the dislocation tanglings at room temperature in specimen S. These photographs were taken at intervals of about 2 s.
TABATA, et al.: DISLOCATIONS IN ACMg SINGLE CRYSTALS
803
Fig. il. Successive stages of a sudden burst of dislocation multiplication by the collective cross-slip of screw dislocations around dislocation tanglings at room temperature in specimen S. These photographs were taken at intervals of about 2 s.
yielding. Moreover, at -8O”C, a sudden burst of dislocation motion at obstacles is not observed as shown in Fig. 12. On the basis of the observations and of the above discusions, it can be concluded that the jerky collective motion of edge and screw dislocations and abrupt multiplication of dislocations by the abrupt collective cross-slip of screw dislocations which give rise to a large do and/or small G in equation (1) are the causes of the serrated yielding. This conclusion supports the model proposed in the previous paper where the relationship between the ~cro~opicaliy observed serrated yielding and the microscopically observed dislocation motions was discussed in detail [8]. As already suggested in the above discussions, the formation of dislocation tangles which can retard many mobile dislocations [16] is quite necessary for the onset of a sudden burst of dislocation motion as
recognized in Figs. 8,9, 10 and 11. From this point of view, it can be considered that some finite plastic strain before the onset of serrated yielding is necessary to form the obstacles which can retard many mobile dislocations [17J. Introduction of vacancies by plastic deformation also plays an important role to enhance the diffusion of magnesium atoms to the dislocations. The dislocation motion in regions between obstacles, however, is not so jerky even at room temperature as shown in Figs. S(a) and (b). This means that the formation of obstacles, i.e., retardation of dislocation motion by obstacles, is more important for the onset of serrated yielding than the enhancement of a diffusion rate by vacancies produced during the deformation before the onset of serrated yielding [IO]. As a conclusion of this section, the ma~ro~~pi~ serrated yielding is caused by the microscopic dislocation motions as the following processes (if-(iv). (i) The
TABATA, et al.: DISLOCATIONS IN ACMg SINGLE CRYSTALS
Fig 12. Behavior of edge and screw dislocations at -80°C in sprdmsn L These photographs are picked up from VTR with au interval of about 0.5 s. dislocation tanghgs are formed in the specimen as the deformation proceeds. (ii) Many mobile dislocations are trapped and slow down in velocity by these dislocation tangling% (iii) These trapped dislocations overcome abruptly the obstacles collectively when the applied stress is increased because of the cooperation of solute pinning and internal stress field of dislocation tanghngs as discussed in the previous paper [8]. (iv) These sudden bursts of dislocation motion cause the abrupt appearance of a slip band with a large displacement and this is detected as serrated yielding on a usual load-elongation record. 4.2 Reliability of dynamic strain aging model on the onset of the serrated yielding in substitutional alloys
Dynamic strain aging model for the onset of serrated yielding proposed the following equation concerning the onset strain cc of serrated yielding under the given strain rate (&)[lo]; E” + p = kex?$QJKT)/4bKNDo
(2)
where Do is the diffusion frequency factor and Q,,,, the effective activation energy for solute migration, is equal to (&,A?), where E, is the activation energy for vacancy diffusion and B is the solute-vacancy binding
energy. In equation (2X 1 is the ef%ctive radius of the atomosphere and b is the Bergers vector. In this model, the increase of vacancy concentration C, and dislocation density p by the strain e is expressed by the C,= K.8’ (3) p = N*e@
(4)
A modified model of dynamic strain aging model for the serrated yielding in substitutional alloys based on the strain aging of mobile dislocations temporarily arrested at obstacles has been also proposed [12]. Many investigators have given the values of m, /I and Q,,,in approximate agreement with other studies from the measurements of the strain rate and temperature dependences of lc using equations (2X (3) and (4) E7,18,191. In the present observation, it becomes clear that abrupt collective cross-slip of screw dislocations is also origin of the serrated yielding as shown in Figs. 10 and II. Since the screw dislocations have only shear component as their stress field, the dynamic strain aging, which is caused by the vacancyassisted lattice diffusion of solute atoms to the edge dislocations, of screw dislocations by magnesium
TABATA, et al.: DISLOCAT!ONS M Al-Mg SXNGLE CRYSTALS atoms cannot be considered in general. Iiowever, if the screw ~si~ations have edge components, for example, if they have jogs on them, solute atoms interact with the parts of jogs on screw dislocations. Moreover, there is some possibility of interaction between screw dis~~tions and sobte atoms when solute atoms coagulate and form the tetragonal distortion. In addition to these interactions, shear modulus effect of solute atoms is important in the case of interaction between screw dislocation and solute atoms. These ekcts of solute atoms suppress the cross slip probability of screw dislocations because mean free length of screw dislocations which can cross slip becomes short and similiar with each other, and enable them to pile up against the obstacles as shown in Figs. 10 and 11. According to the increase of the applied stress, these piled-up ScTew di~~~o~ cross slip colkctive~y because the mean fke length is very similar in every parts of piled-up screw diskations. This is the reason why screw dislocations pile up against the obstacles and cross slip cokctive~y in Al-Mg alloy. As discussed in the above, onset of serrated yielding of Al-Mg alloys is also attributed to the collective motion of screw dislocations at the obstacks. Tberefore, it can be concluded tbat the dynamic strain aging mode& in which the interaction between edge dislooltions and solute atoms is mainly considered [lo], wet fully explain the onset of serrated yictiing of Al-Mg alloys around room temperature and that the physical meaning &,, Q,,,, m, etc., obtained by using equations (2X (3) and (4) is not so Clear.
805
Acknowkfg~ts-The authors are gratefui to Messrs. K. Yoshida, Kamatsu and T. Sakata for their help in maiatenante of tbe electron microscape.
t. B. J. Brindley and P. J. Worthington, Actu metult.17, 1357 (1967). 2. E. 0. Hall, Yield Point Phenamena in Metals and Afloys, Plenum Press, New York (1970). 3. A. T. Thomas. Acra me&~. f4. X363f19661. 4. II Munt and E. Macberau&i Z. ‘Met&k. 57, 552 ww.
5. A. Wijlcr and J. Sehade van Wtstrum, Script0 Met. 5, 159 (1971). 6. S. Miura and H. Yamauchi, Trans. Japan Inst. Metals 13, 82 (1971). 7. P. G. Maccormick, Acta metafl.20,351 (1972). 8. H. Fujita and T. Tab&a, Acta metaff.25 793 (197f). 9. T. T&&a, H. Fujita and N. &da, Mater. W. Engngto be published (f980). 10. A. H. Cottnll, Phil. Nag. 454, 829 (1953). il. W. G. Johnston and J. J. Gilman, J. annf. .* Phvs. _ I% 1259 (1959).
12. R. K. Ham and D. Jaffrey, Phii. Msg. 15, 247 (1%7). 13. H. Fuiita. T. Tabata. N. Sumida. M. ?&tmi. K. Yoshida z&d &f. Komat& Proc o$bth int. Con,l:on H&h Voftage Electron microscopy, ToUIouse, p. 345 (19715). 14. T. Tabata, H. Mori, H. Fuji& and I. Ishikawa, f. pI~ys. Sac. Japan 40,1103 (1976). 15. T. Mori and M. Meshii, Actu Metali. 17, 167 (1969). 16. H. Fuji& J. phys. Sac. Japan 23,1349 (1967). 17. S. Miura, J. Takamura and M, Yam&&a, StiyokswiSiri 16, 144 (1967). @usaction of the Mining and Maui Ass&&on Kyotof. 18. P. G. Maccarmiek, Am metdl. 19,463 (1971). 19. S. R. Masxwcn and B. Ramaswami, Phil. Msg. 21,1025 (1970).
HIROSHI FUJITA
and YASUHIRO NAKAJIMAt
Research Cneter for Ultra-High Voltage Electron Microscopy, Gsaka University, Yamada-Kami, Suita, Osaka 565. Japan (Received 2 September 1979) Abatraet-41 situ d~o~ation of Al-U.3 wt.% Mg single crystals has been carried out to investigate the behavior of dislocations related to serrated yielding (P-L effect) at room temperature and - 80°C. As the formation of dislocation tanglings proceeds, motion of both edge and screw dislocations is retarded around them. The waiting time of mobile dislocations at the tangles is markedly prolonged at room temperature so that dislocations are piled up against the tangles. These piled-up dislocations make jerky motion in a group when the applied stress increases and form the coarse slip bands rapidly. In this process, screw dislocations make cross slip abruptly in a group and many dislocations are suddenly multiplied. Heterogeneous deformation corresponding to the serrated yielding is emphasized by these sudden bursts of dislocation motion. At -SOT, however, the waiting time of mobile dislocations at the dislocation tan&s becomes similar to that in pure alu~um crystal, so that the motion of both edge and screw dislocations becomes reiativciy homogeneous and smooth through the crystat. Ott the basis of the observations, the origin of the serrated yielding in AI-Mg alloy was discussed. RsNous avons deforme in situ des monocristaux d’Al-O,3%Mg (en poids), afin d%tudier le comportement des dislocations lie aux hachures de la limite Clastique (eget P-L) g la temperature ambiante et H -80°C. Au fur et i mesure de la formation d’echeveaux de dislocations, le deplacement da dislocations coin et vis cat ret&& J..e temps d’attcnte dcs dislocations mobiles sur les &heveaux est nettcment plus grand B la temp&ature ambiante, de sorte que ks dislocations s’y empiknt. Ces d&cations empii&s se d&p¢ en groupe de m&&e saccad& Iorsque la contra&e apptiiute augrnmxte et e&4 fommt ra~tdc~~~&~~tAucoursdcce~~desgroup?Jdtdisioatiansvis peuvent partir soudainement en glissement d&vie et se multiplier rapidement. La d&rmation -gene ot aux hachures de la limite tlastique est accenttree par ces variations brutales dam ie d6placement des d&cations. A -8O“C par contre, le temps d’attente des dislocations mobiles aux Ccheveaux devient comparable a celtti observe dam l’aluminium pur, de sorte que le d&placement des dislocations coin et vis est homogtne et regulier dam tout le cristal. Compte term de ces observations, nous discutons de I’origine des hachures it la limite CIastique dam f’alliage Al-J@. h-g-Einkristaile Al-O.3 Gew.-% Mg wurden bei Raumtemperatur tmd -80°C in s&u verform& urn das Verhalten der Versetzungen beim ruckweisen F’lieBen zu untersuchen. Mit dem wachsenden Aufbau von Versetzungskn&teln wird die Bewegung von Stufen- tmd Schraubenversetzungen um die Ktiuel herum vertigert. Die Wartezeit beweglicher Versetzungen ist an den Kniiueln bei Raumtemperatur merklich verliingert, so dag sich Versetzungen gegen die KnPuel aufstauen. Wenn die angelegte Spsnnung erhaht wird, ftihren diese aufgestauten Versetzungen als Gruppe einc ruckweise Bewegung aus und bilden pliitzlich ein grobes Gleitband Bei diesem Prozess quergleiten die Schraubenversetzungen abrupt in einer Gruppe und viele Versetzungen vervielfachen sich plijtzlich. Die heterogene Verformung, die dem ruckweisen PlieDen entspricht, wird durch diese pl&zlichen Verset2~~~~~~ verstirkt. Bei -80°C dagegen ist die Wartezeit beweglicher Versetzungen an den Ver~~~~~uein iihnlich der in reinem Aluminium. Dadurch wird die Bewegung von St&n- und Schraubenversetzungen reiativ homogen und gleichn&iBig. Ausgehend von den Beobachtungen wird die Ursache fur ruckweises PliDen in Al-Mg-Legierungen diskutiert.
and interstitial
1. XNTRODUCI’ION
The serrated yielding (Portevin-Le Chatelier effect) has been extensively studied in both substitutional t Present address:
Kobe
Steel Industry,
Yamaguchi,
Japan. 795
alloys [l,Zj.
This
phenomenon
has
been generally accompanied by the i~orno~~~ deformation 13-53 and the shape and magnitude of serratious strongly depend on the deformation and specimen conditions such as temperature[6], strain rate [7J, amount of strain [S, 91, number of active slip
TABATA, et ai.: DISLOCATIONS IN Al-Mg SJNGLE CRYgTALS
-I!36
systems [9], existence of grain boundaries [8] and so on. Two of the present authors showed that the serrated yielding results from the enhancement of the heterogeneous deformation by the interaction between mobile dislocations and solute atoms 183. Many theories have been proposed to explain the origin of serrated yielding, or mechanism of interaction between solute atoms and dislocations [NJ-123. They can be roughly classified into two groups. One is based on dynamic strain aging model [lo] and the other is derived from Johnston-Gilman dislocation dynamics [II]. Recently, the static strain aging model [12] has also been proposed. As mentioned above, many experiments have been carried out and many theories have been developed on serrated yielding to explain this phenomenon, but there is as yet no clear consensus as to the details of the mechanism. This is mainly due to the lack of dynamic observation of dislocation behavior related to the serrated yielding. From this point of view, the present experiment has been carried out to observe dankly the behavior of both edge and screw dislocations and their temperature dependence in AI-Mg singie crystals,
2. SPECIMENS AND EXPERIMENTAL PROCEDURES 21 Specimens AM.3 wt%Mg singie crystals were grown by a modified Sridgman method in Ar-10% HZ gas after binding seed crystals in a vacuum of 3 x lo-’ torr. TWO sets of crystals named specimen S and E were grown as shown in Fig. 1. In specimen S, the slip direction [110] (primary Burgers vector) makes an angle of 45” with the top surface of the specimen and projection of sfip direction to the top surface is parallel to the tensile axis, as shown in Fig. l(a). In this specimen, the glide path of edge dislocations decreases with decreasing specimen thickness and the behavior of screw dislocations can be mainly observed by electron microscopy. On the other hand, the Burgers vector of primary slip system in specimen E is parallel to the top surface of specimen so that the glide path of screw dislocations decreases with decreasing specimen thickness while the glide path of edge dislocations is not changed as shown in Fig l(b). The tensile axes of specimens E and S are shown in Fig. 2. Chemical composition of the specimens is shown in Table 1.
Fig 1. Geometry of primary siip system of specimen S (a) and specimen E (b).
Fig 2. Tensile ales of specimens S and E
2.2 Experimental procedures The ~xperimcntaI apparatus, operation procedures and electropolishing techniques of spa5mens for in situ deformation have been drcadydtzcrhd in previousppcrs [13,14]. The specimen was continuously stretched in electron microscope using tensile testing specimen holder drived by motor and strain rate was roughly determined as 5-8 x IO-*//s which is the suitable strain rate for appearance of serrated yielding of ACMg alloys around room temperature. The shape and size of thin specimen used for in situ deformation is shown ~emati~Iy in Fig. 3. The thickness of the local region of specimen where dynamic observation of dislocation behavior was carried out was determined as about 10 q or more by the combination of thickness fringes and width of slip traces. Electron microscope used for in situ experiments is Hitachi HU-2000 type operated at 2 MV. Behavior of dislocation was recorded using h&h sensitive image or&icon television camera and video tape recording system. The ordinary image recording with photoplates WBS also used intermittently. Following special precautions have been taken in order to establish the reliability of the experiments.
Table 1. Chemical composition of specimens. 1 Alloy
Al-O.Jwt%Mg
Magnes iuta Iwt%I 0.33
Impurity
content
(wt%I
CU
Si
Fe
Mn
0.004
0.006
0.007
0.002
TABATA, et al.: DISLOCATIONS IN Al-Mg SINGLE CRYSTALS
797
(1O’6e/crr?+s) using high sensitive image orthicon tube and the dislocation motion was usually recorded from the first several seconds of electron irradiation by VTR system. (iii} There are some ~ssibiliti~ of disappearance of serrated yielding when thin specimen is used for in situ deformation. Therefore, it is necessary to examine whether or not the dislocation behavior observed by in situ ~efo~ation experiments exactly correspond to that in bulk specimen. From this point of view, size effect on the deformation mode and magnitude of serration was investigated in specimens E and S as will be described in the following section.
-_-I-3orm 3. EXPERIMENTAL
RESULTS
Fig. 3. Schematic representation of thin specimen used for in situ deformation. Dynamic observation of dislocation behavior was carried out around the region indicated by a dashed line.
3.1 Thickness e&x% on the stress-strain curve and characteristics of serrations
(if A sudden burst of dislocation motion is considered to be usually observed by in situ experiments even in materials which don’t normally exhibit serrated yield because of the uneven friction in the straining stage mechanism Stretching device for in situ deformation used in the present experiment is so smooth that strain can be applied very continuously to the specimen as reported in the previous paper [ 133, Moreover, the dislocation behavior in pure ahnninum single crystals (99.99% in purity) with the same orientations as those of A:-Mg alloys used in the present experiment was observed using this stretching device and compared with those in Al-Mg alloys. The disiocation motion in pure aluminum was not so discontinuous as those in Al-Mg alloys even at low stress level, e.g. at higher temperatures. Evidence has been given by this pre-experiment that the stretching device used in the present experiment for in situ deformation has not so severe uneven friction which cause a sudden burst of dislocation motion. Therefore, it is concluded that dislocation behavior, which is the origin of serrated yielding of Al-Mg alloys, can be observed substantially by in situ deformation method. {ii) The major difficulty in these experiments arise from radiation damage under illumination of electron beam. From this point of view, the microscope should be operated under the threshold voltage of radiation damage. However, at low accelerating voltage, the maximum observable thickness is limited under the critical one above which the behavior of dislocations is the same to those in bulk specimen. Actually, the jerky collective motion of edge and screw dislocations cannot be observed at thin parts of specimen in the present experiment. Therefore, the accelerating voitage was determined as 2 MV and several kinds of devices were considered to suppress the effect of radiation damage as possible as we can. Namely, specimens were observed at low fluxes of electrons
Figures 4 and 5 show the stress-strain curves of specimens S and E with various kinds of thicknesses together with the comparison of mode and magnitude of serrations in bulk and thin specimens at strains pointed by arrows A and A’, respectively. The stress level and total elongation decrease with decreasing specimen thickness in specimen S as shown in Fig. 4. On the other hand the decrease of stress level in the stress-strain curves of specimens E with decrease of specimen thickness is not so large compared with that of specimen S even when the specimen thi&nem is widely changed, as shown in Fig. 5. The magnitude of serrations in thin specimens used for in situ deformation is generally larger than that of bulk specimens, and the drop occurs more rapidly in thin specimens as recognized in Figs. 4 and 5. The magnitude of serrations increases with increasing strain up to 10% strain in thin specimens and 15% strain in bulk specimens and then decreases to the roughly constant value of magnitude in both type of specimens with various thicknesses as the same manner as described in the previous papers [8,9]. The details of configuration of stip bands appeared on the top surface of thin specimen S used for in situ deformation was observed by optical microscopy and compared with that of bulk specimen to examine the size effect on the slip mode at room temperature, as shown in Figs. 6 and 7. As recognized in Fig. 6, slip bands appear homogeneously all over the gauge parts of thin specimen used for in situ deformation and the slip bands arrangement is very similar to that in bufk specimen. Moreover, detaiis of slip bands arc compared in bulk and thin specimens, as shown in Figs. 7(a) and (b). Configuration of slip bands in both specimens are very similar with each other, as recognized by comparing Figs. 7(a) and (b). On the basis of these investigations, it is concluded that the serrated yielding can be observed in thin specimens and that the dislocation behavior observed by in situ defo~ation can be closely related with the serrated yielding of bulk specimens.
790
TABATA, et al.: DISLOCATIONS IN Al-Mg SINGLE CRYSTALS
STRAIN ck) Fig 4. Re~tions~p between stress-strain curves and thickness of specimens S al room temmture. The magnitude and shape of serrations in bulk and thin specimens at the strains pointed by arrows A and A are also shown in squares A and A’, respectively. The thicknesses of specimens are shown in figure. The average thickness d thin specimen used for in s&udeformation is about 3Oqn.
3.2 Behavior of edge dislocations at room temperature in q&men E Edge dislocations move smoothly at the very eariy stage of deformation. As the deformation proceeds, the dislocation tangles are formed by the interaction among mobile dislocations. Once the dislocation tangles arc formed, edge dislocations are trapped by these obstacles and pile up against the dislocation tangles. These edge dislocations abruptly move in a group through the obstacles according to the increase of applied stress. Namely, once obstacles, such as dii location tangles, for the mobile dislocations are
0
IO
formed in specimen, a sudden burst of edge dislocation motion becomes dominant around them. Figure 8 shows an exampie of a sudden burst of edge dislocation motion around obstacles at the early stage of deformation. In Figs. g(a)-+), edge dislocations l-9 are trapped by the dislocation tangle T and then these piled up edge dislocations overcome colloctively a dislocation tangle T at a time as recognized in Fig. g(d). The c&xtive motion d edge disbc&iw becomes more dominant when well deveioped dislo. cation tangles arc formed with increasing strain as shown in Fig. 9. Edge dislocations 1, 2, 3, 4 etc., pile
20 STRAIN
30
40
(W
Fig. 5. Re~tio~shlp between stress-strain curves and thickness of specimen E at room temperature. The magnitude and shape of serrations in bulk and thin specimens at the strains pointed by arrows A and A’ are also shown in squares A and A’, respctively.
TABATA, et al.: DISLOCATIONS IN Al-Mg SlNGLE CRYSTALS
799
Fig. 6. The arrangements of slip bands on the top surface of thin specimen S used for in situ deformation. Specimen wss deformed to the begirting of fracture (about 20”/, strain) in electron microscope at room temperature. Dynamic observation of dislocation behavior was carried out around the regions indicated by a dashed line.
up against a well developed dislocation tangle T one after another as shown in Figs. 9(a)-(d) and edge dislocations l-10 are finally trap& by a dislocation tangle T as recognized in Fig. 9(e). At the next moment, the piled up edge dislocations abruptly overcome the dislocation tangle T in a group as shown in Fig. 9(f). These sudden bursts of edge dislocation motion at dislocation tangles are intermittently repeated, while the specimen is stretched continuously. 3.3 Behavior of screw disiocatimts at mm in speei~ S
Ts in Fig 1qc). These sudden bursts of screw dislocation motion are also repeated intermittently as in the case of edge dislocations, while the specimen is stretched continuously.
temperature
Figure 10 shows the behavior of screw dislocations around dislocation tangles in specimen S at room temperature. When the dislocation tangles Tr, T2 and TJ are formed, screw dislocations l-6 and l”-9” pile up against these dislocation tangles, as recognized in Figs. 10(a) and (b). These piled up screw dislocations suddenly escape out from the obstacks Tr and T2 with abrupt collective cross-slip as shown by arrows in Fig. lo(c) and following screw dislocations l’-10 pile up again at the dislocation tangles TI and TX as recognized in Fig. lo(c). At the dislocation tangle T3 which may be a relatively weak obstacle, piled up screw dislocations l”-9” in Fig. lo(b) overcome collectively and form the coarse slip bands S as recognized in Fig. lo(c). Other group of screw dislocations 1”‘-4”’ begin to pile up again against the dislocation tangle
Fig. 7. Comparison of slip band configuration at about loO/, strain between bulk specimen (a) and thin specimen (b) used for in situ deformation. The thickness of bulk and thin specimens is 1.1 mm and about 20 m respectively.
TABATA, et ak: DISLOCATIONS IN Al-Mg SINGLE CRYSTALS
Fig. 8. Cokctive motion of edge dislocations at the dislocation tang&s at room tampcfature in specimen E. Thase Photographs are picked up from VTR taken at aorraal speed {30 frames/s) with an interval of about 0.5 s.
Figure 11 shows the successive stages of sudden burst of screw dislocation motion around d&cation tar&es at about 10% strain in specimen !S. Many screw dislocations are trapped by the dislocation tangies Tr, T2 and T3 as shown in Figs. ll(aHf). These screw dislocations suddenly make cross slip at a time as shown by arrows in Figs. 11(b), (c) and (d), and many dislocations are multiplied abruptly as recognized in Figs. 11(c)-@). Coarse slip bands are formed by these processes as shown in Figs. 11(c) and (d). These behavior of screw dislocations are very different from those in pure aluminum single crystals in which pileup and coRective cross-slip of screw dislocations are scarcely observed. 3.4 Behavior of edge and screw dislocations at -&PC Figure 12 shows the successive stages of the motion of edge and screw dislocations in specimen E at -80°C at which the magnitude of serrations is very small compared with that at room temperature. As recognized in Fig. 12, both edge (l&) and screw (ls+ dislocations move continuously and pile-up of dislocation group at the dislocation tangles T1 and T2
is not observed so often as in the deformation at room temperature. Consequently, a sudden burst of dislocation motion is scarcely observed at - 80°C. 4 DWXJSSXON 4.1 Origin of serrated yielding As a function of the nucleation and growth of sIip bands, the macroscopic plastic strain rate (i) can be written as;
& = Is(t)d, + N(t)G
ut
where N(t) is the formation rate of slip band and N(t) = j$~(x)dx. do and G are terms describing the initial displacement and growth of slip band [lS]. Thus the abrupt appearance of slip band with a large displacement would cause a serrated yielding on the stress-strain curve. As shown in Figs. 8,9, 10 and 11, a sudden burst of dislocation motion at such obstacles as dislocation tangles is observed corresponding to the serrated yielding. On the other hand, smooth movement of dislocations is observed homogeneously all over the specimen before the onset of the serrated
TABATk et al.: DISLOCATIONS
IN Al-Me SINGLE CRYSTALS
Fig. 9. Successive stages of colktive motion of edge dislocations at the well devdoped dislocation tanglings at room temperature in specimen E. These photographs are picked up from VTR with an interval of about 0.5 s.
TABATA, et al.: DISLOCATIONS
IN ACMg SINGLE CRYSTALS
Fig. 10. Collective motion of screw dislocations around the dislocation tanglings at room temperature in specimen S. These photographs were taken at intervals of about 2 s.
TABATA, et al.: DISLOCATIONS IN ACMg SINGLE CRYSTALS
803
Fig. il. Successive stages of a sudden burst of dislocation multiplication by the collective cross-slip of screw dislocations around dislocation tanglings at room temperature in specimen S. These photographs were taken at intervals of about 2 s.
yielding. Moreover, at -8O”C, a sudden burst of dislocation motion at obstacles is not observed as shown in Fig. 12. On the basis of the observations and of the above discusions, it can be concluded that the jerky collective motion of edge and screw dislocations and abrupt multiplication of dislocations by the abrupt collective cross-slip of screw dislocations which give rise to a large do and/or small G in equation (1) are the causes of the serrated yielding. This conclusion supports the model proposed in the previous paper where the relationship between the ~cro~opicaliy observed serrated yielding and the microscopically observed dislocation motions was discussed in detail [8]. As already suggested in the above discussions, the formation of dislocation tangles which can retard many mobile dislocations [16] is quite necessary for the onset of a sudden burst of dislocation motion as
recognized in Figs. 8,9, 10 and 11. From this point of view, it can be considered that some finite plastic strain before the onset of serrated yielding is necessary to form the obstacles which can retard many mobile dislocations [17J. Introduction of vacancies by plastic deformation also plays an important role to enhance the diffusion of magnesium atoms to the dislocations. The dislocation motion in regions between obstacles, however, is not so jerky even at room temperature as shown in Figs. S(a) and (b). This means that the formation of obstacles, i.e., retardation of dislocation motion by obstacles, is more important for the onset of serrated yielding than the enhancement of a diffusion rate by vacancies produced during the deformation before the onset of serrated yielding [IO]. As a conclusion of this section, the ma~ro~~pi~ serrated yielding is caused by the microscopic dislocation motions as the following processes (if-(iv). (i) The
TABATA, et al.: DISLOCATIONS IN ACMg SINGLE CRYSTALS
Fig 12. Behavior of edge and screw dislocations at -80°C in sprdmsn L These photographs are picked up from VTR with au interval of about 0.5 s. dislocation tanghgs are formed in the specimen as the deformation proceeds. (ii) Many mobile dislocations are trapped and slow down in velocity by these dislocation tangling% (iii) These trapped dislocations overcome abruptly the obstacles collectively when the applied stress is increased because of the cooperation of solute pinning and internal stress field of dislocation tanghngs as discussed in the previous paper [8]. (iv) These sudden bursts of dislocation motion cause the abrupt appearance of a slip band with a large displacement and this is detected as serrated yielding on a usual load-elongation record. 4.2 Reliability of dynamic strain aging model on the onset of the serrated yielding in substitutional alloys
Dynamic strain aging model for the onset of serrated yielding proposed the following equation concerning the onset strain cc of serrated yielding under the given strain rate (&)[lo]; E” + p = kex?$QJKT)/4bKNDo
(2)
where Do is the diffusion frequency factor and Q,,,, the effective activation energy for solute migration, is equal to (&,A?), where E, is the activation energy for vacancy diffusion and B is the solute-vacancy binding
energy. In equation (2X 1 is the ef%ctive radius of the atomosphere and b is the Bergers vector. In this model, the increase of vacancy concentration C, and dislocation density p by the strain e is expressed by the C,= K.8’ (3) p = N*e@
(4)
A modified model of dynamic strain aging model for the serrated yielding in substitutional alloys based on the strain aging of mobile dislocations temporarily arrested at obstacles has been also proposed [12]. Many investigators have given the values of m, /I and Q,,,in approximate agreement with other studies from the measurements of the strain rate and temperature dependences of lc using equations (2X (3) and (4) E7,18,191. In the present observation, it becomes clear that abrupt collective cross-slip of screw dislocations is also origin of the serrated yielding as shown in Figs. 10 and II. Since the screw dislocations have only shear component as their stress field, the dynamic strain aging, which is caused by the vacancyassisted lattice diffusion of solute atoms to the edge dislocations, of screw dislocations by magnesium
TABATA, et al.: DISLOCAT!ONS M Al-Mg SXNGLE CRYSTALS atoms cannot be considered in general. Iiowever, if the screw ~si~ations have edge components, for example, if they have jogs on them, solute atoms interact with the parts of jogs on screw dislocations. Moreover, there is some possibility of interaction between screw dis~~tions and sobte atoms when solute atoms coagulate and form the tetragonal distortion. In addition to these interactions, shear modulus effect of solute atoms is important in the case of interaction between screw dislocation and solute atoms. These ekcts of solute atoms suppress the cross slip probability of screw dislocations because mean free length of screw dislocations which can cross slip becomes short and similiar with each other, and enable them to pile up against the obstacles as shown in Figs. 10 and 11. According to the increase of the applied stress, these piled-up ScTew di~~~o~ cross slip colkctive~y because the mean fke length is very similar in every parts of piled-up screw diskations. This is the reason why screw dislocations pile up against the obstacles and cross slip cokctive~y in Al-Mg alloy. As discussed in the above, onset of serrated yielding of Al-Mg alloys is also attributed to the collective motion of screw dislocations at the obstacks. Tberefore, it can be concluded tbat the dynamic strain aging mode& in which the interaction between edge dislooltions and solute atoms is mainly considered [lo], wet fully explain the onset of serrated yictiing of Al-Mg alloys around room temperature and that the physical meaning &,, Q,,,, m, etc., obtained by using equations (2X (3) and (4) is not so Clear.
805
Acknowkfg~ts-The authors are gratefui to Messrs. K. Yoshida, Kamatsu and T. Sakata for their help in maiatenante of tbe electron microscape.
t. B. J. Brindley and P. J. Worthington, Actu metult.17, 1357 (1967). 2. E. 0. Hall, Yield Point Phenamena in Metals and Afloys, Plenum Press, New York (1970). 3. A. T. Thomas. Acra me&~. f4. X363f19661. 4. II Munt and E. Macberau&i Z. ‘Met&k. 57, 552 ww.
5. A. Wijlcr and J. Sehade van Wtstrum, Script0 Met. 5, 159 (1971). 6. S. Miura and H. Yamauchi, Trans. Japan Inst. Metals 13, 82 (1971). 7. P. G. Maccormick, Acta metafl.20,351 (1972). 8. H. Fujita and T. Tab&a, Acta metaff.25 793 (197f). 9. T. T&&a, H. Fujita and N. &da, Mater. W. Engngto be published (f980). 10. A. H. Cottnll, Phil. Nag. 454, 829 (1953). il. W. G. Johnston and J. J. Gilman, J. annf. .* Phvs. _ I% 1259 (1959).
12. R. K. Ham and D. Jaffrey, Phii. Msg. 15, 247 (1%7). 13. H. Fuiita. T. Tabata. N. Sumida. M. ?&tmi. K. Yoshida z&d &f. Komat& Proc o$bth int. Con,l:on H&h Voftage Electron microscopy, ToUIouse, p. 345 (19715). 14. T. Tabata, H. Mori, H. Fuji& and I. Ishikawa, f. pI~ys. Sac. Japan 40,1103 (1976). 15. T. Mori and M. Meshii, Actu Metali. 17, 167 (1969). 16. H. Fuji& J. phys. Sac. Japan 23,1349 (1967). 17. S. Miura, J. Takamura and M, Yam&&a, StiyokswiSiri 16, 144 (1967). @usaction of the Mining and Maui Ass&&on Kyotof. 18. P. G. Maccarmiek, Am metdl. 19,463 (1971). 19. S. R. Masxwcn and B. Ramaswami, Phil. Msg. 21,1025 (1970).