• TABLE OF CONTENTS
HIDE
 Title Page
 Copyright
 Dedication
 Acknowledgement
 Table of Contents
 Abstract
 Introduction
 Experimental techniques
 Observations and results
 Discussion
 Summary
 Suggestions for future work
 Appendix
 Reference
 Biographical sketch
 Copyright














Title: deformation of grains during cold-rolling
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Table of Contents
    Title Page
        Page i
    Copyright
        Page ii
    Dedication
        Page iii
    Acknowledgement
        Page iv
    Table of Contents
        Page v
        Page vi
    Abstract
        Page vii
        Page viii
        Page ix
    Introduction
        Page 1
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    Experimental techniques
        Page 28
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    Observations and results
        Page 49
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    Discussion
        Page 217
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    Summary
        Page 238
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    Suggestions for future work
        Page 241
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    Appendix
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    Reference
        Page 305
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    Biographical sketch
        Page 309
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    Copyright
        Copyright
Full Text

















THE DEFORMATION OF GRAINS
DURING COLD-ROLLING










By

ROBERT A. ELLIS, JR.


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY









UNIVERSITY OF FLORIDA


1980
































Copyright 1980

by

Robert A. Ellis, Jr.

































Dedicated to my wife, Karen, without whose support

and urging this work could not have been completed.















ACKNOWLEDGMENTS

The author would like to thank the members of his

supervisory committee, especially Dr. F. N. Rhines, for

their help and guidance during the course of this

research.

The author is also grateful to his fellow students

for their help and suggestions, which have aided greatly

in his work.

In addition, the author would like to thank the

National Science Foundation, the University of Florida

and the Department of Materials Science and Engineering

for their financial support during the time he was engaged

in this research.















TABLE OF CONTENTS


Chapter


ACKNOWLEDGMENTS . . . . . .

ABSTRACT . . . . . . . .

I INTRODUCTION . . . . . . .

The Basics of Quantitative
Metallography . . . . .
Measurements on Anisotropic
Structures . . . . . .
The Shapes of Metal Grains . . .
Models of Grain Shape . . . .
Quantitative Studies of Deformation
Grain Boundary Sliding . . . .

II EXPERIMENTAL TECHNIQUES . . . .

Metallographic Sample Preparation
Quantitative Metallography . . .
Bulk Deformation Samples . . .


. . iv


vii


9
. . 1



. 19
S. 22
. . 23
. . -26


OBSERVATIONS AND RESULTS . . . ... 49

Changes in the Appearance of the
Microstructures . ... . 50
Roses.of the Numbers of Intersections 86
Representations of NL(9,0) in Three
Dimensions . . ........ . .117
Empirical Equations for NL(6, ) . . 131
Three-Dimensional Plots of the Mean
Grain Intercept . . . . . .. 133
The Shapes of Individual Grains . .. 139
Bulk Size Changes . . . . . . 140
Comparison of Bulk Sample and Grain
Deformations . . . . . ... 143
Grain Boundary Surface Areas per
Unit Volume . . . . . ... 171
Grain Boundary Edge Lengths per
Unit Volume . . . . . .... .. 190
Tests for Grain Boundary Sliding . . .209
Summary of Results . . . . . .. 215


III


Page


. .















IV DISCUSSION . . . . . .

The Model for the Deformation
Process . . . . . .
An Alternate Model .. . . .
Evidence of Unequal Deformation
in the Grains . . . .
Additional Factors Influencing
the Quantitative Measurements
Summary . . . . . .

V SUMMARY . . . . . . .

VI SUGGESTIONS FOR FUTURE WORK . .


APPENDICES

A EXPERIMENTAL PRINCIPAL VALUES .

B CALCULATED SURFACE AREAS . . .

C CALCULATED EDGE LENGTHS ..

D MEASUREMENT OF AREAL FEATURES IN
ANISOTROPIC MICROSTRUCTURES . .

REFERENCES . . . . . .

BIOGRAPHICAL SKETCH . . . .


. . 217


. . 217
. . 224

S. 229

S. 233
. . 237

. . 238

. . 241




. . 244

. . 261

. . 270


. . 278

. . 305

. . 309














Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy



THE DEFORMATION OF GRAINS
DURING COLD-ROLLING

By

Robert A. Ellis, Jr.

August 1980



Chairman: Frederick N. Rhines
Major Department: Materials Science and Engineering



Quantitative metallographic techniques were used to

study the changes in the shapes of the grains in aluminum,

iron, titanium and zirconium samples during cold-rolling.

The grains deformed in much the same way as the bulk

pieces of metal, becoming longer, wider and thinner in

appearance. However, the quantitative measurements

revealed that the deformation of the grains was not

exactly the same as that of the bulk; the measurements

indicated that the grains tended to be shorter, wider and

thicker than expected from the changes in the dimensions

of the bulk samples.

Saltykov's planar-linear structure model was used

with the oriented NL and PA measurements made in this

vii













study to determine the magnitudes of the oriented compo-

nents of the grain boundary surface areas and edge lengths.

Both the grain boundary surfaces and the grain edges

became increasingly oriented with deformation, as was

expected. However, the total values of surface area and

edge length did not increase as rapidly with deformation

as expected.

For the most part, these differences between the

measurements and the expected values appear to be due to

deficiencies in the models used to describe grain defor-

mation. These models are usually based on "average"

grains, each of which deforms in exactly the same way

as the bulk. It is shown that a model in which some

grains deform less than the bulk, while others deform more,

exhibits the same discrepancies in the measurements which

were seen experimentally.

Examination of a set of aluminum samples, using a

technique which allows differentiation between deformed

and undeformed grains, revealed that some of the grains

were indeed undeformed at deformations as high as a 50%

reduction in thickness. Additionally, it was found that

the larger grains in the pieces appeared to be deforming

before the smaller grains. This difference in behavior

between the differently-sized grains can be explained by

viii













the higher resistance to deformation of the smaller grains

because of their higher ratio of boundary area to volume.

The variations in the deformation behavior of the

grains of different sizes apparently were the cause of the

differences between the expected and actual values of the

quantitative measurements. To accurately predict the

values of the measurements, it is necessary to use a

model which reflects these variations, rather than one

based on the behavior of "average" grains.
















CHAPTER I
INTRODUCTION


There have been many studies which examined the

shapes of the grains in a polycrystalline metal. Most

of the studies, especially the earlier ones, were quali-

tative or semi-quantitative. There have been a few

studies, however, which used the quantitative techniques

developed within the last thirty years or so.

In this study, some of these quantitative techniques

were used to examine the changes in the shape of metal

grains which occur during cold-rolling.



The Basics of Quantitative Metallography

In order to understand the work which has been done

on grain shapes, it is necessary to understand the basic

relationships of quantitative metallography and the

measurement techniques used. These are discussed in the

following sections.


Volume Fraction

One parameter often.of interest is the volume fraction

of a feature in the microstructure, say an a-phase. There

are several techniques of measuring this parameter (1,2).













One method, perhaps the simplest, is through the use

of point counting. In this technique, a network of points

is dispersed uniformly over the structure. The number of

points which fall in the a-phase is counted. Then the

grid is repositioned randomly, and the number of points on

the a-phase is counted again. The total number of points

falling on the a-phase is divided by the total number of

points used to give P, the average fraction of the points

falling on the a-phase. (The bar denotes that this is an

average value.) The volume fraction of the a-phase, V ,
-a
is equal to P.

This technique is illustrated in Figure 1. For this

placement of the grid, four out of sixteen grid points

fall in the a-phase and Pp would be 0.25. If this process
--e
were repeated with different grid placements, and p was

found to be 0.25, the value of V" for this structure would

also be 0.25.

There have been other techniques used to determine

volume fraction. Areal analysis, where the area of the

a-phase is measured through use of a planimeter or some

other technique, also yields VV directly. The average
-a a
areal fraction of a-phase, A, is equal to V Volume

fraction can also be measured through lineal analysis,

where a series of test lines are placed on the structure










































Va = 4/16 = 0.25
V


Figure 1. Determination of volume fraction, V c
through point counting. (Shaded grains
are a-phase.)













and the average fraction of line length which falls on the

a-phase, La, is determined. The volume fraction is equal

to LLT

In summary, the relationships for the volume fraction

are


V =P ~ (I-1)
V P A L

It should be noted that the same techniques can be

used to measure the fraction of microstructural features

such as particles, voids, deformed grains, etc.


Surface Area

Another parameter of interest is the surface of some

type of feature per unit volume, SV. For instance, it

has been shown that the hardness of a metal is directly

related to the value of S for the grain boundaries in the

metal (3).

The value of SV, say for grain boundaries in a single-

phase alloy, is measured through use of a test line (1,2).

A test line of length is placed on the structure and the

number of intersections it makes with the grain boundaries,

n, is counted. The test line is then placed again on the

structure randomly and the measurement made again. The













total number of intersections is then divided by the total

line length to give the value NL. It has been shown that
L*

SV = 2NL (1-2)


This technique is illustrated in Figure 2. The 1 cm. test

line makes two intersections with the grain boundaries,
-1
giving a value of NL of 2 cm. If this measurement were
-1
repeated, and it were found that NL were equal to 2 cm.
2 3
then SV would be equal to 4 cm. /cm .

It should be noted that Equation I-2 is based on

averaging the values of NL over all possible orientations

in space. If the structure is not isotropic, and the values

of NL are not measured in all possible orientations,

Equation I-2 would not yield the proper value of SV. Of

course, it is not possible to actually measure NL in all

orientations in three dimensions, but the experimental

technique should be such that the test line orientations

are as random as possible to minimize anisotropy effects.

This technique can be used to determine the surface

areas of other types of microstructural features. For

instance, the amount of interface between the a- and 8-

phases in a structure, SV can be determined by counting

the number of intersections the test lines make with a-B

phase boundaries.







6























1 cm.











-1
NL = 2/1 cm. = 2 cm.
2 3
S = 2 NL = 4 cm. /cm.

S= 1/NL = 0.5 cm.



Figure 2. Determination of surface area, Sv, and mean
free path, T.













Another parameter which can be determined through NL

measurements is X, the mean grain intercept. This quantity

is equal to the average distance between boundaries in the

structure and is given by

1 2_
1 2 (1-3)
NL S

The value of A is not exactly equal to what is

normally thought of as the average grain diameter, d.

The average grain diameter is generally determined from

the maximum or caliper diameters of the grains. For a

structure composed of uniformly-sized spheres of diameter

D, the value of d would be equal to D, while A would be

equal to 2/3D (2). A is lower than d since it is deter-

mined by averaging the lengths of all the chords through

the spheres, which vary in length from 0 to D.

For multiphase structures, values of A can be computed

for each phase, yielding the mean distance across each

phase. In addition, the mean free path, A defined as

the average separation of a8 interfaces in the structure

can be determined (2) by the equation

Ea
1- L (-4)
2L













Edge Length

Another parameter frequently measured is the length

of grain edge per unit volume, LV. This parameter is

determined by placing a grid with area A on a sectioning

plane. The number of triple points which fall within this

area are counted. The grid is moved and the measurement

is made again. The average number of points which fall

within a unit area is denoted by PA. The length of grain

edge per unit volume is given (2) by


V = 2PA (1-5)


This measurement is illustrated in Figure 3. A test
2
grid with an area of 1 cm. is placed on the structure and

four triple points fall within the area, yielding a value
-2

-2
PA were found to be 4 cm. then LV would be equal to

8 cm./cm.

Edge lengths can also be measured in multiphase

structures. For instance, in a two-phase structure, values

of LV could be determined for a-a-a, a-a-f, a-8-r and

B-B-8 edges.


Number of Grains per Unit Area

The number of grains per unit area on a sectioning

plane can be determined in at least two ways (1,2). One













method is to count the number of grains within a given

area (counting grains which cross out of the area as 1/2)

to determine NA directly. A second method is to count the

number of triple points, P, within a given area, A. The

number of grains is given (1) by


-P
N = (-6)
A A

For the example in Figure 3, where P was four and A
2 -2
was 1 cm. NA would be equal to 2 cm. .



Measurements on Anisotropic Structures

The relationships discussed above are based on average

values of the experimentally measured parameters; these

averages are those obtained (theoretically) by making

measurements in all possible directions or on all possible

planes. The same average value of a parameter could be

obtained from both an isotropic and a highly anisotropic

structure. For this reason, additional techniques and

relationships have been developed to quantify the aniso-

tropy present in many structures.


Oriented Measurements

If any of the quantitative measurements previously

discussed are made on a completely isotropic structure,

the values obtained for the measurements made in different







10















1 cm.





1 cm.














P = 4/1 cm. = 4 cm.


-2
Lv = 2P = 8 cm./.cm.

NA = PA/2 = 2 cm.2



Figure 3. Determination of edge length, LV, and number
of grains per unit area, NA.
.A'













orientations will be very similar. However, if the struc-

ture is anisotropic, there can be large differences in

the measurements made in different orientations. This

provides the basis for one technique of quantifying the

anisotropy of a structure: oriented measurements (4).

Oriented NL or PA measurements are made using the

same techniques as before except that the test line or

plane is kept in one particular orientation and just moved

through the structure. After a set of measurements is made

in one orientation, and an average value is obtained, this

process can be repeated using a different orientation of

test line or plane. The result of these measurements is a

table of measured values of NL or PA versus orientation.

The more anisotropic a structure is, the greater the vari-

ation between the measurements made in different orien-

tations.

The relations previously discussed between NL and S

and between PA and LV differ somewhat for oriented measure-

ments (2):


NL(0,9) = SV(e,)lproj (1-7)


where NL(9,4) is the average value of NL measured in a

particular orientation and S (9,I) .pr is the total

projected area of the surfaces onto a plane which is per-

pendicular to the test lines used to determine NL(9,(), and,













PA(8,) = Lv(0,)proj (1-8)

where PA(6,0) is the average value of PA measured in a

particular orientation and Lv(,)) proj is the total pro-

jected length of the edges in the structure onto a line

which is perpendicular to the test planes used to determine

PA( ,1).


Roses of the Number of Intersections

Saltykov (1,2,4) developed a technique to present

oriented NL measurements graphically, making it easier to

visualize the anisotropy in the structure. These graphs

are known as "roses of the number of intersections."

In this representation, the values of NL measured

in different orientations on a test plane are plotted as

a function of orientation on polar co-ordinate paper.

Figure 4 shows what the roses would look like for an

isotropic structure (a series of circles) and a completely

oriented structure (a set of parallel lines). Partially

oriented structures would have roses whose appearance was

somewhere between these two.

Roses can be determined for various sectioning planes

through a structure, yielding a representation of how the

value of NL varies in three dimensions.
JL















(a) Isotropic structure.


(b) Rose for structure
in (a).


(c) Completely oriented
structure.


(d) Rose for structure
in (c).


Figure 4. Examples of roses of the numbers of intersection.


16


(I













The Saltykov Models of Oriented Structures

Saltykov has proposed (1,2,4) that microstructures

can be divided into four basic types, shown in Figure 5.

The first (Figure 5a) is an isometric or isotropic struc-

ture; the second (Figure 5b) is a linear structure

(typical of a drawn structure); the third (Figure 5c) is

planar (as in a pressed structure); and the fourth (Figure

5d) is a planar-linear structure (as seen in a rolled

structure). Since the planar-linear structure is typical

of those seen in this study, it will be discussed in detail

here.

The planar-linear structure can be thought of as

being composed of three types of elements of surface.

The first type of elements are isometric, with normals

oriented in all directions in space; the :second type are

planar, with elements normal to the rolling plane; and the

third type are linear, with normals perpendicular to the

rolling direction. In other words,


(Sv)Total = (SV)iso + (SV)pl + (SV)lin (1-9)

The values of (SV) iso (SV)pl and (SV)lin can be

determined from NL measurements made in the three principal

directions: (NL)Ii in the rolling direction, (NL)I in the

transverse direction, and (NL)i in the rolling plane normal

direction, as shown in Figure 5d. The relationships are:





















Orientation
Axis


(a) Isometric


(b) Linear


Plane Ple
Plane
(c) Planar (d) Planar-Linear

Figure 5. The four general classes of structure proposed
by Saltykov.


(NL)i


(NL


(NL) I I


(PA I I












(S) iso = 2(NL)

(Sv) p= (NL) (NL)

(S) lin- 2 ) I- ( (I-10)

The total oriented surface area,(SV)pl-lin' is equal

to the sum of (Sv)pl and (Svlin

The degree of orientation of the surfaces, w can be

expressed as the percentage of surface area which is planar

or linear or the combined value:


S (S V)p x 100%
pl (SV)total

S (SV)lin
Slin (SV) total x 100%


S (SV pl-lin x 100% (1-)
pl-lin (S) total

The grain boundary edges in the structure can also be

thought of as composed of three types of elements: iso-

metric, lying in all directions in space; planar, lying in

all directions in the rolling plane; and linear, parallel

to the rolling direction. Thus,


(Lv)total = (Lv)iso + (LV)pl + (Lv)lin (1-12)

The values of each of the components of (LV)total can

be determined from PA measurements on the three principal











planes: (PA) i on the rolling plane, (PA)i on the longitu-
dinal plane perpendicular to the rolling plane, and (PA)i

on a transverse plane perpendicular to the rolling plane.
The relationships, determined by Patterson (5), are:

(Lv)iso = 2(PA)

(Lv)pl = 1[ (PA)r-(PA)II]
(V pl 2 A -A^

(Lv) in = (PA) I-(PA) (I-13)

The total oriented edge length, (LV)pl-lin, is equal

to the sum of (Lv)pl and (LV) lin

The degrees of orientation of the edges, w can
be expressed as:

L (L)pl x 100%
pl (LV)total

L (Lv)in
lin =(LV)total

L ( ( pl-lin
L = (Lv)pl-lin x 100% (1-14)
pl-lin (Lv)total

It should be noted that these equations for the planar-
linear structure can be reduced to those derived for the

other structures; for instance, for the planar structure,
a value of zero is substituted into the equations for

(S) lin'













Patterson (5) has derived equations for determining

the values of (Lv)proj in any direction for the planar-

linear structure. The equations for (Sv)proj in any

direction for this structure are derived in Appendix D.


Hilliard's Analysis of Oriented Structures

Recently, Hilliard (6-8) has developed a general

mathematical treatment to specify and determine anisotropy.

To deal with a system of lines in space, a test array of

lines is superimposed on the structure and the number of

intersections counted. Mathematical procedures, including

use of distribution functions and Fourier transformations,

allow the expression of edge lengths as a function of

direction. To treat the surfaces in a structure, a test

array of surfaces is used. For further details, the

original papers should be consulted.


Shape Factors

There are many attempts in the literature to develop

some single parameter which will describe the shape of

the grains in a metal quantitatively. More than a dozen

of these are discussed by Underwood (1,9). In general,

they are based on some combination of the quantitative

metallography parameters discussed above and are often

based on some assumed grain shape (for example, ellipsoids).














According to Fischmeister (10), "there is only one

simple combination of primary stereological data . that

depends exclusively on the shape of the objects studied

in a two-dimensional section and is unaffected by the

volume fraction, size or size distribution of the objects."

This parameter, F, is given by
2 NL2
2 L
F (I-15)
3T- VVNA

These shape factors will not be discussed in detail,

since they suffer from common drawbacks. As previously

mentioned, many are based on assumed grain shapes and

they are generally based on measurements made on two-

dimensional sections through the structure and, therefore,

do not really describe the three-dimensional structure.



The Shapes of Metal Grains

Several different techniques have been used to examine

the shapes of grains in metals (generally in a relatively

equiaxed, recrystallized condition).

Various investigators have separated the grains in

the metal by embrittling the grain boundaries or infil-

trating a liquid metal down them. Desch (11) examined

the faces of grains from a disintegrated brass and.an

embrittled chromium steel. He found that the grains tended

to approximate.pentagonal dodecahedrons with curved faces













and edges. He later noted (12) that for B-brass the number

of faces per grain ranged from 11 to 20, with 3 to 8 edges

present per face. Similar methods have been used by Hull

(13) and Smith (14) to study the grains in brass. Patterson

(5) separated grains in aluminum with liquid gallium and

examined the distributions of grain volume, the number of

faces per grain and the number of edges per grain. He

found that all three of these distributions were log-

normal and that the number of faces and edges a grain

had was directly proportional to its volume, which had

previously been reported by Williams and Smith (15). The

mean number of faces per grain was between 12 and 13.

It is interesting to note that the shapes of metal

grains are very similar to those found in plant cells (16),

human fat cells (17), and foams (11). Smith (18) has

summarized the literature dealing with extracted grains

and cells. This appears due to the fact that the same

driving force (minimization of surface energy) is present

in each case (19).

It has also been possible to study the shapes of some

grains and cells without having to separate them. Investi-

gations of this type have been conducted by Matzke and

Nastler (20) on froths, by Matzke on vegetable cells and

soap bubble arrays (21) and by Williams and Smith (15) on













an aluminum-tin alloy (microradiography was used to reveal

the shape of the grain boundary phase present).

Examination of the results of these studies (1)

indicates that the distribution of faces per grain and edges

per face lies somewhere between those for a pentagonal

dodecahedron and the g-tetrakaidecahedron proposed as a

grain model by Williams (22). For this reason, the penta-

gonal dodecahedron and the tetrakaidecahedron are often

considered as models for the average grain in the structure.

Another method used to examine grain shapes is serial

sectioning, which consists of taking successive cuts

through the structure. Photographs of the various

sectioning planes can be used to build models of the

structure, as was done by Hopkins and Kraft (23)', or

quantitative measurements can be made on each plane

through the structure. Scheil (24) and Scheil and Wurst

(25) may have been the first to use this technique to

obtain grain size distributions in ingot iron by measuring

the area of each grain on successive sections. More

recent studies have used serial sectioning techniques to

obtain the topological parameters in the structure, such

as the number of edges, faces, corners, as well as grain

volumes, edge lengths, and so on. Papers by Steele (26)

and Kronsbein and Steele (27) describe the techniques in

detail. Craig (28) used serial sectioning to study the













evolution of the grain structure during grain growth; these

results were the basis of a grain growth model developed

by Rhines and Craig (29). The information on grain shape

obtained through serial sectioning techniques agrees with

that obtained in previous studies where the grains were

separated.



Models of Grain Shape

Models of grain structures used to predict or

explain quantitative measurements generally treat the

grains as all being of one size and shape. Common shapes

used to describe isotropic structures are cubes (30) and

spheres (24,31). DeHoff (32) has developed a model using

tetrakaidecahedra to represent the grains; this-shape, as

discussed previously, is similar to the average grain shape

seen in metals.

Deformation of the grain can be modeled by changing

the relative lengths of the axes: a cube becomes a

rectangular parallelopiped, a sphere becomes an ellipsoid

and an equiaxed tetrakaidecahedron becomes nonequiaxed. It

is generally assumed (33) that the relative changes in the

length of the axes should be the same as that of the bulk

piece of metal; for example, the height of the grains in a

piece of metal rolled to 50% reduction in thickness should

be half of that in the undeformed material.













For these various models, it is possible to calculate

what the values of the quantitative parameters would be

and how they would change with deformation.



Quantitative Studies of Deformation

There have been several studies which have quantified

the change in shape of metal grains during deformation.

Tafel and Scholz (31) studied the change in shape

of iron grains in tensile samples. They measured the

lengths of the three major axes of the grains to derive

average values, which they corrected to take into account

the fact that the grains are not always sectioned through

their widest points. They found that the deformation of

the grains varied with both radial and axial position in

the bar. The lowest deformations occurred near the

surfaces of the bars and near the grips. On the average,

the grains deformed less than the samples, which was

contrary to their expectations. They attributed this to

the occurrence of grain boundary sliding, contributing up

to 30% of the radial strain. However, since these tests

were not at elevated temperatures, this explanation does

not seem tenable (see the next section on grain boundary

sliding).

Scheil (24) measured the axial ratios of the ferrite

grains seen on sectioning planes through ingot iron samples.













From frequency distributions of these ratios, he deter-

mined the average axial ratio for the grains at different

amounts of rolling deformation. These axial ratios

tended to be lower than the equivalent specimen axial

ratios, by as much as 20% at higher deformations. He

could not explain this discrepancy.

Perhaps the best known study was performed by

Rachinger (33) on aluminum grains deforming in tension.

He determined the values of NL in the longitudinal and

transverse directions in the samples after 50% elongation,

and calculated the average strain in the grains from

these. The results obtained indicated that the grains

deformed by the same amount as the sample at room

temperature or when strained at a high rate at elevated

temperature. However, when the samples were strained

at a slow rate at temperatures of 2000C or more, the

strain in the grains was much less than that of the sample.

He attributed these discrepancies to grain boundary

sliding and performed additional studies to prove

that this was so. Grid lines scratched on the sample

surfaces and internal oxide markers both showed jumps

at grain boundaries after high temperature, slow strain

rate tests, showing that grain boundary sliding actually

was occurring. Since the sample deformation under

these conditions could be accomplished by moving













the grains relative to each other, instead of deforming

the grains, the strain in the grains was lower than the

strain for the sample.

Thomas et al. (34) measured the values of NL on

longitudinal sections through Ferrovac E samples which

were either drawn or swaged. They found that the value of

NL for both structures was that expected from the specimen

shape change up to about 60% reduction of area; at higher

reductions, both structures had higher NL values than

expected, with the values for the swaged structure higher

than those for the drawn. They attributed this discrep-

ancy to the difficulty of telling the difference between

the grain boundaries and deformation bands at higher

reductions, and the fact that the grains became-wavy,

allowing them to be counted more than once on a sectioning

plane.

Braun (35) measured the anisotropy present in

several cold-worked metals and alloys. He expressed the

anisotropy in terms of a parameter he developed, a, which

is based on the axial ratio of the grains. Instead of

actually measuring the grains and calculating a in each

case, he employed a comparison grid showing structures

with different values of a, similar to the ASTM grain

size grids.













Dunne and Dunlea (36) have applied Saltykov's

planar-linear model to study the grain shape anisotropy

in cold-rolled and recrystallized steel. They found

that the values of NL in the principal directions varied

as would be expected from the bulk deformation up to about

50% reduction of thickness. Above this reduction, the

grains elongated less than the bulk, "indicating that

other processes, as well as grain elongation, are

associated with the bulk shape change." They noted that

the degree of orientation, wSl-lin, approached a limiting

value of approximately 80% at high reductions. When the

cold-rolled samples were annealed, they still retained

much of the lath-like anisotropy seen in the rolled

structure. When cross-rolled samples were annealed,

they were found to have pancake-shaped grains similar to

those seen in the deformed structure.



Grain Boundary Sliding

As mentioned before, one possible explanation for

the strain in the grains of metals being lower than the

strain of the bulk specimen is that grain boundary sliding

is occurring. In this mode of deformation, the change in

shape is accomplished by the relative motion of grains past

each other, with little or no change in shape of the

grains themselves.














This type of behavior is common only at relatively

high temperatures (generally greater than half of the

melting point), which is why the discrepancies seen by

Tafel and Scholz (31) at room temperature in iron were

probably not due to grain boundary sliding. For example,

grain boundary sliding is common in high-temperature

creep of aluminum (37), but does not occur to any signif-

icant amount below about 2000C (38). (However, studies

using a tensile stage in a transmission electron micro-

scope (39) have shown that a small amount of sliding can

occur even at room temperature.) Sliding is also more

common at lower strain rates.

The details of the grain boundary sliding process

will not be discussed here; a comprehensive review has been

prepared by Bush et al. (40).
















CHAPTER II
EXPERIMENTAL TECHNIQUES


The experimental techniques used in this study were

varied, since the basic procedure had to be modified for

each of the four materials--aluminum, iron, titanium and

zirconium--which were used. Those techniques which

were the most widely used are discussed in this chapter,

while those used for special experiments are discussed

where appropriate in later chapters.



Metallographic Sample Preparation

Aluminum

For several reasons, high-purity aluminum was chosen

as the face-centered cubic material to be studied: it

has a single-phased structure which forms few annealing or

deformation twins; it is easily worked and heat treated;

it is relatively easily prepared for metallography; and

its structure can be delineated clearly through use of an

anodized coating and polarized light.

The aluminum used for the samples was taken from

twenty-five pound pigs, intended as remelt stock. The

analysis of the pigs was reported (41) to be:













Al 99.9980 w/o

Si 0.0003 w/o

Fe 0.0009 w/o

Cu 0.0001 w/o

Mg 0.0005 w/o

Ca 0.0002 w/o

Since the cast structure consisted of huge grains

with considerable porosity, it was necessary to refine the

grain size and weld the pores shut through cycles of

working and annealing. Due to the purity of the aluminum,

it would recrystallize on working at room temperature;

therefore, cold-working had to be performed at liquid

nitrogen temperature (-1960C).

Five different sets of samples were prepared, each of

which received a slightly different treatment to break

down the cast structure.

Treatment 1. This treatment began with a 4 in. x

1.5 in. x 0.9 in. block of aluminum, which was rolled

to a 50% reduction of thickness at room temperature and

annealed at 6200C in a circulating air furnace for 30

minutes. The block was then rolled another 50% at liquid

nitrogen temperature and annealed in a salt bath at

62520C for 2 minutes. Half of the block was kept to

prepare metallographic specimens in the annealed














condition; the other half was rolled an additional 50%

at liquid nitrogen temperature.

As will be discussed in more detail in Chapter III,

the annealed structure obtained with Treatment 1 was

far from equiaxed. Since an equiaxed annealed structure

was preferable, a different method of working, similar

to one used to get equiaxed grains in copper (42), was

used in Treatments 2 through 5.

Treatment 2. This treatment consisted of cutting

a block of cast aluminum into six 1 in. x 1 in. x 1 in.

cubes. Each of these cubes was compressed 25% along one

axis at room temperature in a hand-operated hydraulic

press, rotated 90 and compressed 25% along another

axis, and then compressed along the third axis until it

was roughly the original size and shape. Oil was used

as a lubricant between the press faces and the cubes to

minimize barreling. The cubes were then annealed in the

circulating air furnace at 630C for 30 minutes. The

compression along the three perpendicular axes was

repeated, at liquid nitrogen temperature this time. Each

cube was then annealed separately in the salt bath at

6252C for 2 minutes. One cube was kept to prepare

metallographic samples; the others were rolled at liquid

nitrogen temperature to 10, 25, 50, 60 and 75% reduction

of thickness.














Treatments 3 through 5. Each of these treatments

began with a 1 in. x 1 in. x 2 in. piece of cast aluminum.

These pieces underwent the same two cycles of compression

and annealing as the cubes in Treatment 2 except that the

final annealing times were 3 minutes for Treatment 4 and

4 minutes for Treatment 5. After the final anneal, part

of the block was cut off. Then the rest was rolled 10%,

another piece was cut off, and so on, to yield specimens

of 0, 10, 25, 50, 60 and 75% reduction.

All of the deformed material, including mounted

metallographic samples, was stored in a freezer to

minimize the effects of recovery and recrystallization

that could occur at room temperature.

For each reduction in each treatment, metallographic

samples were prepared whose faces were parallel to the

longitudinal, transverse and rolling planes. In addition,

for Treatment 2, samples were prepared of planes

perpendicular to the rolling plane, at 30 and 600 from

the transverse direction (see Figure 6).

Samples were identified by the treatment number, the

amount of reduction, and the sectioning plane.

The sectioning planes were denoted by an "L," a "T"

or an "R," which indicated, respectively, that the

sectioning planes were parallel to the longitudinal,

transverse or rolling planes, or by a "30" or a "60,"























Rolling Direction


30 60


Figure 6. Sectioning planes used.













which meant the sectioning plane was 30 or 600 from

the transverse plane. For example, a designation of

2-50-30 would be used to identify a sample which had

undergone Treatment 2 before rolling, had been reduced

50% in rolling, and was sectioned on a plane perpendicular

to the rolling plane and 300 from the transverse plane;

the designation 4-25-T would be used for a sample which

had undergone Treatment 4 before rolling, had been

reduced 25% in rolling, and was sectioned parallel to the

transverse plane.

The metallographic samples were mounted in Caulk

NuWeld, a cold-setting plastic used for making denture

bases, to avoid recrystallization due to the high tempera-

tures and pressures used in mounting samples in a thermo-

setting plastic, such as Bakelite. Holes were drilled

through the backs of the mounts and screws put in to

provide electrical contacts for the anodizing process.

The specimens were ground on 120, 180, 320 and 600

grit SiC paper, using water and liquid hand soap as

lubricants. They were then ground on 600 Soft Microcut

paper, with kerosene as the lubricant. This greatly

reduced the required polishing time. Rough polishing

was done on a billiard cloth using a slurry of 1200 grit

emery powder in water, with hand soap as a lubricant

during the later stages of the polishing. Final polishing













was done on a Microcloth using a slurry of 3200 grit

emery in water, with hand soap as the lubricant.

To prevent changes in the microstructure of the

deformed samples during preparation, they were alternately

ground or polished and immersed in an ice water bath to

keep them cold.

Since most etchants will not delineate the structure

of high-purity aluminum well, an anodizing process was

used instead. When viewed under polarized light, the

grains show up in different shades of gray, depending

on their orientation. Essentially all of the grain

boundaries can be seen, since, by rotating the stage

slightly, the shades of the grains are changed and

boundaries which were not evident before become clear.

Very small orientation differences (such as those between

subgrains) can be seen. In addition, annealed grains

are one shade of gray throughout and change color

uniformly across the grain as the stage is rotated;

deformed grains show color gradients across them and do

not change color uniformly as the stage is rotated.

Anodizing was done using an electrolyte consisting

of 33 ml. of hydrofluoric acid and 13.6 gm. of boric acid

in enough water to make a liter of solution. A graphite

cathode was used. With a specimen-to-cathode distance

of 1 in. and a voltage of 20 V, the process took 1 to













1 1/2 minutes. Stirring was necessary, but could not be

too violent or swirling patterns formed across the sample

surface. All of the anodizing solution had to be care-

fully rinsed from the sample before drying to prevent

attack of the anodized film by residual hydrofluoric

acid.

If it was necessary to repolish an an anodized speci-

men, the polishing time could be greatly reduced by removing

most of the oxide first by immersing the sample for one

minute in a solution of 5 ml. of hydrofluoric acid in

100 ml. of water.


Iron

The body-centered cubic material used in this study

was Armco iron. It was chosen because it is (essentially)

a single-phase structure which does not form any appre-

ciable number of deformation or annealing twins, it is

easily worked, and it is easy to prepare for metallographic

study.

The iron was obtained as hot-rolled 3 in. x 12 in. x

0.4 in. strips. There was no analysis available for this

lot, but it is thought to approximate the standard

analysis (43), which is:













Fe 99.96 w/o

C 0.012 w/o

P 0.005 w/o

S 0.025 w/o

Si Trace

The only preparation necessary before the final

rolling was removal of surface oxide by pickling in

dilute hydrochloric acid.

After a piece was cut from the strip, the rest was

rolled at room temperature, with pieces being cut off at

25, 50, 60 and 75% reduction.

Metallographic specimens sectioned parallel to the

longitudinal, transverse and rolling planes were prepared

for each reduction. These were identified in the same

manner as the aluminum samples, with an "Fe" for iron

replacing the treatment number; for example, a designation

of Fe-10-R would be used for an iron sample which had

been reduced 10% during rolling and was sectioned parallel

to the rolling plane. Bakelite was used as the mounting

material.

The samples were ground on 120, 180, 320 and 600 grit

SiC papers, using water and hand soap for lubricants. The

rough polishing was done on a Microcloth with 6 p diamond

paste, using Metadi fluid as the lubricant. Final

polishing was done on a Microcloth with 1 p (heavy)













diamond paste, using Metadi fluid as the lubricant. The

only special precautions necessary during polishing were

to dry the samples well between steps and to store them

in a desiccator to prevent rusting.

The structure was delineated by etching with 2%

Nital. To show up all of the grain boundaries, it was

often necessary to overetch the samples.


Titanium

One of the hexagonal close-packed materials

examined was high-purity titanium. It was obtained in

the form of rolled strips of varying lengths, with a

thickness of 0.32 cm. and a width of 1.53 cm. The purity

was 99.99% with 0.01% of unknown impurities.

Since the structure was very fine, the material was

annealed for a long time to increase the grain size after

recrystallization. Annealing was done in a circulating

air furnace at 6700C for 6 hours. Except for a surface

layer of oxide, there were no apparent ill effects from

annealing in air instead of the usual vacuum, no second

phase (oxide or hydride) was observable within the

sample, and the ductility was very good. It has been

suggested (44) that this type of heat treatment would

produce an oxygen-rich layer lying immediately beneath

the oxide, and that this layer would not deform in the













same manner as the bulk of the sample, resulting in

nonuniform deformation. However, the samples do not

show any obvious difference in structure between the

center of the strip and the outside. The surface oxide

layer was easily removed by pickling in a solution of

10 ml. nitric acid and 90 ml. hydrofluoric acid. This

pickling treatment may also have reduced the thickness

of any oxygen-rich layer that was present, decreasing

any influence it would have had on the deformation

process.

The strips were then rolled at room temperature with

pieces being cut off at 0, 10, 25, 50, 60 and 75% reduc-

tion. Metallographic samples were prepared of the

longitudinal, transverse and rolling planes from each

reduction. These were identified as before; for example,

a designation of Ti-50-L would be used for a titanium

sample which had undergone a 50% reduction during rolling

and was sectioned parallel to the longitudinal plane.

It was necessary to mount the samples in Plastimet,

a very hard thermosetting plastic. Otherwise, the mount

would polish away much faster than the titanium, resulting

in a rounded surface.

The laboratory-built automatic grinding and polishing

apparatus shown in Figure 7 was used to prepare six

samples at a time. Grinding was done on 120, 180, 320






























(a) Complete apparatus.


(b) Close-up of sample holder with six samples.

Figure 7. Automatic polishing apparatus.













and 600 grit SiC papers (30 minutes for each grit size)

with running water as the lubricant. Polishing was done

on Microcloths using 1 p and 0.3 p alumina (2 hours with

1 p, 1 hour with 0.3 p). The alumina was applied as a

very dilute water slurry which was continuously dripped

from a pitcher onto the wheel. A magnetic stirrer in the

pitcher kept the alumina in suspension.

The samples were then etched for 10 seconds with a

solution of 10 ml. hydrofluoric acid, 5 ml. nitric acid

and 85 ml. water. After etching, they were repolished

with 0.3 p alumina, then re-etched for 25 seconds. This

etching and repolishing step was necessary to remove the

disturbed layer present and reveal the true structure.


Zirconium

There were several problems which appeared in using

the titanium (which will be discussed in detail in

Chapter III). It was suggested (44) that they could be

avoided by using commercial-purity zirconium, rolled at

1000C. This was obtained as large, half-inch thick,

cold-rolled flats, from which a 3 in. x 6 in. piece was

cut for use in this study. The composition of commercial-

purity zirconium.is (45):













Zr 97.88%

Hf 1.90%

O 0.07%

C 0.15%

The zirconium was annealed for 6 hours at 6700C in a

circulating air furnace.

The block was kept at 1000C during rolling by immer-

sion in a boiling water bath between passes. Pieces

were cut off at 0, 10, 25, 50, 60 and 75% reduction.

Metallographic samples were prepared with sectioning

planes parallel to the longitudinal, the transverse and

the rolling planes. These were identified as before;

for example, a designation of Zr-75-T would indicate a

zirconium sample which had been reduced 75% during rolling

and was sectioned on a plane parallel to the transverse

plane. Diallyl phthalate, a fairly hard thermosetting

plastic, was used as the mounting material.

The automatic polisher was used for these samples,

with the same grinding and polishing schedule as for the

titanium. It was not necessary to etch and repolish the

samples, since the etchant used was also a chemical polish

and removed the disturbed layer.

This etchant was a solution of 10 ml. hydrofluoric

acid, 45 ml. nitric acid and 45 ml. water, applied by

swabbing for 30-60 seconds. To avoid staining of the













sample, the swabbing had to be continued under the rinse

water until all of the etchant was washed off. This

etchant left an optically active coating which behaved

the same way as the anodized coating on the aluminum

(except that it was in shades of brown instead of gray).

However, the experimental results, which will be discussed

in detail in Chapter III, indicate that this coating

may not be as sensitive to small orientation differences

as the anodized coating on the aluminum samples.



Quantitative Metallography

There were two principal quantitative measurements

made on these samples. The first was the oriented NL

count, which is a count of the number of intersections

per unit length of test line that the grain boundaries

make with test lines placed on the structure in specific

orientations. The second was a count of the number of

grain boundary triple points per unit area of sectioning

plane, PA. These were discussed in detail in Chapter I.

A Bausch and Lomb Research II metallograph was used

for all measurements. This provided the polarized

light needed for counting the aluminum and zirconium

samples, as well as the bright-field illumination used for

the iron and titanium. Also, the metallograph had a













rotating stage indexed in 10 increments which facilitated

the making of the oriented NL counts.

The intersection counts were done using a test line

reticule in the metallograph. The magnification was

adjusted to give approximately 10 intersections with

grain boundaries per test line length. With 30 placements

of the test line, this magnification usually yielded a

coefficient of variance of less than 5%. For the iron

and the titanium, this was at 600X; for the zirconium,

it was at 400X. All of the aluminum specimens were

counted at 50X, although the number of intersections was

below 10 for many samples, since this was the minimum

magnification available. At each magnification, the

test line length was measured using a ruled slide.

For Treatments 1 and 2 of the aluminum, NL counts

were done at each 150 of orientation on the sample faces.

This was accomplished by aligning a reference direction

(e.g., the transverse direction) on the sample with the

test line and setting the index of the rotating stage on

00. The test line was then placed at 30 different

positions on the sample, and the number of intersections

with grain boundaries counted. The stage was then rotated

150, and the process repeated. Due to symmetry, it was

only necessary to make measurements through 90 of arc

on each specimen.













To minimize sampling bias, the placements of the

test line were spaced as uniformly as possible over the

central area of the specimen. Edges were avoided to

prevent surface effects from influencing the results;

however, this was probably not necessary, since a com-

parison with measurements made using the whole surface

of the specimens did not produce any statistically

significant results.

The samples of the aluminum from Treatments 3 through

5, the iron, the titanium and the zirconium, were measured

in a similar way, except that NL counts were made only in

the rolling direction, the transverse direction and the

rolling plane-normal direction.

The orientations of the counts were expressed with

reference to the transverse direction and the rolling

plane through use of the two angles, 8 and (, shown in

Figure 8. The angle 6 increased from 00 in the trans-

verse direction to 900 in the longitudinal direction; the

angle ( increased from 0 in the rolling plane to 900 in

the rolling plane-normal direction. As an example, an NL

count taken on specimen 2-10-30 (0 = 300) at 450 from the

rolling plane (4 = 450) would be referred to as NL (300,

450); one taken on 2-10-R (( = 00) in the rolling direction

(6 = 90) would be expressed as NL (900, 00).








































Figure 8. Angles used to describe orientation of test
lines.













The triple point counts were done using a square

grid in the metallograph eyepiece as the test area. This

test area was placed uniformly at 30 positions over the

central area of the specimen, and the number of triple

points within the area was counted. The size of the test

area was measured using the ruled slide at each magni-

fication.

When the aluminum and zirconium samples were counted,

it was often necessary to rotate the stage some to show

up all of the grain boundaries. The index lines on the

stage were used to return it to the proper orientation

before the actual measurement was made.



Bulk Deformation Samples

In order to compare the deformation of the grains

to that of the bulk samples, it was necessary to measure

how the height, width and length of the bulk sample

changed with deformation. Since this could not be done

on the same pieces used for the metallographic specimens,

another set of blocks was prepared, one for each material,

that had received the same pre-annealing treatment

(Treatment 2 for the aluminum).

After the original dimensions were measured, the

blocks were rolled 5% under the same conditions as













before. The new dimensions were recorded, the blocks

rolled another 5%, and so on, up to 80% reduction.

There were two problems encountered during this

procedure. First, the length was sometimes hard to

measure due to the fact that the samples did not always

stay flat at higher reductions. This problem was solved

by dividing the original volume by the height and width

at that reduction and using this as the length. The

second problem was barreling of the aluminum samples.

The other materials exhibited very slight amounts of

convex barreling; the aluminum showed greater (although

still not very large) amounts of concave barreling

(Figure 9). Therefore, the widths of the aluminum

sample were taken as the average value over the contour.

























(a) Convex.


(b) Concave.


Figure 9. Barreling during
perpendicular to


rolling. (Sectioning plane
rolling direction.)
















CHAPTER III
OBSERVATIONS AND RESULTS


As a piece of metal is rolled, it is compressed

perpendicular to the rolling plane and is elongated in

the rolling direction and, to a lesser extent, in the

transverse direction. This change in shape is accom-

plished by deformation of the grains within the piece.

It is generally assumed (33) that, unless grain

"boundary sliding" occurs, each of the grains in the

piece of metal deforms in the same manner as the bulk;

for example, if the length of the bulk sample increases

by a factor of 2, the length of each grain also increases

by a factor of 2 and the value of NL in the rolling

direction decreases by a factor of 2. Also, the grains

are assumed to retain the same positions relative to

each other, so that the number of grains on any given

cross-section remains constant.

The results of this study indicate that this is not

true for cold-rolled aluminum and iron (the results for

titanium and zirconium are questionable, due to problems

encountered with these microstructures). At reductions

as high as 50%, some of the grains appeared still to be

undeformed. The NL measurements indicated that the













grains elongated less than the bulk sample in the rolling

direction, elongated more than.the bulk sample in the

transverse direction, and were compressed less than the

bulk sample in the rolling plane-normal direction. Also,

fewer grains appeared on longitudinal and transverse

sectioning planes thanwere expected, while more appeared

on rolling plane sections. In spite of all this, there

was no sign of any significant amount of grain boundary

sliding, as indicated by internal markers.

The deformation of the grains, therefore, was the

same as the bulk sample only in a gross sense; that is,

both tended to become longer, wider and thinner with

reduction. They were quite different individually.



Changes in the Appearance of the Microstructures

During rolling, the microstructures of all the

materials changed greatly. The shape of the grains

changed from equiaxed to greatly elongated and flattened,

as expected. Various types of deformation structures

appeared within the grains, including deformation twins

for the hexagonal close-packed metals. However, the

deformation was not uniform, as had been expected; there

were large differences in the deformation of adjacent

grains, and deformation gradients could be observed even














within individual grains. The rest of this section dis-

cusses the changes in microstructure observed for each

material.


Aluminum

The microstructures of the "Treatment 2" aluminum

samples are shown in Figures 10 through 15.

The grains in the undeformed samples (Figure 10) were

relatively equiaxed and did not appear to be of widely

differing sizes. Each grain anodized to one uniform

color, confirming that it was undeformed.

The microstructural appearance of the samples that

had been reduced 10% (Figure 11) was indistinguishable

from that of the undeformed samples. Most of the grains

still appeared to be equiaxed, and only a few grains

showed the nonuniformity of color that is associated

with deformation.

Many more grains appeared to be deformed in the

samples that had been reduced 25% (Figure 12). The

grains which showed signs of deformation often appeared

to be the larger grains present on the section. A flat-

tening and an elongation of the grains were beginning to

become apparent.

By 50% reduction (Figure 13), almost all of the

grains were deformed, with only a few small undeformed


















































(a) Transverse section. Transverse direction is hori-
zontal. 50X.

Figure 10. Microstructure of aluminum specimens from
Treatment 2, no reduction.






























(b) Longitudinal section. Rolling direction is hori-
zontal. 50X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 50X.


Figure 10. (continued)


















































(a) Transverse section. Transverse direction is hori-
zontal. 50X.

Figure 11. Microstructure of aluminum specimens from
Treatment 2, 10% reduction.





























(b) Longitudinal section. Rolling direction is hori-
zontal. 50X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 50X.


(continued)


Figure 11.


















































(a) Transverse section. Transverse direction is hori-
zontal. 50X.

Figure 12. Microstructure of aluminum specimens from
Treatment 2, 25% reduction.






























(b) Longitudinal section. Rolling direction is hori-
zontal. 50X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 50X.


(continued)


Figure 12.


















































(a) Transverse section. Transverse direction is hori-
zontal. 50X.

Figure 13. Microstructure of aluminum specimens from
Treatment 2, 50% reduction.






























(b) Longitudinal section. Rolling direction is hori-
zontal. 50X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 50X.


(continued)


Figure 13.


















































(a) Transverse section. Transverse direction is hori-
zontal. 50X.

Figure 14. Microstructure of aluminum specimens from
Treatment 2, 60% reduction.






























(b) Longitudinal section. Rolling direction is hori-
zontal. 50X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 50X.


(continued)


Figure 14.


"RAW"



















































(a) Transverse section. Transverse direction is hori-
zontal. 50X.

Figure 15. Microstructure of aluminum specimens from
Treatment 2, 75% reduction.







63






















(b) Longitudinal section. Rolling direction is hori-
zontal. 50X.

























(c) Rolling plane section. Rolling direction is hori-
zontal. 50X.


(continued)


Figure 15.













grains apparent.* The grains had definitely become

elongated and flattened.

No undeformed grains could be seen in the samples

reduced 60 and 75% (Figures 14 and 15). The trend to

becoming elongated and flattened continued, resulting in

very long, wide, thin grains.

Examination of the microstructure of individual

grains revealed an inhomogeneity of deformation within

the grains themselves. At lower reductions, a grain

often appeared undeformed over most of its area and

highly deformed over a small area. The highest deforma-

tion gradients were often adjacent to grain boundaries

and triple points (see Figure 16), implying that the

deformation of a grain is influenced by the neighboring

grains. No subgrains were observed, but the grains in

highly deformed samples often showed a "blocky" appear-

ance, suggesting the presence of diffuse dislocation

arrays which might have sharpened into subgrain boundaries

if the deformation had been at a higher temperature.

The microstructures of the samples from Treatments 3

through 5 were indistinguishable from those of Treatment 2.



*It is probable that the number of undeformed grains is
higher than would be estimated from examination of these
photographs, since the probability of a small grain ap-
pearing on any given cross-section is very low.





























(a) At triple points. 200X.


(b) At grain boundary. 100X.

Figure 16. Deformation gradients within grains of
"Treatment 1" aluminum samples with 50%
reduction in thickness.













The samples resulting from Treatment 1 differed only in

that the undeformed grains were much wider and longer

than they were thick.


Iron

The microstructures of the iron samples are shown in

Figures 17 through 21.

Although the crystal structures of the aluminum and

the iron are different, their grains were of almost

identical appearance throughout deformation.

It was not possible to tell directly whether the

iron grains had deformed, as it was for the aluminum,

where polarized light is effective. However, some of the

deformed grains did show some type of internal features

upon etching, presumably as a result of etching at the

dislocations present in the deformed structure; the per-

centage of these grains may be assumed to be related to

the number of deformed grains present. It could be seen

that the percentage of these grains increased with defor-

mation. This implies that the number of deformed grains

increased with deformation, as in the case of aluminum.



















































(a) Transverse section. Transverse direction is hori-
zontal. 400X.

Figure 17. Microstructure of iron specimens, no reduc-
tion.






























(b) Longitudinal section.
zontal. 400X.

























(c) Rolling plane section.
zontal. 400X.

Figure 17. (continued)


Rolling direction is hori-


Rolling direction is hori-



















































(a) Transverse specimen. Transverse direction is hori-
zontal. 400X.

Figure 18. Microstructure of iron specimens, 25% reduc-
tion.































(b) Longitudinal section.
zontal. 400X.


Rolling direction is


(c) Rolling plane section. Rolling direction is hori-
zontal. 400X.


Figure 18. (continued)


hori-



















































(a) Transverse section. Transverse direction is hori-
zontal. 400X.

Figure 19. Microstructure of iron specimens, 50% reduc-
tion.





















7
- -^^-^'^
F 7 .-*i < '-c.--


(b) Longitudinal section.
zontal. 400X.


(c) Rolling plane section.
zontal. 400X.


Rolling direction is hori-


Rolling direction is hori-


(continued)


Figure 19.



















































(a) Transverse section. Transverse direction is hori-
zontal. 400X.

Figure 20. Microstructure of iron specimens, 60% reduc-
tion.































(b) Longitudinal section. Rolling direction is hori-
zontal. 400X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 400X.


(continued)


Figure 20.



















































(a) Transverse section. Transverse direction is hori-
zontal. 400X.

Figure 21. Microstructure of iron specimens, 75% reduc-
tion.


















*- .








'C-




--rs~ c --. -

_` - --'-


(b) Longitudinal section.
zontal. 400X.


Rolling direction is hori-


(c) Rolling plane section. Rolling direction is hori-
zontal. 400X.


Figure 21. (continued)













Titanium

The appearance of the deformed titanium microstruc-

tures was very different from those of the aluminum and

iron.

The undeformed structure was relatively equiaxed, as

can be seen in Figure 22. With as little as 10% reduction,

large numbers of twins had appeared (Figure 23). The

number of twins had increased greatly by 25% reduction

(Figure 24). These twinned grains often appeared in

"clumps," with the twin boundaries seemingly continuous

across the grain boundaries, making it impossible to

tell exactly where the grain boundaries occurred. By

50% reduction (Figure 25), the structure had become so

distorted that the grain boundaries could no longer be

seen clearly.

The scatter of the quantitative results for the

titanium samples, discussed later in this chapter, is

probably due to the difficulty in determining the

position of the grain boundaries in twinned areas. No

counts could be made on the most highly deformed samples,

due to the lack of obvious grain boundaries.


Zirconium

It was necessary to minimize the amount of twinning

to examine the grain structure of a deformed hexagonal



















































(a) Transverse section. Transverse direction is hori-
zontal. 300X.

Figure 22. Microstructure of titanium specimens, no
reduction.






























(b) Longitudinal section. Rolling direction is hori-
zontal. 300X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 300X.


Figure 22. (continued)




















































(a) Transverse section. Transverse direction is hori-
zontal. 300X.

Figure 23. Microstructure of titanium specimens, 10%
reduction.































(b) Longitudinal section. Rolling direction is hori-
zontal. 300X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 300X.


(continued)


Figure 23.



















































(a) Transverse section. Transverse direction is hori-
zontal. 300X.

Figure 24. Microstructure of titanium specimens, 25%
reduction.






























(b) Longitudinal section. Rolling direction is hori-
zontal. 300X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 300X.


(continued)


Figure 24.



















































(a) Transverse section. Transverse direction is hori-
zontal. 300X.

Figure 25. Microstructure of titanium specimens, 50%
reduction.






























(b) Longitudinal section. Rolling direction is hori-
zontal. 300X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 300X.


Figure 25. (continued)













close-packed metal. This was done by using commercially

pure zirconium, rolled at 1000C. Although twinning still

occurred, the amount was minimal.

In general, the microstructures of the deformed

samples were very similar to those observed in aluminum

and iron, with the addition of some twinning. These

microstructures may be seen in Figures 26 through 31.

At higher reductions, there often appeared to be a

number of deformed grains present which were much larger

than the rest of the grains. As discussed in a later

section of this chapter, these large grains were probably

actually several smaller grains of almost identical

orientation.



Roses of the Number of Intersections

The deformation of the grains in three dimensions

was studied quantitatively through the use of Saltykov's

"roses of the number of grain boundary intersections."

determined on several sectioning planes for each reduction

of thickness. These roses are polar plots of the oriented

NL measurements discussed in Chapters I and II. They give

an indication of how the dimension of the average grain in

a specified direction changes with deformation. The

higher the NI count, the smaller the dimension of the

average grain in that direction.













































AIAL-


(a) Transverse section. Transverse direction is hori-
zontal. 200X.

Figure 26. Microstructure of zirconium specimens, no
reduction.






























(b) Longitudinal section. Rolling direction is hori-
zontal. 200X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 200X.


(continued)


Figure 26.



















































(a) Transverse section. Transverse direction is hori-
zontal. 200X.

Figure 27. Microstructure of zirconium specimens, 10%
reduction.






























(b) Longitudinal section. Rolling direction is hori-
zontal. 200X.


(c) Rolling plane section. Rolling direction is hori-
zontal. 200X.


(continued)


Figure 27.



















































(a) Transverse direction. Transverse direction is'hori-
zontal. 200X.

Figure 28. Microstructure of zirconium specimens, 25%
reduction.




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