The interpretation of roll textures of face-centred cubic metals

THE

INTERPRETATION FACE-CENTRED E.

R.

W.

OF ROLL TEXTURES CUBIC METALS*

JONES?

and

E.

A.

OF

FELLt

Evidence from two different approaches is shown from which it is concluded that a mixture and (112)[11i] textures describes the roll texture of f.c.c. metals better than (123)[412]. L’INTERPRETATION

DES STRUCTURES DE LAMINAGE CUBIQUES A FACES CENTREES

(1lO)[i12]

DES METAUX

Les resultats de deux travaux differents permettent aux auteurs de conclure qu’un melange des textures (100)[112] et (112j[ll l] decrit mieux les textures de laminage des metaux cubiques a faces cent&es que la texture (123)[412]. DIE

DEUTUNG

VON WALZTEXTUREN

KUBISCH-FLACHENZENTRIERTER

METALLE

Der Vorschlag, dass eine Mischung von (110)[712] und (112)[ 1li] Texturen die Walztextur kubischfliichenzentrierterMetalle besser als (123)[412] beschreibt, wird von zwei verschiedenen Gesichtspunkten aus begriindet. INTRODUCTION

The textures interpreted

produced

for many

(llO)[il2]

of the major

either

of the

two methods

and (112)[lli].(1)

with the theoretical

classical

AN

of view then, a means of deciding descriptions

to the rolling

direction

X-ray

and revolved

camera

axis.

of a fibre texture,

complicated fit the

textures

observed

have

(111)

been

figures

proposed

more

closely

used is as follows:

If a narrow strip be cut from a rolled sheet parallel

sheet normal. More

and

X-RAY METHOD OF DISTINGUISHING BETWEEN POSSIBLE TEXTURES

is a single maximum in the rolling direction and reverse rolling direction about 23” away from the

which

is very necessary,

have been used in the present work.

The first approach

positions

textures.

In particular, it has been found that in the (111) pole figure there

this point

between various

the advent of counter spectrometers it has found that all the “peaks” in the pole

figures do not coincide of

metals have been

years in terms

and minor roll textures With been

From

in f.c.c.

The resulting

direction.

it can be mounted about

diffraction

pattern

will be that

the fibre axis being the rolling

A similar strip cut parallel

verse direction

in an

its longitudinal

to the trans-

will give the indices for this direction

and of these that due to Hu, Sperry and Beckc2) has

and, from the two, the texture is completely

been quite widely used, e.g. by Smallman(3) and Calnan.(4) This description fits the [ill] pole figure

This technique

defined.

thus enables the texture to be defined

maxima

with two photographs only, though, of course, it does not give the pole figures. Such an experiment

should be at 22” from the sheet normal but is quite

has been done on nickel sheet 0.004 in. thick which

inadequate

had been

quite

well

apart

from

the

for describing

fact the

that

(200)

the

and the

(220)

As long as the symbol for the texture is merely used as a label it matters little whether it is accurate or not.

However,

the texture

if it is necessary to calculate from

the modes

of deformation

operating

TABLE

in the sheet, the accuracy

not the average

Description

for other properties.

t The Mond Nickel Company Ltd., Wigan Street, Birmingham 16.

1

METALLURGICA,

VOL.

appears

Rolling plane

1

Rolling direction

Transverse direction

712

lil il0 121

of the description Major roll Minor roll “Beck” texture

Found in fibre axis determinations

* Received February 1, 1957. ACTA

98 per cent and the results

which agrees with none of the theoretical given and which is not perpendicular to

or

becomes extremely important because a description which is the average of two others for X-ray reflections is in general

rolled

It will be seen that the rolling direction as [223] textures

the way in which anisotropic properties such as elastic moduli or magnetic properties vary with direction

cold

of the analysis are given in Table 1.

pole figures.

D

& R

5, DECEMBER

Division, 1957

689

iii

412

110 and 111

ACTA

690

the

observed

transverse

METALLURGICA,

directions.

This

value

based on the centre of a very dense 111 reflection the X-ray

diffraction

some 40’

in comparison

photograph with

the 200 and 220 reflections.

direction

of the major

roll textures

and minor

YOUNG’S

Another way of distinguishing the variation

orientation

in the sheet.

in a cubic

crystal

is on

of 25” for from axes

agree with those and neither

the roll direction nor the transverse direction with the axes of the “Beck” texture.

is to study

1957

This suggests that it is

derived for the transverse

OF

5,

which spreads over the value

probably due to overlapping of reflections (111) and (112) fibre axis materials. The

VARIATION

VOL.

agrees

MODULUS

between the textures

of elastic

modulus

with

It can be shown(5)

the Young’s

modulus

that

E in any olled Cu Sheet.

direction is given by 1 - = a -

E

where

is a function

f(a)

the stress axis.

of the direction

cosines

of

It will be noted that a maximum

in

E arises from a maximum

in f(a).

In the case of a sheet with perfect function axis

f(a)

makes

equations

depends with

are given

texture

this

solely on the angle the stress

the roll

direction.

below,

The

0 in each

relevant

case

being

measured from the rolling direction. f(a)

=

g,

-

b4

cos

28 + &

x sin se -

1 _ 1242

FIG. 1.

modulus to be used as a criterion for choosing between descriptions of textures. The fourth quadrant Fig. 1 shows the variation in Young’s modulus cold rolled

copper

It is obvious

sheet as measured

that the experimental

better fitted by a mixture

-

since Weerts

1

modulus

6fi

sin 48

in

obtained the

= f

f(a)

=

+ i4

cos

28 + &

cos

& - g8cos 2e + & 11

+-p 422/E

sin 28 +

(ii2)[11i]

ae

appropriate

process in

imposes

addition

to

in rolled

sheet

sin 48

symmetry

about

the

crystal

where

(123)[412]

the

rolling

the roll direction

symmetry.

A

similar

expression, in which 8 is replaced by (-0) must therefore be superimposed. This is equivalent to discarding the sine terms. The amended equations are plotted in Fig. 1. The difference between the curves sufficiently marked for the variation

and

rolling

directions

and (llO)[ilZ]

will not tit the experimental facts since both textures give higher values for (fa) in the transverse direction. (112)[11i] direction.

which

On the evidence

The presence of the sine terms means that there is asymmetry about the rolling direction. This is not

In fact

be present

has its greater

some texture

like

in the rolling

f(a)

DISCUSSION

cos 48

--!% 841/E

and minor

texture.

the same value for Young’s

transverse

There must therefore f(a)

by Weerts.@)

of the major

it is clear that a mixture of (123)[412] (1 lo)[i12]

of in

results are much

roll textures than by the (123)[412]

48 -

cos

asmming equal mixture (110)[112] and (112)[1111 (after Weerts)

RD

bf(a)

is obviously of Young’s

therefore cription

so far advanced

it would appear

that the sole merit of the (123)[412] is that it explains

terms of a single texture. It is inconsistent fibre axis work on nickel and the Young’s work

on copper,

both

be explained by some (llO)[i12] and (112)[lli]. It vary

des-

the (111) pole figure in

of which mixture

must of

with the modulus

apparently

textures

like

will be noted that Weerts’ observed results less widely than would have been expected.

It seems probable that this is due to scatter of the textures about their ideal positions which would smear the peaks out. Such a scatter has previously been invoked by one of us(‘) in producing a calculated pole figure, Fig. 2, which is strongly reminiscent

E.

R.

W.

JONES

AND

E.

A.

FELL:

ROLL

TEXTURES

rolling

OF

directions.

close agreement

F.C.C.

691

METALS

These values

are in surprisingly

with the spreads found in the fibre

axis work, which may be regarded as support for the hypothesis that a pole figure can be described in terms

of the proportions

their spreads. results

of

figures

was

It would

an experiment obtained

planes, and an attempt

of ideal textures

be interesting

for

in which different

and

to have the

a set of pole crystallographic

made to calculate all but one

of them from parameters obtained from that one. The analysis might well be extended to a prediction of the variation of the elastic properties with direction in the sheet. ACKNOWLEDGMENT The authors wish to thank the Mond Nickel Company for permission to publish this paper. REFERENCES

FIQ. 2. Calcula;ted (111) pole figure (llO)[i12].

texture. Standard deviation about RD 10” Standard devia.tion about TD 5’

of the texture calculated texture

by

deviations

pole

of silver given by Smallman.(3) figure

a Gaussian

was derived distribution

of 5” and 10’ about

from with

the

The ideal

standard

the transverse

and

1. C. BARRETT StructwreofMetaZa pp. 395,396. McGraw-Hill, New York. 2. Hn SPERRYend W. BECK Trans. Anaer. Inst. Min. (Met&.) Engm. 194,86 (1952). 3. R. E. SMALLMAN J. Imt. Met. 84, 1, 10 (Sept. 1955). 4. E. A. CALNAN J. Inst. Met. 85, No. 1, 11 (Sept. 1956). 5. WOOSTER Crystal Physics p. 252. Cambridge University Press. 6. J. WEERTS 2. MettuZZk. 25, 101 (1933). 7,. E. R. W. JONES J. Inst. Met. 84, No. 13, 504 (1956).