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The work-hardening of anthracene single crystals
THE
WORK-HARDENING
OF ANTHRAGENE P. M.
SINGLE
CRYSTALS*
ROBINSONt
Single stage work-hardening is observed when anthracene single cry&Is are deformed in sheer with the (001) slip plane parallel to the plane of shear and with either the [OlOJor [I IO] slip directions parallel to the stress axis. Three stage work-hardening is observed when appreciable amounts of slip occur in the two slip directions in the basal plane. The rates of hardening during stages I and II am then dependent cm the orientation of the slip directions with respect to the stress axis. Latent hardening of the inactive slip system occurs when the crystal is deformed in one of the slip directions. Latent softening may be induced by either reversing the slip direction or, in the case of deformation in [loo], by an intermediate deformation in the [OlO] direction. The work-hardening of anthraoene and the latent hardening and softening are explained in terms of the elastic interaction between glide diafocations. It is though that stage I work-hardening occurs when there is predominantly easy glide in one slip direction in the basal plans and that stage II occurs when glide dislocetions of different Burgem vector produced by duplex slip in the basal plane interact to form sessile dislocation locks. DURC~SSE~~ PAR ECROUISSAGE DE MONO~RISTAU~ D’A~THRACE~E Un durcissement par Bcrouissage caract&& per un seul stade est observe quand des monoeristaux d’anthracbne sont dBformBs en cisaillement avec le plan de glissement (001) parall&le au plan de cisaillement et avec les directions de glissement soit [OlO] soit [llO] parrtll&les8. l’axe de contrainte. Un durcissement par Bcrouisaagecaracterise par trois stades est observe dans Ie caa ot des augmentations appr&iables du glissement se produisent dens lea deux directions de glissement du plan de base. Les taux de durcissement durant lee stades I et II dependent alors de I’orientation des directions de glissement par rapport & l’axe de oontrainte. Un durcissement latent du systeme de glissement inactif se produit quand Ie cristal est deform6 dans l’une des directions de glissement. Un ramollissement latent peut %re induit soit par inversion de la direction de glissement, soit, dans Is caa de deformation suivant [ 1001, par une d&formation intermtidiaire dans la direction [OlO]. Le durcissement par Bcrouissege de l’anthra&ne ainsi que le duroissement latent et le ramollissement latent sont expliqu& au moyen de l’interaction tSlastiqueentre Ies dislocations glissiles. L’auteur pense que le stade I du durciesement par Bcrouissage se produit quand il y a p&dominance d3 glissement facile dans une des directions de glissement du plan de base et que Ie stade II se produit quand les dislocations glissiles de vecteurs de Burgers diff&ents produites par un glissement double dans le plan de base interagisssnt pour former des noeuds de dielocations sessiles. VERFESTIGUNG VON ANTHRAZENEINKRISTALLEN Die Verfestigung von Anthrazeneinkristallen erfolgt in einem einzigen Bereich, wenn bei Scherverformung die (OOl)-Ebene parallel zur Scherebene und entweder die [OlO]-oder die [llO]-Gleitriehtung in drei Bereichen wird beobachtet, wenn b&r&chtparallel zur S~~~~~ Iiegt. Eine Ve~~tigu~ lithe Abgleitung in den beiden Gleitrichtungen in der Bssisebene erfolgt. Die Verfestigungsgeschwindigkeiten in den Bereichen I und XI hiingen else von der Orientierung der Gleitrichtungen beziiglich der Spannungsachse ab. Late&e Verfestigung des inaktiven Gleitsystems tritt auf, wenn der Kristall in einer der Gleitrichtkann induziert werden, wenn die Gleit~cht~ umgekehrt ungen verformt wird. Late&e Entf~ti~~ wirt, oder im Falle der Verformung in [ lOO]-Richtung durch eine Zwischenverformung in [OlO]-Riohtung. Die Verfestigung von Anthrazen sowie die Iatente Verfestigung und Entfestigung werden auf Verfestigung im Bereiab I tritt vermutWechselwirkungen zwischen Gleitverseteungen zuriickgefm. Iich dann auf, wenn die Einfachgleitung hauptsi3ohlich in einer Gleitrichtung erfolgt. Der Bereich 11 tritt auf, wenn Gleitversetzungen mit verschiedenem Burgersvektor und durch Doppelgleitung crzeugt in der Basisebene in Wec~el~k~g treten und unbewegliche Ve~tzungss~r~n bilden.
1. INTRODUCTION
In recent years much attention has been given to the work-hardening of plastic materials, particularly f.c.c. and c.p.h. metals. ~~0) Progress towards a unified theory of work-hardening has become progressively slower as the experimental evidence has mounted. This has been partly due to the difficulty in reconciling seemingly oimflicting experimental results and partly to the different interpretations of the sa.me results by various groups of workers. * Received September 26,1967. t Commonwealth Scientific and
Industrial Research Organization, Division of Tribophysics, University of Melbourne, Victoria, AustraIia. ACTA METALLURGICA, 5
VOL. IS, APRIL
1968
545
The development of the theory has been hindered h a certain extent by the lack ofun~mbi~ous correlations between the form of the stress-strain curves and the slip systems operating at any particular time. In the course of an invest&&ion of defects in moleou1ar orystals, it became evident that anthracene and naphthalene single crystals exhibited unusual workhar dening behaviour, the type and extent of which could be easily controlled experimentally. In order to plaoe the work-hardening charitcteristics of anthrracene in perspective, it is desirable to first consider briefly th e various theories proposed for the workhardening of metals.
546
ACTA
METALLURUICA,
Three stage work-hardening is observed with single C@XL~S of f.c.c. metals and it is generally agreed that stage I is characterised by easy glide on a single slip system with a low rate of work-hardening. It is thought that the hardening during this stage is due to the interaction between the elastic strain fields of individual dislocations,(lss’ the formation of dipole and dipole clusters,(s~B)the interaction of glide dislocations with point defects,@) or the interaction of glide dislocation with forest dislocations.(‘) The rate of work-hardening increases during stage II and appears to have a constant relationship to the modulus of rigidity of the metal.c4) There has been much controversy over the mechanism of hardening during stage II, but the various theories can be grouped as (1) the pile-up theories, where hardening is thought to be primarily due to long range internal stresses from piled-up groups of dislocations interacting with glide dislocations;(1*3) (2) forest theories, in which hardening is attributed to a decrease in the mean free path of the glide dislocations, either by slip on secondary systems or by the formation of dislocation tangles;(4s7’ and (3) jog theories, in which the motion of dislocations is hindered by the formation of jogs and thesubsequent production of vacancies during their non-conservative motion.(s*6) The various theories have in common the postulation that dislocation climb or cross-slip is responsible for the decrease in the rate of workhardening during stage III. In c.p.h. metals, which at low temperatures deform predominantly by slip on the basal plane, onb stage I although the dislocation hardening is observed, (11~16) arrangements after deformation appear to be complex.(a*1s.17-z2)The situation is somewhat complicated by the possibility of secondary slip on pyramidal planes. (16) The most unambiguous determinations of the rate of work-hardening in c.p.h. metals were carried out by Washburn et al.,(11-14) who deformed zinc single crystals in shear with the basal plane parallel to the plane of shear. They observed single stage work-hardening for all orientations of the slip direction with respect to the stress axis. Many of the theories proposed to account for the observed rate of work-hardening during easy glide in c.p.h. metals are somewhat similar to those proposed for stage I in f.c.c. metals. (2-5*17) The observation of sessile dislocation loops formed from the condensation of vacancies on the basal plane of zincP) has led to the suggestion that such loops play a major role in the work-hardening of c.p.h. metals.(1**20) Some observations indicate that the vacancy loop concentration increases during deformation.(zO) As three equivalent
VOL.
16,
1966
slip directions exist in the basal plane of c.p.h. metals, hardening may also arise due to the interaction of dislocations of different Burgers vector in the same plane. f20) Recent work on the deformation behaviour of anthracene and naphthalene,(23-26)both of which have a monoclinic structurei(20) has shown that slip may occur in the basal plane in the [llO] direction as well as in the [OlO] direction reported earlier.(27szs) Single stage work-hardening with extensive easy glide is observed when crystals deform in tension by slip in either slip direction.t26) There is no evidence to data of extensive slip on planes other than the basal plane. The occurrence of two crystallographically non-equivalent slip directions in the one active slip plane is somewhat unusual, the closest parallel case being the three equivalent slip directions in the basal plane of c.p.h. metals. In the present investigation, the crystals were uubjetted to a constrained deformation in shear, with the basal plane parallel to the plane of shear. This allowed both slip directions in the basal plane to be activated simultaneously. By rotating the crystal with respect to the stress axis, and still keeping the slip plane parallel to the plane of shear, it was possible to obtain either single stage or three stage work-hardening and to vary the extent of the various stages and the rates of hardening. Therefore, the onset of the various stages of work-hardening could be studied in a system which is free from the complicating effects of possible slip on secondary slip planes. 2. MATERIALS
AND EXPERIMENTAL PROCEDURE
The material used was Hopkins and Williams Blue Fluorescent Grade anthracene further purified by recrystallization, chromatography on an alumina column and zone-refining. The final purity was better than 30 ppm total impurity, which was the limit of resolution of analysis by mass spectroscopy. Single crystals 12 cm long and 3 mm dia. were grown at a rate of 0.1 cm/hr in Pyrex tubes in a Bridgeman furnace with the upper zone 12’C above and the lower zone 12°C below the melting point. After removing from the Pyrex tubes, the crystal surfaces were polished in a bath of toluene. X-ray analysis showed that the crystals exhibited a high degree of perfection and etch-pitting on the basal plane with a mixed acid etch(B) revealed only occasional low angle boundaries. The dislocation density, as estimated from the occurrence of etch-pits, was 103-lo5 dislocations/cm2. The crystals selected for the shear tests were those
ROBINSON:
WORK
HARDENING
547
ANTHRACEXE
single crystals in tension. (%) The rate of work-hardening during easy glide wa8 46-60 g/mml/lOOo/o strain, and appeared to be unaffected by the density of grownin di81ocations in the cry&al. Deformations of up to 40% were observed before failure occurred by fracture on the basal plane. Single stage work-hardening was no longer observed when one of the Slip direction8 w&8 at a small angle (<5”) to the stress axis 80 that under the conditions of constrained deformation a small amount of slip occurred in the second slip direction. For such orientations, a fairly extensive region of easy glide was observed, followed by a second stage of more rapid work-hardening (Fig. 1) once t.he strees resolved along the secondary slip system exceeded the critical shear stress for Slip in that direction. A linear relation between stress and strain was observed during the second stage as well as during stage I. When extensive slip occurred in bwo directions, that is for large angles bet.ween a slip direction and the stress axis, three stage work-hardening was obtained (Fig. 1). The rat,es of work-hardening during stages I and II increased, and the extent of stage I decreased, as the angle between the slip direction and the st,rcss axis became larger (Fig. 2). For large misoricntations. extremely high rates of work-hardening were observed compared with those during easy glide in a single slip direction. During stage TTI, the rat,e of work-hardening decreased prior t,o failure by fra&ure on the basal plane. When the stress axis bisected the angle between
with the baaal plane perpendicular to the rod axis. These cry8tals were cleaved into approximately 1 in. lengths. The design of the shear jig wa8 such that when these rods were placed in position the basal plane Wa8 parallel to the plane of shear. The slip direction8 in the basal plane were then orientated with respect to the stress axis by making u8e of the birefringent nature of anthracene when viewed normal to the basal plane. A line on a rotatable section at the centre of an angular scale on one side of the shear jig was viewed through the length of the crystal and the crystal rotated until a single lino was seen. The [ 1001 direction in the basal plane was then parallel to the zero line at the centre of the angular scale. The zero line could be set at any desired angle to the stress axis and in this way any orientation of the slip directions in the basal plane could be readily obtained. 3. RESULTS 3.1 Orientation dependence of the stress-strain curses Single stage work-hardening with a long region of easy glide was observed when crystals were deformed with the basal plane parallel to the plane of shear and with either the [OIO] or [llO] slip directions parallel to the stress axis (Fig. 1). The critical resolved shear stress for plastic deformation to begin at 298’K in either the [OlO] or [ 1lo] direction8 was 13-l 5 g/mm2, in agreement with the result.8 obtained on deforming 70
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STRAIN
FIO. 1. Shear stress vs. sheer strain curves for anthraceno single crystals deformed by slip in the basal plane in the [OlO]and [ I lo] directions and in B direction bisecting those two, showing single stage work-hardoning when slip occurs in a single direction and thrm stage work-hardcning when duplex slip occurs.
0 !!?!f
~--__.-__.._... IO ANGLE
: 20 BETWEEN
[IIO]
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Flo. 2. The orientation dependence of the ratm of workhardening during atuges I and II when tho stress axis lies between [l IO] and [ITO’I.
_
548
ACTA
METALLURQICA,
VOL.
16,
1968
two slip directions, rapid rates of work-hardening were observed in stages I and II and cleavage fracture often occurred before the onset of stage III. This is presumably because the fracture stress in the basal plane is exceeded before the stress resolved in the slip dire&ion is large enough to initiate stage III. 3.2 Lxtent hardening of inactive slip system Prior deformation in the [llO] direction led to an increase in the critical shear stress for slip in the [OiO] direction during subsequent deformation (Fig. 3) and vice-versa. The stress was higher than would be expected if deformation had continued in the original direction (Fig. 3). Although single stage work-hardening was still observed, pre-straining in the [llO] direction had a marked effect on the rate of workhardening in the [OlO] direction, the increase in hardening depending on the amount of pre-strain. 3.3 Latent softening by reversing slip direction When crystals were deformed plastically in either the [OlO] or [ 1lo] directions and then rotated through 180”, the stress necessary for plastic flow in the reverse direction was lower than that necessary for continued flow in the original direction. The decrease in flow stress was small because of the low rates of workhardening in either slip direction. The softening effect was more readily observable after giving the crystal a small plastic strain to harden the latent slip system and to increase the rate of work-hardening .during subsequent deformation in the forward s,ud reverse directions in the system. For example, Fig. 4 shows 50
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FIQ. 4. Shear street vs. eheer strain ourvee for an anthracene eingle crystal deformed by slip in the bassal plene in the [OlO] and then in the [OTO]direction, showing latent eoftaning of the dormant elip system. Cry&al givenesmell prior deformation in [l lo] direction.
the latent softening in the [OIO] direction in a crystal which had been given a small prior strain in the [l lo] direction. Single stage work-hardening was observed on deforming in the reverse direction with little detectable change in rate from that in the original direction. 3.4 Latent direction
softening
by deformation
in second slip
Three stage work-hardening was observed when the crystals were deformed with the [ 1001directionparallel to the stress axis so that both the [l lo] and [ 1101 slip directions were activated. A series of crystals were deformed in this manner into stage II, unloaded and then deformed in the [OlO] direction to various strains. On reloading in the [lOO] direction, it was found that the stress at which plastic deformation began was lower than the flow stress necessary to continue deformation during the original straining in the [lOO] direction (Fig. 5). The latent softening in the [lOO] direction was dependent on the shear strain during the intermediate deformation in the [OlO] direction (Fig. 6). Deformation in the [OlO] direction prior to deforming in the [lOO] direction had a pronounced effect in increasing the extent of stage I and in decreasing the rate of work-hardening during this stage (Fig. 7).
1 4. DISCUSSION
STRAIN
FIG. 3. Sheer etresa vs. shear strain curves for an anthracene single oryetal deformed by slip in the base1 plane in the [OlO] direction after prior deform&ion in the [I IO] direction, ehowing 18b3nt hardening of the dormant slip system.
The deformation of anthracene single crystals in shear is of interest from the point of view of workhardening theories because either single stage or three stage work-hardening can be obtained depending on the orientation of a slip direction with respect to the stress axis. Theories of work-hardening generally
ROBINSON:
[IOdllS
WORK
HARDENING
[OlO$/S
A
OF
bkA
A
SHEAR
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STRAIN
FIU. 6. Shear stress va. shear strain curvea for an anthracene singlecrystal deformedin the [ lOO]direction,then in the [OlO]direction, and finally m-deformed in the [lOO] direction, showing latent softening introduced by the intermediate deformation in [OlO].
revolve around the mechanism underlying the rapid hardening during stage II. This stage is only observed in anthracene when appreciable slip takes place in two directions in the basal plane. Some indication of the process by which the interaction of glide dislocations of different Burgersvectorinthe basal planegives rise to hardening is given by the observations of latent softening. Rapid hardening occurs during stage II when crystals are deformed in the [lOO] direction so that slip occurs equally in the [llO] and [liO] slip directions. An intermediate deformation in the [OlO] direction, however, reduces the flow stress in the [lOO]
direction, indicating that the original hardening is probably due to an elastic interaction between the glide dislocations rather than a process which gives rise to jogs or point defects. The probable mechanism of hardening is that [llO] and [liO] glide dislocations interact to form sessile [lOO] dislocations. When the crystal is deformed in the [OlO] direction, the flow stress in the [loo] direction is reduced due to the reaction of the [OlO] dislocations with the sessile [lOO] locks to form mobile [llO] dislocations.
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FIG. 6. The percentage reduction in flow stress in the [IOO] direction due to an intermediate deformation in the [OlO] direction, aa a function of the shear strain during the intermediate deformation.
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0.01
I
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Fro. 7. Shear stress vs. shear strain curves for anthracene single crystals, showing the incmased extent of stage I work-hardening induced by prior deformation in the [OlO] direction.
660
ACTA
METALLURGICA,
The orientation dependence of the work-hardening can be acoounted for on the basis of the interaotion between dislocation8 of the same Burgers vector and the formation of sessile dislocation look8 when dislocation8 of different Burgers vector approach one another. The low rates of work-hardening observed during the extensive easy glide in either the [OlO] or [llO] directions and the decree in flow stress on reversing the slip direction indicate that the hardening is probably due to the interaction between the stress fields of the glide dislocation, as proposed by Seeger and oo-workers(1-3) for easy glide in c.p.h. metals. The contribution to the work-hardening from the intersection of the glide dislocations with grownin dislocations, which will probably have [OOl] Burger8 veotor,(25) is thought to be minor as the rate of hardening during easy glide does not appear to be sensitive to the density of grown-in dislocations, at lea& within the limits of the current experiments. The rate of hardening during easy glide in one slip direction increases rapidly and the extent of the stage decreases as glide dislocations of another Burgers vector in the basal plane are introduced, either concurrently with theprimaryglidedislocationsbya slight misorientation between the slip direction and the stress axis or by a small prior deformation in a second slip direction. The results indicate that the formation of sessile dislocation locks between the primary and secondary glide dislocations is extremely effective in raising the rate of hardening during stage I. Single stage work-hardening may be expected to continue as long as the density of such sessile dislocation locks is insufficient to have the overall effect of decreasing the long easy glide of the primary glide dislocations. Stage II work-hardening does not begin until a stress level is reached at which the critical resolved shear stress for massive slip to begin in the second slip direction is exceeded. This correspond8 to the formation of a high density of sessile dislocations, which lead to rapid hardening due to the decrease in the distance that the glide dislocations in the two directions can move before encountering a sessile lock. The density of such locks will depend on the amount of slip in each of the two active slip directions, thus explaining the orientation dependence of the rate of hardening during stage II. The observed latent hardening of the inactive slip system during deformation in one slip direction can also be readily explained by the formation of such sessile dislocations on subsequent deformation on the originally inactive system. On the basis of the rapid work-hardening being due to the formation of sessile dislocation locks, stage III hardening begins when the stress level is sufficiently
VOL.
16,
1968
high to allow dislocation climb around the sessile looks to take place. The present results indicate that in anthracenc the occurrence and extent of the various stages of workhardening are dependent on the degree to which slip ocours in one or more slip directions in the basal plane. The only similar work on the work-hardening of metals in which slip has been rigorously confined to one plane is that of Washburn et aZ.(*l-“’ with zinc single crystals. Although duplex slip in the basal plane of zinc led to an increased rate of workhardening, no second stage work-hardening was observed. This could possibly be due to the dislocation looking being weak compared with the situation in anthraoene where the [llO] glide dislocat.ion is associated with a stacking fault(2s) and may therefore form strong locking points. As the deformation in anthracene is confined to one slip plane, many of the theories advanced for stage II work-hardening in metals are inapplicable. For example, it is unlikely that there will be an appreciable contribution to the work-hardening due to the production of jogs or point defects during deformation, as slip does not occur on intersecting slip planes and the intersection of glide dislocations with grown-in forest dislocations produces comparatively little work-hardening. However, the processes giving rise to work-hardening in anthracene appear to be quite similar in many respects to those proposed by Seeger and co-workers(1-3~S”-S’) to account for t.he various stage8 of hardening in f.c.c. metals. They attribute the work-hardening as being due to long range stresses between glide dislocation8 and the onset of stage II to be an increase in these stresses due partly to the formation of sessile locks formed between primary glide dislocations and those on secondaryslipplanes.(32) 5. CONCLUSIONS 1. The crystal structure and the active slip systems in anthracene enable the work-hardening characteristics to be examined under conditions which eliminate from consideration many of the theories proposed for the work-hardening of metals. 2. Single stage work-hardening is observed when anthracene single crystals are deformed in shear with the basal plane parallel to the plane of shear and with the [OlO] or [IlO] slip directions parallel to the stress axis. 3. If one of the slip directions makes a small angle (
WORK
ROBINSON:
4. Three stage work-hardening orientation that
with
appreciable
tions.
respect
5. Latent
stress
is such
in two direc-
during
stage8
I
on orientation.
hardening
when the
when the
axis
of slip occur
of work-hardening
and II are dependent occurs
to the
amounts
The rates
is observed
HARDENING
of the
crystal
inactive
is deformed
slip system in one of the
slip dire&ions. 6. Lat,ent
softening
have been deformed II
arc
extent
then
occurs
deformed
in the
of stage I hardening
direction
when
crystals
in the [lOO] direction
can be increased
which
into stage
[OlO] direction.
on deforming
The
in the [lo01
by a prior deformation
in
the [OlO] direction. 7. It is thought when there direction
that stage I work-hardening
is predominantly
when glide dislocations produced
by duplex
of different
8. The senile
dislocation
dislocations
in one slip
stage
II occurs
Burger’s
slip in the basal
to form sessile dislocation producing
easy glide
in the basal plane and that
occurs
vector
plane interact
locks. locks
can be broken
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REFERENCES 1. .i. SEEOER, H. KROX~~ULLER,9. .MADERand H. TRAUBLE, Phil. Maa. 6. 639 11961). 2. A. SEEOE~ &d H.‘TRACBLE, 2. Met&k. 51,435 (1960). 3. S. M~ER, A. SEFXXER and H. THIUUNQER, J. appl. Phye. 54. 3376 (1963). 4. U. KUHLMASN-WIISDORF. Tran8. metall. Sot. AIME 224, 1047 (1962). ’ 5. P. B. HImcH, Relation between the Structure and Mechanical Prove&e8 of M&la. D. 39. H.M.S.O. (1963). 6. I’. B. *HIR&, D&Q&. Faraday Sot.‘ So.’ 38. 111 (1964).
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7. 2. S. BA~INSKI, Phil. Mag. 4,393 (1969). 8. Z. S. BASINSKI and S. J. BASINSKI, Phil. Mag. 9, 61 (1964). 9. F. J. WORZALA and W. H. ROBIXSOS, Phil. Mag. 16, 939 (1967). IO. H. J. LEVIN~TEIN and W. H. ROBINSON, J. appl. Phys. 33.3149 (1963). 11. E. H. ED&ARD$ and J. WASHBURN, Trans. Am. Ivat. Min. Engf-8200, 1239 (1954). 12. C. H. Lr, J. WASHBL-RN and E. R. PARKER, Trans. Am. In&. Min. Engre 107, 1223 (1953). 13. H. DR~LYARD,J. WASHBURN 8nd E. R. PARKER, Trans. Am. Zn8t. Min. Engra 197, 1226 (1953). 14. E. H. EDWARDS, J. WASHBURN and E. R. PARKER, Trane. Am. Inat. Min. &ngr8 197, 1525 (1953). 16. W. PFEIPFER, Phya. Status Solidi 2, 1727 (1962). 16. M. B&EK, Phyr. Skztwr Solidi S, 2169 (1963). 17. J. S. LALLY and P. B. HIRSCH, Phil. Msg. 12,595 (1965). 18. A. BEROAEZAN, A. FO~RDE~JX and S. AJIELISCHX, Acta Met. 9, 464 (1961). 19. M. BO&K and P. KsATOCHVfL, Phya. St&U8 SOlidi 6, 169 (1964). 20. P. KRATOCHV~L,PhiE. Mag. 13,267 (1966). 21. M. Bo&K, P. LuK.~~, B. SMOLA and M. ~VABOV~, Phya. Statw Solidi 7, 173 (1964). 22. A. SEEOER, H. KRONMULLER, 0. BOSER and Y. RAIT, Phye. St&w, Solidi 3, 1107 (1963). 23. P. M. ROBINSON and H. G. SCOTT, Phys. Statue Solidi 20, 461 (1967). 24. P. M. ROBINSON and H. G. SCOTT, Actu Met. 16, 1230 (1967). 25. P. M. ROBIXSOS and H. G. SCOTT, Acfa Met. 16, 1581 (1967). 26. A. I. KITAIOORODSKI, Organic Chemical Cryelollography, Izd. Aked. Nauk SSSR. Moscow (1955): EngliahTranal. by Consultants Bureau kntmpri& Inc: ‘( 196y). 27. A. KOCHENDORFER, Z. Kriat. 97,263 (1937). 28. R. H. GORDON, Acta Met. 13, 199 (1965). 29. P. M. ROHINSON and H. G. SCOTT, J. Cryst. Urouth, to be published.
30. A. SEEGER and M. WILKENS, 2nd Int. Symv. Reinstatofle in Wissemchaft und Technik, W&=&n, Akademieverlsg,
Berlin (1966).
SEP.OER, North Amoricen Aviation Scienw Report (1967). 32. U. NSSMANN, Phys. St&c8 Solidi 12, 723 (1965) 31. A.
de? 1965. Contra
WORK-HARDENING
OF ANTHRAGENE P. M.
SINGLE
CRYSTALS*
ROBINSONt
Single stage work-hardening is observed when anthracene single cry&Is are deformed in sheer with the (001) slip plane parallel to the plane of shear and with either the [OlOJor [I IO] slip directions parallel to the stress axis. Three stage work-hardening is observed when appreciable amounts of slip occur in the two slip directions in the basal plane. The rates of hardening during stages I and II am then dependent cm the orientation of the slip directions with respect to the stress axis. Latent hardening of the inactive slip system occurs when the crystal is deformed in one of the slip directions. Latent softening may be induced by either reversing the slip direction or, in the case of deformation in [loo], by an intermediate deformation in the [OlO] direction. The work-hardening of anthraoene and the latent hardening and softening are explained in terms of the elastic interaction between glide diafocations. It is though that stage I work-hardening occurs when there is predominantly easy glide in one slip direction in the basal plans and that stage II occurs when glide dislocetions of different Burgem vector produced by duplex slip in the basal plane interact to form sessile dislocation locks. DURC~SSE~~ PAR ECROUISSAGE DE MONO~RISTAU~ D’A~THRACE~E Un durcissement par Bcrouissage caract&& per un seul stade est observe quand des monoeristaux d’anthracbne sont dBformBs en cisaillement avec le plan de glissement (001) parall&le au plan de cisaillement et avec les directions de glissement soit [OlO] soit [llO] parrtll&les8. l’axe de contrainte. Un durcissement par Bcrouisaagecaracterise par trois stades est observe dans Ie caa ot des augmentations appr&iables du glissement se produisent dens lea deux directions de glissement du plan de base. Les taux de durcissement durant lee stades I et II dependent alors de I’orientation des directions de glissement par rapport & l’axe de oontrainte. Un durcissement latent du systeme de glissement inactif se produit quand Ie cristal est deform6 dans l’une des directions de glissement. Un ramollissement latent peut %re induit soit par inversion de la direction de glissement, soit, dans Is caa de deformation suivant [ 1001, par une d&formation intermtidiaire dans la direction [OlO]. Le durcissement par Bcrouissege de l’anthra&ne ainsi que le duroissement latent et le ramollissement latent sont expliqu& au moyen de l’interaction tSlastiqueentre Ies dislocations glissiles. L’auteur pense que le stade I du durciesement par Bcrouissage se produit quand il y a p&dominance d3 glissement facile dans une des directions de glissement du plan de base et que Ie stade II se produit quand les dislocations glissiles de vecteurs de Burgers diff&ents produites par un glissement double dans le plan de base interagisssnt pour former des noeuds de dielocations sessiles. VERFESTIGUNG VON ANTHRAZENEINKRISTALLEN Die Verfestigung von Anthrazeneinkristallen erfolgt in einem einzigen Bereich, wenn bei Scherverformung die (OOl)-Ebene parallel zur Scherebene und entweder die [OlO]-oder die [llO]-Gleitriehtung in drei Bereichen wird beobachtet, wenn b&r&chtparallel zur S~~~~~ Iiegt. Eine Ve~~tigu~ lithe Abgleitung in den beiden Gleitrichtungen in der Bssisebene erfolgt. Die Verfestigungsgeschwindigkeiten in den Bereichen I und XI hiingen else von der Orientierung der Gleitrichtungen beziiglich der Spannungsachse ab. Late&e Verfestigung des inaktiven Gleitsystems tritt auf, wenn der Kristall in einer der Gleitrichtkann induziert werden, wenn die Gleit~cht~ umgekehrt ungen verformt wird. Late&e Entf~ti~~ wirt, oder im Falle der Verformung in [ lOO]-Richtung durch eine Zwischenverformung in [OlO]-Riohtung. Die Verfestigung von Anthrazen sowie die Iatente Verfestigung und Entfestigung werden auf Verfestigung im Bereiab I tritt vermutWechselwirkungen zwischen Gleitverseteungen zuriickgefm. Iich dann auf, wenn die Einfachgleitung hauptsi3ohlich in einer Gleitrichtung erfolgt. Der Bereich 11 tritt auf, wenn Gleitversetzungen mit verschiedenem Burgersvektor und durch Doppelgleitung crzeugt in der Basisebene in Wec~el~k~g treten und unbewegliche Ve~tzungss~r~n bilden.
1. INTRODUCTION
In recent years much attention has been given to the work-hardening of plastic materials, particularly f.c.c. and c.p.h. metals. ~~0) Progress towards a unified theory of work-hardening has become progressively slower as the experimental evidence has mounted. This has been partly due to the difficulty in reconciling seemingly oimflicting experimental results and partly to the different interpretations of the sa.me results by various groups of workers. * Received September 26,1967. t Commonwealth Scientific and
Industrial Research Organization, Division of Tribophysics, University of Melbourne, Victoria, AustraIia. ACTA METALLURGICA, 5
VOL. IS, APRIL
1968
545
The development of the theory has been hindered h a certain extent by the lack ofun~mbi~ous correlations between the form of the stress-strain curves and the slip systems operating at any particular time. In the course of an invest&&ion of defects in moleou1ar orystals, it became evident that anthracene and naphthalene single crystals exhibited unusual workhar dening behaviour, the type and extent of which could be easily controlled experimentally. In order to plaoe the work-hardening charitcteristics of anthrracene in perspective, it is desirable to first consider briefly th e various theories proposed for the workhardening of metals.
546
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Three stage work-hardening is observed with single C@XL~S of f.c.c. metals and it is generally agreed that stage I is characterised by easy glide on a single slip system with a low rate of work-hardening. It is thought that the hardening during this stage is due to the interaction between the elastic strain fields of individual dislocations,(lss’ the formation of dipole and dipole clusters,(s~B)the interaction of glide dislocations with point defects,@) or the interaction of glide dislocation with forest dislocations.(‘) The rate of work-hardening increases during stage II and appears to have a constant relationship to the modulus of rigidity of the metal.c4) There has been much controversy over the mechanism of hardening during stage II, but the various theories can be grouped as (1) the pile-up theories, where hardening is thought to be primarily due to long range internal stresses from piled-up groups of dislocations interacting with glide dislocations;(1*3) (2) forest theories, in which hardening is attributed to a decrease in the mean free path of the glide dislocations, either by slip on secondary systems or by the formation of dislocation tangles;(4s7’ and (3) jog theories, in which the motion of dislocations is hindered by the formation of jogs and thesubsequent production of vacancies during their non-conservative motion.(s*6) The various theories have in common the postulation that dislocation climb or cross-slip is responsible for the decrease in the rate of workhardening during stage III. In c.p.h. metals, which at low temperatures deform predominantly by slip on the basal plane, onb stage I although the dislocation hardening is observed, (11~16) arrangements after deformation appear to be complex.(a*1s.17-z2)The situation is somewhat complicated by the possibility of secondary slip on pyramidal planes. (16) The most unambiguous determinations of the rate of work-hardening in c.p.h. metals were carried out by Washburn et al.,(11-14) who deformed zinc single crystals in shear with the basal plane parallel to the plane of shear. They observed single stage work-hardening for all orientations of the slip direction with respect to the stress axis. Many of the theories proposed to account for the observed rate of work-hardening during easy glide in c.p.h. metals are somewhat similar to those proposed for stage I in f.c.c. metals. (2-5*17) The observation of sessile dislocation loops formed from the condensation of vacancies on the basal plane of zincP) has led to the suggestion that such loops play a major role in the work-hardening of c.p.h. metals.(1**20) Some observations indicate that the vacancy loop concentration increases during deformation.(zO) As three equivalent
VOL.
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slip directions exist in the basal plane of c.p.h. metals, hardening may also arise due to the interaction of dislocations of different Burgers vector in the same plane. f20) Recent work on the deformation behaviour of anthracene and naphthalene,(23-26)both of which have a monoclinic structurei(20) has shown that slip may occur in the basal plane in the [llO] direction as well as in the [OlO] direction reported earlier.(27szs) Single stage work-hardening with extensive easy glide is observed when crystals deform in tension by slip in either slip direction.t26) There is no evidence to data of extensive slip on planes other than the basal plane. The occurrence of two crystallographically non-equivalent slip directions in the one active slip plane is somewhat unusual, the closest parallel case being the three equivalent slip directions in the basal plane of c.p.h. metals. In the present investigation, the crystals were uubjetted to a constrained deformation in shear, with the basal plane parallel to the plane of shear. This allowed both slip directions in the basal plane to be activated simultaneously. By rotating the crystal with respect to the stress axis, and still keeping the slip plane parallel to the plane of shear, it was possible to obtain either single stage or three stage work-hardening and to vary the extent of the various stages and the rates of hardening. Therefore, the onset of the various stages of work-hardening could be studied in a system which is free from the complicating effects of possible slip on secondary slip planes. 2. MATERIALS
AND EXPERIMENTAL PROCEDURE
The material used was Hopkins and Williams Blue Fluorescent Grade anthracene further purified by recrystallization, chromatography on an alumina column and zone-refining. The final purity was better than 30 ppm total impurity, which was the limit of resolution of analysis by mass spectroscopy. Single crystals 12 cm long and 3 mm dia. were grown at a rate of 0.1 cm/hr in Pyrex tubes in a Bridgeman furnace with the upper zone 12’C above and the lower zone 12°C below the melting point. After removing from the Pyrex tubes, the crystal surfaces were polished in a bath of toluene. X-ray analysis showed that the crystals exhibited a high degree of perfection and etch-pitting on the basal plane with a mixed acid etch(B) revealed only occasional low angle boundaries. The dislocation density, as estimated from the occurrence of etch-pits, was 103-lo5 dislocations/cm2. The crystals selected for the shear tests were those
ROBINSON:
WORK
HARDENING
547
ANTHRACEXE
single crystals in tension. (%) The rate of work-hardening during easy glide wa8 46-60 g/mml/lOOo/o strain, and appeared to be unaffected by the density of grownin di81ocations in the cry&al. Deformations of up to 40% were observed before failure occurred by fracture on the basal plane. Single stage work-hardening was no longer observed when one of the Slip direction8 w&8 at a small angle (<5”) to the stress axis 80 that under the conditions of constrained deformation a small amount of slip occurred in the second slip direction. For such orientations, a fairly extensive region of easy glide was observed, followed by a second stage of more rapid work-hardening (Fig. 1) once t.he strees resolved along the secondary slip system exceeded the critical shear stress for Slip in that direction. A linear relation between stress and strain was observed during the second stage as well as during stage I. When extensive slip occurred in bwo directions, that is for large angles bet.ween a slip direction and the stress axis, three stage work-hardening was obtained (Fig. 1). The rat,es of work-hardening during stages I and II increased, and the extent of stage I decreased, as the angle between the slip direction and the st,rcss axis became larger (Fig. 2). For large misoricntations. extremely high rates of work-hardening were observed compared with those during easy glide in a single slip direction. During stage TTI, the rat,e of work-hardening decreased prior t,o failure by fra&ure on the basal plane. When the stress axis bisected the angle between
with the baaal plane perpendicular to the rod axis. These cry8tals were cleaved into approximately 1 in. lengths. The design of the shear jig wa8 such that when these rods were placed in position the basal plane Wa8 parallel to the plane of shear. The slip direction8 in the basal plane were then orientated with respect to the stress axis by making u8e of the birefringent nature of anthracene when viewed normal to the basal plane. A line on a rotatable section at the centre of an angular scale on one side of the shear jig was viewed through the length of the crystal and the crystal rotated until a single lino was seen. The [ 1001 direction in the basal plane was then parallel to the zero line at the centre of the angular scale. The zero line could be set at any desired angle to the stress axis and in this way any orientation of the slip directions in the basal plane could be readily obtained. 3. RESULTS 3.1 Orientation dependence of the stress-strain curses Single stage work-hardening with a long region of easy glide was observed when crystals were deformed with the basal plane parallel to the plane of shear and with either the [OIO] or [llO] slip directions parallel to the stress axis (Fig. 1). The critical resolved shear stress for plastic deformation to begin at 298’K in either the [OlO] or [ 1lo] direction8 was 13-l 5 g/mm2, in agreement with the result.8 obtained on deforming 70
30007-
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601
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/W’
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005
006
0.07
5
x-
STRAIN
FIO. 1. Shear stress vs. sheer strain curves for anthraceno single crystals deformed by slip in the basal plane in the [OlO]and [ I lo] directions and in B direction bisecting those two, showing single stage work-hardoning when slip occurs in a single direction and thrm stage work-hardcning when duplex slip occurs.
0 !!?!f
~--__.-__.._... IO ANGLE
: 20 BETWEEN
[IIO]
__.._ .3 STRESS
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Flo. 2. The orientation dependence of the ratm of workhardening during atuges I and II when tho stress axis lies between [l IO] and [ITO’I.
_
548
ACTA
METALLURQICA,
VOL.
16,
1968
two slip directions, rapid rates of work-hardening were observed in stages I and II and cleavage fracture often occurred before the onset of stage III. This is presumably because the fracture stress in the basal plane is exceeded before the stress resolved in the slip dire&ion is large enough to initiate stage III. 3.2 Lxtent hardening of inactive slip system Prior deformation in the [llO] direction led to an increase in the critical shear stress for slip in the [OiO] direction during subsequent deformation (Fig. 3) and vice-versa. The stress was higher than would be expected if deformation had continued in the original direction (Fig. 3). Although single stage work-hardening was still observed, pre-straining in the [llO] direction had a marked effect on the rate of workhardening in the [OlO] direction, the increase in hardening depending on the amount of pre-strain. 3.3 Latent softening by reversing slip direction When crystals were deformed plastically in either the [OlO] or [ 1lo] directions and then rotated through 180”, the stress necessary for plastic flow in the reverse direction was lower than that necessary for continued flow in the original direction. The decrease in flow stress was small because of the low rates of workhardening in either slip direction. The softening effect was more readily observable after giving the crystal a small plastic strain to harden the latent slip system and to increase the rate of work-hardening .during subsequent deformation in the forward s,ud reverse directions in the system. For example, Fig. 4 shows 50
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FIQ. 4. Shear street vs. eheer strain ourvee for an anthracene eingle crystal deformed by slip in the bassal plene in the [OlO] and then in the [OTO]direction, showing latent eoftaning of the dormant elip system. Cry&al givenesmell prior deformation in [l lo] direction.
the latent softening in the [OIO] direction in a crystal which had been given a small prior strain in the [l lo] direction. Single stage work-hardening was observed on deforming in the reverse direction with little detectable change in rate from that in the original direction. 3.4 Latent direction
softening
by deformation
in second slip
Three stage work-hardening was observed when the crystals were deformed with the [ 1001directionparallel to the stress axis so that both the [l lo] and [ 1101 slip directions were activated. A series of crystals were deformed in this manner into stage II, unloaded and then deformed in the [OlO] direction to various strains. On reloading in the [lOO] direction, it was found that the stress at which plastic deformation began was lower than the flow stress necessary to continue deformation during the original straining in the [lOO] direction (Fig. 5). The latent softening in the [lOO] direction was dependent on the shear strain during the intermediate deformation in the [OlO] direction (Fig. 6). Deformation in the [OlO] direction prior to deforming in the [lOO] direction had a pronounced effect in increasing the extent of stage I and in decreasing the rate of work-hardening during this stage (Fig. 7).
1 4. DISCUSSION
STRAIN
FIG. 3. Sheer etresa vs. shear strain curves for an anthracene single oryetal deformed by slip in the base1 plane in the [OlO] direction after prior deform&ion in the [I IO] direction, ehowing 18b3nt hardening of the dormant slip system.
The deformation of anthracene single crystals in shear is of interest from the point of view of workhardening theories because either single stage or three stage work-hardening can be obtained depending on the orientation of a slip direction with respect to the stress axis. Theories of work-hardening generally
ROBINSON:
[IOdllS
WORK
HARDENING
[OlO$/S
A
OF
bkA
A
SHEAR
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-4NTHRACENE
STRAIN
FIU. 6. Shear stress va. shear strain curvea for an anthracene singlecrystal deformedin the [ lOO]direction,then in the [OlO]direction, and finally m-deformed in the [lOO] direction, showing latent softening introduced by the intermediate deformation in [OlO].
revolve around the mechanism underlying the rapid hardening during stage II. This stage is only observed in anthracene when appreciable slip takes place in two directions in the basal plane. Some indication of the process by which the interaction of glide dislocations of different Burgersvectorinthe basal planegives rise to hardening is given by the observations of latent softening. Rapid hardening occurs during stage II when crystals are deformed in the [lOO] direction so that slip occurs equally in the [llO] and [liO] slip directions. An intermediate deformation in the [OlO] direction, however, reduces the flow stress in the [lOO]
direction, indicating that the original hardening is probably due to an elastic interaction between the glide dislocations rather than a process which gives rise to jogs or point defects. The probable mechanism of hardening is that [llO] and [liO] glide dislocations interact to form sessile [lOO] dislocations. When the crystal is deformed in the [OlO] direction, the flow stress in the [loo] direction is reduced due to the reaction of the [OlO] dislocations with the sessile [lOO] locks to form mobile [llO] dislocations.
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.
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FIG. 6. The percentage reduction in flow stress in the [IOO] direction due to an intermediate deformation in the [OlO] direction, aa a function of the shear strain during the intermediate deformation.
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0.01
I
0.02
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Fro. 7. Shear stress vs. shear strain curves for anthracene single crystals, showing the incmased extent of stage I work-hardening induced by prior deformation in the [OlO] direction.
660
ACTA
METALLURGICA,
The orientation dependence of the work-hardening can be acoounted for on the basis of the interaotion between dislocation8 of the same Burgers vector and the formation of sessile dislocation look8 when dislocation8 of different Burgers vector approach one another. The low rates of work-hardening observed during the extensive easy glide in either the [OlO] or [llO] directions and the decree in flow stress on reversing the slip direction indicate that the hardening is probably due to the interaction between the stress fields of the glide dislocation, as proposed by Seeger and oo-workers(1-3) for easy glide in c.p.h. metals. The contribution to the work-hardening from the intersection of the glide dislocations with grownin dislocations, which will probably have [OOl] Burger8 veotor,(25) is thought to be minor as the rate of hardening during easy glide does not appear to be sensitive to the density of grown-in dislocations, at lea& within the limits of the current experiments. The rate of hardening during easy glide in one slip direction increases rapidly and the extent of the stage decreases as glide dislocations of another Burgers vector in the basal plane are introduced, either concurrently with theprimaryglidedislocationsbya slight misorientation between the slip direction and the stress axis or by a small prior deformation in a second slip direction. The results indicate that the formation of sessile dislocation locks between the primary and secondary glide dislocations is extremely effective in raising the rate of hardening during stage I. Single stage work-hardening may be expected to continue as long as the density of such sessile dislocation locks is insufficient to have the overall effect of decreasing the long easy glide of the primary glide dislocations. Stage II work-hardening does not begin until a stress level is reached at which the critical resolved shear stress for massive slip to begin in the second slip direction is exceeded. This correspond8 to the formation of a high density of sessile dislocations, which lead to rapid hardening due to the decrease in the distance that the glide dislocations in the two directions can move before encountering a sessile lock. The density of such locks will depend on the amount of slip in each of the two active slip directions, thus explaining the orientation dependence of the rate of hardening during stage II. The observed latent hardening of the inactive slip system during deformation in one slip direction can also be readily explained by the formation of such sessile dislocations on subsequent deformation on the originally inactive system. On the basis of the rapid work-hardening being due to the formation of sessile dislocation locks, stage III hardening begins when the stress level is sufficiently
VOL.
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1968
high to allow dislocation climb around the sessile looks to take place. The present results indicate that in anthracenc the occurrence and extent of the various stages of workhardening are dependent on the degree to which slip ocours in one or more slip directions in the basal plane. The only similar work on the work-hardening of metals in which slip has been rigorously confined to one plane is that of Washburn et aZ.(*l-“’ with zinc single crystals. Although duplex slip in the basal plane of zinc led to an increased rate of workhardening, no second stage work-hardening was observed. This could possibly be due to the dislocation looking being weak compared with the situation in anthraoene where the [llO] glide dislocat.ion is associated with a stacking fault(2s) and may therefore form strong locking points. As the deformation in anthracene is confined to one slip plane, many of the theories advanced for stage II work-hardening in metals are inapplicable. For example, it is unlikely that there will be an appreciable contribution to the work-hardening due to the production of jogs or point defects during deformation, as slip does not occur on intersecting slip planes and the intersection of glide dislocations with grown-in forest dislocations produces comparatively little work-hardening. However, the processes giving rise to work-hardening in anthracene appear to be quite similar in many respects to those proposed by Seeger and co-workers(1-3~S”-S’) to account for t.he various stage8 of hardening in f.c.c. metals. They attribute the work-hardening as being due to long range stresses between glide dislocation8 and the onset of stage II to be an increase in these stresses due partly to the formation of sessile locks formed between primary glide dislocations and those on secondaryslipplanes.(32) 5. CONCLUSIONS 1. The crystal structure and the active slip systems in anthracene enable the work-hardening characteristics to be examined under conditions which eliminate from consideration many of the theories proposed for the work-hardening of metals. 2. Single stage work-hardening is observed when anthracene single crystals are deformed in shear with the basal plane parallel to the plane of shear and with the [OlO] or [IlO] slip directions parallel to the stress axis. 3. If one of the slip directions makes a small angle (
WORK
ROBINSON:
4. Three stage work-hardening orientation that
with
appreciable
tions.
respect
5. Latent
stress
is such
in two direc-
during
stage8
I
on orientation.
hardening
when the
when the
axis
of slip occur
of work-hardening
and II are dependent occurs
to the
amounts
The rates
is observed
HARDENING
of the
crystal
inactive
is deformed
slip system in one of the
slip dire&ions. 6. Lat,ent
softening
have been deformed II
arc
extent
then
occurs
deformed
in the
of stage I hardening
direction
when
crystals
in the [lOO] direction
can be increased
which
into stage
[OlO] direction.
on deforming
The
in the [lo01
by a prior deformation
in
the [OlO] direction. 7. It is thought when there direction
that stage I work-hardening
is predominantly
when glide dislocations produced
by duplex
of different
8. The senile
dislocation
dislocations
in one slip
stage
II occurs
Burger’s
slip in the basal
to form sessile dislocation producing
easy glide
in the basal plane and that
occurs
vector
plane interact
locks. locks
can be broken
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by
sign.
REFERENCES 1. .i. SEEOER, H. KROX~~ULLER,9. .MADERand H. TRAUBLE, Phil. Maa. 6. 639 11961). 2. A. SEEOE~ &d H.‘TRACBLE, 2. Met&k. 51,435 (1960). 3. S. M~ER, A. SEFXXER and H. THIUUNQER, J. appl. Phye. 54. 3376 (1963). 4. U. KUHLMASN-WIISDORF. Tran8. metall. Sot. AIME 224, 1047 (1962). ’ 5. P. B. HImcH, Relation between the Structure and Mechanical Prove&e8 of M&la. D. 39. H.M.S.O. (1963). 6. I’. B. *HIR&, D&Q&. Faraday Sot.‘ So.’ 38. 111 (1964).
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7. 2. S. BA~INSKI, Phil. Mag. 4,393 (1969). 8. Z. S. BASINSKI and S. J. BASINSKI, Phil. Mag. 9, 61 (1964). 9. F. J. WORZALA and W. H. ROBIXSOS, Phil. Mag. 16, 939 (1967). IO. H. J. LEVIN~TEIN and W. H. ROBINSON, J. appl. Phys. 33.3149 (1963). 11. E. H. ED&ARD$ and J. WASHBURN, Trans. Am. Ivat. Min. Engf-8200, 1239 (1954). 12. C. H. Lr, J. WASHBL-RN and E. R. PARKER, Trans. Am. In&. Min. Engre 107, 1223 (1953). 13. H. DR~LYARD,J. WASHBURN 8nd E. R. PARKER, Trans. Am. Zn8t. Min. Engra 197, 1226 (1953). 14. E. H. EDWARDS, J. WASHBURN and E. R. PARKER, Trane. Am. Inat. Min. &ngr8 197, 1525 (1953). 16. W. PFEIPFER, Phya. Status Solidi 2, 1727 (1962). 16. M. B&EK, Phyr. Skztwr Solidi S, 2169 (1963). 17. J. S. LALLY and P. B. HIRSCH, Phil. Msg. 12,595 (1965). 18. A. BEROAEZAN, A. FO~RDE~JX and S. AJIELISCHX, Acta Met. 9, 464 (1961). 19. M. BO&K and P. KsATOCHVfL, Phya. St&U8 SOlidi 6, 169 (1964). 20. P. KRATOCHV~L,PhiE. Mag. 13,267 (1966). 21. M. Bo&K, P. LuK.~~, B. SMOLA and M. ~VABOV~, Phya. Statw Solidi 7, 173 (1964). 22. A. SEEOER, H. KRONMULLER, 0. BOSER and Y. RAIT, Phye. St&w, Solidi 3, 1107 (1963). 23. P. M. ROBINSON and H. G. SCOTT, Phys. Statue Solidi 20, 461 (1967). 24. P. M. ROBINSON and H. G. SCOTT, Actu Met. 16, 1230 (1967). 25. P. M. ROBIXSOS and H. G. SCOTT, Acfa Met. 16, 1581 (1967). 26. A. I. KITAIOORODSKI, Organic Chemical Cryelollography, Izd. Aked. Nauk SSSR. Moscow (1955): EngliahTranal. by Consultants Bureau kntmpri& Inc: ‘( 196y). 27. A. KOCHENDORFER, Z. Kriat. 97,263 (1937). 28. R. H. GORDON, Acta Met. 13, 199 (1965). 29. P. M. ROHINSON and H. G. SCOTT, J. Cryst. Urouth, to be published.
30. A. SEEGER and M. WILKENS, 2nd Int. Symv. Reinstatofle in Wissemchaft und Technik, W&=&n, Akademieverlsg,
Berlin (1966).
SEP.OER, North Amoricen Aviation Scienw Report (1967). 32. U. NSSMANN, Phys. St&c8 Solidi 12, 723 (1965) 31. A.
de? 1965. Contra