MECHANICAL CONTRIBUTIONS TO THE PLANE-STRAIN DEFORMATION
AND RECRYSTALLIZATION TEXTURES OF AL-KILLED STEEL
by
PRACHEESHWAR SWAROOP MATHUR
B. Tech., Indian Institute of Technology, Kanpur
(1967)
S. M., Massachusetts Institute of Technology
(1968)
Submitted in Partial Fulfillment of the Requirements
for the Degree of
DOCTOR OF SCIENCE
at the
Massachusetts Institute of Technology
June 1972
D
Signature of Author
Department of Metallurgy and Materials Science
May 5, 1972
Certified by
Thesis Supervisor
Zoo
A~
.11
Accepted by
Chairman, Departmental Committee on Graduate Students
Archives
JUL 5 1972
LIBRARIES
ii
MECHANICAL CONTRIBUTIONS TO THE PLANE-STRAIN DEFORMATION
AND RECRYSTALLIZATION TEXTURES OF AL-KILLED STEEL
by
PRACHEESHWAR S. MATHUR
Submitted to the Department of Metallurgy and Materials Science on
May 5, 1972 in partial fulfillment of the requirements of the
degree of Doctor of Science
ABSTRACT
This work is concerned with the texture changes which underlie
the reduction dependence of the plastic anisotropy of cold rolled
and recrystallized killed-steel strip. The earlier observations of
Whiteley and Wisel on the maxima in the intensity of rolling plane
{lll and in the anisotropy parameter, Rf, were repeated and extended
by introducing into the cold-reduction step the variable of deformation-zone geometry (i.e. A, the ratio of the mean height of the zone
to its length). A range of A < 1 to A = 4 was covered by cold rolling (< 1) and strip drawing (from 1 to 4). Pole figures after rolling reductions of about 98% are changed abruptly as if by a 550 rotation of part of the stable texture around the transverse direction.
It is suggested that the mechanism is localized flow in macroscopic
bands along maximum shear planes as strain hardening capacity is
exhausted. There is both mechanical and metallographic evidence of
such bands. Assigning a shear texture to them modifies the parent
texture in a way which is consistent with the pole figures. As A
becomes > 1, strain and texture gradients appear and the texture
inversion occurs in the more strained regions at smaller total reductions -- after as little as 40% for surface layers with A = 4.
The mechanism appears not to be changed,however, only accelerated
in terms of the imposed reduction. Implications for practical
texture control are discussed.
Thesis Supervisor:
Title:
Walter A. Backofen
Professor of Metallurgy and Materials Science
TABLE OF CONTENTS
Page
ABSTRACT ----------------------------------------------------------
1i
LIST OF FIGURES ---------------------------------------------------
v
LIST OF TABLES ----------------------------------------------------
viii
ACKNOWLEDGEMENTS --------------------------------------------------
ix
INTRODUCTION ------------------------------------------------------
1
EXPERIMENTAL PROCEDURES -------------------------------------------
3
Choice of Process --------------------------------------------
3
Design of Experiments ----------------------------------------
6
Material and Specimen Preparation ----------------------------
8
Texture Measurements -----------------------------------------
10
Microscopy ---------------------------------------------------
11
RESULTS -----------------------------------------------------------
11
The Homogeneous Deformation Texture --------------------------
11
Inhomogeneous Deformation and Texture Gradients --------------
20
IMPLICATIONS FOR TEXTURE CONTROL ----------------------------------
33
SUMMARY AND CONCLUSIONS -------------------------------------------
36
REFERENCES --------------------------------------------------------
37
APPENDIX I -
Procedural Details ---------------------------------
40
APPENDIX II -
The Uniformity of Rolling Texture ------------------
48
iv
-
Stereographic Rotation of Ideal Rolling
Textures in {100} and {110} Projections ----------
51
Stereographic Rotation of the Ideal Shear
Textures of Iron in {lOO1} and {110}
Projections --------------------------------------
54
Gradients in {lOO} Reflection Intensity for A > 1
56
SUGGESTIONS FOR FUTURE RESEARCH -----------------------------------
58
BIOGRAPHICAL NOTE -------------------------------------------------
60
APPENDIX III
APPENDIX IV
APPENDIX V
-
-
v
LIST OF FIGURES
Pagj
Figure
1
Deformation zone geometry for strip drawing (a) and
rolling (b). -------------------------------------------
4
2
Cold rolling pole figures: {100}, {llO}, and {111}.
Cumulative reductions noted on each. Ideal fiber
textures identified by A, B, and C. Fiber axis is
<110> along the R.D. for A, <110> 600 from the R.D.
toward the sheet normal for B, and <111> along the
sheet normal for C.------------------------------------
12
Strain and reduction dependence of rolling-plane reflection intensities. The insert shows the more usual
method of plotting directly against cumulative reduction. --------------------------------------------------
14
Ideal fiber textures from Fig. 2 in a {1lll} projection
in (a) and after a + 550 rotation around the T.D. in
(b). --------------------------------------------------
15
Ideal shear (or torsion) textures for iron in a {1lll}
projection in (a) and after a + 350 rotation around the
T.D. in (b). The 350 rotation in (b) leads to pole
reinforcement at 55' from the sheet normal. ------------
17
6
Shear bands after 99% cold rolling reduction.-----------
19
7
Strain and reduction dependence of {111} reflection
intensities from the drawing plane of strip reduced
with different A. The various a-r combinations for
any A are noted in each case. Curve u is for the
homogeneously cold rolled strip of Fig. 3. Curve s
(filled symbols) represents near-surface reflections;
curve c (open symbols) is from the center.--------------
21
8
The {l00} companion to Fig. 7.
--------------------------
22
9
The variation with depth, At, below the surface
(where At/to = 0) of {111} reflection intensities
in strip reduced different amounts with several A. -----
23
3
4
5
vi
Fiqure
Pagi
The A dependence of the imposed (or apparent) strain, Ei,
for the {111} inversion in Fig. 7 and for the appearance
of edge cracking, Rolling A is known only to be < 1. --
25
The effect of friction on surface-reflection intensities
from strip drawn with constant A = 1.5 and a = 6 .------
26
Strain and reduction dependence of {111} reflection intensities from the drawing plane of strip reduced with
different A and then recrystallized. The various a-r
combinations for any A are noted in each case. All
measurements are from the surface. Curve u is
"recrystallized" from Fig. 3.
---------------------------
27
13
The {100} companion to Fig. 12.-------------------------
28
14
Pole figures from different locations in strip cold drawn
a total of 80% with A = 2 and a = 120. Location is defined by At/to: 0.05 is just below the surface, at a
depth of 5% of the drawn thickness; 0.44 is near the
center; 0.20 is about midway between surface and center.
Ideal textures from Figs. 2 and 4a are included. -------
30
Scanning-electron micrographs of edge cracking in the
99% cold rolled strip of Fig. 6 and in the 80% colddrawn strip from which the pole figures in Fig. 14
were taken. Cracks penetrate only about 20% of the
thickness in the drawn strip.---------------------------
32
Variation of rolling-plane {100} and {111} intensity
through the thickness of strips cold rolled to various
cumulative reduction. ----------------------------------
49
11-2
{111} pole figures of 80% and 92% cold-rolled strips. --
50
III-1
Ideal fiber textures A, B and C in {100} and {110} pole
figures (a); and rotated + 550 around T.D. (b). A and
B are two partial fiber textures with fiber axis <110>
parallel to R.D. (A), and at 600 to R.D. toward N.D.
(B); C is a complete fiber texture with fiber axis
<111> parallel to N.D. ---------------------------------
53
10
11
12
15
II-1
vii
Page
Figure
IV-1
V-1
Ideal orientations of the shear texture in iron in {lOO1}
and {110} projections and rotated + 350 around T.D. ----
55
Variation of rolling-plane {00} reflection intensity as
a multiple of random through the thickness of strips
drawn to various cumulative reductions with constant A
and a. -------------------------------------------------
57
viii
LIST OF TABLES
Table
1
Strip Drawing Conditions -----------------------------------
7
2
Composition ------------------------------------------------
9
3
Some Mechanical Properties ---------------------------------
9
I-1
Conditions for Pole Figure Determination -------------------
44
1-2
Conditions of Diffractometry -----------------------------
45
ix
ACKNOWLEDGEMENTS
The author is grateful to Professor W.A. Backofen for his help,
guidance and encouragement throughout the course of this work.
He also wishes to thank Mr. R.L. Whiteley of Bethlehem Steel
Corporation for providing the sheet steel used in the research.
Discussions with members of the Metals Processing Laboratory are
gratefully acknowledged.
Special thanks are due Miss Jean L.
DiMauro for typing the manuscript.
The research program was generously supported by the American
Iron and Steel Institute.
1
MECHANICAL CONTRIBUTIONS TO THE PLANE-STRAIN DEFORMATION
AND RECRYSTALLIZATION TEXTURES OF AL-KILLED STEEL
INTRODUCTION
The crystallographic textures of wrought metals are commonly classed
according to the processes by which they are produced, e.g. rolling, wire
drawing, deep drawing.2,3
This implies that the strain state is defined
by the shape change imposed in processing, or that straining is homogeneous.
In many practical operations the implication is a reasonable one.
It can happen, however, that the strain state is not fully known from just
the external shape-change; local variations are possible depending upon
the geometry of the deformation zone in the processing system.
A useful
index of that geometry is the ratio of the mean zone thickness, II,to the
zone contact-length, L, or A = I/L (Fig. 1).
Many effects of processing
respond to changes in A. One of interest here is the amount of redundant
strain in a given reduction; there are good theoretical grounds4 for expecting it to increase with A, and experiment has shown it to be an approximately single-valued and linear function of A irrespective of the
particular reduction and zone contour, e.g. die angle.5-7
Strain dis-
tribution, also, has been found to be strongly dependent on A.7 ,8
It seemed reasonable therefore, as a starting point in the present
work, to suppose that texture would be sensitive to A level and even
2
subject to some control through control of A. Ferritic low-carbon steel
strip was the material choice because it can be given a texture by planestrain reduction and annealing which causes large amounts of useful
plastic anisotropy.l*
The texture of cold-rolled ferrite is known from earlier pole figure
studies, and there is no serious argument about how it ought to be de2 3 9 14
cribed. 9 ~14 The recrystallization texture is also well known. , , '
A number of mechanical studies after recrystallization have emphasized
14 15
i values and the intensity of rolling-plane X-ray reflections.1, ,
In cold rolled and recrystallized killed-steel there is a maximum in '
after about 80% reduction and, somewhat later, at , 98%, a maximum in
the intensity of rolling-plane {lll}.
Texture gradients have been studied as well, although there is
still some controversy over their origin.
Roll-gap friction can con-
tribute to the gradients but from weighing all of the evidence friction
appears not to influence cold rolling texture to a depth greater than
*
The usual index of plastic anisotropy is the width-to-thickness
strain ratio in the uniaxial tension test; this is designated
as R (which often represents roll radius as well) or r (which
might now be confused with strip reduction). The average, R',
from measurements at 00, 450, and 90* to the rolling direction
is commonly reported. Drawability usually impoves with
increasing R.1
3
16 -20
about 5% of the strip thickness even when there is no lubricant.
There is other evidence that large A, i.e. > 1, or what has been called
"high-body rolling", also contributes, even more importantly, to texture
gradients. 20
Background in this area, however, is extremely limited,
and adding to it was another goal of the present work.
EXPERIMENTAL PROCEDURES
Choice of Process:
The A for each of two plane-strain reductions
is defined in Fig. 1. The process in Fig. la is strip drawing through
a die of semi-angle a; mean thickness, F, is taken to be the circular
arc midway through the deformation zone, drawn normal to both die
faces, and L is the interface length.
A
In these terms,
~
L r (2 - r)
where a is in radians and r = 1
-
(1)
(h1 /h0 ) is the reduction in the pass.
For strip rolling (Fig. lb),
Az ~
h0
R (2 - r)
where R is roll radius, h0 is entering thickness, and r is again the
fractional reduction in the pass; the usual approximation is made of
L ~ Aii~.
0
Thus the equivalent die angle in a rolling reduction is
(2)
4
L
a
r
2-r)
(b)
-4Rr ( 2 -r )=
CI
(2-r
Figure 1. Deformation zone geometry for strip drawing (a)
and rolling (b).
5
rh '
In cold strip rolling A tends to lie near 1 because a horizontally
directed friction force large enough for the rolls to "bite" and deliver
well-lubricated strip cannot usually be developed with A much larger than
that.
To fix A at any level, however, is nearly tantamount to making roll
size, R, a variable, for only then could a sequence of constant-reduction
passes be made on any given lot of material.
To achieve constant A in a
given mill r could be lowered in succeeding passes, but then r would no
longer be an independent variable and would eventually become extremely
small and difficult to control.
To avoid such complications, the process choice for much of this work
was plane-strain strip drawing.
As Eq. 1 shows, A can be held constant
now for given r by fixing the die angle, a; and as Eq. 3 shows, this is
equivalent to reducing R along with strip thickness in rolling to produce
the same effect.
drawing.
There are, however, two related disadvantages to strip
One is that the final cumulative reduction (Er) will not be as
large as in rolling because the applied tension encourages drawing failure as the material's strain hardening capacity is exhausted.
Its effect
in these experiments was to limit the total strip-drawing reduction to
Er ~ 90%.
The other disadvantage for present purposes is that the low
rolling-A magnifies frictional stresses.
In low-A drawing, the effect
again contributes to a total allowable reduction less than that in rolling.
Accordingly, the highest cumulative reductions in the work about
6
to be described (Er ~ 99%) were still reached by rolling under conditions
which could be controlled only to the extent that A was always kept < 1
(in a range of about 0.3 to 0.5).
in strip drawing.
The range of A > 1 is easy to explore
Although the high end of that range, e.g. A > 2, is
not usually entered in practical rolling it was important to do so here,
to establish the trends which carry down to lower A.
There is good reason to expect that textures will be essentially
the same in strip which has been rolled and drawn the same amount in
plane strain under identical conditions of deformation-zone geometry
and friction.
The displacement boundary conditions, i.e. the shape
changes, which determine the kind of texture that develops in a given
material are the same.
The processes differ only in the hydrostatic
part of their stress systems.
This expectation is borne out by the
findings.
Design of Experiments:
Experimental conditions for strip drawing
are summarized in Table I. Each A was produced by different combinations
of a and r to see if texture did depend on the variables which fix A, at
least within the range of values in Table I.
The drawing apparatus was almost a copy of that used by Rogers and
Coffin 2 1 in their study of plane-strain strip drawing, although without
the provision for measuring die load.
A different pair of tungsten-
carbide inserts was used for each die angle.
A constant r was maintained
7
TABLE I
STRIP DRAWING CONDITIONS
(Terms are defined in Eq.
r, %
A
1
1.5
2
1 and Fig. 1)
30
10.0
60
20.0
120
40.0
30
6.7
60
13.5
120
27.0
30
5.0
60
10.0
120
20.0
60
4
120
120
5.0
10.0
10.0
8
by changing the die-face separation after each pass by inserting pieces of
hardened-steel shim stock between the backs of the inserts and the outside
casing in which they were mounted.
machine at 1.0 in/min.
Drawing was done in an Instron testing
Other procedural details are given in Appendix I.
A Teflon coating was the usual lubricant.*
by Alexander's
22
method, was about 0.08.
The friction coefficient,
Friction effects were studied
for A = 1.5 with a = 60 and r = 0.135 by lubricating some strips with an
ordinary washing soap and water solution.
Drawing forces now were about
twice as large as those with Teflon, which meant that the friction coefficient (from an analysis by Wistreich 23 ) was raised to about 0.20.
Material and Specimen Preparation:
The test material was an an-
nealed and temper-rolled aluminum-killed steel of ASTM grain Size No. 7
processed to yield a nearly random orientation.
Its composition and
some mechanical properties are given in Tables II and III.
Drawing specimens were 1-in wide, 12-in long (along the rolling
direction) and surface ground to a uniform thickness which varied from
batch to batch but was about 0.2 in. They were "pointed" by rolling
half their length so as to pass through the drawing die and then
cleaned and lubricated.
Periodically during the reduction sequence
pieces about 4-in long were cut off for the texture studies.
*
Emeralon 323 from the Acheson Colloid Co.
9
TABLE II
COMPOSITION
Mn
C
Al
Si
Ni
Cr
S
Cu
P
Mo
Sn
0.33
0.052
0.05
0.01
0.01
0.01
0.004
0.004
0.002
0.002
0.002
TABLE III
SOME MECHANICAL PROPERTIES
Test Direction
I
_________
*
+
Tensile
Strength (psi)
R
00 (R.D.)
0.93
450
1.0
900 (T.D.)
0.97
________
___
0.98
= (R0 + 2R4 5 + R90
n is the slope of a log a - log s plot
0.25
45,000
0.26
44,500
0.24
45,500
10
The recrystallization treatment after cold working involved heating
in vacuum to 1300*F over a six-hour period, soaking for 28 hours at 1300*F,
and finally furnace cooling.
Texture Measurements:
These were made at different locations in a
reduced strip, from the surface to center.
Each location was exposed by
etching at room temperature in a 50:50 hydrogen peroxide and phosphoric
acid bath.
The surface location was also reached by etching away material,
usually from 1 to 3% of the sample thickness; this proved to be enough to
avoid frictional complications with the Teflon lubricant used here.
There were two kinds of measurements:
parallel to the exposed surface (I
figures. 24
line intensities from planes
and I{100}) and Schulz-type pole
The latter were constructed using a Siemen's texture goniom-
eter and are plotted with intensity contours based on unit intensity
from a random iron-powder sample.
Line intensities are integrated in-
tensities and are plotted after normalizing with respect to the same
line from a random sample, i.e. Io, using Harris' method for doing
this.25
All line-intensity data are given with their 90% confidence
limits; at the surface these are based on measurements at three or
four different areas from each side of the strip, while six different
areas were usually scanned for any one interior location.
detail is found in Appendix I.
Further
11
Microscopy:
The as-drawn and rolled edges were sometimes examined,
after degreasing only, in the scanning electron microscope.
Strips were
also nickel-plated and sectioned for more conventional metallographic
work (Appendix I).
RESULTS
The Homogeneous Deformation Texture:
This is the base for evaluating
A effects and was produced here by cold rolling with A < 1. The result
was a texture uniform through the thickness and, over a large reductionrange, no different from what has already been reported. 9-1
details are given in Appendix II.).
(Supporting
The two <110> fiber textures normally
assigned to cold-rolled steel have been overlaid on the pole figures in
Fig. 2,although a slight improvement in the description could be made with
the recent suggestion, from work on cold-rolled niobium, to substitute
<320> for the fiber axis.26
A <111> fiber texture around the normal to
the rolling plane is also called for by the intense central region in
the {111} pole figures, especially that for 98% reduction.
The new observation appears in the last reduction step, 98% to 99%
(an increase in the logarithmic thickness-strain, c = kn [1/(1-Er)],
of 3.9 to 4.6).
It is most clear in the {111} pole figures where the
central intensity-peak is nearly halved while that at 550 toward the
rolling direction is raised almost 40%.
4.
Companion changes in the other
12
R. D.
R.D.
{Il0}
80%
I
\r
\B
T. D.
R. D.
-
--
T.D.
R. D.
R.D.
92%
1.5
4
3
1.5
T. D.
R.D.
D.
i18
4
T. D.
2
R D.
R.D.
{100}
98%
98%
0.5
-
432
1-
1.5
2
0.5
R 5
T. D.
T. D.
8
R.D.
6
3
T.D.
R.D.
T. D.
Figure 2.
Cold rolling pole figures: {100}, {110}, and {111},
Cumulative reductions noted on each. Ideal fiber
textures identified by A, B, and C. Fiber axis is
<110> along the R.D. for A, <110> 60' from the R.D.
toward the sheet normal for B, and <111> along the
sheet normal for C.
T. D.
13
pole figures are a 30% drop in the {110} peak and a 50% gain in the interior {100} peak, near the intersection of the <110> fiber textures.
A high-reduction texture change has also been found in cold-rolled niobium, in {100} and {111} pole figures; in {100} the interior peak was
doubled while in {111} the central peak was hardly changed as the 550
peak became about three times as strong as that at the center. 26
Reflection intensities from rolling-plane {111} and {100},
i.e. Ill}/I
and I{100} /,
are related to the cumulative reduction
in Fig. 3. Measurements for each reduction were made at 4-5 locations
between the strip surface and center and were sufficiently alike to be
combined.
The trends for cold-rolled material parallel those in Fig. 2,
with a {111} peak somewhat better defined now at Er ~ 98%.
One way of producing the major textural change in Fig. 2 (from
Er = 98%
+
99%) is simply to rotate the ideal orientations of some
fraction of the sample by 55* around the transverse direction.
That
has been done in Fig. 4 with a {111} projection which shows that all
components now reinforce at 550 from the rolling-plane normal while
the central region is spread out.
The same rotation for {110} and
{100} projections also shows that changes in high-intensity regions
follow those in Fig. 2 (See Appendix III).
The mechanism for producing such a rotation might be found in
an area of overlap between continuum mechanics and crystal plasticity.
14
%r,%
40
60
99
98
95
90
80
7-
6
Recrystallized
4-
Cold Rol led
10
3--
2-2
3
2
90
92
94
96
98
0I
IXroo
Cold Rolled
(100)
Recrystallized
00
0
3
2
4
6
Figure 3. Strain and reduction dependence of rolling-plane
reflection intensities. The insert shows the more
usual method of plotting directly against cumulative reduction.
15
R.D.
(a)
A ---
..
-
....
----------
..---
T.D.
L--------
.D
-A
R.D.
B
C
rotated 550
~~~
(b)
550
.----
-
T. D.
Figure 4. Ideal fiber textures from Fig. 2 in a {111}
projection in (a) and after a + 550 rotation
around the T.D. in (b).
16
The inversion in the upward trend in {111} comes after large reductions
when the strain hardening rate (which has not yet been measured in plane
strain at such large strains) is probably low and perhaps even vanishing.
Were all strain hardening to disappear flow could be expected on the
macroscopic maximum-shear surfaces, or along the continuum slip lines
at 450 to a frictionless interface.
Shear strain in stably flowing
volumes around these surfaces in a non hardening solid would be of the
order of 1*; without strain hardening and, if the zone is sufficiently
thick, with any adiabatic heating the flow could become unstable and
still larger localized shear develop, even to the point of fracture.
There would be no need to change crystallographic deformation mechanisms.
The effect on rolling texture would enter from the shear
texture in the locally flowing zones.
This texture is known for
iron, 27 and its ideal orientations are given with reference to the
shear plane in a {111} projection in Fig. 5a.
To fit the argument
being developed, Fig. 5a ought to be rotated 450 around its transverse direction and then compared with the rolling pole-figures.
The comparison is a more useful one, however, if the rotation is
350 instead, as in Fig. 5b.
*
Now two ideal orientations reinforce
With two orthogonal zonesthe shear displacement in one is the
amount by which the other thickens. In each zone, therefore,
shear displacement and thickness are roughly the same so that
the shear strain is n 1.
17
shear
direction
shear
plane
(a)
0
V
0
-7
R.D.
rotated 350
7
0
o
(10)
< 12>
1~
112}
< Il>
(110{
{110)
< I Il>
<001>
v
0
V
o0
550
(b)
0
0
I
Figure 5.
V T.D.
Ideal shear (or torsion) textures for iron in a {1l1}
projection in (a) and after a + 350 rotation around
the T.D. in (b). The 35* rotation in (b) leads to
pole reinforcement at 550 from the sheet normal.
18
(three poles overlap) at the 55* peak in the {lll} pole figures in Fig. 2.
The same exercise for {110} and {100} projections (Appendix IV) also produces a pole redistribution consistent with that in the 98
-+
99% reduction-
step in Fig. 2. The implication, of course, is that the shear planes are
inclined at 350 to the rolling plane, not 450, as they could be owing to
some friction and other uncertainties in the slip-line field in an actual
rolling reduction.
Although the argument is somewhat speculative there is nothing speculative about the shear zones or bands that it calls for.
There is ex-
cellent metallographic evidence for them, beginning with Adcock 28 in
1922.
They appear after heavy cold-rolling reduction and almost always
at an angle of 30-40* to the rolling plane.
All reported observations
seem to be for flat rolled non-ferrous materials,29-33 although some
excellent pictures from what may be a more nearly axisymmetric reduction on a low-carbon steel have been published by Cockcroft.34
An
example from the 99% reduced strip of the present work is given in
Fig. 6. Metallographic contrast is poor in Fig. 6 but sheared zones
are visible.
From many such observations on this material the volume
fraction of its bands was estimated to be not less than about 15%.
That amount may be quite enough for noticeably transferring <111>
poles from the normal toward the rolling direction, as in Fig. 2.
Just the presence of such bands is good support for the premise
that the hardening rate does decay in plane strain.
19
Figure 6. Shear bands after 99% cold rolling reduction.
20
The distinction between shear bands and shear cracks must be subtle.
At the edge of a strip, where the hydrostatic part of the roll-gap stress
system is substantially reduced and even tension may develop, the band
will first become a crack.
That was the observation here at Er > 98%,
shear cracks at the edge becoming shear bands inward from the edge.
Therefore shear cracks are also a symptom of this localized flow which,
it is being argued, may act to modify a previously stabilized texture.
Inhomogeneous Deformation and Texture Gradients:
The effect of
A > 1 on deformation-texture development is largely summarized in
Figs. 7 and 8 with the strip drawing reduction dependence
of I{lll/I
and I{1o}/I o for the different A. The curves marked u are from Fig. 3
for the cold rolled and uniformly textured strips.
The other trend
lines and data represent the center, c and surface, s. The c and s
curves are plotted with data gathered in making gradient determinations
of the kind found in Fig. 9; more gradient data are given in Appendix V.
It seems clear from Figs. 7 and 8 that curve c is about the same as
u, as it ought to be since it represents a principal plane.
For A = 1
there is not yet any texture gradient, and c and s are indistinguishable.
For A > 1 there are differences, and for A = 1.5 and 2 in Fig. 7 there
is also indication of some a-effect on the reduction dependence; with
a
30, Il l}/I
seems to be raised a small amount. The broad,
dotted bands are drawn to accommodate any a effect and the scatter in
the data (which tends to characterize such measurements).
21
Ir, %
Er,%
20
40
60
70
80
20
90
85
60
40
70
9C
85
80
2
a* r%
.30
A
620
a r%
.
12 40
.
A
3 6.7
612.5
1 1227
0
A=2
0(11
C
- 3
_
-.
____c--
a' r%C
1
2-
0
A
6 10
m
12206
r%
3-a,
5
U12
10
TO
6
EA
0
2
0
2
Figure 7. Strain and reduction dependence of {111} reflection
intensities from the drawing plane of strip reduced
with different A. The various a,-r combinations for
any A are noted in each case. Curve u is for the
homogeneously cold rolled strip of Fig. 3. Curve s
(filled symbols) represents near-surface reflections;
curve c (open symbols) is from the center.
1(100)
10
1(100)
I0
OL
0
2
2
0
Figure 8. The {100} companion to Fig. 7.
E
N)~
rNa
23
A=1.5,I
j{
6*
Ir=80%
62%
3
Io
5O/%
29%
0
2
3
o
~~aIo
E r=60%-
3
10
r=83%0/
240%
26%1%
(
sufae)(srfce(ener
10
0igue9
(Surface)
Figure 9.
h
20
arainwt
40
30
At
to(Surface)
depth,
0
10
30
20
40
1t9eowtesufc
50
At
(oCenter)
The variation with depth, At, below the surface
= 0) of {111} reflection intensities
(where t/t
in strip resuced different amounts with several A.
24
The I f
/I
in Fig. 7 is strongly dependent on Er and A, This
particular intensity has a peak value at the surface after an imposed
strain, e
(or reduction, Zri), for all but A = 1 when
than the total reduction limit.
Ei
was larger
The pattern is an extension of the
rolling results (Fig. 3).
There is some uncertainty in picking Ei
from Fig. 7 and what has been done is to let it be defined by the
maximum in the upper side of the dotted band.
The A-dependence in
Fig. 10 is too strong, however, to be seriously affected by that
uncertainty:
the strain for inversion falls with increasing A from
its highest level in rolling when A is < 1. The peak I{ll /I falls
also, although not so regularly.
Held
18
has suggested that the cumulative reduction for the re-
lated peak in the anisotropy parameter, If, of recrystallized material
is sensitive to friction.
The possibility was tested here at the
surface for A = 1.5 with the results in Fig. 11.
Intensity levels
are changed, but Ei is not.
Measurements on cold drawn and recrystallized strips are summarized in Figs. 12 and 13.
alent.
Rolling and A = 1 are again nearly equiv-
The I{lll}/Io pattern is not basically changed, although
intensity levels are raised as others have shown them to be in
rolled strip (cf. Figs. 7 and 12).14,35
The I{100}/o pattern is
changed by recrystallization and resembles that previously observed
25
99
4
-]98
95
3 -
C
90
cracking
21--
IF-
85
80
1111
70
inversion
(E)
-160
40
20
OL
I
I
I
I
0
1
2
3
4
Figure 10.
The A dependence of the imposed (or apparent) strain,
e.-,for the {111} inversion in Fig. 7 and for the
appearance of edge cracking. Rolling A is known only
to be < 1.
26
Er,/
20
l
3KF
40
I
60
70
80
|
85
90
|
|____
soa p
1(100)
10
2H
Teflon
0
21-
Teflon
1(Il1 )
I0
I -
0
0
2
6
Figure 11.
The effect of friction on surface-reflection intensities
from strip drawn with constant A = 1.5 and a = 60.
27
r,%
70
80
85
90
5
4
3
0(II
2
0
4
3
Jo
2
OL
0
Figure 12.
2
0
2
Strain and reduction dependence of {111} reflection
intensities from the drawing plane of strip reduced
with different A and then recrystallized. The
various a-r combinations for any A are noted in each
case. All measurements are from the surface. Curve
u is "recrystallized" from Fig. 3.
2
I(1oo)
I0
0
2
'(100)
I0
OL
0
2
0
8
Figure 13.
2
8
The {100} companion to Fig. 12.
r%)
CO
29
for rolling, '51
in
1
except that as A is increased above 1 the upward trend
00/}1 0 begins at smaller reductions.
At this point pole figures were invoked to find reasons for such
behavior, especially that to be seen in Fig. 7. Material reduced 80%
at A = 2 (when Er. ~ 65%) was chosen for the study.
The {100}, {110},
and {111} pole figures at c and s locations and at an intermediate one
as well
are given in Fig. 14.
At the center they compare well with
those for 80% rolling reduction in Fig. 2. Moving from center to
surface, there are changes in Fig. 14 which resemble those produced
by the last reduction-step in Fig. 2, from 98 to 99%, which brought
in Fig. 14 the central intensity-
on the rolling-texture inversion:
peak of the {111} is nearly halved while that 550 away is now doubled;
the {110} peak is lowered by about 40%; and there is some gain, perhaps
50%, in the interior {100} peak.
Figure 9 indicates a similar change
for the {111} peak around the normal direction.
are lower in Fig. 14 than in the 98
Measured intensities
99% step in Fig. 2, but so is
-+
the overall reduction.
Because trends are alike ---
through the thickness in an in-
homogeneously strained material in Fig. 14 and with reduction in one
homogeneously strained in Fig. 2 ---
it
that their explanations might be, too.
seemed reasonable now to think
On that basis, the texture
gradient must derive from a gradient of the same macroscopic shear
which produced the uniformly distributed inversion in Fig. 2.
There
30
R.D.
R.D.
R.D.
{Ioo} {1001~
~
{uo}
10
N
{IuI}
B
\Bj
A0.5
.-.BC
2 1.5N
\B
c
0.5
I
5
0.\
)\\Bo
c.5\
T.
1
AC
15/' A~
1
\B
/
j
A
B
1'
CB1
At0.44 (center)
R.D.
R.D.
R.D.
{I00}
{nIo}
T.D.
0.5-
{III}
[------.2
,-
2.5
=
Figur
P
.
2
(su5
fen
TD
14.
00.5
IT..T
4T.D.
"t
to
R.D.
0.2
R.D.
R.D.
{I10}
J1001
{II
0.5
0515j
5
3
21.
1.51.
5
35 2
2
1.51.
3.5-
rm
2re1.5cluded
ig02.5d4
2.5
TD.
1
05
T. .
2.5
2
T.
4
t 0.5(surface)
Figure 14.
Pole figures from different locations in strip cold drawn
a total of 80% with A = 2 and a~ = 120. Location is defined
by At/t :0.05 is just below the surface, at a depth of 5%
of the Krawn thickness; 0.44 is near the center; 0.20 is
about midway between surface and center. Ideal textures
from Figs. 2 and 4a are included.
31
is good evidence of such a gradient in the shear cracks at the edges of
strips after drawing beyond Ei.
An example from the material of Fig. 14
is given in Fig. 15 along with one from the cold-rolled strip shown
earlier in Fig. 6. The rolled strip is cracked through the thickness,
while for A = 2 the cracks penetrate only about 20% of the thickness or
to about the depth in Fig. 9 at which I{lll1/Io begins climbing.
The
implication in this is that the {111} inversion begins where strainhardening rate first drops down to some more or less critical upper
limit for shear flow.
Texture inversion is therefore initiated at the
surface because strain gradients rise with A7,8 and strain hardening
rate is tied fairly directly to the effective or equivalent strain
(with an inverse relationship).
The imposed e. for inversion must
therefore fall as A rises, as it is shown to in Fig. 10.
Also
plotted in Fig. 10 are the imposed strains at which edge cracks
were first clearly seen.
Their A-dependence closely parallels that
of e . These strains are larger, presumably because the shear bandto-crack conversion requires more strain, but their closeness is
evidence that e. is determined by localized shear flow.
The shear
cracks after 80% reduction at A = 2 (Fig. 15) were followed inward
from the edge and observed to turn into shear-bands.
The problem with Fig. 10 is that it
requires very large strain
gradients for which there is little independent experimental support.
If the strain for inversion in rolling at
£
~ 4 is the critical level
32
Figure 15.
Scanning-electron micrographs of edge cracking in the
99% cold rolled strip of Fig. 6 and in the 80% colddrawn strip from which the pole figures in Fig. 14
were taken. Cracks penetrate only about 20% of the
thickness in the drawn strip.
33
which must be reached for all A, the surface-to-center strain ratio must
then be close to 8 at A = 4, nearer 5 at A = 2, and about 2 at A = 1.5.
Related work on hardness (and strain) gradients in initially annealed
copper suggests a maximum ratio of 4, or perhaps somewhat more, for
A ~ 4 and no more than about 2 for A ~ 2.7
The roughly factor of 2
difference between that work and this may reflect different strain
hardening characteristics and different measurement techniques, or
it may mean that a critical-strain inversion criterion is too simple.
The lower I 11/I
at E: as A is raised is perhaps to be explained
as a result of the redundant character of the straining in which two
principal axes are rotated away from those of the strip, i.e. the
pulling and thickness directions.
IMPLICATIONS FOR TEXTURE CONTROL
The findings show that there is a mechanical basis for close and
perhaps even useful control of texture.
Although real textures are
complex, their ideal components are about all that can be accommodated
in analysis of texture-controlled behavior.
In the past, however, this
has not been a serious limitation to such analysis, and that is why
only two components known to be important in Al-killed steel strip are
singled out for comment here:
{111} and {100} in the rolling plane.
34
{111}:
Control of {111} is very much an exercise in control of the
inversion, or of Er
(or Eg)
in Figs. 7 and 12.
Suppressing the in-
version must allow Ifill/10 to continue rising; hastening it cuts off
that trend.
Therefore to intensify {111}, macroscopic shearing ought
to be avoided in reductions with A < 1. Restoring enough strain hardening capacity to disperse localized flow should have that effect.
What seems called for is repeated low-A reduction, to below Er , and
annealing.
This general approach has been tried for maximizing if,
but without conclusive results. 36
It might work better if practiced
on killed-steel strip with stricter regard for maximizing the cold
reduction but stopping short of an upper limit, which is at the i
peak (below Er.) if that is the emphasis.
Should interest focus
more on elastic constants, e.g. as in maximizing Young's modulus,
then Er
is a more logical upper limit.
To promote lower Il
/I,
macroshearing can be induced at smaller imposed reductions by raising
A; gradients are unavoidable now with surface layers being the first
to undergo the inversion (Figs. 7 and 9).
{100}:
The reduction dependence of {100} in either cold worked
or recrystallized material seems unrelated to the macroshearing.
strip rolling the characteristic upward turn in I{100}o1/
In
after re-
crystallization starts before the {111} inversion at Er , which was
first pointed out by Whiteley and Wise.1
With increased A both re-
ductions are lowered (cf. Figs. 12 and 13) and eventually come
35
together at around Er = 50% when A = 2. There is little basis in these
data for anticipating how {100} will be affected by repeated reduction
and annealing; perhaps some enhancement will be found with reductions
greater than that for the up-turn in I{100} /o'
An unfortunate practical complication is that I is driven down
more rapidly by increasing {100} than it is raised by increasing {111}.
As Whiteley and Wise 1 have shown, the peak in if vs. Er is determined
more by the up-turn in {100} than the inversion in {111}.
With low A,
therefore, raising i would have to be concerned more with suppressing
{100} than with the comparatively easier task of increasing {111}.
What this appears to mean is that the proposed macroshearing development has little influence on the Rf peak.
Perhaps the most obvious
merit of increased {100} would be in magnetic-material processing
when it should make some improvement in permeability. 37
The greatest practical problem is to use these findings in strip
rolling, a basically low-A operation.
From Eq. 2, A > 1 requires
R/h0 < 10 (where R is now the roll radius) when the reduction per
pass is r ~ 10%; with larger r, the R/h0 falls, e.g. when r ~ 25%,
R/he
3 for A > 1. These are low values of R/h0 , more common to
heavy-section hot rolling and cluster-mill cold rolling; they must
also reflect roll flattening so that the apparent R/h0 (based on
measured roll radius) may have to be smaller still for A > 1. But
this is hardly a serious disadvantage in strip rolling, for the
36
inhomogeneous deformation under A > 1 is only occasionally useful.
What
has been given here are some guide lines for the control of that kind of
deformation.
SUMMARY AND CONCLUSIONS
The mechanical factors of total reduction and deformation-zone
geometry can have strong effects on both the deformation and recrystallization textures of killed-steel strip.
When the height of
the zone is less than its length, or the ratio A is < 1, texture is
uniform through the thickness but undergoes an inversion, largely
in the intensity of {111} in the rolling plane, after a reduction
of about 98%.
Inversion has been associated with the formation of
shear bands as an outgrowth of diminished strain hardening capacity
and the development of shear texture in the bands which changes the
previously stable rolling texture.
As A becomes > 1, texture gradi-
ents appear and the inversion occurs at smaller total reduction,
beginning at the surface where straining is most advanced.
The
implications for control of the plastic-anisotropy parameter are
discussed.
37
REFERENCES
1.
R. L. Whiteley and D. E. Wise: "Relationship among Texture, Hot
Mill Practice and the Deep Drawability of Sheet Steel", Flat
Rolled Products-III, p. 47, Interscience Publisher, Chicago, 1962.
2.
C. S. Barrett and T. B. Massalski:
McGraw-Hill, New York, 1966.
3.
I. L. Dillamore and W. T. Roberts: "Preferred Orientation in
Wrought and Annealed Metals", in Met. Rev. 1965, Vol. 10, p. 271.
4.
A. P. Green: "Plane Strain Theories of Drawing", Proc. Instn.
Mech. Engrs., 1960, Vol. 174, No. 31, p. 847.
5.
R. M. Caddell and A. G. Atkins: "The Influence of Redundant Work
When Drawing Through Conical Dies", Journal of Enqineering for
Industry, Trans. ASME, Series B, 1967, Vol. 89, p. 1.
6.
R. W. Johnson and G. W. Rowe, "Redundant Work in Drawing Cylindrical
Stock", J. Inst. Metals, 1968, Vol. 96, p. 97.
7.
J. J. Burke, Sc. D. Thesis, Department of Metallurgy and Materials
Science, M.I.T., Cambridge, Mass., 1968.
8.
B. B. Hundy and A. R. E. Singer, "Inhomogeneous Deformation in
Rolling and Wire Drawing", J. Inst. Metals, Vol. 83, 1955, p. 401.
9.
F. Haessner and H. Weik: "Untersuchungen der Walz-und
Rekristallisationstexturen von Karbonyleisen", Arch. Eisenhuettenw.9
1956, Vol. 27, p. 153.
10.
M. Moller and H. Stablein: "Walztexturen von Transformatorenstahl",
Arch. Eisenhuettenw., 1958, Vol. 29, p. 377.
11.
J. Bennewitz: "Untersuchungen uber die Walztextur von Eisen und
Kubisch-raumzentrierten Eisenlegierungen", Arch. Eisenhuettenw.,
1962, Vol. 33, p. 393.
12.
H. Takechi, H. Kato, and S. Nagashima: "Rolling and Annealing
Textures of Low Carbon Steel Sheets", Trans. TMS-AIME, 1968,
Vol. 242, p. 56.
in Structure of Metals, p. 541,
38
13.
P. N. Richards and M. K. Ormay: "Preferred Orientations in
Commercial Cold-Reduced Low Carbon Steels", Trans. TMS-AIME,
1969, Vol. 245, p. 715.
14.
R. H. Goodenow and J. F. Held: "Recrystallization of Low Carbon
Titanium Stabilized Steel", Met. Trans., 1970, Vol. 1, p. 2507
15.
M. Fukuda: "Mathematical Analysis on the Relation between
Crystallographic Texture and Lankford r Value in Steel Sheets",
Trans. ISIJ, 1968, Vol. 8, p. 68.
16.
I. L. Dillamore and W. T. Roberts: "Crystallographic Texture
Variations through Rolled Aluminum and Copper Sheet", J. Inst.
Metals, (1963-64), Vol. 92, p. 193.
17.
C. S. Stickels: "Surface Texture in Iron and Steel", Trans.
TMS-AIME, 1967, Vol. 239, p. 1857.
18.
J. F. Held: "The Effect of Inhomogeneous Textures on Mechanical
Properties of Low Carbon Steel Sheets", Trans. TMS-AIME, 1967,
Vol. 239, p. 573.
19.
F. Haessner and D. Mayer-Rosa: "Uber den Aufbau der Walztextur
kubisch raumzentrierter Metalle und Legierungen", Z. Metallk.,
1967, Vol. 58, p. 12.
20.
R. A. Vandermeer and J. C. Ogle: "Texture Inhomogeneities in
Cold-Rolled Niobium", Trans. TMS-AIME, 1969, Vol. 245, p. 1511.
21.
H. C. Rogers, Jr. and L. F. Coffin: "Influence of Pressure on
the Structural Damage in Metal Forming Processes", Trans. ASM,
1967, Vol. 60, p. 672.
22.
J. M. Alexander: "The Effect of Coloumb Friction in the Plane
Strain Compression of a Plastic Rigid Material", J. Mech. and
Phys. Solids, 1955, Vol. 3, p. 233.
23.
J. W. Wistreich: "Investigation of the Mechanics of Wire
Drawing", Proc. Instn. Mech. Engrs., 1968, Vol. 174, p. 847.
24.
L. G. Schulz: "A Direct Method of Determining Preferred
Orientation of a Flat Reflection Sample Using Geiger Counter
X-Ray Spectrometer", J. Appl. Phys., 1948, Vol. 20, p. 1030.
25.
G. B. Harris: "Ouantitative Measurement of Preferred
Orientation in Rolled Uranium Bars", Phil. Mag., 1952,
Vol. 43, p. 113.
39
26.
R. A. Vandermeer and J. C. Ogle: "The Development of Preferred
Orientations in Cold Rolled Niobium", Trans. TMS-AIME, 1968,
Vol. 242, p. 1317.
27.
W. A. Backofen and B. B. Hundy: "Torsion Texture of 70:30 Brass
and Armco Iron", Trans. AIME, 195 3, Vol. 197, p. 61.
28.
F. Adcock: "The Internal Mechanism of Cold Work and Recrystallization in Cupro Nickel", J. Inst. Metals, 1922, Vol. 27, p. 73.
29.
J. D. Grogan: in Communication on Adcock's paper, J. Inst. Metals,
1922, Vol. 27, p. 103.
30.
M. Cook and T. L. Richards: "The Structural Changes in Copper
Effected by Cold Rolling and Annealing", J. Inst. Metals, 1940,
Vol. 66, p. 1.
31.
M. Cook and T. Ll. Richards: "The Structural Changes Effected in
70:30 Brass Strip by Cold Rolling and Annealing", J. Inst. Metals,
1943, Vol. 69 p. 351.
32.
W. T. Roberts: in "Discussion on Preferred Orientation", J. Inst.
Metals, 1954, Vol. 82, p. 654.
33.
S. L. Couling, J. F. Pashak, and L. Sturkey: "Unique Deformation
and Aging Characteristics of Certain Magnesium-Base Alloys",
Trans. ASM, 1959, Vol. 51, p. 94.
34.
M. G. Cockraft: "Ductile Fracture in Cold Working Operations",
in Ductility, p. 199, ASM Metals Park, Ohio, 1968.
35.
J. T. Michalak and R. D. Schoone: "Recrystallization and Texture
Development in a Low-Carbon, Aluminum-Killed Steel", Trans. TMSAIME, 1968, Vol. 242, p. 1149.
36.
K. Matsudo, T. Shimomura and Y. Hashimoto, "Effect of Two-Stage
Cold Rolling-Annealing Process on Deep Drawability of Low Carbon
Rimmed Steel Sheet", Report of Tech. Res. Inst., Nippon Kokan Ltd.,
1966.
37.
S. Chikazumi: "Magnetic Anisotropy", in Physics of Magnetism,
p. 128, John Wiley and Sons, Inc., London, 1964.
40
APPENDIX I
PROCEDURAL DETAILS
Strip Drawing:
The drawing apparatus was almost a copy of that used
by Rogers and CoffinI in their study of plane-strain strip drawing, although without the provision for measuring the drawing load.
A wedge-
shaped orifice for two dimensional strip drawing was provided with a pair
of tungsten carbide dies inserted in die holders which were made of low
carbon steel heat treated to a hardness of Rc 45.
Three pairs of dies
with flat surfaces and semi die angles of 30, 6* and 120 were used.
The die holders were supported by the walls of a rectangular hole
(2.2 in. x 2.1 in.) in a thick steel cylinder of 5-in. diameter.
This
cylinder, of 2-in. height, was resting on a 6-in. diameter and 1.25 in.thick steel base-plate having a 2.5-in. diameter hole.
Everything was
then bolted through a 0.5-in. thick aluminum "washer" to the top of the
Instron Machine (in the cavity provided for the load cell.)
The gap
between the dies could be adjusted by inserting pieces of hardened
steel shimstock of various thicknesses between the die holders and the
sides of the rectangular hole.
Strips used were about 12-in. long.
They were surface ground to
uniform thickness and width which varied from batch to batch but were
about 0.2-in. and 1-in., respectively.
Strips were "pointed" by rolling
half their length so as to pass through the drawing die.
After cleaning
41
with acetone, Teflon was sprayed on the thicker part of the strip and
allowed to dry.
The dies were cleaned with acetone and the rolled
portion of the strip inserted into the gap which had been set for the
desired reduction of the undeformed and Teflon-coated portion.
The
rolled portion of the strip was tightly gripped in wedge-type jaws
mounted on the moving crosshead of the Instron machine and pulled
at a constant speed of 1-in/minute.
All strips were drawn at constant A by keeping r constant during
repeated drawing through the same pair of dies.
A constant r was
maintained by changing the die-face separation after each pass.
The coefficient of friction for Teflon coated strip was determined by Alexander's 2 method which involves plane-strain compression
of lubricated strip.
lubrication.
It was a reasonable choice for dry, solid-film
With liquid lubrication, however, a veritcally aligned
drawing operation provides a better and more nearly uniform supply
of the lubricant than plane-strain compression; liquid is much more
easily displaced from the latter.
Therefore the friction coefficient
with the soap and water solution was evaluated in drawing.
This was
done according to an analysis by Wistreich3 and involved the comparison of drawing forces for Teflon-lubricated and liquid-lubricated
strips of the same thickness reduced the same amount in dies of the
same design.
It is assumed in doing this that the value for Teflon,
42
derived from compression, applies in drawing as well.
Reduction
details were A = 1.5 from a = 6* and r = 0.135.
Drawing loads were measured for this purpose by attaching a load
cell to the moving crosshead of the Instron machine.
The inverted
load cell was bolted on top of an adapter-cylinder of 1-in. wall
thickness and 3-in. height with its base plate bolted to the moving
cross head of the Instron machine.
screwed into the load cell.
The wedge-type jaws were now
Drawing loads for six successive passes
with r = 0.135 and cumulative reductions up to 70% were measured for
both kinds of strips.
In each pass the drawing loads were always
uniform and showed a variation of no more than + 5%.
The ratio of
drawing loads for two strips, in identical passes, was always
2.1 + 0.07.
Using the coefficient of friction for Teflon coated
strip (0.08) as the base, that for soap and water lubrication was
calculated to be 0.2.
Rolling:
A quantity of strip was cold rolled to 99% reduc-
tion in thickness.
Cumulative reduction up to 80% was carried
out on a two-high laboratory mill with unlubricated 5-in.
diameter rolls.
For further reduction, up to 99%, a four-high
mill with 1-5/8-in. diameter work rolls was used, with lubrication only in the last step of the reduction.
43
Texture Measurement:
Experimental conditions for pole figure
determination are given in Table I-1.
made with a GE X-RD5 diffractometer.
given in Table 1-2.
Line-intensity measurements were
Conditions of diffractometry are
The intensities are always represented as a mul-
tiple of the intensities from a random sample.
As reported by Takechi,
Kato, and Nagashima, 4 random samples were prepared by spraying -325
mesh electrolytic-iron powder on a glass microscope slide with a fine
coating of silicone grease to act as binder.
For line intensity measurements, integrated intensity, i.e. the
area under a peak, was used as a measure of line intensity.
area was measured graphically.)
(The
The intensity ratios (with respect
to the same lines in a random sample) were normalized to avoid any
effect of surface preparation, sample thickness, and instrumental
errors.
It was done as proposed by Harris
5
who has shown that the
measured ratio of intensity, I{hkZ}, from textured material to that
from a random sample, Io, is related to the actual ratio as
I[{hkU
1
k
I hkj(
measured
where k depends on variables noted above.
from the X-ray source is constant,
1
_
real
As the power emanating
44
TABLE I-1
CONDITIONS FOR POLE FIGURE DETERMINATION
Radiation . . . . . . .
Filter
Slits
.
.
.
.
.
* Mo K
* Zr
* Diverging:
2 x 1 cm
Receiving:
4 x 1 cm
Rotation of specimen in its own plane . . . . 36*/minute
Rotation of specimen in a plane
perpendicular to its own . . . . . . . . . .
0.5*/minute
45
TABLE 1-2
CONDITIONS OF DIFFRACTOMETRY
Radiation
Mo K
. . .
Filter
Slits
. . .
Zr, 0.002-in thick
Diverging,
.
30
Receiving, 0.20
Scanning speed
. . . . . . 2-in/minute
46
{hkk}
1o
=
n
(2)
real
provided summation is done over a large number of peaks.
Summing
both sides of Eq. 1 and using Eq. 2
f{hk}]
o
k.n
measured
or
k =1
hkt}
n0
measured
or
I{hk}
o
{hkk}
j
real
L
measured
1
{hk}
n
Io
measured
This is the ratio plotted in all the reflection intensity measurements.
Summation was done over the first thirteen lines (n = 13).
Microscopy:
examination.
Strips were nickel-plated before metallographic
Mounted in bakelite, samples were mechanically polished
and etched with 1%Nital solution for observation under the optical
47
microscope.
Specimens whose edges were examined by scanning electron
microscopy to observe edge cracking were only cleaned with acetone.
For grain-size measurement, a piece of undeformed strip was mounted
in bakelite so as to have the rolling plane as the plane of polish.
After adequate mechanical polishing and etching with 1% Nital solution
four micrographs were taken.
as proposed by Hilliard.6
A.S.T.M. grain size No. was determined
Mean linear intercept measurements were
made with the Hilliard circle, with at least four arbitrary, non
overlapping circle placements on each photograph to insure accuracy.
APPENDIX I -
REFERENCES
1.
H. C. Rogers, Jr. and L. F. Coffin: "Influence of Pressure on
the Structural Damage in Metal Forming Processes", Trans. ASM,
1967, Vol. 60, p. 672.
2.
J. M. Alexander: "The Effect of Coloumb Friction in the Plane
Strain Compression of a Plastic Rigid Material", J. Mech. and
Phys. Solids, 1955, Vol. 3, p. 233.
3.
J. W. Wistreich: "investigation of the Mechanics of Wire
Drawing", Proc. Instn. Mech. Engrs., 1968, Vol. 174, p. 867.
4.
H. Takechi, H. Kato, and S. Nagashima: "Rolling and Annealing
Textures of Low Carbon Steel Sheets", Trans. TMS-AIME, 1968
Vol. 242, p. 56.
5.
G. B. Harris: "Ouantitative Measurement of Preferred
Orientation in Rolled Uranium Bars", Phil. Mag., 1952,
Vol. 43, p. 113.
6.
J. E. Hilliard: "Estimating Grain Size by the Intercept
Method", Metal Progress, 1964, Vol. 85, No. 5, p. 99.
48
APPENDIX II
THE UNIFORMITY OF ROLLING TEXTURE
The {100} and {111} reflection intensities from the rolling-plane
of strips cold rolled to various cumulative reductions showed no variation with position in the strip (Fig. II-1).
Also, the'{lll} pole
figures from positions near the center of the strips cold rolled to
80% and 92% reduction (Fig. 11-2) are similar to those from positions
near the surface of the same strips (Fig. 2).
These provide suf-
ficient basis to conclude that the deformation texture developed in
cold rolled strip is uniform through the thickness of the strip.
Xr=
980/
Ir=
990/
91%/
(100)
60%
40%
-
-
10
o~
-:
2I
I
I
I
10
20
30
40
(Gee
I
I
0
10
(Surface)
20
30
At
40
50
0
(Ce nter)
(Surface)
At
50
(Cen ter)
S0
5
4
I0
10
2 -
2O
(Surface)
Figure II-l.
At
to
(Center)
I
3
10
0
(Surface)
-
I
I
30
20
At
to
40
50
(Center)
Variation of rolling plane {100} and {111} intensity through the
thickness of strips cold rolled to various cumulative reduction.
11
5 4
Figure 11-2.
7
{111} pole figures of 80% and 92% cold-rolled strips.
Cn
C0
51
APPENDIX III
STEREOGRAPHIC ROTATION OF IDEAL ROLLING TEXTURES
IN {100} AND {110} PROJECTIONS
The ideal rolling textures, A, B, and C, are shown in Fig. III-la
for {100} and {110} projections.
A and B are similar to that reported
by Bennewitz. 1 A has <110> as fiber axis parallel to N.D. (the sheet
normal) and is limited to a + 550 rotation of {001} <110> around it.
In B, the <110> fiber axis lies at 600 from R.D. towards N.D. with a
+ 350 rotation of {554} <225> around it. In C, the fiber axis is
<111> parallel to N.D. and the rotation is a full 3600 around it.
The new positions of these fiber textures after a + 550 rotation
around T.D. are shown in Fig. III-lb.
The rotated {lOO} projection shows a concentration of ideal
textures near the "interior" high intensity region to be seen in
the {100} pole figures of Fig. 2. This would explain the increase
in intensity of this region in Fig. 2 (98%
different trend in {110}.
-* 99%).
There is a
Before rotation there is a marked
intersection of ideal textures at o 300 from the center towards
N.D. (Fig. III-la).
With rotation, however, this spreads out
over a 20-350 range which is held responsible for the drop in
the high-intensity region of the {110} pole figures of Fig. 2
(98%
+
99%).
52
APPENDIX III
1.
-
REFERENCES
J. Bennewitz: "Untersuchungen uber die Walztextur von Eisen und
Kubisch-raumzentrierten Eisenlegierungen", Arch. Eisenhuettenw.,
1962, Vol. 33, p. 393.
53
R.D.
R.D.
{oo}
* N
(n o}
N
-~.
(a)
-N.
ISN
L... . .
..
. .. .
>IT.D.
T. D.
A
B
C
R. D.
--
R.D
(100){
110
rotated 55*
rotated 550
(b)
T D.
Figure III-1.
-
Ideal textures A, B and C in {l00} and {110} pole
figures (a); and rotated + 550 around T.D. (b).
A and B are two partial fiber textures with fiber
axis <110> parallel to R.D. (A), and at 60* to
R.D. toward N.D. (B); C is a complete fiber
texture with fiber axis <111> parallel to N.D.
D
54
APPENDIX IV
STEREOGRAPHIC ROTATION OF THE IDEAL SHEAR TEXTURES
OF IRON IN {100} AND {110} PROJECTIONS
The ideal orientations in the shear texture of iron are shown in
f100} and {110} projections in Fig. IV-la.
To fit the argument being
developed in Fig. 5, a rotation of these ideal orientations by + 350
around T.D. (Fig. IV-lb) is imposed to simulate the new rolling-plane
texture.
A cluster of ideal orientations in the rotated {100} pro-
jection near the position of the "interior" high-intensity region of
the {100} pole figure of Fig. 2 shown by dotted region is thus
offered as the explanation of the rise in the intensity in this
region in Fig. 2 (98%
-.-
99%).
55
(100)
(110)
shear
direction
shear
direction
O1
I7
00
she ar
Pla ne
0
(a)
0
COC
V
{1 10)
< 112>
0
(112)
<I ll>
< I II>
(11 0)
R.D.
-~-P,
0
35
rotated 35*
El
S7
V
C
0
T. D.
Figure IV-1.
Ideal orientations of the shear texture in iron in
{100} and {110} projections and rotated + 350 around
T.D.
(b)
56
APPENDIX V
GRADIENTS IN {100} REFLECTION INTENSITY FOR A > 1
The variation with depth, At, below the surface (where At/t 0 = 0)
of {100} reflection intensities from strips reduced different amounts
with several A is shown in Fig. V-1.
The data from positions near the
center (At/t 0 = 0.50) were used to plot curve c in Fig. 8. Extrapolated
values of I{100}1 o were used in the absence of measurements at the
center.
57
I
1.5, a= 6*
2
1(100)
I0
0
62%
i!N2 ,a=6*
2
1(100)
29
3
=2
A2
2
(100)
--
10
..---
48%
0
2
(100)
I0
I
0
0
(Surface)
Figure V-1.
10
30
20
t
to
40
50
(Center)
Variation of rolling-plane {lOO} reflection intensity as a
multiple of random through the thickness of strips drawn to
various cumulative reductions with constant A and a.
58
SUGGESTIONS FOR FUTURE RESEARCH
There are three areas for further investigation, briefly outlined
below.
1.
Texture Sharpening:
Increasing Illl}/Io without raising I{100}/o
is essentially what is implied here. The reason for such interest
is the correlation between large R (Plastic Anisotropy Ratio) and
large I{ll}/I{100}.
drawability.
The large R in turn contributes to greater
The proposed experiments would involve controlled-A
reductions to levels just below those that will be known to bring
an increase in I{100}
o after recrystallization.
would be recrystallization.
The next step
Repeating the sequence may lead to
both interesting and useful results.
The variables would be A
(in a range of direct interest in rolling, e.g. 0.5 - 1.5),
cumulative reduction, and the recrystallization practice.
2.
Mechanical Control of Texture in Non Ferrous Metals:
There is
reason to believe that macroshear and texture inversion are not
at all unique to low carbon steel sheet and strip.2,3
A
parallel study of the mechanical contributions to the planestrain deformation and recrystallization textures of non ferrous
materials would test the hypotheses of macroshear and shear
texture development in shear bands, suggested in this study.
59
It may also provide some information about R and/or AR control in
such materials.
3.
Plane Strain vs, Axisymmetric Strain Hardening:
Strain hardening
in iron to large strain has been studied in detail in recent years.
The medium for much of this work has been axisymmetric reductions
by wire drawing.4
When straining is axisymmetric, however, macro-
shear is prevented because of the difficulty of accumulating
shear on unchanging macroscopic shear surfaces in axisymmetric
reduction.
Therefore the strain hardening behavior, especially
as the strain hardening rate falls, may be markedly different in
the two cases.
Considering the practical importance of plane-
strain reduction in sheet processing, this deformation mode is
an appropriate area for similar study.
REFERENCES
1.
M. Fukuda: "Mathematical Analysis on the Relation between
Crystallographic Texture and Lankford r Value in Steel Sheets",
Trans. ISIJ, 1968, Vol. 8, p. 68.
2.
M. Cook and T. Ll. Richards: "Fundamental Aspects of the Cold
Working of Metals", J. Inst. Metals, 1950-51, Vol. 78, p. 463.
3.
R. F. Braybrook and E. A. Calnan: "Some Observations on the
Development of Face-Centered Cubic Rolling Textures",
J. Inst. Metals, 1956-57, Vol. 85, p. 11.
4.
G. Langford and M. Cohen: "Strain Hardening of Iron by Severe
Plastic Deformation", Trans. ASM, 1969, Vol. 62, p. 623.
60
BIOGRAPHICAL NOTE
The author is the eldest son of Mr. Parmeshwar Sarup Mathur and
Mrs. Gopal Rani Mathur of Moradabad, U.P. India.
Born on December 19,
1945, he graduated with a Bachelor of Science degree from Agra
University in 1962.
He received the degree of Bachelor of Technology
in Metallurgical Engineering from Indian Institute of Technology,
Kanpur, India in 1967 and was judged to be the best graduating student
in Metallurgical Engineering.
thesis award the same year.
He also received the best Bachelor's
He then entered Massachusetts Institute
of Technology and received the degree of Master of Science from the
Department of Metallurgy and Materials Science in 1968.
After work-
ing with the Division of Sponsored Research at Massachusetts Institute
of Technology for a brief period he started on his doctoral program
in 1969.
The author is a member of Sigma Xi, American Society for Metals,
and the American Institute of Mining, Metallurgical and Petroleum
Engineers.