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).

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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).