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The initiation of plastic flow in copper
THE
INITIATION
OF
R. F. TINDER?
PLASTIC
FLOW
IN COPPER*
and J. WASHBURNt
The continuous shear stress shear strsin behavior for tubular polycrystalline specimens of copper and its dilute alloys deformed in torsion at room temperature w8.s studied using 8 strain resolution of the order of IO-*. Irrevemible plestic deformation beg8n at the smallest me8snreable stresses. Tlxe sm8ll but messurebb spparent elestic regions observed in Jl specimens very ne8r zero applied stress are thought to be associated with the small unrecoverable pm&reins produced during the handling and gripping operations. These apparent elestic regions were completely absent in specimens deformed following the introduction of fresh, mobile dislocations into their gage section surfaces. The addition of solute concentr8tions up to 0.1 at O/caluminum in copper had little effect upon the movement of these fresblv introduced disloc8tions. Polvcrvsmlline copper strain hssdens readilv at room temner8ture and exhibits a discontinuous plastic behavior only following prior straining.” The anehxst~cunloading beh8vior is also demonstrated for annesled Conner snecimeus. It is suggested tb8t plastic deformation st& by ihe motion of s few favorably oriented dislocetion segments that can glide over great enough distances to form strong new intemctions with other dislocrttions. INITIATION
DE L’ECOULEMENT
PLASTIQUE
DANS
LE CUIVRE
Les auteurs Btudient en continu le comportement 8 18 deformation par oission d’eohantillons de cuivre et de quelques uns de ses 8llieges dilues soumis 8 torsion temp&r8ture ambiante avec une sensibilite de mesure de l’ordm de lo-*. 11sconstatent qu’une deformation plastique irreversiblese produit d&sla plus petite tension mesur8ble. Les domains 8pp8mnts &stiques, sont petits nmis memrables, observes dans ie es8 de tous les spt%imens pour une tension appliquee t&s proche de zero, peuvent selon les auteurs dtre associes 8ux predefonoations non-restaumbles produites dumnt 1s m8nipul8tion et le serrctge des Bprouvettes. Ces regions elastiques 8 parentes sont entierement absentes d8ns le 08s des Bch8ntillons dont lea surf8ces de mesure ont pre$ ablement recu de nouvelles dislocetions mobiles. L’introduction dans le onivre de teneurs en aluminium dissous all8nt jusqu’8 0,l oAat., produit peu d’effet sup le mouvement des disloc8tions,nouvellementintroduites. Lecuivre polycristallindurcit8i~mentp8r deformation8temperature 8mbiante et ne montre un comportement plastique discontinu qu’8pres deform8tion pr&minaire. Les 8uteurs montrent eg8lement le complement an&stique z%la d&charged’~ch~ti~ons de cuivre recuits. Les auteurs suggerent que la deform&ion plr&ique commence p8r ie mouvement de quelques segments de dislocetion favorablement orient& qui peuvent se deplacer SUPdes distances suf&xunment grsndes pour former de nouvelles et importantes interactions 8vec d’autres dislocations. DAS ANFANGSSTADIUM
DES PLASTISCHEN
FLIEDENS
VON KUPFER
RBbrenfijrmige polykristalline Proben au8 Kupfer und verdiinnten Kupferlegierungen wurden bei Raumtemperatur in Torsion verformt. Dabei wurde die Schubs~un~s-Sohe~n~u~e mit einer Autlijsung der Schsmng von der Gr6~enor~~g lo-* kont~uierlich a~genommen. Irreversible pls&ische Verformmg bebei den kleinsten meilbaren Spamnmgen. Die kleinen, aber mellbaren dastischen Bereiche, die bsi 8llen Proben g8nz nshe dem Nullpunkt der rangelegtenSp8nnung beobechmt wurden, sind vermutlich eine Folge der geringen nicht erholberen Vorverformungen, die beim Umgehen mit den Proben und bei ihrer Befestigung auftreten. Diese anscheinend elastischen Bereiche fehlten vijllig bei Proben, die nsch der Einfiihrung frischer beweglicher Versetzungen in die Oberfhiche des zur Messung benutzten Abschnitts verformt wurden. Die Hinzuftigung von Ve~reinigungskonzentrationen bis 0. I Atom % Aluminium in Kupfer hatte auf die Bewegung dieser frisch eingefuhrten Versetmmgen nur geringen EinlluB. Bei R8um~rn~r8t~ seigt ~iykrista~~~ Kupfer durchweg Verfestigung, d~kontinuierliches plastischea Verh8lten tritt mu xmch Vorverformung auf. D8s 8nelastische Verhdten bei Entlastung wird an 8uxgeghihten Kupferproben gezeigt. Nach Ansicht der Autoren setst die plastische Verformung mit der Bewegung einiger weniger giinstig orientierterVersetzungssegmente ein, die i.ibergeniigend weite Entfernungen gleiten konnen, urn in starke Weohselwirkung mit anderen Versetzungen treten zu konnen. INTRODUCTION
Of the few studies that have been conducted in the pre-macroyield region of the stress-strain curve, the work of Young(l) is, perhaps, of greatest interest to the present investigation. Using an etch pit technique on high purity copper crystals containing as few dislocations as 50/mmz, Young was able to demonstra~ the * Received April 22, 1963; revised July 1, 1963. Pert of 8 thesis submitted to the Grrtduate School of Engineering, University of C8lifomi8, September 1962, by R. F. Tinder in partial fulfillment of the requirements for the Ph.D. degree. t Dep8rtment of Mettallurgy, Washington Stete Univemity, Pullman, W8sbington. $ Dep8rtment of Miner81 Technology, University of Califomie, Berkeley, Calif. ACTA METALLURGICA,
VOL.
12, FEBRUARY
1964
129
irreversible movement of grown in surface segment at stresses as low as about 4 g[mm2. Dislocations that moved at stresses of about 10 g/mm2 also moved back part way following the removal of the stress. His studies further showed that in such crystals multi. plication of dislocations occurred at resolved stresses of about 18 gfmm2. Other important work in this area has been chiefly concerned with the development of a theory for the microstrain region. Based upon the assumption that one Frank-Read source is active per grain, Thomas and Averbach(2) concluded that for polycrysta~~e coppep the plastic “microstrain” should increase monotonically with stress and be independent of grain
130
ACTA
METALLURGICA,
size. (They detected deviation from elastic stressstrain behavior above about 1000 psi using a strain sensitivity of about 1 x 10es.) Their interpretation of results was later questioned by Brown and Lukens@) who reasoned that the number of Frank-Read sources should be uniform throughout the material and independent of grain size, and that the only barriers to dislocations in the microstrain region are grain boundaries. The latter authors developed a theory which gives the microstrain as yp a psP(a - a,J2/Ga, where D is the grain diameter, p8 the density of sources, o the applied stress, u,, the stress to activate the first Frank-Read source and G is the shear modulus. According to their model, the microstrain region begins with the stress, g,,, which first activates a source, and ends at the macroyield point where slip bands are formed. Presumably, the dislocations which are generated by sources in the microstrain region pile up qn grain boundaries and eventually produce the required stress concentrations needed to activate new sources in the adjoining grains. No systematic investigation of the effect of solute impurity on the initial plastic behavior of metals has yet been reported in the literature. The present investigation was designed to study the preyield plastic behavior of polycrystalline copper at a considerably greater strain resolution (of the order of 1OW) than that used in any of the previous investigations and to determine the effect of freshly introduced dislocations and substitutional impurities on the initial plastic behavior.
VOL.
12, 1964
During tightening of the grips, the specimen was subjected to small sporadic torques in both directions from zero. As soon as each torque was detected it was reduced to zero by manual adjustment of the driving mechanism. These torques, which could be measured, were usually kept below about f0.3 g/mm2, f0.5 g/mm2, and ~2.0 g/mm2 in stress magnitude for specimens having wall thicknesses of 1.27 mm, 0.509 mm and 0.127 mm, respectively. However, the specimens were subjected to these stresses many times (ten or more in each direction from zero) during a normal clamping operation. Other small stresses exerted on the specimen during gripping (e.g. from bending moments and axial forces) were no doubt present but no measure of these was made. The specimens were tested in torsion at 20% at a load rate of about 0.1 g/mm2/sec over test periods ranging from about 5 set to 10 min in duration. The testing equipment consisted of a torsional loading apparatus, a nulling and zero suppression circuit through which the output signals from the stress and strain sensing systems were fed, and an X-Y recorder which was powered by a voltage regulator. The stress and strain sensing systems were so constructed that only torsional stresses and angular displacements were recorded. In addition the ’ sensing systems were somewhat temperature compensating provided that the temperature changes were small and uniform over the loading apparatus. A detailed description of the loading apparatus will be published elsewhere. Extreme care was taken to minimize the noise level EXPERIMENTAL PROCEDURE AND RESULTS due to mechanical vibrations, thermal-mechanical Tubular polycrystalline specimens were machined effects and extraneous electric fields. This was from OFHC copper of 99.995 per cent purity and from accomplished by shock mounting the entire loading various dilute alloys containing up to 1.0 at. y0 apparatus on a basement floor, placing all testing aluminum in OFHC copper. The gage sections were equipment in a plastic enclosure, and shielding all 19 mm long and had an outside diameter of 6.6 mm leads with proper grounding. When operating under and wall thicknesses of 1.27 mm, 0.509 mm, and 0.127 favorable conditions the noise level was reduced to a mm. Their overall length was 31.7 mm. The specimens range of from 1 to 4 x 10m9 in strain magnitude. were annealed in open end Vycor tubes at 900°C for The residual noise was predominantly a regular 14 hr under a pressure of 1OW Torr and then cooled to vibration of about 6 c/s and was averaged out of the room temperature at a rate of less than G”C!/min. data presented below. The drift rate was negligible The final average grain size was usually somewhat over the periods of testing. The uncertainty of larger than the wall thickness although the grains did absolute zero stress was estimated to be less than not always extend t*hrough the specimen wall. The f0.05 g/mm2 for most tests. specimens were removed from the Vycor tubes by Calibrations of the stress and strain sensing allowing them to slide very gently down the tube and systems were made independently and were found to onto a cotton bed. To minimize deformation due to be linear well beyond the ranges used in this investigahandling each specimen was picked up from its bed tion. The scale factors based upon the outside diameter with special split cylinder teflon tweezers which sus- of the tube gage sections were 0.361 g/mm2 and pended the specimen by the upper gage section shoulder 8.95 x 10-s per inch graph paper, respectively, for during transportation to the testing apparatus. the stress and strain axes. Typical X-Y recordings
TINDER
AND
WASHBURN:
THE
INITIATION
Total shear strain yT (scale:
,
FLOW
IN COPPER
131
, )
recording of stress-strain curve for an unannealed mild-steel E
FIG. 1. Typical X-Y
for unannealed
OF PLASTIC
mild steel and annealed OFHC copper
curves are drawn to a common
origin and reveal a
specimens are shown in Figs. 1 and 2. No significant
small apparent
plastic strain was detected
g/mm 2. At higher stresses plastic strain increased in a smooth continuous manner at a rate that depended
study.
However,
in steel over the range of
measureable
creep was detected
in
elastic limit of the order of about 2
mild steel when held at about 25 g/mm2 for periods of 5
upon the purity.
min of more.
same order of magnitude
The shear moduli
for polycrystalline
The apparent elastic limits are of the as those observed in copper
specimens of aluminium, copper, zinc, and mild steel were determined from the slopes of the shear stress-
by Young”). However, even these limits may have been associated with the unavoidable prestrains
total shear strain curves near zero applied stress. With the exception of steel, these values were consis-
The as-annealed
tently higher than those measured at ordinary
to a “gripping
resolutions
but were in substantially
strain
good agreement
with values obtained from ultrasonic measurements.(4) Results for as-annealed polycrystalline specimens of copper and its dilute alloys, differing in purity each by about an order of magnitude, Fig. 3.
Only the plastic
are represented
component
in
of the strain is
shown, the elastic part having been subtracted.
The
produced
during the handling or gripping operations. specimens
fatigue”
were, in effect, subjected
in torsion within the range of
about kO.5 g/mm2 for specimens having intermediate wall thickness. The combined stresses due to gripping could have hardened the specimens sufficiently to have produced
the observed
apparent
elastic limits.
Since
the prestrains were likely to have been greatest in the specimens of thinnest wall, an increase in apparent elastic limit with decreasing wall thickness would be expected. The results of this investigation are
ACTA
132
FIG. 2. X-Y
METALLURGICA,
VOL.
12, 1964
recording of stress-strain curve for a polycrystalline specimen annealed at 9OO’C for 1.5 hr.
consistent with this hypothesis. Specimens having wall thicknesses of 1.27 mm, 0.509 mm, and 0.127 mm exhibited detectable plastic deformation beginning at stresses averaging about 1 g/mm2, 2 g/mm2 and 6 g/mms, respectively. Furthermore, an increase in the apparent elastic limit was often observed in a particular specimen immediately following a prior straining which exceeded the first apparent elastic limit. This is demonstrated in Fig. 6. When copper specimens were prestrained before testing or were unloaded and tested a second time they exhibited a discontinuous plastic behavior. Figure 4 shows this effect in a polycrystalline OFHC copper @ecimen following a 10% compressive prestrain and a one-week room temperature anneal. Zinc, in comparison, (also Fig. 4) shows no apparent elastic limit and deforms in a smooth continuous
OFHC-copper
manner following a similar compressive prestram and an eight hour room temperature anneal. The effect of freshly introduced dislocations on the mechanical behavior of a variety of copper specimens varying in purity and wall thickness was studied by bombarding the gage section surfaces with 27 1~(av.) Al,O, particles forced from the nozzle of a White abrasive unit. The impact of the alumina particles introduced a high density of dislocations in the surface layers of the grains in the gage section while leaving unchanged the parts of the specimen near the clamps. The nature of this surface damage was studied by the etch pit technique using Livingston’s etch(s) on polycrystalline OFHC copper discs which had received the same annealing treatment as the specimens. The dislocation arrangements around regions locally deformed by particle impingement are
TINDER
AND WASHBURN:
P
I
c
II m Ip
P /
0
4
8
OFHC 0.1 At. 0.1 At. 1.0 At.
12
THE
INITIATION
OF PLASTIC
FLOW
IN COPPER
133
copper % Al % Fe % Al
16
20
Y,xlOe FIG. 3. Effect of alloying on the initial plastic behavior of copper. Specimen wall thickness 0.509 mm.
16
(b) Fro. 5. Photographs of etched polycrystalline OFHCcopper discs following a 1.5 hr QOOOC anneal and bombardment with 27 ,u (av.) Al,O, particles. x 110.
shown
in Fig.
5 for grains
Samples of the stress-strain
having
(111)
surfaces.
test series performed
specimens before and after bombardment
on
are represen-
ted in Fig. 6, for an OFHC copper specimen having a intermediate wall thickness (0.509 mm), and in Fig. 7, for a specimen of a dilute copper alloy containing 0.1 at. o/o aluminum having a wall thickness of 0.509 mm. Bombardment of the gage section surface was accomplished at zero applied stress following test II. All four tests on a given specimen were performed
in
the consecutive order given by the roman numerals, without release of the specimen from the grips. For simplicity the curves have all been shifted to a common origin. The apparent elastic limit and discontinuous plastic behavior which were always observed in Fro. 4. Initial plastic behavior of copper and zinc following a 10% compressive prestrain. Specimen wall thickness 0.509 mm.
prestrained specimens were completely absent in tests III following surface deformation but reappeared in
ACTA
METALLURGICA,
VOL.
12, 1964
16
0
6
4
8
20
12
16
Yp x
IO8
24
28
FIG. 8. Initial anelastic unloading behavior of an OFHC copper specimen having a wall thickness of 0.509 mm. st Following Surface Deformation
curve IV. which
Furthermore,
were
made
reveal that the plastic 0
4
8
Y,
I2
I6
20
down
to the lowest
deformation
x IO8
6. Effect of surface deformation on an OFHC copper specimen having a wall thickness of 0.509 mm.
specimens small
of large
deformation
was irreversible
on
mm)
up to 1 at.%
However,
Surface
OFHC
wall thickness (.127
curves
deformation
measureable.
performed
wall thickness
similar results.
hysteresis
surface
stresses
studies
copper containing
half-cycle
following
(1.27 and
copper
mm)
and
on alloys
aluminum
of
pfoduced
similar tests produced
no
effect on steel specimens. The
unloading
behavior
copper specimen
16
for an annealed
cycle tests were performed given
14
OFHC
is shown in Fig. 8. The three half-
by the roman
in the consecutive
numerals.
Detectable
order reverse
plastic strain during unloading occurred for maximum stresses above 4 g/mm2 which is in fair agreement with Young’s
etch
pit
small percentage The
observations.
However,
only
a
of the total strain was recovered. apparently
not
returned to its initial state even by application
dislocation
network
was
of a
reverse stress, as shown in Fig. 9. The reverse plastic
SecondTest
lZ
Third Test Following Surface Defurmotion Fourth Test
Ip.
“0
4
8 Yp x
12
I6
20
108
Yl
0
II 40
I 00
II
I 120
II 160
I
First
deformationc
II: IE
Second Third
deformationC deformation=)
I 200
11 240
I
It
II
260
320
Yp x 106
Fm. 5. Effect of surface deformation on an OFHC copper specimen containing 0.1 at.% aluminium, and having a wall thickness of 0.509 mm.
FIN. 9. Test series showing Bauschinger effect in an OFHC-copper specimen annealed at 900°C for 1.5 hr.
TINDER
AND
WASHBURN:
THE
INITIATION
strain was smaller than that which would be predicted from a simple bowing model. DISCUSSION
Plastic deformation begins in these tests at a stress too low for operation of Frank-Read sources. At 5 g/mms the critical length for a Frank-Read source in copper is 0.2 mm. This is greater than the subgrain size and of the same order as the wall thickness of the specimen. However, at the highest stress levels employed, this type of dislocation multiplication may have contributed to the strain. The simplest model that can be proposed to explain the small plastic strains observed in these experiments is the bowing of elements of the three-dimensional dislocation network between fixed nodes. Assuming a dislocation density of lo6 to lo6 cm/cmsaft.er annealing this model can account for the observed magnitude of the strains. However, if.most of the plastic strain is attributed to motion of a very large number of dislocation segments through an average distance that is small compared to the distances between neighboring dislocations in the network, then it becomes difficult to explain the substantial irreversibility of the strain and the great fluctuations in strain rate that occurred during loading of prestrained specimens. The results suggest that an important fraction of the total strain, in the initial stages of deformation, involved motion of a few favorably situated dislocation segments through distances large enough to form new interactions (e.g. node formation) with other elements of the three dimensional network. If this were so, then most elements of the network must have been relatively immobile, making little or no contributibn to the strain. The reduction in the number of mobile segments due to interactions during prior straining (by gripping or actual testing) would necessarily be manifested as an increase in apparent elastic limit in subsequent tests as was observed. However, the use of higher strain resolutions than that used in this investigation would, no doubt, reveal dislocation movement in these apparent elastic regions. In an annealed crystal the greatest part of the total length of dislocation line exists in two-dimensional arrays. Most of these subgrain boundaries contain dislocations with at least two different Burgers vectors and are immobile except for displacements that are small compared to the average spacing between dislocations in the array. Within the subgrains there are some relatively isolated dislocation lines which in some regions probably approach a It is reasonable to three-dimensional network.
OF PLASTIC
FLOW
IN
COPPER
136
assume that most parts, even of this network, have reached positions of metastability for both climb and glide motion during annealing. In general, the nodes that fix the positions of the ends of a segment will not lie on the same (111) layer of atoms. Therefore, most segments will be heavily jogged. Only rarely will a length of dislocation lie on or nearly on a (Ill} plane. We propose that the start of plastic deformation, as observed in these experiments, corresponds to glide, over distances comparable to the spacing between dislocations in the three-dimensional network, of the few segments lying most nearly on (111) and having Burgers vectors most nearly parallel to the direction of the applied stress. In many caf4es, particularly where one end of the segment terminates at an external surface, the glide may involve little or no increase in the total length of dislocation line. Figure 10 shows a particular example where a dislocation cuts across a subgrain from one small angle boundary to another. In cases like this there is no tendency for the line to return to its original position when the stress is removed. Also, if the plastic strain is mostly due to rather large displacements of a few segments, then the chance is very great that many of these will intersect other dislocations during their motion, forming new nodes. They will then -be unable to return to their original position even if the direction of the stress is reversed. Motion of a favorably oriented segment may also lead to glide of the less mobile dislocations that join it at its ends. Consider, for example, the elements of a dislocation network shown in Fig. 11. Suppose that dislocations AA’ and BB’ pass from one subgrain boundary to another, as shown in Fig. 10, but have formed attractive junctions with dislocation CC’ (if the stress tends to move dislocations AA’ and BB’ in
A
FIG. 10. A particularexample of a dislocation segment that could move a long distance when a small stress is applied.
136
ACTA
METALLURGICA,
their glide planes as indicated by the arrows) then the dislocation CC’ may be caused to move in its glide plane by motion of the nodes, P, P’, 0 and 0’ along the glide plane intersections. This might happen even though the stress exerts no force on CC’ or even a small foroe in the opposite direction. The important point is that the triple nodes in a three-dimensional network are not necessarily fixed points when a stress is applied. Motion of some segments of dislocation at G
FIG. 11. Coopera,tivemotion of severel dislocation segments by glide of nodes.
one part of the network may start a progressive rearrangement that can spread through a larger volume of crystal. The total plastic strain would then be due to both bowing out of individual dislocation segments between adjacent nodes and to a cooperative bowing of larger parts of a network. Presumably, this would involve motion of dislocations through distances large enough to form new interactions with other less mobile elements of the three-dimensional network. The large effect due to introduction of new dislocations at the surfaces of the specimen gauge length was clear evidence that the small plastic strains being measured were not localized at stress concentrations in the grip sections. These tests also show that the mobility of dislocations in the dilute (0.1 o/o Al) solid solution was approximately equal to that in OFHC copper. They suggest that the smaller strain rate observed in the annealed condition for the alloy specimens compared to that of pure copper was due to a smaller number of moving dislocation segments rather than a lower dislocation velocity. However, further experiments are needed for certain interpretation of impurity and solute element effects. Because of the low stresses involved in these experiments, it is of interest to consider their significance relative t,o the Peierls-Nabarro stress in
VOL.
12, 1964
copper. However, if the Peierls-Nabarro stress is defined as the stress required at absolute zero to move a dislocation that is straight on an atomic scale and lying in a position of minimum core energy,@) then none of the quantitative theories(r) are detailed enough to permit an estimate of its magnitude from these results. The theory is particularly incomplete for close packed crystals. For a dislocation that is split into partials it is not even certain which directions in the glide plane correspond to minimum core energy. Assume that the lowest core energy can be achieved when one of the two partials is either pure edge or pure screw, then, for a given Burgers vector and glide plane there are four such directions. If the PeierlsNabarro stress is important, a curved dislocation that is moving would tend to develop straight segments; the angles between adjacent segments being either 150’ or 120’ where the line passed from one preferred direction into another. Transmission electron microscopy of copper does not show any preference for particular orientation of dislocation lines relative to crystallographic directions. Therefore, if straight segments do form they must be very short (less than a few hundred interatomic distances). This means that a meaningful analysis of the Peierls-Nabarro stress must be based on thermally activated generation of kinks at the ends of these short segments. For the case where a dislocation segment is caused to move by motion of the triple nodes at its ends, the important consideration should be generation of kinks at the nodes. CONCLUSIONS
(1) Measurable plastic strains are produced in annealed polycrystalline copper and dilute solid solutions of aluminum in copper by applied stresses as low as about 2 g/mms. However, even these apparent elastic limits may be associated with the unavoidable prestrains produced during handling and gripping of the specimens. (2) Even the smallest plastic strains of the order of 10-s are largely irreversible. They are not recovered on removing the applied stress and the amount of strain produced by subsequent loading in the reverse direction is not as great as would be expected from a simple dislocation bowing model. (3) Introducing new dislocations at the surface of a specimen by bombarding with 27 p alumina particles greatly increases the amount of plastic strain in the pre-yield range. Under these conditions irreversible plastic deformation begins at the smallest measurable stresses. (4) In prestrained specimens pre-yield plastic strain does not increase smoothly with increasing
TINDER
AND
WASHBURN:
THE
stress. Marked fluctuations in strain rate resulting in irregular stress-strain curves.
INITIATION
OCCUR
AGKNO~EDGMENTS
The authors are grateful to the Office of Naval Research and in particular to Dr. Julius Harwood for support of their experiments. The help of Ira Pratt in the solution of some experimental problems is also greatly appreciated.
OF PLASTIC
FLOW
IN COPPER
137
REFERENCES 1. F. W. YOUNC3, JR., J. Appl. Phya. 82, 1815 (1961),and88, 963 (1962). 2. D. A. TEOU snd B. L. A~ERBAGH, Aeta Met, 7,69 (1959). 3. N. BROWN and K. F. LUKEXS, Acta Met. S, 106 (1961). 4. W. P. MASON, Phyeieol Acouatica and the Properties of Solids,p. 17. D. Van Nostrand, Primeton, N. J. (1958). 5. J. D. LIVINGSTON, J. AppZ. Whys. 81, 1071 (1960). 6. F. R. N. NAB-O, Proc. Phya. Sot. &mad.59, 256 (1947). 7. J. FRIEDEL, Eleotmn iW&rompy and Strength of Cryat&, p. 605. J. Wiley, New York (1963).
INITIATION
OF
R. F. TINDER?
PLASTIC
FLOW
IN COPPER*
and J. WASHBURNt
The continuous shear stress shear strsin behavior for tubular polycrystalline specimens of copper and its dilute alloys deformed in torsion at room temperature w8.s studied using 8 strain resolution of the order of IO-*. Irrevemible plestic deformation beg8n at the smallest me8snreable stresses. Tlxe sm8ll but messurebb spparent elestic regions observed in Jl specimens very ne8r zero applied stress are thought to be associated with the small unrecoverable pm&reins produced during the handling and gripping operations. These apparent elestic regions were completely absent in specimens deformed following the introduction of fresh, mobile dislocations into their gage section surfaces. The addition of solute concentr8tions up to 0.1 at O/caluminum in copper had little effect upon the movement of these fresblv introduced disloc8tions. Polvcrvsmlline copper strain hssdens readilv at room temner8ture and exhibits a discontinuous plastic behavior only following prior straining.” The anehxst~cunloading beh8vior is also demonstrated for annesled Conner snecimeus. It is suggested tb8t plastic deformation st& by ihe motion of s few favorably oriented dislocetion segments that can glide over great enough distances to form strong new intemctions with other dislocrttions. INITIATION
DE L’ECOULEMENT
PLASTIQUE
DANS
LE CUIVRE
Les auteurs Btudient en continu le comportement 8 18 deformation par oission d’eohantillons de cuivre et de quelques uns de ses 8llieges dilues soumis 8 torsion temp&r8ture ambiante avec une sensibilite de mesure de l’ordm de lo-*. 11sconstatent qu’une deformation plastique irreversiblese produit d&sla plus petite tension mesur8ble. Les domains 8pp8mnts &stiques, sont petits nmis memrables, observes dans ie es8 de tous les spt%imens pour une tension appliquee t&s proche de zero, peuvent selon les auteurs dtre associes 8ux predefonoations non-restaumbles produites dumnt 1s m8nipul8tion et le serrctge des Bprouvettes. Ces regions elastiques 8 parentes sont entierement absentes d8ns le 08s des Bch8ntillons dont lea surf8ces de mesure ont pre$ ablement recu de nouvelles dislocetions mobiles. L’introduction dans le onivre de teneurs en aluminium dissous all8nt jusqu’8 0,l oAat., produit peu d’effet sup le mouvement des disloc8tions,nouvellementintroduites. Lecuivre polycristallindurcit8i~mentp8r deformation8temperature 8mbiante et ne montre un comportement plastique discontinu qu’8pres deform8tion pr&minaire. Les 8uteurs montrent eg8lement le complement an&stique z%la d&charged’~ch~ti~ons de cuivre recuits. Les auteurs suggerent que la deform&ion plr&ique commence p8r ie mouvement de quelques segments de dislocetion favorablement orient& qui peuvent se deplacer SUPdes distances suf&xunment grsndes pour former de nouvelles et importantes interactions 8vec d’autres dislocations. DAS ANFANGSSTADIUM
DES PLASTISCHEN
FLIEDENS
VON KUPFER
RBbrenfijrmige polykristalline Proben au8 Kupfer und verdiinnten Kupferlegierungen wurden bei Raumtemperatur in Torsion verformt. Dabei wurde die Schubs~un~s-Sohe~n~u~e mit einer Autlijsung der Schsmng von der Gr6~enor~~g lo-* kont~uierlich a~genommen. Irreversible pls&ische Verformmg bebei den kleinsten meilbaren Spamnmgen. Die kleinen, aber mellbaren dastischen Bereiche, die bsi 8llen Proben g8nz nshe dem Nullpunkt der rangelegtenSp8nnung beobechmt wurden, sind vermutlich eine Folge der geringen nicht erholberen Vorverformungen, die beim Umgehen mit den Proben und bei ihrer Befestigung auftreten. Diese anscheinend elastischen Bereiche fehlten vijllig bei Proben, die nsch der Einfiihrung frischer beweglicher Versetzungen in die Oberfhiche des zur Messung benutzten Abschnitts verformt wurden. Die Hinzuftigung von Ve~reinigungskonzentrationen bis 0. I Atom % Aluminium in Kupfer hatte auf die Bewegung dieser frisch eingefuhrten Versetmmgen nur geringen EinlluB. Bei R8um~rn~r8t~ seigt ~iykrista~~~ Kupfer durchweg Verfestigung, d~kontinuierliches plastischea Verh8lten tritt mu xmch Vorverformung auf. D8s 8nelastische Verhdten bei Entlastung wird an 8uxgeghihten Kupferproben gezeigt. Nach Ansicht der Autoren setst die plastische Verformung mit der Bewegung einiger weniger giinstig orientierterVersetzungssegmente ein, die i.ibergeniigend weite Entfernungen gleiten konnen, urn in starke Weohselwirkung mit anderen Versetzungen treten zu konnen. INTRODUCTION
Of the few studies that have been conducted in the pre-macroyield region of the stress-strain curve, the work of Young(l) is, perhaps, of greatest interest to the present investigation. Using an etch pit technique on high purity copper crystals containing as few dislocations as 50/mmz, Young was able to demonstra~ the * Received April 22, 1963; revised July 1, 1963. Pert of 8 thesis submitted to the Grrtduate School of Engineering, University of C8lifomi8, September 1962, by R. F. Tinder in partial fulfillment of the requirements for the Ph.D. degree. t Dep8rtment of Mettallurgy, Washington Stete Univemity, Pullman, W8sbington. $ Dep8rtment of Miner81 Technology, University of Califomie, Berkeley, Calif. ACTA METALLURGICA,
VOL.
12, FEBRUARY
1964
129
irreversible movement of grown in surface segment at stresses as low as about 4 g[mm2. Dislocations that moved at stresses of about 10 g/mm2 also moved back part way following the removal of the stress. His studies further showed that in such crystals multi. plication of dislocations occurred at resolved stresses of about 18 gfmm2. Other important work in this area has been chiefly concerned with the development of a theory for the microstrain region. Based upon the assumption that one Frank-Read source is active per grain, Thomas and Averbach(2) concluded that for polycrysta~~e coppep the plastic “microstrain” should increase monotonically with stress and be independent of grain
130
ACTA
METALLURGICA,
size. (They detected deviation from elastic stressstrain behavior above about 1000 psi using a strain sensitivity of about 1 x 10es.) Their interpretation of results was later questioned by Brown and Lukens@) who reasoned that the number of Frank-Read sources should be uniform throughout the material and independent of grain size, and that the only barriers to dislocations in the microstrain region are grain boundaries. The latter authors developed a theory which gives the microstrain as yp a psP(a - a,J2/Ga, where D is the grain diameter, p8 the density of sources, o the applied stress, u,, the stress to activate the first Frank-Read source and G is the shear modulus. According to their model, the microstrain region begins with the stress, g,,, which first activates a source, and ends at the macroyield point where slip bands are formed. Presumably, the dislocations which are generated by sources in the microstrain region pile up qn grain boundaries and eventually produce the required stress concentrations needed to activate new sources in the adjoining grains. No systematic investigation of the effect of solute impurity on the initial plastic behavior of metals has yet been reported in the literature. The present investigation was designed to study the preyield plastic behavior of polycrystalline copper at a considerably greater strain resolution (of the order of 1OW) than that used in any of the previous investigations and to determine the effect of freshly introduced dislocations and substitutional impurities on the initial plastic behavior.
VOL.
12, 1964
During tightening of the grips, the specimen was subjected to small sporadic torques in both directions from zero. As soon as each torque was detected it was reduced to zero by manual adjustment of the driving mechanism. These torques, which could be measured, were usually kept below about f0.3 g/mm2, f0.5 g/mm2, and ~2.0 g/mm2 in stress magnitude for specimens having wall thicknesses of 1.27 mm, 0.509 mm and 0.127 mm, respectively. However, the specimens were subjected to these stresses many times (ten or more in each direction from zero) during a normal clamping operation. Other small stresses exerted on the specimen during gripping (e.g. from bending moments and axial forces) were no doubt present but no measure of these was made. The specimens were tested in torsion at 20% at a load rate of about 0.1 g/mm2/sec over test periods ranging from about 5 set to 10 min in duration. The testing equipment consisted of a torsional loading apparatus, a nulling and zero suppression circuit through which the output signals from the stress and strain sensing systems were fed, and an X-Y recorder which was powered by a voltage regulator. The stress and strain sensing systems were so constructed that only torsional stresses and angular displacements were recorded. In addition the ’ sensing systems were somewhat temperature compensating provided that the temperature changes were small and uniform over the loading apparatus. A detailed description of the loading apparatus will be published elsewhere. Extreme care was taken to minimize the noise level EXPERIMENTAL PROCEDURE AND RESULTS due to mechanical vibrations, thermal-mechanical Tubular polycrystalline specimens were machined effects and extraneous electric fields. This was from OFHC copper of 99.995 per cent purity and from accomplished by shock mounting the entire loading various dilute alloys containing up to 1.0 at. y0 apparatus on a basement floor, placing all testing aluminum in OFHC copper. The gage sections were equipment in a plastic enclosure, and shielding all 19 mm long and had an outside diameter of 6.6 mm leads with proper grounding. When operating under and wall thicknesses of 1.27 mm, 0.509 mm, and 0.127 favorable conditions the noise level was reduced to a mm. Their overall length was 31.7 mm. The specimens range of from 1 to 4 x 10m9 in strain magnitude. were annealed in open end Vycor tubes at 900°C for The residual noise was predominantly a regular 14 hr under a pressure of 1OW Torr and then cooled to vibration of about 6 c/s and was averaged out of the room temperature at a rate of less than G”C!/min. data presented below. The drift rate was negligible The final average grain size was usually somewhat over the periods of testing. The uncertainty of larger than the wall thickness although the grains did absolute zero stress was estimated to be less than not always extend t*hrough the specimen wall. The f0.05 g/mm2 for most tests. specimens were removed from the Vycor tubes by Calibrations of the stress and strain sensing allowing them to slide very gently down the tube and systems were made independently and were found to onto a cotton bed. To minimize deformation due to be linear well beyond the ranges used in this investigahandling each specimen was picked up from its bed tion. The scale factors based upon the outside diameter with special split cylinder teflon tweezers which sus- of the tube gage sections were 0.361 g/mm2 and pended the specimen by the upper gage section shoulder 8.95 x 10-s per inch graph paper, respectively, for during transportation to the testing apparatus. the stress and strain axes. Typical X-Y recordings
TINDER
AND
WASHBURN:
THE
INITIATION
Total shear strain yT (scale:
,
FLOW
IN COPPER
131
, )
recording of stress-strain curve for an unannealed mild-steel E
FIG. 1. Typical X-Y
for unannealed
OF PLASTIC
mild steel and annealed OFHC copper
curves are drawn to a common
origin and reveal a
specimens are shown in Figs. 1 and 2. No significant
small apparent
plastic strain was detected
g/mm 2. At higher stresses plastic strain increased in a smooth continuous manner at a rate that depended
study.
However,
in steel over the range of
measureable
creep was detected
in
elastic limit of the order of about 2
mild steel when held at about 25 g/mm2 for periods of 5
upon the purity.
min of more.
same order of magnitude
The shear moduli
for polycrystalline
The apparent elastic limits are of the as those observed in copper
specimens of aluminium, copper, zinc, and mild steel were determined from the slopes of the shear stress-
by Young”). However, even these limits may have been associated with the unavoidable prestrains
total shear strain curves near zero applied stress. With the exception of steel, these values were consis-
The as-annealed
tently higher than those measured at ordinary
to a “gripping
resolutions
but were in substantially
strain
good agreement
with values obtained from ultrasonic measurements.(4) Results for as-annealed polycrystalline specimens of copper and its dilute alloys, differing in purity each by about an order of magnitude, Fig. 3.
Only the plastic
are represented
component
in
of the strain is
shown, the elastic part having been subtracted.
The
produced
during the handling or gripping operations. specimens
fatigue”
were, in effect, subjected
in torsion within the range of
about kO.5 g/mm2 for specimens having intermediate wall thickness. The combined stresses due to gripping could have hardened the specimens sufficiently to have produced
the observed
apparent
elastic limits.
Since
the prestrains were likely to have been greatest in the specimens of thinnest wall, an increase in apparent elastic limit with decreasing wall thickness would be expected. The results of this investigation are
ACTA
132
FIG. 2. X-Y
METALLURGICA,
VOL.
12, 1964
recording of stress-strain curve for a polycrystalline specimen annealed at 9OO’C for 1.5 hr.
consistent with this hypothesis. Specimens having wall thicknesses of 1.27 mm, 0.509 mm, and 0.127 mm exhibited detectable plastic deformation beginning at stresses averaging about 1 g/mm2, 2 g/mm2 and 6 g/mms, respectively. Furthermore, an increase in the apparent elastic limit was often observed in a particular specimen immediately following a prior straining which exceeded the first apparent elastic limit. This is demonstrated in Fig. 6. When copper specimens were prestrained before testing or were unloaded and tested a second time they exhibited a discontinuous plastic behavior. Figure 4 shows this effect in a polycrystalline OFHC copper @ecimen following a 10% compressive prestrain and a one-week room temperature anneal. Zinc, in comparison, (also Fig. 4) shows no apparent elastic limit and deforms in a smooth continuous
OFHC-copper
manner following a similar compressive prestram and an eight hour room temperature anneal. The effect of freshly introduced dislocations on the mechanical behavior of a variety of copper specimens varying in purity and wall thickness was studied by bombarding the gage section surfaces with 27 1~(av.) Al,O, particles forced from the nozzle of a White abrasive unit. The impact of the alumina particles introduced a high density of dislocations in the surface layers of the grains in the gage section while leaving unchanged the parts of the specimen near the clamps. The nature of this surface damage was studied by the etch pit technique using Livingston’s etch(s) on polycrystalline OFHC copper discs which had received the same annealing treatment as the specimens. The dislocation arrangements around regions locally deformed by particle impingement are
TINDER
AND WASHBURN:
P
I
c
II m Ip
P /
0
4
8
OFHC 0.1 At. 0.1 At. 1.0 At.
12
THE
INITIATION
OF PLASTIC
FLOW
IN COPPER
133
copper % Al % Fe % Al
16
20
Y,xlOe FIG. 3. Effect of alloying on the initial plastic behavior of copper. Specimen wall thickness 0.509 mm.
16
(b) Fro. 5. Photographs of etched polycrystalline OFHCcopper discs following a 1.5 hr QOOOC anneal and bombardment with 27 ,u (av.) Al,O, particles. x 110.
shown
in Fig.
5 for grains
Samples of the stress-strain
having
(111)
surfaces.
test series performed
specimens before and after bombardment
on
are represen-
ted in Fig. 6, for an OFHC copper specimen having a intermediate wall thickness (0.509 mm), and in Fig. 7, for a specimen of a dilute copper alloy containing 0.1 at. o/o aluminum having a wall thickness of 0.509 mm. Bombardment of the gage section surface was accomplished at zero applied stress following test II. All four tests on a given specimen were performed
in
the consecutive order given by the roman numerals, without release of the specimen from the grips. For simplicity the curves have all been shifted to a common origin. The apparent elastic limit and discontinuous plastic behavior which were always observed in Fro. 4. Initial plastic behavior of copper and zinc following a 10% compressive prestrain. Specimen wall thickness 0.509 mm.
prestrained specimens were completely absent in tests III following surface deformation but reappeared in
ACTA
METALLURGICA,
VOL.
12, 1964
16
0
6
4
8
20
12
16
Yp x
IO8
24
28
FIG. 8. Initial anelastic unloading behavior of an OFHC copper specimen having a wall thickness of 0.509 mm. st Following Surface Deformation
curve IV. which
Furthermore,
were
made
reveal that the plastic 0
4
8
Y,
I2
I6
20
down
to the lowest
deformation
x IO8
6. Effect of surface deformation on an OFHC copper specimen having a wall thickness of 0.509 mm.
specimens small
of large
deformation
was irreversible
on
mm)
up to 1 at.%
However,
Surface
OFHC
wall thickness (.127
curves
deformation
measureable.
performed
wall thickness
similar results.
hysteresis
surface
stresses
studies
copper containing
half-cycle
following
(1.27 and
copper
mm)
and
on alloys
aluminum
of
pfoduced
similar tests produced
no
effect on steel specimens. The
unloading
behavior
copper specimen
16
for an annealed
cycle tests were performed given
14
OFHC
is shown in Fig. 8. The three half-
by the roman
in the consecutive
numerals.
Detectable
order reverse
plastic strain during unloading occurred for maximum stresses above 4 g/mm2 which is in fair agreement with Young’s
etch
pit
small percentage The
observations.
However,
only
a
of the total strain was recovered. apparently
not
returned to its initial state even by application
dislocation
network
was
of a
reverse stress, as shown in Fig. 9. The reverse plastic
SecondTest
lZ
Third Test Following Surface Defurmotion Fourth Test
Ip.
“0
4
8 Yp x
12
I6
20
108
Yl
0
II 40
I 00
II
I 120
II 160
I
First
deformationc
II: IE
Second Third
deformationC deformation=)
I 200
11 240
I
It
II
260
320
Yp x 106
Fm. 5. Effect of surface deformation on an OFHC copper specimen containing 0.1 at.% aluminium, and having a wall thickness of 0.509 mm.
FIN. 9. Test series showing Bauschinger effect in an OFHC-copper specimen annealed at 900°C for 1.5 hr.
TINDER
AND
WASHBURN:
THE
INITIATION
strain was smaller than that which would be predicted from a simple bowing model. DISCUSSION
Plastic deformation begins in these tests at a stress too low for operation of Frank-Read sources. At 5 g/mms the critical length for a Frank-Read source in copper is 0.2 mm. This is greater than the subgrain size and of the same order as the wall thickness of the specimen. However, at the highest stress levels employed, this type of dislocation multiplication may have contributed to the strain. The simplest model that can be proposed to explain the small plastic strains observed in these experiments is the bowing of elements of the three-dimensional dislocation network between fixed nodes. Assuming a dislocation density of lo6 to lo6 cm/cmsaft.er annealing this model can account for the observed magnitude of the strains. However, if.most of the plastic strain is attributed to motion of a very large number of dislocation segments through an average distance that is small compared to the distances between neighboring dislocations in the network, then it becomes difficult to explain the substantial irreversibility of the strain and the great fluctuations in strain rate that occurred during loading of prestrained specimens. The results suggest that an important fraction of the total strain, in the initial stages of deformation, involved motion of a few favorably situated dislocation segments through distances large enough to form new interactions (e.g. node formation) with other elements of the three dimensional network. If this were so, then most elements of the network must have been relatively immobile, making little or no contributibn to the strain. The reduction in the number of mobile segments due to interactions during prior straining (by gripping or actual testing) would necessarily be manifested as an increase in apparent elastic limit in subsequent tests as was observed. However, the use of higher strain resolutions than that used in this investigation would, no doubt, reveal dislocation movement in these apparent elastic regions. In an annealed crystal the greatest part of the total length of dislocation line exists in two-dimensional arrays. Most of these subgrain boundaries contain dislocations with at least two different Burgers vectors and are immobile except for displacements that are small compared to the average spacing between dislocations in the array. Within the subgrains there are some relatively isolated dislocation lines which in some regions probably approach a It is reasonable to three-dimensional network.
OF PLASTIC
FLOW
IN
COPPER
136
assume that most parts, even of this network, have reached positions of metastability for both climb and glide motion during annealing. In general, the nodes that fix the positions of the ends of a segment will not lie on the same (111) layer of atoms. Therefore, most segments will be heavily jogged. Only rarely will a length of dislocation lie on or nearly on a (Ill} plane. We propose that the start of plastic deformation, as observed in these experiments, corresponds to glide, over distances comparable to the spacing between dislocations in the three-dimensional network, of the few segments lying most nearly on (111) and having Burgers vectors most nearly parallel to the direction of the applied stress. In many caf4es, particularly where one end of the segment terminates at an external surface, the glide may involve little or no increase in the total length of dislocation line. Figure 10 shows a particular example where a dislocation cuts across a subgrain from one small angle boundary to another. In cases like this there is no tendency for the line to return to its original position when the stress is removed. Also, if the plastic strain is mostly due to rather large displacements of a few segments, then the chance is very great that many of these will intersect other dislocations during their motion, forming new nodes. They will then -be unable to return to their original position even if the direction of the stress is reversed. Motion of a favorably oriented segment may also lead to glide of the less mobile dislocations that join it at its ends. Consider, for example, the elements of a dislocation network shown in Fig. 11. Suppose that dislocations AA’ and BB’ pass from one subgrain boundary to another, as shown in Fig. 10, but have formed attractive junctions with dislocation CC’ (if the stress tends to move dislocations AA’ and BB’ in
A
FIG. 10. A particularexample of a dislocation segment that could move a long distance when a small stress is applied.
136
ACTA
METALLURGICA,
their glide planes as indicated by the arrows) then the dislocation CC’ may be caused to move in its glide plane by motion of the nodes, P, P’, 0 and 0’ along the glide plane intersections. This might happen even though the stress exerts no force on CC’ or even a small foroe in the opposite direction. The important point is that the triple nodes in a three-dimensional network are not necessarily fixed points when a stress is applied. Motion of some segments of dislocation at G
FIG. 11. Coopera,tivemotion of severel dislocation segments by glide of nodes.
one part of the network may start a progressive rearrangement that can spread through a larger volume of crystal. The total plastic strain would then be due to both bowing out of individual dislocation segments between adjacent nodes and to a cooperative bowing of larger parts of a network. Presumably, this would involve motion of dislocations through distances large enough to form new interactions with other less mobile elements of the three-dimensional network. The large effect due to introduction of new dislocations at the surfaces of the specimen gauge length was clear evidence that the small plastic strains being measured were not localized at stress concentrations in the grip sections. These tests also show that the mobility of dislocations in the dilute (0.1 o/o Al) solid solution was approximately equal to that in OFHC copper. They suggest that the smaller strain rate observed in the annealed condition for the alloy specimens compared to that of pure copper was due to a smaller number of moving dislocation segments rather than a lower dislocation velocity. However, further experiments are needed for certain interpretation of impurity and solute element effects. Because of the low stresses involved in these experiments, it is of interest to consider their significance relative t,o the Peierls-Nabarro stress in
VOL.
12, 1964
copper. However, if the Peierls-Nabarro stress is defined as the stress required at absolute zero to move a dislocation that is straight on an atomic scale and lying in a position of minimum core energy,@) then none of the quantitative theories(r) are detailed enough to permit an estimate of its magnitude from these results. The theory is particularly incomplete for close packed crystals. For a dislocation that is split into partials it is not even certain which directions in the glide plane correspond to minimum core energy. Assume that the lowest core energy can be achieved when one of the two partials is either pure edge or pure screw, then, for a given Burgers vector and glide plane there are four such directions. If the PeierlsNabarro stress is important, a curved dislocation that is moving would tend to develop straight segments; the angles between adjacent segments being either 150’ or 120’ where the line passed from one preferred direction into another. Transmission electron microscopy of copper does not show any preference for particular orientation of dislocation lines relative to crystallographic directions. Therefore, if straight segments do form they must be very short (less than a few hundred interatomic distances). This means that a meaningful analysis of the Peierls-Nabarro stress must be based on thermally activated generation of kinks at the ends of these short segments. For the case where a dislocation segment is caused to move by motion of the triple nodes at its ends, the important consideration should be generation of kinks at the nodes. CONCLUSIONS
(1) Measurable plastic strains are produced in annealed polycrystalline copper and dilute solid solutions of aluminum in copper by applied stresses as low as about 2 g/mms. However, even these apparent elastic limits may be associated with the unavoidable prestrains produced during handling and gripping of the specimens. (2) Even the smallest plastic strains of the order of 10-s are largely irreversible. They are not recovered on removing the applied stress and the amount of strain produced by subsequent loading in the reverse direction is not as great as would be expected from a simple dislocation bowing model. (3) Introducing new dislocations at the surface of a specimen by bombarding with 27 p alumina particles greatly increases the amount of plastic strain in the pre-yield range. Under these conditions irreversible plastic deformation begins at the smallest measurable stresses. (4) In prestrained specimens pre-yield plastic strain does not increase smoothly with increasing
TINDER
AND
WASHBURN:
THE
stress. Marked fluctuations in strain rate resulting in irregular stress-strain curves.
INITIATION
OCCUR
AGKNO~EDGMENTS
The authors are grateful to the Office of Naval Research and in particular to Dr. Julius Harwood for support of their experiments. The help of Ira Pratt in the solution of some experimental problems is also greatly appreciated.
OF PLASTIC
FLOW
IN COPPER
137
REFERENCES 1. F. W. YOUNC3, JR., J. Appl. Phya. 82, 1815 (1961),and88, 963 (1962). 2. D. A. TEOU snd B. L. A~ERBAGH, Aeta Met, 7,69 (1959). 3. N. BROWN and K. F. LUKEXS, Acta Met. S, 106 (1961). 4. W. P. MASON, Phyeieol Acouatica and the Properties of Solids,p. 17. D. Van Nostrand, Primeton, N. J. (1958). 5. J. D. LIVINGSTON, J. AppZ. Whys. 81, 1071 (1960). 6. F. R. N. NAB-O, Proc. Phya. Sot. &mad.59, 256 (1947). 7. J. FRIEDEL, Eleotmn iW&rompy and Strength of Cryat&, p. 605. J. Wiley, New York (1963).