- Email: [email protected]
Easy glide of cubic metal crystals
EASY J.
GARSTONE,?
GLIDE R.
OF CUBIC
W.
K.
METAL
CRYSTALS*
HONEYCOMBE,:
and
G.
GREETHAM:
The structural features associated with easy glide in high-purity aluminum crystals have been studied The temperature dependence of the phenonemon has been by microscopic and X-ray methods. examined on identically oriented crystals over the range -196°C to 2OO”C, while the influence of specimen-length has been studied at room temperature. An examination of the orientation dependence of the stress-strain curves of copper single crystals confirms the results of Rosi in so far as easy glide ends at a value of the resolved shear stress o,, such that cr, - 7, (critical resolved shear stress) is constant. However, it is shown that the length of the easy-glide range varies because of the existence of a size factor, demonstrated by experiments on crystals of identical orientation, but of different sizes. The effect of thin electro-deposits and, in particular, of alloying additions on the extent of easy glide, has been investigated. The view is advanced that easy glide ends as a result of secondary slip arising prematurely in the Examination of this model gives the result that ~Jo,, is constant, iu vicinity of dislocation pile-ups. accord with the experimental results. The value of 7e determines the extent of easy glide, and from this Variation in the length of the slip path and follows an explanation of the temperature dependence. consequently of the number of pile-ups, is put forward as an explanation of the orientation dependence of the phenomenon. GLISSEMENT
FACILE
DE
CRISTAUX
CUBIQUES
METALLIQUES
Les traits structuraux de cristaux d’aluminium de haute puret8, associCs ou glissement facile, ont &8 Btudibs par des m&hodes de rayons X et microscopiques. L’effet de la t,emp&rature sur le ph&nom&ne a BtB examine sur des cristaux identiquement, orient& pour le domaine de -196°C jusqu’it 2OO”C, tandis que l’influence de la longueur de 1‘8chantillon a BtB BtudiBe iL la tempbrature ambiante. Un examen de l’effet de l’orientation SUI‘ les courbes tension-dbformation de monocristaux de cuivre confirme les r&&tats de Rosi dans la mesure ofi le glissement facile se termine B une valeur de la tension de cisaillement r&solue crOtelle que a 0 - 7e (tension critique de cisaillement r&olue soit constant. 11 est cependant d&nontri: (par des experiences sur des cristaux d’orientations identiques mais de tailles diff&entes) que la longueur du domaine du glissement facile varie, B cause de l’existence d’un facteur de taille. L’effet de fins dBp8ts blectrolytiques et,, en particulier, d’additions d’alliages sur I’ampleur du glissement facile a 6th BtudiB. L’hypothBse est &mise que le glissement facile se termine avec l’apparition pr&maturbe d’un glissement secondaire aux environs d’empilements de dislocations. L’examen de ce mod&le donne le r&sultat que 7Jo,, est constant en accord avec les rbsultats exp&imentaux. La valeur de 7, determine 1’8tendue du glissement facile et de ceci rt%ulte I’explication de I’influence de la tempt%ature. Une variation de la longueur de glissement et, par consbquent, du nombre d’empilements est avancbe pour expliquer l’influence de I’orientation sur le ph&nom&ne. “EASY
GLIDE”
IN
KUBISCHEN
METALLKRISTALLEN
An Reinstaluminium-Kristallen wurden die mit easy glide zusammenhlingenden strukturellen Veriinderungen (Gleitlinien, Knickbiinder usw.) mikroskopisch und rijntgenographisch untersucht. Ausserdem wurde an Kristallen gleicher Orientierung die Temperaturabhiingigkeit dieses Verfestigungsbereichs zwischen -196OC und 200°C verfolgt, wiihrend eine Untersuchung iiber den Einfluss der Probenl&nge bei Raumtemperatur erfolgte. Eine Nachprtifung der Orientierungsabhiingigkeit der Verfestigungskurve van Kupfer-Einkristallen bestiitigt insoweit die Ergebnisse von Rosi, als der easy-glide-Bereich bei einem Schubspannungswert o0 endigt, fiir den o0 - 7. (kritische Schubspannung) konstant ist. Es wird jedoch gezeigt, dass die Variation der Llinge des easy-glide-Bereichs auf die Existenz eines GrGssen-Effektes zuriickgeht, der durch Experimente an Kristallen mit gleicher Orientierung aber verschiedenem Querschnitt nachgewiesen wird. Weiterhin wurde der Einfluss diinner elektrolytisch abgeschiedener Schichten und insbesondere von Zulegierungen auf die Ausdehnung des easy-glide-Bereichs untersucht. Die Autoren sind der Auffassung, dass das Ende des easy glide van sekundiirer Gleitung herrtirt, die in der S&ho \-on Versetzungsaufstauungen vorzeitig einsetzt,. Eine Nachpriifung dieses Modells fiihrt in ‘iTbereirrstimmung mit den experimentellen Ergebnissen zu dem Resultat, dass 7,/o,, konstant ist. Der Wert van 7c bestimmt somit die Ausdehnung des easy glide-Bereichs, woraus such eine ErklBrung der Temperat,urabhBngigkeit folgt. Die Orientierungsabhkngigkeit der Erscheinung wird damit erkliirt, dass sich mit der Orientierung die LBnge des Gleitwegs und somit aurh dir Zahl der Aufstauungen Bndert.
* Received November 10, 1955. t Atomic Energy Research Establishment, Harwell. formerly $ Metallurgy Department, University of Sheffield, England. ACTA
METXLLURGICB,
VOL.
4,
SEPTEMBER
19.56
Metallurgy 455
Department,
University
of Sheffield.
England.
ACTA
486
METALLURGICA,
1. INTRODUCTION
Hexagonal give
shear-stress
plastic strains.
strain
curves
However,
1956
which determine
large
is much
cubic metal crystals where the
stress-strain curves are normally bolic.
up to
The rate of strain hardening
less than in comparable
4,
glide depends on the rotations occurring in kink bands,
metal crystals to a first approximation
linear
VOL.
approximately
para-
it has been known for some time that
them.
when secondary
As these rotations
temperature,
the easy-glide
crystals
of identical
different
temperatures
have
shown
that this stage of
ceases when slip on more than
one system begins. In recent hardening
can occur in pure metal crystals regardless
studied.
system
takes
occurrence that
the
place
and
provided
is uninterrupted
of inhomogeneities. parabolic
behavior
metal crystals arose from the formation bands and slip on other systems. partly
based
aluminum
by
on experimental
additions
of
cubic
of deformation
This opinion
work
carried
2.
the
Masingc3) considered
stress-strain
The effects
slip on a single
m-as
out on
crystals by Masing and Raffelsiefer,t4) who
square
wire
through
and
size and
with copper crystals
observations
have also been
of electrodeposited
films and of
to copper crystals have also been
The aluminum of the
at three
by X-ray
The role of crystal
PREPARATION
cation
critically
deformed
has been investigated
of the
on aluminum
and examined
methods.
orientation
alloying
structure,
clear that
orientation
on which metallographic
linear
of their crystal
it has become
Results will be presented
microscopic
made.
years
shorter.
to assess the important
crystals, and to propose a general explanation
very low hardening from the yield-point to as much as 20% plastic strain. More recently, Maddin, MathewHibbardc2)
within
variables in easy glide in both pure metals and in alloy phenomenon.
little or no hardening
range becomes
This paper is an attempt
exceptions to this behavior occur; notably, Von Goler and Sachs(l) showed that 70130 brass crystals exhibited
son and
slip occurs
are larger the higher the
OF
CRYSTALS
crystals were prepared by a modifi-
critical-strain (99.99%
strained
method
pure).
(29/o elong.)
a gradient furnace,
being 600-630°C.
from
Long
0.125-in.
lengths
of the
were
passed
wire
the highest temperature
In this way crystals
up to 22 in.
found that crystals with orientations near [loo] or [ill]
long were prepared and could be cut into a number of
hardened
identical
parabolically,
gave initially more
rapid
whereas
crystals
near [ 1 lo]
a linear hardening hardening
curve followed by a Rosi and parabolic curve.
specimens
(4 in. long).
similar cross-section
Copper
crystals
of
(0.125 in.) were prepared from the
melt, using a split graphite mold.
The copper used in
Mathewsonc5) also found a linear law with aluminum
these experiments was OFHC, which was subsequently
crystals
up to 2%
twice vacuum-melted
showed
that
aluminum
elongation.
Liicke
and Langec6)
heated to eliminate volatile bonding
on the crystal orienAndrade
agents.
Unless
these
critical
resolved
found that gold and silver crystals
greatly
from
extent
depended
of
this
not only
linear
region
in
tation, but also on the purity of the material. and Henderson”) behaved region
in a similar manner to aluminum, of linear hardening,
frequently
called,
temperature
became
of deformation.
was markedly
in graphite which had previously
been thoroughly
the
restricted
or “easy greater
and the
glide,” the
as it is
lower
the
The range of easy glide
in silver crystals when these
g/mm2). For the investigation three square-sectioned the dimensions in. Identically
found
working
with
aluminum
Jaoul
crystals,
that the range of easy glide decreased
as the
purity was reduced from 99.995 to 99.8%. Metallographic aluminum,
have shown that deformation
on
bands and
unpredicted slip on other planes occur in the early stages of deformation in crystals which would be expected
to deform
on one set of planes.
Rosi,(is)
using both silver and copper single crystals, found that
polished
glide.
Sawkill
and
being 0.250, 0.188,
the length in each case was four
oriented crystals of different sizes were
(100 ml) electrolyte 27.
The
the aluminum
copper
crystals
The crystals
accidental
g/l.)
acid
across the cell of
were polished
(1000
were carefully
to avoid
crystals were
(900 ml) perchloric
with a voltage
orthophosphoric acid approximately 1.8.
axial alignment.
multiple
a special
crystals from a common source,
in an ethyl alcohol
occurrence
have suggested that the range of easy
(~40-60
seed crystal.
designed
of sporadic
the
varied
also grown in separate molds from parts of the same
the end of the linear hardening was associated with the Honeycombeo4)
of the size effect,
Prior to deformation,
studies,‘93 107lit 12) principally
low value
of the specimens
impurities
in the metals had the same effect.
copper
graphite mold was made which allowed the growth of
had a thin oxide film, and in general the presence of Crussard,(s)
were taken,
stress of the
the characteristic
and 0.125 in. square;
and
precautions
shear
at
mounted, bending
in aqueous
a voltage
of
using a jig
and to ensure
The ends of each crystal were held
in steel cups by using Woods
metal for the copper
GARSTONE’et
crystals,
and
a special
aluminum
for
EASY
GLIDE
487
the
The copper crystals were deformed
aluminnm crystals.
primarily in a Polanyi-type a.luminum
solder
al.:
crystals
were
tensile machine, while the strained
in a Hounsfield
t,ensometer which was adapted to carry out tests both at -196°C and at 200°C in addition to deformation at, room temperature. 3. EXPERIMENTAL ALUMINUM
The microstructural
RESULTS CRYSTALS
features
WITH
associated
glide were most readily studied on aluminum
with easy crystals.
Furthernlore~ the fact that very long crystals could be prepared by the strain-anneal eliminate
t’he orientation
specimens,
method made it easy to by using identical
variable
and the effect of crystal length
could
Fra. “. Same es Fig. 1. X-ray micrograph )/ 20.
be
&tidied within wide limits. microscopically
and by X-ray
further examination
diffraction
methods.
A
was carried out at a later stage
m-hen the rate of hardening had increased considerably. It was established
that both
band, bands of secondary
types
of deforn~ation
slip, and kink bands were
present during the region of easy glide. show an optical micrograph
Figs. 1 and 2
and an X-ray micrograph
from the same face of a crystal taken just after the end of easy glide (approx.
4.4oj
elongation);
reveals two sets of deformation the operative them.
Optical
slip bands
the Iatter
bands, one parallel to
and the others normal
examination
slip in the regions of either type of deformation Little
X-ray
asterism
to
did not show secondary
was observed
at this
band. stage
(Fig. 3). After FXG. 1. Aluminum crystal 04B 4.4% elongation at room temperature. Optical micrograph x 250.
The work confirmed as the occurrence the orientation
earlier investigations
of easy glide depended
of the crystal.
somewhat.
elongation)
heavier
the stress-strain
deformations
(--S-9”,0
curve became
paral colic
and marked strain hardening had taken place.
in so far
markedly
on
Crystals in which more
than one slip system were predicted to operate from t,he earliest8 stages of deformation, in particuiar crystals
near [loo]
and [Ill]
and on the boundary
between these poles, gave no region of easy glide and showed marked strain hardening of the deformation.
Large
bands
from the beginning of secondary
slip
were observed, but kink bands were absent. Particular attention was paid to those crystals the orientation
of w-hich fell well within the stereographic
triangle a,nd which gave regions of easy glide. The deformation was interrupted at a point near the end of the easy-glide region and the crystals were examined
Frc. 3. Crystal OPB after 4.4% elongation, X-ray Laue photograph.
X -ray
ACTA
485
METALLURGICA,
VOL.
FIG. 4. Xiuminum crystal 04B aft,er ??.S?(,elongation at! room temperst,ure. Optical micrograph s 250.
micrographs
confirmed
more heavily disoriented
and that the major disorien-
tations
with the kink bands rather
were associated
mi~rograph compared
after
w&h Fig.
crystal at the earlier stage. correspondingly
Fig. 5 is t,he X-ray
S.%o;b elongation,
directly
Microscopic
slip.
deformed
-196”C,
(Fig. 6; cf. Fig. 3).
at room temperature
(Fig. 7);
however,
system in
(Fig. 4) and
in cryst~als deformed
2OO”C, t,he kink bands were more ~rononnced, secondary
slip was observed in them.
in these latter larger those
numbers occurring
crystals of
be
did not reveal any marked
evidence of slip other t,han on the primary crystals
can
on the same
The X-ray asterisms were
more pronounced
examination
which
2 taken
at and
The slip bands
were coarser and contained
individual
slip
lamellae
after similar deformations
than
at lower
temperatures.
Fm. 5. &me ~b3Fig. 4. X-ray micrograph X 20.
1956
FIG. 6. Same as Fig. 4. X-ray LRUCphot~gr5ph.
that the crystals had become
than the bands of secondary
4,
(b) Terwperature Dependence qf Easy Glide Cryst,als -196’C,
of
room
examined increwed rate
orientation
temperature,
and
after approximately
deformat,ion. the
identical
The
lengt,h
deformed
t’he same amount
of
t,he easy-glide
as the t~el~perat~~e of testing fell; of
subsequent
decreasing temperature.
at
2OO”C, and were
hardening
of
range
hotvever,
increased
with
crystals
3% a,
For exampIe,
b, and c (Fig. 10) showed this behavior quite clearly, the
crysta,l deformed
easy-glide For
a given
asterism
in liquid
nitrogen
range of approximately deformation,
increased
with
t,he extent,
increasing
of
an
X-ray
ten~perature
test (Figs. 6 and 9). This ~-as qualitatively with the disorientations
giving
1Ot.b shear strain.
observed in the X-ray
micro-
graphs which resulted primarily from the formation kink bands (Figs. 5 and 8). Microscopic
of
correlated of
observations
showed clearly that the size and spacing of t,he kink
FIG. 7. Aluminum crystal 04A deformed to SY/, elong&ion at - 196°C. Optical micrograph x 250.
GARSTONE
et al.:
EASY
4. EXPERIMENTAL RESULTS COPPER CRYSTALS
FIG. 8. Same m Fig. 7. Y-ray micrograph ~20.
bends increased with the temperature. there is a correlation
introduced
by the
stress-strain
curves
orientations. glide
kink hands.
part
orientation.
on
of
shear
copper
crystals
of
various
Roth the slope and length of the ensyof
the
stress-strain
However, stress
curves
va~ry with
Rosi has shown that this part
of the cnrve is associated Two ident,ically oriented crystals (17~4 17b), one 9 in.
WITH
Rosi,(la) and Cupp and Chalmerso5) have published
It seems that
between the length of the onsy-
glide range and the ~sorientat,ions
489
GLIDE
which
with a constant is
independent
increment of
crystal
long, the other 3 in. long, which had received the same
orientation.
The present work, while confirming
treatment,
observation,
not only for copper but also dilute alloys,
range.
were deformed
to the end of the easy-glide
The load-extension
curves are shown in Fig. 11.
M’hilo the curves are not identical, glide is similar in each case. carried
out
complete,
after
the
the range of easy
An X-ray
easy-glide
revealed little difference
exan&stion
deformation in X-ray
of the
Furthermore, a survey of crystalsrevealed noticeable dif-
ferences only within 1 mm of the grips. X-ray micrographs revealed the presence deformation bands t.hroughout both crystals.
shows that variations in the easy-glide range can arise from the differences in the size and surface condition of the crystals tested.
was
asterism
between the two crystals, t)he length
this
(a) Urieratatkm
Dependence
of the &ress-strain
Fig. 1% shows the shear stress-shear strain curves for a number of oopper crystals of diflerent orientations (Fig. 12b), all of which would
of fine
Curse
linear hardening mation.
be expected
at t,he heginning
to show
of plusti-ticdefor-
These diger from R,osi’s results in so far as
the length of the easy-glide range is bigger by at least
FJG. 9. Same 89 Fig. 7, X-ray Laue photogmph.
FIG. LX. K&em hardening of two identicz&y oriented aluminum crysttils of different lengths. 17it-3 in. long. 17b-9 in. long.
ACTA
METALLURGICA,
VOL.
4,
1956
on coppep and copper-silver single cr@als
TABLE 1. Data
7
T(
(de4
text)
00
-
1
63:” 56”
cu-49 CU-50
cu-51
56’ 59” w 48’ 433 4gc 49” 46”
cu-43 cu-48 CU.53 Cu.42 cu-40 CU-38 CU-44 cu.45 CU-55 cu.35
64
343-O 37” 334 3.5” 37” 42’ 49’ 43” 0
( I i
I 1
i;): 89 3s 38 48 44 41 49 37 46 ti’i
:;o 39” 48” 49’
0 % 46”
ext.
dev.
86 58 58 59 6f 64 65 57 53 55 50 53 57
142 13x 108 136 106 121 127 123 120 122 100 117 134
78 80 59 77
73 63 71 57
77 45 5; 62 66 67 6i 50 64 ii
535
1230 485 770
635 “53 384
635 253 3x4
__
-1
_I
60
79
i /
1.86
2.31 l.id 1.89 1.95
i
2.8
/
_ext. 1.65 2.38
2.22 2.38 2.2 2.31 2.79 3.18 2.65
ii:
68 83 59 i9
-_.
dev.
2.93 2.43 2.7 2.54 2.35
2.16 2.16 2.22 2
2.21
2.37:
_ cll-Ag
1B 2C 3F
alloys
47” 4.7” 50”
595 232 386
232 386 ,I
-
-_....-._
/
2.07 2.09
j
2.00
-
Note: In this table, X,, is the angle between the specimen axis and the normal to the slip plane: & is the angle between the specimen axis and the shp direction; -rc (dev) is the critical resolved shear stress determined by the first deviation from Hooke’s law; 7c (ext) is the critical resolved shear stress determined by extrapolation of the stress/strain ourve to zero strain; cr, is the stress at which the extrapolated easy-glide range meets the extrapolation of t,he rapid-hardening part of the curve.
a factor
of
2.
However,
they
confirm
that
linear
The resolved critical shear stress for glide (TJ is not?
hardening
ends at a value of the shear stress o. such
constant.
that a0 -
-rC is approximately
where -r, is
differences in purity of the crystals as grown, in part
glide.
to structural
the
critical
resolved
shear
essential results are tabulated
constant, stress
for
in Table 1.
The
The variation differences
to the difficulty Added
can in part be attributed due to mosaics,
of handling
determining
rC precisely,
very gradually.
specimens.
uncertainty
in
as the curves
change slope
Bearing these di~culties
in mind, the
degree of constancy extent
and in part
such fragile
to this there is considerable
to
of (r. -
T, is quite surprising.
of easy glide is a maximum
decreases as the [loo]-[ill]
boundary
The
near [l lO] and is approached.
(b) Microstructure The
crystals
deformation, microscope SHEAR
WEAR
STRAIN
STRAIN
u-ere
and many
electropolished
were examined
prior
to
under
the
at various st,ages during the deformation,
“1.
-/.,
Fro. 12a. Shear-stress/shear-strain curves of copper crystals of various orientations.
/
1
PIG. 12b. Orie~t‘atiolls of rapper crystals of Fig. 1%.
GARSTONE
et al.:
EASY
GLIDE
To overcome
491
this trouble,
three crystals of different
sizes (&, &, and g in. diam.)
but of identical
orien-
tation were grown in separate molds from parts of the same
seed
removed
crystal.
without
The
smallest
crystal
could
damage from the single mold.
be Fig.
13 shows the shear stress-shear strain curves for three crystals of different sizes prepared in this way.
It
clear that the amount
with
decreasing
crystal
of easy glide increases
size.
Furthermore,
range ends at approximately 0
0
1
I
I
2
SHEAR
STRAIN
13. Shear-stress/shear-strain oriented copper crystals of different R, t in. diam.; C, ;dr in. diam.
Slip
on
the
predicted
curves of identically sizes. A, # in. diem.:
system
occurred
exclusively
during the region of easy glide, but slip on
secondary
systems
was detected
after
the end of easy
fairly
soon
operative
secondary
plane
in limited glide.
regions The
was the cross-slip
first identified by Maddin, Mathewson, however,
first plane
and Hibbard;t2)
at higher stresses the majority
of the other
(111) planes operate at least locally. (c)
of the recent results”9 13) on easy glide
in the extent of linear hardening
metals of comparable gations
have
of easy glide, presumably
causing
dislocation
Andrade
and Henderson(7)
on silver crystals
pile-ups
below
the
by
surface.
found that an oxide film
would markedly
reduce the linear
part of the stress-strain curve. A copper crystal was plated with 10,000 A of Ni, but this did not eliminate easy glide, and slip appeared on the surface as in the case of unplated ever, the further
addition
crystals.
How-
of 10,OOOA of chromium
did result in the elimination
in copper, silver, and gold shows that there is a wide variation
There is already some evidence that surface coatings
of the linear hardening
region (Fig. 14).
Crystal Xize
Comparison
(d) Electroplating of Crystals will reduce the extent
primary
the easy-glide
the same resolved shear
stress.
3
o/o
FIG.
is
purity.
used
different
crystals, the existence
even with
As the various investisizes
of a size-effect
and
shapes
of
was possible.
Copper crystals of three sizes $, &, and Q in. square of identical orientation
were grown in a triple graphite
(e) Alloying Particular
attention
for other shows
alloying
typical
elements
shear
The critical resolved
Repeatedly
and 600 g/mm2.
however, the smallest crystal did
such as gold.
stress-shear
crystals of three alloys containing
groups characterized
it was found that the largest crystal gave
15 for 0.3,
shear stresses fall into three
Furthermore,
the stress-strain curves
also fall into three families, the greatest range of easy glide being shown by the crystals silver
from the mold.
Fig.
curves
by the average values 240, 450,
difficulty
it undamaged
strain
approximately
not always behave in the expected manner, due to the of removing
give similar results
0.6, and 1.0% by weight of silver.
mold, and each crystal was tested in a similar manner. the least easy glide;
has been paid to dilute alloys
of silver in copper, but experiments
content.
Closer
with the highest
examination
of the
curves
reveals that, as in the case of pure copper, the end of easy glide occurs at approximately
twice the critical
resolved shear stress for glide. In the curves of Fig.
15 the slopes of the linear
range are very similar.
This arises from the fact that
crystals
oriented
fairly
closely
to each
other
were
chosen so that the effect of the alloying element could be more readily determined. The slope is clearly more a function of orientation than of composition. Metallographic SHEAR
STRAIN
‘/_
FIG. 14. Effect of surface coatings on the range in two similarly oriented copper crystals (1) unplated, (2) nickel-chromium plated.
observations
revealed
of easy glide in all crystals examined easy-glide
that the end was associated
with the localized occurrence of unpredicted secondary slip. Some secondary slip was observed prior to the end of easy glide, but this was usually associated with
492
ACTA
METALLURGICA,
VOL.
As
4,
the
resolved
1956
secondary
slip
operates
at
macroscopic
shear stresses below those which would
expected
to produce
slip on the secondary
stress concentrators
must exist locally
shear stress sufficiently dislocations
to cause glide.
seem to be the most
centrators in a deformed
to raise the Pile-ups
likely
single crystal.
from the head of a dislocation
OOW
20
30
SHEAR
40
50
STRAIN
60
Pij
is the local
of three
9 477(1 f(0) determines
surface defects such as pits or scratches, which would The first operative
be expected to act as stress-raisers.
slip plane was again found to be the crossbut in most
co the applied
shear
in the pile-up, and
r the distance from it measured in units of
the secondary
slip plane,
stress,
“/,
FIG. 15. Typical shear-stress/shear-strain curves dilute copper silver alloy crystals. x-o.3 3F -0.6 weight per cent silver. lB-1.0
secondary
(~0)
pile-up is:
stress, n the number of dislocations
70
of
stress con-
Stroh(l7) has shown that the stress at a point
where
be
planes,
crystals
all the octahedral
Y)Oo
which plane is the first to operate in system.
A Frank-Rea’d
source on any system near a pile-up
will operate when the local stress Pij reaches a critical value ,ub/l, which is approximately stress, so the above expression
7, the critical shear
becomes:
planes were found to operat,e locally sooner or later. 5. DISCUSSION
The
general
viewpoint on easy glide has been by Cottrell,(16) who distinguishes between
crystallized laminar
flow resulting
and the subsequent or less parabolic interpreted
in a linear stress-strain
turbulent hardening
curve
flow resulting in a more curve.
Koehler(22)
pile-ups.
However,
agreed, and the present experiments
it is
confirm,
that the end of easy glide is in fact characterized planes.
Now
of unpredicted
The possibility
of sporadic
The transition
flow can be understood dislocations
unpredicted
hardening
jogs
subsequent
(2)
K2ao
Eshelby,
Frank, and Nabarro(l*) (TO77
n=_-__
slip be
planes
by virtue interstitial
which
give rise to
of the generation and
of of
Y) ~- = K,o,
iub where d is the length of the pile-up. Substituting
values of T and n in (1). 7, - = constant (10
This means that secondary slip starts and consequently easy glide ends when the resolved shear stress on the
mation. However, an important question yet to be answered is: What decides when this transition takes
primary system reaches a given multiple of the critical
The effect of such variables
orient,ation,
purity,
size of specimen,
vacancy
d(1 -
have shown that
for-
place?
and
by
from laminar to turbulent
in terms of the interaction
on different
increased
sub
slip on other octahedral
within the region of easy glide cannot nevertheless excluded.
L
r=
sources takes place, while he
of dislocation
the occurrence
sources in the crystal
head of the pile-up.
has
postulates that the more rapid hardening is due to the interaction
of dislocation
will determine the distance (L) of the source from the
the linear region as that in which exhaus-
tion of the Frank-Read
widely
The distribution
as temperature, and effect
of
surface films on the extent of easy glide must all be explained.
resolved shear stress 7,.
In the present experiments,
the ratio has been found to be approximately
2 both
for pure copper and the dilute alloys with silver.
The
longer easy-glide ranges in the alloys can be explained simply as necessary for the local stress to build up to
GARSTONE
a value approaching stress
so
et&.:
493
GLIDE
that of the critical resolved shear
markedly
increased
by
alloying.
Other
factors being equal, the present theory indicates the critical
EASY
resolved
that
shear stress T, determines
the
extent of easy glide. As Rosi has pointed out,, the results on the effect of impurities
on easy glide have not been unambiguous.
When a finely dispersed occur
second phase is present, the
pile-ups
would
in the vicinity
particles
and at an early stage of the deformation,
thus leading t,o rapid hardening.
of the
small
Carlsen and Honey-
eombe(rs) have shown in aluminum 3.3% copper single crystals
that
linear
super-saturated
l~arde~ng
only
occurs
in the
solid solution, and ordinary parabolic
hardening occurs when a finely dispersed second phase is present. As the temperature increases,
of deformation
is lowered,
7,
so again an increase in the extent of easy
glide would
be expected.
experiments
of Andrade
described
above.
This is confirmed and Hendersonc7)
Lowering
the
tem~rature
reduces the amount of slip per slip band. temperatures,
by the
and those also
At, elevated
the slip bands will be coarser and the
stresses around the pile-ups should lead earlier to the occurrence
of secondary
on aluminum
have
slip.
The above experiments
confirmed
this view:
est,ablished
that
given &ress is reached, tation
dependence
evaluating
an explanation
of easy
the slope
This is a minimum
glide
slip direction.
can be sought
for orientations axis rotates
towards
the primary
elongated,
length of t,he slip direction
increases.
Mot,t(20) is followed
during
that,
pass out of the crystal,
locations
since it would
If the view of
easy
glide,
by the present experiments,
small crystals of identical plotting copper
is now for dis-
to escape if the slip path is increased.
is well supported
dislo-
then the change in
be more difficult
show that, large crystjals harden
is
so that the
slope of the stress-strain curve with orientation explained,
and
is approached,
The salient feature of this transition
that the slip plane becomes
cations
in
curve.
near [IlO],
boundary
a
of the orien-
a/a of the stress-strain
increases as the [loo]-[llI] i.e. as the tension
glide ends when
easy
more rapidly
orientation.
This which than
Furthermore,
o/a against the length of the slip direction for crystals of different
orientation
4 LENGTH
OF
I
,
I
I
I
5
6
7
5
9
SLIP
DIRECTION
mm.
FIG. 16. Relation between the rate of hardening o/u and the length of the slip direction.
to be particularly
pronounced
this is, in fact’, what Andrade
with small
crystals;
and Henderson
found.
One final point which needs some discussion
is the
question of where the pile-ups occur in the deformed crystals.
In aluminum the obvious
sites of secondar-y
slip are primarily the deformatiol~ bands, as the above experiments
have
pronounced,
but closer spaced at lower temperatures;
indicated.
this means that secondary
These
bands
are less
slip will occur at a later
stage, for the critical pile-ups will require more deformation to form them.
secondary
slip is observed in kink bands at a much earlier stage at 200°C than during deformation at -196°C. Having
1
101 3
does, in fact,
give an approximately linear correlation (Fig, l(i). The effect, of surface fihns is also evidence in support
At higher temperatures (200°C) in the bands are heavier for a given
the distortions deformation, spondingly
and secondary
slip occurs
earlier stage.
Of course, it could be postulated are initiated develop,
by local
secondary
cause further secondary
felt that deformation distances
that
expected to make It is doubtful apply
to
crystals, vations
the
t,hat kink bands slip and, as they
slip.
However,
it is
bands must play a significant
role, as it is only when pile-ups large
at a corre-
the
a substantial
whether behavior
are spaced at, fairly
specimen
size
the above of
could
be
difference.
certain
e.g. 70/30 brass, although of easy glide were made
considerations highly
alloyed
the early obseron this material.
Here, the linear region of the curve is almost parallel to the strain axis and the lack of hardening appears to be related to the occurrence
of a yield phenomenon.
Piercg, Cahn, and Cottrell(z~) have recently shown that in brass crystals, slip propagates through the specimen in the linear zone.
Furt,hermore, slip in brass crystals
is much coarser and more grouped than in crystals of copper and its dilute alloys. ACKNOWLEDGMENTS
of the above a,rgument , since such films would tend to retain dislocations within the crystal, thereby reducing
One of us (G. G.) is indebted to the Department for Scientific and Indust’rial Research for a studentship. We gratefully acknowledge the helpful comments of
the easy-glide range.
our eollea~gues at all st,ages of the work.
These
effects would be expected
ACTA
494
METALLURGICA,
REFERENCES 1. F. VON GBLER and G. SACHS 2. Physik. 55, 581 (1929). 2. R. MADDIN. C. H. MATHEWSON. and W. R. HIBBARD Trans. A&r. Inst. Min. Met.’ Eng. 175, 86 (1948); ibid. 185,527 (lS50). 3. G. MASING Lehrbuch der ull~emeinen Metallkunde Berlin, Springer-Verlag (1950). 4. G. MASING and J. RAFFELSIEFER 2. Metallkunde 41. 65 (1950). 5. F. D. ROSI and C. H. MATHEWSON Trans. Amer. Inst. Min. Met. Eng. 188, 1159 (1950). 6. K. LOCKE and H. LANGE 2. Metallkunde 43., 55 (1952). 7. E.N. DA C. ANDRADE and C. HENDERSON Phil. Trans. A244, 177 (1951). 8. B. JAOUL and C. CRUSSARD Camp. Rend. 234, 700 (1952). 9. K. WT. CAHN J. Inst. Miletrtls79, 448 (1951).
VOL.
4,
1956
10. R. K. CHEN and C. H. MATHEWSON J. Metals 3, 653 (1951). 11. R. W. K. HONEYCO~C~BE J. Inst. Metrrls 80, 49 (1951). 12. E. A. CALNAN Acta. Cryst. 5,557 (1952). 13. F. D. Rosr J. Metals 6, 1009 (1954). 14. J. SAWKILL and R. W. K. HONEYCOXBE Acta, Met. 2, 8.54 (1954). 15. C. R. CUPP and B. CHALMERS Actn Met. 2, 803 (1954). 16. A. H. COTTRELL Prog. in &fetal Physics 4; 205 (1953). 17. A. N. STROH Proc. ROJJ. s’oc. A223, 404 (1954). 18. J. D. ESHELBY, F. C. FR_&NK, and F. R. S. NABARRO Phil. Mng. 42, 351 (1951). 19. K. M. CARLSEN and R. W. K. HONE~~OXBE J. Inst. Metals 83, 449 (1955). 20. N. F. IfOTT Phil. Mao. 44. 742 (1953). 21. G. R. PIERCY, R. W. CAHN, md A. H. COT'~RELL Acta Met. 3, 331 (1955). 22. J. S. KOEHLER Phys. Rec. 86, 5” (1952).
GARSTONE,?
GLIDE R.
OF CUBIC
W.
K.
METAL
CRYSTALS*
HONEYCOMBE,:
and
G.
GREETHAM:
The structural features associated with easy glide in high-purity aluminum crystals have been studied The temperature dependence of the phenonemon has been by microscopic and X-ray methods. examined on identically oriented crystals over the range -196°C to 2OO”C, while the influence of specimen-length has been studied at room temperature. An examination of the orientation dependence of the stress-strain curves of copper single crystals confirms the results of Rosi in so far as easy glide ends at a value of the resolved shear stress o,, such that cr, - 7, (critical resolved shear stress) is constant. However, it is shown that the length of the easy-glide range varies because of the existence of a size factor, demonstrated by experiments on crystals of identical orientation, but of different sizes. The effect of thin electro-deposits and, in particular, of alloying additions on the extent of easy glide, has been investigated. The view is advanced that easy glide ends as a result of secondary slip arising prematurely in the Examination of this model gives the result that ~Jo,, is constant, iu vicinity of dislocation pile-ups. accord with the experimental results. The value of 7e determines the extent of easy glide, and from this Variation in the length of the slip path and follows an explanation of the temperature dependence. consequently of the number of pile-ups, is put forward as an explanation of the orientation dependence of the phenomenon. GLISSEMENT
FACILE
DE
CRISTAUX
CUBIQUES
METALLIQUES
Les traits structuraux de cristaux d’aluminium de haute puret8, associCs ou glissement facile, ont &8 Btudibs par des m&hodes de rayons X et microscopiques. L’effet de la t,emp&rature sur le ph&nom&ne a BtB examine sur des cristaux identiquement, orient& pour le domaine de -196°C jusqu’it 2OO”C, tandis que l’influence de la longueur de 1‘8chantillon a BtB BtudiBe iL la tempbrature ambiante. Un examen de l’effet de l’orientation SUI‘ les courbes tension-dbformation de monocristaux de cuivre confirme les r&&tats de Rosi dans la mesure ofi le glissement facile se termine B une valeur de la tension de cisaillement r&solue crOtelle que a 0 - 7e (tension critique de cisaillement r&olue soit constant. 11 est cependant d&nontri: (par des experiences sur des cristaux d’orientations identiques mais de tailles diff&entes) que la longueur du domaine du glissement facile varie, B cause de l’existence d’un facteur de taille. L’effet de fins dBp8ts blectrolytiques et,, en particulier, d’additions d’alliages sur I’ampleur du glissement facile a 6th BtudiB. L’hypothBse est &mise que le glissement facile se termine avec l’apparition pr&maturbe d’un glissement secondaire aux environs d’empilements de dislocations. L’examen de ce mod&le donne le r&sultat que 7Jo,, est constant en accord avec les rbsultats exp&imentaux. La valeur de 7, determine 1’8tendue du glissement facile et de ceci rt%ulte I’explication de I’influence de la tempt%ature. Une variation de la longueur de glissement et, par consbquent, du nombre d’empilements est avancbe pour expliquer l’influence de I’orientation sur le ph&nom&ne. “EASY
GLIDE”
IN
KUBISCHEN
METALLKRISTALLEN
An Reinstaluminium-Kristallen wurden die mit easy glide zusammenhlingenden strukturellen Veriinderungen (Gleitlinien, Knickbiinder usw.) mikroskopisch und rijntgenographisch untersucht. Ausserdem wurde an Kristallen gleicher Orientierung die Temperaturabhiingigkeit dieses Verfestigungsbereichs zwischen -196OC und 200°C verfolgt, wiihrend eine Untersuchung iiber den Einfluss der Probenl&nge bei Raumtemperatur erfolgte. Eine Nachprtifung der Orientierungsabhiingigkeit der Verfestigungskurve van Kupfer-Einkristallen bestiitigt insoweit die Ergebnisse von Rosi, als der easy-glide-Bereich bei einem Schubspannungswert o0 endigt, fiir den o0 - 7. (kritische Schubspannung) konstant ist. Es wird jedoch gezeigt, dass die Variation der Llinge des easy-glide-Bereichs auf die Existenz eines GrGssen-Effektes zuriickgeht, der durch Experimente an Kristallen mit gleicher Orientierung aber verschiedenem Querschnitt nachgewiesen wird. Weiterhin wurde der Einfluss diinner elektrolytisch abgeschiedener Schichten und insbesondere von Zulegierungen auf die Ausdehnung des easy-glide-Bereichs untersucht. Die Autoren sind der Auffassung, dass das Ende des easy glide van sekundiirer Gleitung herrtirt, die in der S&ho \-on Versetzungsaufstauungen vorzeitig einsetzt,. Eine Nachpriifung dieses Modells fiihrt in ‘iTbereirrstimmung mit den experimentellen Ergebnissen zu dem Resultat, dass 7,/o,, konstant ist. Der Wert van 7c bestimmt somit die Ausdehnung des easy glide-Bereichs, woraus such eine ErklBrung der Temperat,urabhBngigkeit folgt. Die Orientierungsabhkngigkeit der Erscheinung wird damit erkliirt, dass sich mit der Orientierung die LBnge des Gleitwegs und somit aurh dir Zahl der Aufstauungen Bndert.
* Received November 10, 1955. t Atomic Energy Research Establishment, Harwell. formerly $ Metallurgy Department, University of Sheffield, England. ACTA
METXLLURGICB,
VOL.
4,
SEPTEMBER
19.56
Metallurgy 455
Department,
University
of Sheffield.
England.
ACTA
486
METALLURGICA,
1. INTRODUCTION
Hexagonal give
shear-stress
plastic strains.
strain
curves
However,
1956
which determine
large
is much
cubic metal crystals where the
stress-strain curves are normally bolic.
up to
The rate of strain hardening
less than in comparable
4,
glide depends on the rotations occurring in kink bands,
metal crystals to a first approximation
linear
VOL.
approximately
para-
it has been known for some time that
them.
when secondary
As these rotations
temperature,
the easy-glide
crystals
of identical
different
temperatures
have
shown
that this stage of
ceases when slip on more than
one system begins. In recent hardening
can occur in pure metal crystals regardless
studied.
system
takes
occurrence that
the
place
and
provided
is uninterrupted
of inhomogeneities. parabolic
behavior
metal crystals arose from the formation bands and slip on other systems. partly
based
aluminum
by
on experimental
additions
of
cubic
of deformation
This opinion
work
carried
2.
the
Masingc3) considered
stress-strain
The effects
slip on a single
m-as
out on
crystals by Masing and Raffelsiefer,t4) who
square
wire
through
and
size and
with copper crystals
observations
have also been
of electrodeposited
films and of
to copper crystals have also been
The aluminum of the
at three
by X-ray
The role of crystal
PREPARATION
cation
critically
deformed
has been investigated
of the
on aluminum
and examined
methods.
orientation
alloying
structure,
clear that
orientation
on which metallographic
linear
of their crystal
it has become
Results will be presented
microscopic
made.
years
shorter.
to assess the important
crystals, and to propose a general explanation
very low hardening from the yield-point to as much as 20% plastic strain. More recently, Maddin, MathewHibbardc2)
within
variables in easy glide in both pure metals and in alloy phenomenon.
little or no hardening
range becomes
This paper is an attempt
exceptions to this behavior occur; notably, Von Goler and Sachs(l) showed that 70130 brass crystals exhibited
son and
slip occurs
are larger the higher the
OF
CRYSTALS
crystals were prepared by a modifi-
critical-strain (99.99%
strained
method
pure).
(29/o elong.)
a gradient furnace,
being 600-630°C.
from
Long
0.125-in.
lengths
of the
were
passed
wire
the highest temperature
In this way crystals
up to 22 in.
found that crystals with orientations near [loo] or [ill]
long were prepared and could be cut into a number of
hardened
identical
parabolically,
gave initially more
rapid
whereas
crystals
near [ 1 lo]
a linear hardening hardening
curve followed by a Rosi and parabolic curve.
specimens
(4 in. long).
similar cross-section
Copper
crystals
of
(0.125 in.) were prepared from the
melt, using a split graphite mold.
The copper used in
Mathewsonc5) also found a linear law with aluminum
these experiments was OFHC, which was subsequently
crystals
up to 2%
twice vacuum-melted
showed
that
aluminum
elongation.
Liicke
and Langec6)
heated to eliminate volatile bonding
on the crystal orienAndrade
agents.
Unless
these
critical
resolved
found that gold and silver crystals
greatly
from
extent
depended
of
this
not only
linear
region
in
tation, but also on the purity of the material. and Henderson”) behaved region
in a similar manner to aluminum, of linear hardening,
frequently
called,
temperature
became
of deformation.
was markedly
in graphite which had previously
been thoroughly
the
restricted
or “easy greater
and the
glide,” the
as it is
lower
the
The range of easy glide
in silver crystals when these
g/mm2). For the investigation three square-sectioned the dimensions in. Identically
found
working
with
aluminum
Jaoul
crystals,
that the range of easy glide decreased
as the
purity was reduced from 99.995 to 99.8%. Metallographic aluminum,
have shown that deformation
on
bands and
unpredicted slip on other planes occur in the early stages of deformation in crystals which would be expected
to deform
on one set of planes.
Rosi,(is)
using both silver and copper single crystals, found that
polished
glide.
Sawkill
and
being 0.250, 0.188,
the length in each case was four
oriented crystals of different sizes were
(100 ml) electrolyte 27.
The
the aluminum
copper
crystals
The crystals
accidental
g/l.)
acid
across the cell of
were polished
(1000
were carefully
to avoid
crystals were
(900 ml) perchloric
with a voltage
orthophosphoric acid approximately 1.8.
axial alignment.
multiple
a special
crystals from a common source,
in an ethyl alcohol
occurrence
have suggested that the range of easy
(~40-60
seed crystal.
designed
of sporadic
the
varied
also grown in separate molds from parts of the same
the end of the linear hardening was associated with the Honeycombeo4)
of the size effect,
Prior to deformation,
studies,‘93 107lit 12) principally
low value
of the specimens
impurities
in the metals had the same effect.
copper
graphite mold was made which allowed the growth of
had a thin oxide film, and in general the presence of Crussard,(s)
were taken,
stress of the
the characteristic
and 0.125 in. square;
and
precautions
shear
at
mounted, bending
in aqueous
a voltage
of
using a jig
and to ensure
The ends of each crystal were held
in steel cups by using Woods
metal for the copper
GARSTONE’et
crystals,
and
a special
aluminum
for
EASY
GLIDE
487
the
The copper crystals were deformed
aluminnm crystals.
primarily in a Polanyi-type a.luminum
solder
al.:
crystals
were
tensile machine, while the strained
in a Hounsfield
t,ensometer which was adapted to carry out tests both at -196°C and at 200°C in addition to deformation at, room temperature. 3. EXPERIMENTAL ALUMINUM
The microstructural
RESULTS CRYSTALS
features
WITH
associated
glide were most readily studied on aluminum
with easy crystals.
Furthernlore~ the fact that very long crystals could be prepared by the strain-anneal eliminate
t’he orientation
specimens,
method made it easy to by using identical
variable
and the effect of crystal length
could
Fra. “. Same es Fig. 1. X-ray micrograph )/ 20.
be
&tidied within wide limits. microscopically
and by X-ray
further examination
diffraction
methods.
A
was carried out at a later stage
m-hen the rate of hardening had increased considerably. It was established
that both
band, bands of secondary
types
of deforn~ation
slip, and kink bands were
present during the region of easy glide. show an optical micrograph
Figs. 1 and 2
and an X-ray micrograph
from the same face of a crystal taken just after the end of easy glide (approx.
4.4oj
elongation);
reveals two sets of deformation the operative them.
Optical
slip bands
the Iatter
bands, one parallel to
and the others normal
examination
slip in the regions of either type of deformation Little
X-ray
asterism
to
did not show secondary
was observed
at this
band. stage
(Fig. 3). After FXG. 1. Aluminum crystal 04B 4.4% elongation at room temperature. Optical micrograph x 250.
The work confirmed as the occurrence the orientation
earlier investigations
of easy glide depended
of the crystal.
somewhat.
elongation)
heavier
the stress-strain
deformations
(--S-9”,0
curve became
paral colic
and marked strain hardening had taken place.
in so far
markedly
on
Crystals in which more
than one slip system were predicted to operate from t,he earliest8 stages of deformation, in particuiar crystals
near [loo]
and [Ill]
and on the boundary
between these poles, gave no region of easy glide and showed marked strain hardening of the deformation.
Large
bands
from the beginning of secondary
slip
were observed, but kink bands were absent. Particular attention was paid to those crystals the orientation
of w-hich fell well within the stereographic
triangle a,nd which gave regions of easy glide. The deformation was interrupted at a point near the end of the easy-glide region and the crystals were examined
Frc. 3. Crystal OPB after 4.4% elongation, X-ray Laue photograph.
X -ray
ACTA
485
METALLURGICA,
VOL.
FIG. 4. Xiuminum crystal 04B aft,er ??.S?(,elongation at! room temperst,ure. Optical micrograph s 250.
micrographs
confirmed
more heavily disoriented
and that the major disorien-
tations
with the kink bands rather
were associated
mi~rograph compared
after
w&h Fig.
crystal at the earlier stage. correspondingly
Fig. 5 is t,he X-ray
S.%o;b elongation,
directly
Microscopic
slip.
deformed
-196”C,
(Fig. 6; cf. Fig. 3).
at room temperature
(Fig. 7);
however,
system in
(Fig. 4) and
in cryst~als deformed
2OO”C, t,he kink bands were more ~rononnced, secondary
slip was observed in them.
in these latter larger those
numbers occurring
crystals of
be
did not reveal any marked
evidence of slip other t,han on the primary crystals
can
on the same
The X-ray asterisms were
more pronounced
examination
which
2 taken
at and
The slip bands
were coarser and contained
individual
slip
lamellae
after similar deformations
than
at lower
temperatures.
Fm. 5. &me ~b3Fig. 4. X-ray micrograph X 20.
1956
FIG. 6. Same as Fig. 4. X-ray LRUCphot~gr5ph.
that the crystals had become
than the bands of secondary
4,
(b) Terwperature Dependence qf Easy Glide Cryst,als -196’C,
of
room
examined increwed rate
orientation
temperature,
and
after approximately
deformat,ion. the
identical
The
lengt,h
deformed
t’he same amount
of
t,he easy-glide
as the t~el~perat~~e of testing fell; of
subsequent
decreasing temperature.
at
2OO”C, and were
hardening
of
range
hotvever,
increased
with
crystals
3% a,
For exampIe,
b, and c (Fig. 10) showed this behavior quite clearly, the
crysta,l deformed
easy-glide For
a given
asterism
in liquid
nitrogen
range of approximately deformation,
increased
with
t,he extent,
increasing
of
an
X-ray
ten~perature
test (Figs. 6 and 9). This ~-as qualitatively with the disorientations
giving
1Ot.b shear strain.
observed in the X-ray
micro-
graphs which resulted primarily from the formation kink bands (Figs. 5 and 8). Microscopic
of
correlated of
observations
showed clearly that the size and spacing of t,he kink
FIG. 7. Aluminum crystal 04A deformed to SY/, elong&ion at - 196°C. Optical micrograph x 250.
GARSTONE
et al.:
EASY
4. EXPERIMENTAL RESULTS COPPER CRYSTALS
FIG. 8. Same m Fig. 7. Y-ray micrograph ~20.
bends increased with the temperature. there is a correlation
introduced
by the
stress-strain
curves
orientations. glide
kink hands.
part
orientation.
on
of
shear
copper
crystals
of
various
Roth the slope and length of the ensyof
the
stress-strain
However, stress
curves
va~ry with
Rosi has shown that this part
of the cnrve is associated Two ident,ically oriented crystals (17~4 17b), one 9 in.
WITH
Rosi,(la) and Cupp and Chalmerso5) have published
It seems that
between the length of the onsy-
glide range and the ~sorientat,ions
489
GLIDE
which
with a constant is
independent
increment of
crystal
long, the other 3 in. long, which had received the same
orientation.
The present work, while confirming
treatment,
observation,
not only for copper but also dilute alloys,
range.
were deformed
to the end of the easy-glide
The load-extension
curves are shown in Fig. 11.
M’hilo the curves are not identical, glide is similar in each case. carried
out
complete,
after
the
the range of easy
An X-ray
easy-glide
revealed little difference
exan&stion
deformation in X-ray
of the
Furthermore, a survey of crystalsrevealed noticeable dif-
ferences only within 1 mm of the grips. X-ray micrographs revealed the presence deformation bands t.hroughout both crystals.
shows that variations in the easy-glide range can arise from the differences in the size and surface condition of the crystals tested.
was
asterism
between the two crystals, t)he length
this
(a) Urieratatkm
Dependence
of the &ress-strain
Fig. 1% shows the shear stress-shear strain curves for a number of oopper crystals of diflerent orientations (Fig. 12b), all of which would
of fine
Curse
linear hardening mation.
be expected
at t,he heginning
to show
of plusti-ticdefor-
These diger from R,osi’s results in so far as
the length of the easy-glide range is bigger by at least
FJG. 9. Same 89 Fig. 7, X-ray Laue photogmph.
FIG. LX. K&em hardening of two identicz&y oriented aluminum crysttils of different lengths. 17it-3 in. long. 17b-9 in. long.
ACTA
METALLURGICA,
VOL.
4,
1956
on coppep and copper-silver single cr@als
TABLE 1. Data
7
T(
(de4
text)
00
-
1
63:” 56”
cu-49 CU-50
cu-51
56’ 59” w 48’ 433 4gc 49” 46”
cu-43 cu-48 CU.53 Cu.42 cu-40 CU-38 CU-44 cu.45 CU-55 cu.35
64
343-O 37” 334 3.5” 37” 42’ 49’ 43” 0
( I i
I 1
i;): 89 3s 38 48 44 41 49 37 46 ti’i
:;o 39” 48” 49’
0 % 46”
ext.
dev.
86 58 58 59 6f 64 65 57 53 55 50 53 57
142 13x 108 136 106 121 127 123 120 122 100 117 134
78 80 59 77
73 63 71 57
77 45 5; 62 66 67 6i 50 64 ii
535
1230 485 770
635 “53 384
635 253 3x4
__
-1
_I
60
79
i /
1.86
2.31 l.id 1.89 1.95
i
2.8
/
_ext. 1.65 2.38
2.22 2.38 2.2 2.31 2.79 3.18 2.65
ii:
68 83 59 i9
-_.
dev.
2.93 2.43 2.7 2.54 2.35
2.16 2.16 2.22 2
2.21
2.37:
_ cll-Ag
1B 2C 3F
alloys
47” 4.7” 50”
595 232 386
232 386 ,I
-
-_....-._
/
2.07 2.09
j
2.00
-
Note: In this table, X,, is the angle between the specimen axis and the normal to the slip plane: & is the angle between the specimen axis and the shp direction; -rc (dev) is the critical resolved shear stress determined by the first deviation from Hooke’s law; 7c (ext) is the critical resolved shear stress determined by extrapolation of the stress/strain ourve to zero strain; cr, is the stress at which the extrapolated easy-glide range meets the extrapolation of t,he rapid-hardening part of the curve.
a factor
of
2.
However,
they
confirm
that
linear
The resolved critical shear stress for glide (TJ is not?
hardening
ends at a value of the shear stress o. such
constant.
that a0 -
-rC is approximately
where -r, is
differences in purity of the crystals as grown, in part
glide.
to structural
the
critical
resolved
shear
essential results are tabulated
constant, stress
for
in Table 1.
The
The variation differences
to the difficulty Added
can in part be attributed due to mosaics,
of handling
determining
rC precisely,
very gradually.
specimens.
uncertainty
in
as the curves
change slope
Bearing these di~culties
in mind, the
degree of constancy extent
and in part
such fragile
to this there is considerable
to
of (r. -
T, is quite surprising.
of easy glide is a maximum
decreases as the [loo]-[ill]
boundary
The
near [l lO] and is approached.
(b) Microstructure The
crystals
deformation, microscope SHEAR
WEAR
STRAIN
STRAIN
u-ere
and many
electropolished
were examined
prior
to
under
the
at various st,ages during the deformation,
“1.
-/.,
Fro. 12a. Shear-stress/shear-strain curves of copper crystals of various orientations.
/
1
PIG. 12b. Orie~t‘atiolls of rapper crystals of Fig. 1%.
GARSTONE
et al.:
EASY
GLIDE
To overcome
491
this trouble,
three crystals of different
sizes (&, &, and g in. diam.)
but of identical
orien-
tation were grown in separate molds from parts of the same
seed
removed
crystal.
without
The
smallest
crystal
could
damage from the single mold.
be Fig.
13 shows the shear stress-shear strain curves for three crystals of different sizes prepared in this way.
It
clear that the amount
with
decreasing
crystal
of easy glide increases
size.
Furthermore,
range ends at approximately 0
0
1
I
I
2
SHEAR
STRAIN
13. Shear-stress/shear-strain oriented copper crystals of different R, t in. diam.; C, ;dr in. diam.
Slip
on
the
predicted
curves of identically sizes. A, # in. diem.:
system
occurred
exclusively
during the region of easy glide, but slip on
secondary
systems
was detected
after
the end of easy
fairly
soon
operative
secondary
plane
in limited glide.
regions The
was the cross-slip
first identified by Maddin, Mathewson, however,
first plane
and Hibbard;t2)
at higher stresses the majority
of the other
(111) planes operate at least locally. (c)
of the recent results”9 13) on easy glide
in the extent of linear hardening
metals of comparable gations
have
of easy glide, presumably
causing
dislocation
Andrade
and Henderson(7)
on silver crystals
pile-ups
below
the
by
surface.
found that an oxide film
would markedly
reduce the linear
part of the stress-strain curve. A copper crystal was plated with 10,000 A of Ni, but this did not eliminate easy glide, and slip appeared on the surface as in the case of unplated ever, the further
addition
crystals.
How-
of 10,OOOA of chromium
did result in the elimination
in copper, silver, and gold shows that there is a wide variation
There is already some evidence that surface coatings
of the linear hardening
region (Fig. 14).
Crystal Xize
Comparison
(d) Electroplating of Crystals will reduce the extent
primary
the easy-glide
the same resolved shear
stress.
3
o/o
FIG.
is
purity.
used
different
crystals, the existence
even with
As the various investisizes
of a size-effect
and
shapes
of
was possible.
Copper crystals of three sizes $, &, and Q in. square of identical orientation
were grown in a triple graphite
(e) Alloying Particular
attention
for other shows
alloying
typical
elements
shear
The critical resolved
Repeatedly
and 600 g/mm2.
however, the smallest crystal did
such as gold.
stress-shear
crystals of three alloys containing
groups characterized
it was found that the largest crystal gave
15 for 0.3,
shear stresses fall into three
Furthermore,
the stress-strain curves
also fall into three families, the greatest range of easy glide being shown by the crystals silver
from the mold.
Fig.
curves
by the average values 240, 450,
difficulty
it undamaged
strain
approximately
not always behave in the expected manner, due to the of removing
give similar results
0.6, and 1.0% by weight of silver.
mold, and each crystal was tested in a similar manner. the least easy glide;
has been paid to dilute alloys
of silver in copper, but experiments
content.
Closer
with the highest
examination
of the
curves
reveals that, as in the case of pure copper, the end of easy glide occurs at approximately
twice the critical
resolved shear stress for glide. In the curves of Fig.
15 the slopes of the linear
range are very similar.
This arises from the fact that
crystals
oriented
fairly
closely
to each
other
were
chosen so that the effect of the alloying element could be more readily determined. The slope is clearly more a function of orientation than of composition. Metallographic SHEAR
STRAIN
‘/_
FIG. 14. Effect of surface coatings on the range in two similarly oriented copper crystals (1) unplated, (2) nickel-chromium plated.
observations
revealed
of easy glide in all crystals examined easy-glide
that the end was associated
with the localized occurrence of unpredicted secondary slip. Some secondary slip was observed prior to the end of easy glide, but this was usually associated with
492
ACTA
METALLURGICA,
VOL.
As
4,
the
resolved
1956
secondary
slip
operates
at
macroscopic
shear stresses below those which would
expected
to produce
slip on the secondary
stress concentrators
must exist locally
shear stress sufficiently dislocations
to cause glide.
seem to be the most
centrators in a deformed
to raise the Pile-ups
likely
single crystal.
from the head of a dislocation
OOW
20
30
SHEAR
40
50
STRAIN
60
Pij
is the local
of three
9 477(1 f(0) determines
surface defects such as pits or scratches, which would The first operative
be expected to act as stress-raisers.
slip plane was again found to be the crossbut in most
co the applied
shear
in the pile-up, and
r the distance from it measured in units of
the secondary
slip plane,
stress,
“/,
FIG. 15. Typical shear-stress/shear-strain curves dilute copper silver alloy crystals. x-o.3 3F -0.6 weight per cent silver. lB-1.0
secondary
(~0)
pile-up is:
stress, n the number of dislocations
70
of
stress con-
Stroh(l7) has shown that the stress at a point
where
be
planes,
crystals
all the octahedral
Y)Oo
which plane is the first to operate in system.
A Frank-Rea’d
source on any system near a pile-up
will operate when the local stress Pij reaches a critical value ,ub/l, which is approximately stress, so the above expression
7, the critical shear
becomes:
planes were found to operat,e locally sooner or later. 5. DISCUSSION
The
general
viewpoint on easy glide has been by Cottrell,(16) who distinguishes between
crystallized laminar
flow resulting
and the subsequent or less parabolic interpreted
in a linear stress-strain
turbulent hardening
curve
flow resulting in a more curve.
Koehler(22)
pile-ups.
However,
agreed, and the present experiments
it is
confirm,
that the end of easy glide is in fact characterized planes.
Now
of unpredicted
The possibility
of sporadic
The transition
flow can be understood dislocations
unpredicted
hardening
jogs
subsequent
(2)
K2ao
Eshelby,
Frank, and Nabarro(l*) (TO77
n=_-__
slip be
planes
by virtue interstitial
which
give rise to
of the generation and
of of
Y) ~- = K,o,
iub where d is the length of the pile-up. Substituting
values of T and n in (1). 7, - = constant (10
This means that secondary slip starts and consequently easy glide ends when the resolved shear stress on the
mation. However, an important question yet to be answered is: What decides when this transition takes
primary system reaches a given multiple of the critical
The effect of such variables
orient,ation,
purity,
size of specimen,
vacancy
d(1 -
have shown that
for-
place?
and
by
from laminar to turbulent
in terms of the interaction
on different
increased
sub
slip on other octahedral
within the region of easy glide cannot nevertheless excluded.
L
r=
sources takes place, while he
of dislocation
the occurrence
sources in the crystal
head of the pile-up.
has
postulates that the more rapid hardening is due to the interaction
of dislocation
will determine the distance (L) of the source from the
the linear region as that in which exhaus-
tion of the Frank-Read
widely
The distribution
as temperature, and effect
of
surface films on the extent of easy glide must all be explained.
resolved shear stress 7,.
In the present experiments,
the ratio has been found to be approximately
2 both
for pure copper and the dilute alloys with silver.
The
longer easy-glide ranges in the alloys can be explained simply as necessary for the local stress to build up to
GARSTONE
a value approaching stress
so
et&.:
493
GLIDE
that of the critical resolved shear
markedly
increased
by
alloying.
Other
factors being equal, the present theory indicates the critical
EASY
resolved
that
shear stress T, determines
the
extent of easy glide. As Rosi has pointed out,, the results on the effect of impurities
on easy glide have not been unambiguous.
When a finely dispersed occur
second phase is present, the
pile-ups
would
in the vicinity
particles
and at an early stage of the deformation,
thus leading t,o rapid hardening.
of the
small
Carlsen and Honey-
eombe(rs) have shown in aluminum 3.3% copper single crystals
that
linear
super-saturated
l~arde~ng
only
occurs
in the
solid solution, and ordinary parabolic
hardening occurs when a finely dispersed second phase is present. As the temperature increases,
of deformation
is lowered,
7,
so again an increase in the extent of easy
glide would
be expected.
experiments
of Andrade
described
above.
This is confirmed and Hendersonc7)
Lowering
the
tem~rature
reduces the amount of slip per slip band. temperatures,
by the
and those also
At, elevated
the slip bands will be coarser and the
stresses around the pile-ups should lead earlier to the occurrence
of secondary
on aluminum
have
slip.
The above experiments
confirmed
this view:
est,ablished
that
given &ress is reached, tation
dependence
evaluating
an explanation
of easy
the slope
This is a minimum
glide
slip direction.
can be sought
for orientations axis rotates
towards
the primary
elongated,
length of t,he slip direction
increases.
Mot,t(20) is followed
during
that,
pass out of the crystal,
locations
since it would
If the view of
easy
glide,
by the present experiments,
small crystals of identical plotting copper
is now for dis-
to escape if the slip path is increased.
is well supported
dislo-
then the change in
be more difficult
show that, large crystjals harden
is
so that the
slope of the stress-strain curve with orientation explained,
and
is approached,
The salient feature of this transition
that the slip plane becomes
cations
in
curve.
near [IlO],
boundary
a
of the orien-
a/a of the stress-strain
increases as the [loo]-[llI] i.e. as the tension
glide ends when
easy
more rapidly
orientation.
This which than
Furthermore,
o/a against the length of the slip direction for crystals of different
orientation
4 LENGTH
OF
I
,
I
I
I
5
6
7
5
9
SLIP
DIRECTION
mm.
FIG. 16. Relation between the rate of hardening o/u and the length of the slip direction.
to be particularly
pronounced
this is, in fact’, what Andrade
with small
crystals;
and Henderson
found.
One final point which needs some discussion
is the
question of where the pile-ups occur in the deformed crystals.
In aluminum the obvious
sites of secondar-y
slip are primarily the deformatiol~ bands, as the above experiments
have
pronounced,
but closer spaced at lower temperatures;
indicated.
this means that secondary
These
bands
are less
slip will occur at a later
stage, for the critical pile-ups will require more deformation to form them.
secondary
slip is observed in kink bands at a much earlier stage at 200°C than during deformation at -196°C. Having
1
101 3
does, in fact,
give an approximately linear correlation (Fig, l(i). The effect, of surface fihns is also evidence in support
At higher temperatures (200°C) in the bands are heavier for a given
the distortions deformation, spondingly
and secondary
slip occurs
earlier stage.
Of course, it could be postulated are initiated develop,
by local
secondary
cause further secondary
felt that deformation distances
that
expected to make It is doubtful apply
to
crystals, vations
the
t,hat kink bands slip and, as they
slip.
However,
it is
bands must play a significant
role, as it is only when pile-ups large
at a corre-
the
a substantial
whether behavior
are spaced at, fairly
specimen
size
the above of
could
be
difference.
certain
e.g. 70/30 brass, although of easy glide were made
considerations highly
alloyed
the early obseron this material.
Here, the linear region of the curve is almost parallel to the strain axis and the lack of hardening appears to be related to the occurrence
of a yield phenomenon.
Piercg, Cahn, and Cottrell(z~) have recently shown that in brass crystals, slip propagates through the specimen in the linear zone.
Furt,hermore, slip in brass crystals
is much coarser and more grouped than in crystals of copper and its dilute alloys. ACKNOWLEDGMENTS
of the above a,rgument , since such films would tend to retain dislocations within the crystal, thereby reducing
One of us (G. G.) is indebted to the Department for Scientific and Indust’rial Research for a studentship. We gratefully acknowledge the helpful comments of
the easy-glide range.
our eollea~gues at all st,ages of the work.
These
effects would be expected
ACTA
494
METALLURGICA,
REFERENCES 1. F. VON GBLER and G. SACHS 2. Physik. 55, 581 (1929). 2. R. MADDIN. C. H. MATHEWSON. and W. R. HIBBARD Trans. A&r. Inst. Min. Met.’ Eng. 175, 86 (1948); ibid. 185,527 (lS50). 3. G. MASING Lehrbuch der ull~emeinen Metallkunde Berlin, Springer-Verlag (1950). 4. G. MASING and J. RAFFELSIEFER 2. Metallkunde 41. 65 (1950). 5. F. D. ROSI and C. H. MATHEWSON Trans. Amer. Inst. Min. Met. Eng. 188, 1159 (1950). 6. K. LOCKE and H. LANGE 2. Metallkunde 43., 55 (1952). 7. E.N. DA C. ANDRADE and C. HENDERSON Phil. Trans. A244, 177 (1951). 8. B. JAOUL and C. CRUSSARD Camp. Rend. 234, 700 (1952). 9. K. WT. CAHN J. Inst. Miletrtls79, 448 (1951).
VOL.
4,
1956
10. R. K. CHEN and C. H. MATHEWSON J. Metals 3, 653 (1951). 11. R. W. K. HONEYCO~C~BE J. Inst. Metrrls 80, 49 (1951). 12. E. A. CALNAN Acta. Cryst. 5,557 (1952). 13. F. D. Rosr J. Metals 6, 1009 (1954). 14. J. SAWKILL and R. W. K. HONEYCOXBE Acta, Met. 2, 8.54 (1954). 15. C. R. CUPP and B. CHALMERS Actn Met. 2, 803 (1954). 16. A. H. COTTRELL Prog. in &fetal Physics 4; 205 (1953). 17. A. N. STROH Proc. ROJJ. s’oc. A223, 404 (1954). 18. J. D. ESHELBY, F. C. FR_&NK, and F. R. S. NABARRO Phil. Mng. 42, 351 (1951). 19. K. M. CARLSEN and R. W. K. HONE~~OXBE J. Inst. Metals 83, 449 (1955). 20. N. F. IfOTT Phil. Mao. 44. 742 (1953). 21. G. R. PIERCY, R. W. CAHN, md A. H. COT'~RELL Acta Met. 3, 331 (1955). 22. J. S. KOEHLER Phys. Rec. 86, 5” (1952).