Title: Structural evolution in nickel during annealing subsequent to hot deformation
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Title: Structural evolution in nickel during annealing subsequent to hot deformation
Physical Description: xviii, 183 leaves : ill. ; 28 cm.
Language: English
Creator: Smeal, Charles Robert, 1932-
Publication Date: 1965
Copyright Date: 1965
 Subjects
Subject: Physical metallurgy   ( lcsh )
Thermal analysis   ( lcsh )
Nickel   ( lcsh )
Heat -- Transmission   ( lcsh )
Metallurgical and Materials Engineering thesis Ph. D
Dissertations, Academic -- Metallurgical and Materials Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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Thesis: Thesis - University of Florida.
Bibliography: Bibliography: leaves 179-183.
General Note: Manuscript copy.
General Note: Vita.
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Bibliographic ID: UF00098415
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000561362
oclc - 13516534
notis - ACY7291

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STRUCTURAL EVOLUTION IN NICKEL DURING
ANNEALING SUBSEQUENT TO HOT

DEFORMATION
















By

CHARLES ROBERT SMEAL


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
April, 1965













ACKNOWLEDGMENTS


The author would like to express his gratitude to the chairman of

his supervisory committee, Dr. F. N. Rhines, not only for many discus-

sions and suggestions pertaining to the problem but also for his constant

encouragement. Research which eventually evolved into this thesis was

performed under the supervision of Dr. R. E. Reed-Hill and the author

would like to acknowledge his debt to many aspects of that work. The

author is also indebted to Dr. R. T. DeHoff for his suggestions concern-

ing the quantative metallographic-measurements.

The author would like ,ts; thank Dr. H. H. Sisler and Dr. R.

Stoufer for serving on his supervisory committee.

The electron photomicrograph in Chapter II is the work of Mr.

E. J. Jenkins.











TABLE OF CONTENTS




ACKNOWLEDGMENTS . . . . . . . . . . . . .

LIST OF TABLES . . . . . . . . . .. . .

LIST OF FIGURES . . . . . . . . . . . . .

KEY TO SYMBOLS . . . . . . . . . ... . .

ABSTRACT . . . . . . . . . . . .. .

Chapter

I INTRODUCTION . . . . . . . . . . .

Purpose of the Study and Definition of
Hot Working . . . . . .. . . .
Previous Studies . . . . . . ... .
Hot working . . . . . . ... .
Annealing after hot working. .. . .....


II EXPERIMENTAL MATERIAL, APPARATUS AND
PROCEDURES . . . . . . . . .

Experimental Material . . . . .
Experimental Apparatus . . . .
Experimental Procedures . . . . .
Preparation of tensile bars . .
Extension of tensile bars . . .
Metallography . . . . . .
Quantitative metallography . . .

III EXPERIMENTAL RESULTS . . . . .


Metallographic Observations . . . . . .
General observations . . . . . . .
Observations pertaining directly to
the initiation and early stages
of growth ef strain-free grains .. ...
Volume Fraction Strain-free Material .. . ...
Number of Strain-free Grains Per Unit
Area and Per Unit Volume .. . . ......
Growth Rates . . . . . . ... .
Surface Area Measurements .. . ........


. . . 13
. . . 13
. . . 15
17
. . . 21

. . . 29


29
29









TABLE OF CONTENTS--Continued

Page

IV DISCUSSION ...... . . . ................ 7

Aspects of the Hot-worked Structure .. . .. 75
Distortion of the grain boundary network . 76
Dislocations not associated with a
boundary network . . . . . . . 81
Formation of a subgrain boundary network 82
Serrated boundaries .............. 86
Strain-free grains . . . . . . . 89
Summary . . . . . . . . ... ... 99
Annealing after Hot Working . . .... . . 102
The initiation of strain-free grains
during working and their growth
during annealing . . . . . . 102
The growth of strain-free grains and
the effects of temperature upon
growth ...... . ............... . 107
Summary. .......... . . . . . 122
A Review of the Proposed Mechanism and a
Discussion of Its Applicability to Other
Studies of Annealing after Hot Working
and to Studies of Annealing after
Cold Working . . . .. . . . .... 123
A review of the mechanism. .... . . . 123
Predictions based on the proposed
mechanism compared with results
from other studies of hot working. . . ... 125
Application of the proposed mechanism
to annealing after cold working .. . . 140

V CONCLUSIONS. .......... . . . . . . 143

APPENDICES ............. . . ......... 145

LIST OF REFERENCES. .......... . . . . . . . 179










LIST OF TABLES


Table Page

1 Certified analysis of Nickel 200, heat 513A . . ... 11

2 List of all specimens worked(at 75000 and annealed
bt 7500C, 7000C and 6700) with measured extensions
and reductions in area (sections mounted for
metallographic examination). . . . . . . ... 30

3 Microstructural positions occupied by strain-free
grains at various annealing times for specimens
worked at 7500C and annealed at 7500C. . . . . .. 36

4 Volume fraction strain-free material for specimens
worked at 7500C and annealed at 7500C, 700C and
6700C . . . . . . . . .. . ... . 42

5 Number of strain-free grains per unit area and per
unit volume for specimens worked at 7500C and
annealed at 7500C, 7000C and 6700C . . . . .... 48

6 Grain boundary intercepts (excluding twin boundary
intercepts) for strain-free grains, (NL)NE, for
specimens worked at 7500C and annealed at 7500C,
7000C and 6700C . . . . . . . . . .. 49

7 Growth rates for annealing temperatures of 7500C,
7000C and 6700C ... . . . ... . . . .. . 52

8 Maximum intercept of largest unimpinged grain for
specimens worked at 7500C and annealed at 7500C,
7000C and 6700C . . . . . . . . . . . 53

9 Growth rates calculated from the expression
G (SV)O-N = dVV/dt for specimens worked at
7500C, 7000C and 6700C .. . . . . . . 58

10 Experimental measurements of surface area per
unit volume with strain-free material on at least
one side of the boundary, (SV) with strained
material on at least one side of the boundary,
(SV)old, and the total surface area, (SV)lot'
for specimens worked at 7500C and anneale at
7500C, 700C and 6700C . . . . .. .. .. 61








LIST OF TABLES--Continued


11 Calculated values of surface area per unit volume
with: (1) strain-free material on both sides of
the boundary, (Sy)N-N; (2) strained material on
both sides of the boundary, (Sv)o-o; and (3)
strained material on one side of the boundary and
strain-free material on the other side, (Sy)o-N
(the migrating interface area) for specimens
worked at 7500C and annealed at 7500C, 7000C and
6700C. . . . . . . . . . .66

12 Influence of rate of extension on the apparent
total strain in the grains calculated from the
expression: e = [(NL)T/(NL)L]2/3-1. Nickel
200. Hot-working temperature = 7050C. . . . . ... 77

13 Experimental values of VV compared to those
calculated from the expressions VV = 1-exp-
LLVG22 (upper limit) and VV = 1-exp-
(wLVG t2)/3 (lower limit) for specimens
worked at 7050C and annealed at 7500C, 7000C
and 6700C... .. . . .. . ... .... 110

14 A listing of initial and final grain sizes, values
of n from the equation VV = 1-exp-ktn, and times
necessary for 50 per cent of the structure to
become strain free (to 5) for all available data
on annealing after hot working of Nickel 200 . . .. 127

15 Data which illustrate the effects of initial grain
size upon the type of position at which strain-free
grains are formed and upon the final grain sizes ..... 128

16 Data which illustrate the effects of working
temperature upon: (1) type of positions at which
strain-free grains are formed, (2) growth rate and
(3) final grain sizes .. .. .. . . . . . 133

17 Data which illustrate the effects of rate of working
upon the type of positions at which strain-free
grains are formed and upon the final grain sizes ..... 136

18 Data which illustrate the effects of extent of
working upon the type position at which strain-
free grains are formed and upon the final grain
sizes . . . ... . .. . . .. . . . . 137







LIST OF TABLES--Continued


able Page

19 A summary of the effects of the experimental
variables upon: (1) the type of position at
which strain-free grains are formed, (2) growth
rates and (3) final grain sizes . . . . . ... .141

20 An outline of the conditions of working and
experimental materials for the various studies
of hot working......... ... ... .... . 147

21 Measured chord lengths and calculated values
for the number of grains per mm3 having a
certain average diameter. . . . . . . . 169












LIST OF FIGURES


Figure Page

1 A sketch of the high temperature deformation
apparatus . . . . . .. . . . . 12

2 A sketch of the tensile bar used for the hot
working and annealing experiments . . . . .... 14

3 A photomicrograph of the structure which re-
sulted from the final 25-minute anneal at
7500C. 400x . . . . . . . . . . . 16

4 Electron photomicrograph illustrating the
grooved surface produced on a specimen
polished and etched as described in the
text. 13,000X, ....... ..... ...... . 20

5 A photomicrograph which illustrates the three
basic types of intercept counts performed in
this study. Boundaries with strained material
on at least one side are marked (2) and bound-
aries with strain-free material on at least one
side are marked (3). Polarized light. 400X . . . 25

6 A plot of (NA)corrected/NA versus VV for speci-
mens from all three annealing temperatures.
Specimen numbers are indicated beside the ex-
perimental points ............. ..... 27

7 Selected photomicrographs from the group of
specimens worked at 7500C and annealed at 7500C
(a) immediately before deformation, (b) 0 seconds
anneal, (c) 45 seconds anneal, (d) 120 seconds
anneal, (e) 720 seconds anneal. Polarized light.
400X. . . . . . . . . ........ 31

8 Photomicrographs chosen to illustrate the various
positions occupied by small, strain-free grains.
Polarized light. 1000X . . . . . . . . 38

9 Volume fraction strain-free material versus
annealing time for specimens worked at 7500C
and annealed at 7500C . . . . .... . . 44








LIST OF FIGURES--Continued


Figure Page

10 Volume fraction strain-free material versus
annealing time for specimens worked at 7500C
and annealed at 7000C ........ .......... 45

11 Volume fraction strain-free material versus
annealing time for specimens worked at 7500C
and annealed at 6700C . . . . . . . 46

12 Number of strain-free grains per unit volume
versus annealing time for specimens worked at
7500C and annealed at 7500C, 7000C and 6700C . . ... 50

13 Maximum intercept of largest unimpinged grain
versus annealing time for specimens worked at
7500C and annealed at 7500C, 7000C and 6700C . . ... 54

14 Surface area per unit volume separating strain-
free from strained material (the migrating
interface area) versus annealing time for
specimens worked at 7500C and annealed at 7500C. . 55

15 Surface area per unit volume separating strain-
free from strained material (the migrating
interface area) versus annealing time for
specimens worked at 7500C and annealed at 7000C. ..... 56

16 Surface area per unit volume separating strain-
free from strained material (the migrating
interface area) versus annealing time for
specimens worked at 7500C and annealed at 6700C. ..... 57

17 Total boundary area per unit volume, (Sv)total'
versus annealing time for specimens worked at
7500C and annealed at 7500C ...... . . . . 62

18 Total boundary area per unit volume, (SV) a
versus annealing time for the specimens w rked
at 7500C and annealed at 7000C .. . . ..... 63

19 Total boundary area per unit volume, (SV)toal
versus annealing time for the specimens worked
at 7500C and annealed at 6700C .. . . ..... 64

20 Boundary area per unit volume with strained
material on both sides of boundary, (SV)o-,
versus annealing time for specimens worked at
7500C and annealed at 7500C . . . . . . . 68









LIST OF FIGURES--Continued


Figure Page

21 Boundary area per unit volume with strained
material on both sides of boundary, (Sv)o_,'
versus annealing time for specimens worked at
7500C and annealed at 7000C . . .... . . . . 69

22 Boundary area per unit volume with strained
material on both sides of the boundary,
(SV)O-o, versus annealing time for specimens
worked at 7500C and annealed at 6700C . . . . .. 70

23 Boundary area per unit volume with strain-
free material on both sides of the boundary,
(SV)N-N, versus annealing time for specimens
worked at 7500C and annealed at 7500C . . . . .. 71

24 Boundary area per unit volume with strain-
free material on both sides of the boundary,
(SV)N-N, versus annealing time for specimens
worked at 7500C and annealed at 7000C . . . . .. 72

25 Boundary area per unit volume with strain-
free material on both sides of the boundary,
(SV)N-N, versus annealing time for specimens
worked at 7500C and annealed at 6700C . . . . .. 73

26 A plot of measured total extension versus
calculated e for Nickel 200. Specimens
extended at 05C and 0.009/minute. . . . . ... 78

27 A plot of the ratio of the calculated e to the
measured total extension versus hot-working
temperature. Nickel 200. Rate of extension *
0.75/minute. Total extension = 37 per cent . . .. 79

28 Schematic diagram of the development of sub-
grain boundary networks during hot working.
The extent of working increases from I through
3. The direction of working is indicated . . . .. 83

29 Average subgrain size as a function of hot-
working temperature for copper worked at various
rates. Method and rate of working are indicated
on end curve (4, 46) ......... ......... 85








LIST OF FIGURES--Continued


Figure Page

30 A plot of ln(l/l-VV) versus annealing time for
specimens worked at 7500C and annealed at 7500C,
7000C and 6700C . . . . . . ...... 94

31 An electron photomicrograph of a presumably
strain-free grain with a scalloped boundary
growing at an old grain boundary. IO,OOOX. . . 96

32 A photomicrograph illustrating the growth of
a strain-free grain from a strained grain
apparently of nearly the same orientation.
Polarized light. 1000X ...... ..... ..... 97

33 Schematic diagram of the partition of total
dislocation content between subgrain boundaries
and miscellaneous lattice distortions as a
function of rate and amount of hot working .... 101

34 A plot of 1/tc versus I/T(oK) for VV = 0.05 . . .. 104

35 A plot of experimental growth rates (calculated
from G-(Sv)o-N = dVv/dt versus I/T(OK)) . . . .. 105

36 A plot of calculated and experimental values
of VV versus annealing time for specimens
worked at 7500C and annealed at 7500C. Solid
lines indicate calculated limits of circled
points experimental values. . . . . . . . Ill

37 A plot of calculated and experimental values
of VV versus annealing time for specimens worked
at 7500C and annealed at 7000C. Solid lines
indicate calculated limits and circled points
experimental values . . . . . ... . . 112

38 A plot of calculated and experimental values
of VV versus annealing time for specimens
worked at 7500C and annealed at 6700C. Solid
lines indicate calculated limits and circled
points experimental values. . . . . . . . 113

39 A plot of (Sv)o-N versus VV which includes all
values obtained from specimens annealed at
7500C, 7000C and 6700C. ... . . . . . . 115









LIST OF FIGURES--Continued


Figure

40 A plot of (SV)O-N versus VV for hot-worked
silicon iron deformed to a strain of 0.45
at 8120C and annealed at 8120C. The data
were taken from the study by English and
Backofen . . . . . . . . . .. . .

41 A plot of (SV)O_0 versus VV which includes
all values obtained from specimens annealed
at 75000, 7000C and 6700C .. . . ... ......

42 A plot of diamond pyramid hardness versus
annealing time for specimens extended 38
per cent at 7550C and annealed at 7550C .. . .....

43 A plot of (SV)N-N versus VV which includes
all values obtained from specimens annealed
at 7500C, 7000C and 6700C . . . . . .. . .

44 Photomicrographs obtained from partially
annealed specimens (worked and annealed at
70500) having initial NL's of (a) 18/mm, and
(b) 41/mm. Note the number of strain-free
grains which have formed at old grain edges
(triple points in two dimensions). 200X .. . ....

45 A photomicrograph obtained from a specimen
of Nickel 200 worked at 8550C but not
annealed. Note the presence of strain-free
or nearly strain-free grains at many of the
old grain triple points (edge in three
dimensions). 200X . . . . . . ... . .

46 A photomicrograph obtained from a specimen of
Nickel 200 worked at a rate of 0.009/minute but
not annealed. Note the large number of strain-
free or nearly strain-free grains which have
formed at old grain triple points (edges). 200X .

47 A three-dimensional representation of the rela-
tionship between grain size, working temperature
and degree of working for electrolytic copper
fully annealed after working (from reference 21) .

48 Photomicrographs of specimens worked at 7-500C
and annealed at 7500C. Annealing times are
indicated. Polarized light. 400X . . . .....








LIST OF FIGURES--Continued


Figure Page

49 Photomicrographs of specimens worked at 7500C
and annealed at 7000C. Annealing times are
indicated. Polarized light. 400X. . . . . ... 157

50 Photomicrographs of specimens worked at 7500C
and annealed at 6700C. Annealing times are
indicated. Polarized light. 400X. . . . . ... 163

51 A plot of cumulative per cent of total number
of grains with a certain mean diameter versus
log or the mean diameter. . . . . . . ... 171












KEY TO SYMBOLS


A a constant

B a constant

eg the average longitudinal strain in the grains calculated
from the equation given by Rachinger (43)

G the growth rate calculated from the equation G (Sv)o-N
dVv/dt

k a constant

k a particular size class in Spektor's equation

K1 a geometrical constant

K2 a geometrical constant

K3 a geometrical constant

LV the length of grain edge per unit volume possessed by
strain-free grains--the nucleating edge

n a constant in the equation VV I-exp-ktn indicative of
the microstructural position at which new grains form

nk.l the number of chords per unit length of line in the kth
size class

nkl the number of chords per unit length of line in the size
class k+l

NA the number of strain-free grains per unit area of
metallographic surface

(NA)T the number of triple points per unit area which are at
least partially surrounded by strain-free grains

NL the number of intercepts per unit length of random line
made with a particular structural feature

(NL)L the number of boundary intercepts per unit length of line
oriented parallel to the tensile axis








(NL)NE the number of grain boundary intercepts per unit length of
random line with strain-free grains on at least one side
of the boundary

(NL)new the number of boundary intercepts per unit length of ran-
dom line with strain-free grains on at least one side of
the boundary

(NL)old the number of boundary intercepts per unit length of ran-
dom line with strained grains on at least one side of the
boundary

(NL)T the number of boundary intercepts per unit length of line
oriented perpendicular to the tensile axis

(NL)total the total number of boundary intercepts per unit length of
random line

Np the total number of points which fall on the microstruc-
tural feature of interest

NV the number of strain-free grains per unit volume

(NV)kA the number of particles per unit volume with mean diameter
k&

Pp the fraction of the total number of applied points which
fall on a particular type of microstructural feature

QG The "activation energy" for grain boundary migration cal-
culated from growth rates obtained from the equation
G (SV)o-N = dVV/dt

QT the "activation energy" for the evolution from a strained
material to strain-free grains

R the gas constant

Sy the surface area per unit volume possessed by the feature
of interest

(SV)new the boundary area per unit volume with strain-free grains
on at least one side of the boundary

(SV)N-N the boundary area per unit volume with stain-free grains
on both sides of the boundary

(SV)old the boundary area per unit volume with strained material
on at least one side of the boundary









(Sv)o-N the boundary area per unit volume separating strained
material and strain-free grains--the migrating interface

(Sv)o-0 the boundary area per unit volume with strained material
on both sides of the boundary

(Sv)total the total boundary area per unit volume

t time

T temperature

tc the annealing time at which any specified fraction of the
structure is strain-free

to.5 the annealing time at which 50 per cent of the structure
is strain free

Vy the volume fraction strain-free grains

A the interval length

VV the standard error of the volume fraction strain-free
grains








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

STRUCTURAL EVOLUTION IN NICKEL DURING ANNEALING
SUBSEQUENT TO HOT DEFORMATION

By

Charles Robert Smeal

April, 1965

Chairman: F. N. Rhines
Major Department: Department of Metallurgical and
Materials Engineering


The evolution of structure during annealing after hot working was

studied in Nickel 200. Attention also was directed to the structural

changes which occur during hot working. Metallographic observations and

quantitative metallographic measurements were used to characterize the

structures formed during both processes. Quantitative metallographic

procedures were used to measure: (1) the volume fraction strain-free

grains, (2) the number of strain-free grains, (3) the growth rate of the

strain-free grains, and (4) various types of boundary area.

Results indicated that the structure of hot-worked Nickel 200 is

characterized by some or all of the following features: (I) grain

elongation, (2) dislocations not associated with a boundary network, (3)

subgrains, (4) serrated grain boundaries, and (5) new grains formed dur-

ing working. The prominence and even the appearance of any of these

features in a material of high or moderate stacking-fault energy depended

upon the working conditions.










A study of specimens annealed at 750, 700, and 6700C after work-

ing at 7500C resulted in the following characterization of the evolution

from strained material to strain-free grains:

1. All grains which exist in the completely annealed
structure are formed at essentially zero annealing
time.

2. These grains are formed preferentially at old grain
edges and to a lesser degree at old grain boundaries.

3. Many strain-free grains grow preferentially into one
of the strained grains sharing the edge or boundary
at which it is growing.

4. The boundary between strained material and strain-
free grains migrates at a constant linear rate
throughout the annealing period.

A mechanism for the initiation of new grains during hot working

and the growth of these grains during annealing is proposed. This mech-

anism explains the close relationship between the structure formed during

hot working and the structural evolution during annealing after hot work-

ing. Most of the results from other studies of annealing after hot work-

ing are explicable on the basis of this mechanism.


xviii











CHAPTER I


INTRODUCTION


Only a few investigations of the structural evolution during and

after hot working have been performed. As a result, the structural

changes which occur during hot working and during annealing after hot

working are poorly understood. The importance of these changes is becom-

ing increasingly obvious. It is now apparent that some of the physical

properties of metals and alloys depend to a considerable extent upon

structural details which may be altered by hot working. For example,

Petrova et al. (1)* noted that hot-rolled nickel (8000C followed by a

water quench) exhibited a stress-rupture life 25 times that of a similar,

unworked specimen quenched from 8000C. A second example is the unique

combination of room temperature strength and ductility obtained from hot-

worked aluminum by Whitwham and Herenguel (2). In both cases, the im-

provements in properties were attributed to the structures produced by

hot working.

Hot working is an indispensable process in the fabrication of

most metals and alloys. Only through this process is it possible to

break down the form and structure of the cast material into useful shapes

with desirable properties. Not only are the majority of all metals and

alloys hot worked in at least the initial stages of fabrication, but also

a considerable amount of metal is marketed in the hot-worked condition.


*Numbers in parentheses pertain to entries in the List of
References.









The potential benefits from a thorough understanding of the structural

evolution during and after hot working are therefore substantial.

It is, however, very difficult to study the structural evolution

during and after hot working utilizing the usual industrial choices of

working conditions. Temperatures and rates of working are usually so

high that it is almost impossible to observe the hot-worked structure by

the usual methods. Thus, it is often concluded that recovery processes

operate during hot working to remove all evidence of the deformation.

This viewpoint is, at best, an oversimplification. Although there is no

doubt that some evolution of structure does occur during working, by far

the greatest changes occur during the high-temperature dwell subsequent

to working. The final structure, therefore, depends not only on the

working conditions, but also on the conditions of cooling. On the other

hand, at slow rates of working recovery processes may almost keep pace

with the deformation so that the final structure again shows little or no

evidence of working. Hence a study of the structural evolution during

and after hot working requires a judicious choice of working conditions.

Appropriate conditions vary with the material.

Not only do the experimentally convenient working conditions fall

outside the usual range for hot working, but alsothey fall within a

range about which very little is known. For this reason, a study utiliz-

ing the experimental conditions will yield results which may be applied

in several ways. On the one hand, these results can be extrapolated into

the usual hot-working region and thus add to the understanding of that

process. On the other hand, it is possible to produce structures utiliz-

ing the experimental working conditions which cannot be produced by any







other working procedure. Although the mechanical properties of these

structures are largely unknown, there exist some indications that un-

usual combinations of strength and ductility may be obtained. There are

also indications that certain working conditions may produce hot-worked

structures which exhibit considerable high-temperature stability. This

stability may well be combined with unusual mechanical properties. In

addition, studies utilizing the experimental conditions may provide a

bridge between the structural changes which occur during creep and those

which occur during hot working. Eventually, it may be possible to formu-

late a mechanism which will account for the structural changes which oc-

cur during and after hot working over the complete range of deformation

rates and temperatures.


Purpose of the Study and Definition of Hot Working

This research is a study of the evolution from a strained mate-

rial to a strain-free structure which occurs during the annealing of hot-

worked Nickel 200. This evolution depends to a considerable extent upon

the structure produced during working and hence on the working condi-

tions. The purpose of this study is therefore to determine the influence

of working conditions upon the structural evolution during annealing

after hot working and to characterize this evolution by determinations of

volume fraction strain-free grains, growth rates, number of strain-free

grains, the effects of annealing temperature, and a microstructural his-

tory of the process.

For the purposes of this study, hot working will be defined as

deformation which occurs at a high enough temperature that the usual









crystallographic deformation mechanisms of slip and twinning are accom-

panied by diffusion controlled processes such as dislocation climb and

boundary migration. Moreover, the rate of extension is many orders of

magnitude above those experienced in creep. In addition, the working

conditions must be such that the structure which obtains at any time dur-

ing the working or annealing periods can be successfully "quenched-in."

In this study, the possibility of structural evolution during the trans-

fer from the heating device to the quench tank was eliminated by the

novel procedure of extending the deformation very slightly into the

quenching period.


Previous Studies

Hot working

The structural changes which occur during annealing after hot

working depend to a considerable extent upon the structure which exists

upon the completion of working, i.e., upon the working conditions. For

this reason, it is necessary to inquire to what extent the structural

changes which occur during hot working have been investigated. This in-

quiry must be tempered by the realization that hot-worked structures are

usually unstable, and their stability decreases (for a particular mate-

rial) with increasing temperature and rate of deformation. An extreme

example, noted by Leguet, Whitwham and Herenguel (3), was the complete

recrystallization of OFHC copper in as little as one-fifth of a second

after a moderate reduction by rolling at 7000 C and at a rate of

lOOm/minute. For this reason, only those investigations will be consid-

ered in which the high temperature structure was preserved by a severe







quench immediately after working, or those in which observations were

made at the working temperature.

Since the structural evolution during working is best character-

ized by the microstructural changes which occur during it, these changes

will be made the basis of the discussion. Contained in the following

paragraphs are outlines of and comments upon observations of slip lines,

serrated boundaries, subgrains, and the formation of new grains obtained

from previous studies of hot working. The interrelations amongst these

characteristics will be further clarified in the discussion of the ex-

perimental results (Chapter IV).

A knowledge of the conditions of working and of the materials in-

volved in the various studies is necessary for a complete understanding

of the published observations. In order to clarify the presentation,

these are included as Appendix A.

Slip lines.--Slip lines are the manifestation on an external sur-

face of dislocation movement on a definite crystallographic plane and in

a specific direction. Observations made (under the optical microscope)

on high temperature slip in copper (3, 4), nickel (5, 6), an austenitic

stainless steel (7), and 70-30 brass are in substantial agreement. Slip

lines first appeared at low total deformations and became more widely

spaced with increasing working temperature. Above a certain temperature

they were no longer visible under the microscope. This type of observa-

tion must not be construed as indicating that deformation by slip did not

occur above a certain temperature. Studies with the electron microscope

have revealed high temperature slip lines too fine to be seen optically.









These studies also showed that with increasing working temperature, the

active slip planes became more closely spaced and slip on any one plane

smaller in amount (8).

Grain boundary serrations.--Grain boundary serrations are the

sharp offsets which are formed in grain boundaries during hot working.

They have been observed in a wide variety of hot-worked metals and alloys.

Among these are: Nickel (1, 6, 9), nickel-aluminum alloys (6), nickel-

copper alloys (6), nichrome (10), an austenitic steel (7), magnesium (11,

12), zirconium (13), and uranium (10). Observations on the character and

conditions for the formation of grain boundary serrations are in general

agreement. Serrations appear only within a certain range of working tem-

peratures. Below a characteristic temperature, serrations are either

absent or unresolvable. Above a considerably higher temperature they are

destroyed by recrystallization along old grain boundaries (I). Within

their temperature range of existence, serrations become better defined

with increasing temperature and amount of working (1, 7, 9). Serrations

also vary in appearance with the working conditions. Low temperatures

and fast rates result in more or less straight sides, while high tempera-

tures and low rates tend to yield a more "wavey" or scalloped appearance

(9). An increase in grain size results in less prominent serrations (10).

Subrains.--Subgrains are small regions slightly misoriented with

respect to each other which are formed within grains under certain condi-

tions of working or at working and annealing. Well-defined subgrains

have been observed to form quite readily during hot working in torsion

(14, 15, 16, 17, 18, 19), by forging (4), by rolling (3), and in tension

(6, 10). The degree of development of subgrain boundaries depends not







only on the stacking-fault energy of the material but also on the working

conditions. Materials of low stacking-fault energy such as 70-30 brass

form few and poorly developed subgrain boundaries even under the most

favorable conditions (3). On the other hand, aluminum, with a high

stacking-fault energy, forms subgrains readily during hot working (3, 14,

16). In fact, with sufficient deformation, subgrain boundaries in alumi-

num develop to the point where they can not be distinguished from grain

boundaries (14, 19). Nickel falls between these extremes, but its be-

havior is much closer to that of aluminum than to that of 70-30 brass.

The ease of subgrain formation during hot working may possibly

be related to an increase in stacking fault energy with temperature.

Swann and Nutting (20) have observed that the stacking-fault energy of a

copper-7 per cent aluminum alloy increased abruptly above a certain tem-

perature. If this behavior is general, it would lead one to expect the

formation of better defined subgrains as the temperature of working is

increased.

The formation of new grains during workinq.--The formation of new

grains during working has been a controversial subject. Hardwick and

Tegart (14) noted that the structures of hot-worked nickel and copper

were at least partially occupied by grains which they believed formed

during working. Leguet et al. (3) challenged this conclusion on the

basis of their study which showed working and annealing (formation of new

grains) to be separate and successive. These authors believed that the

new grains observed by Hardwick and Tegart were formed during the very

short time subsequent to working but prior to quenching. This was most

probably the case. Rhines et al. (9), however, have noted the presence

of a large number of very small grains in the structure of hot-worked









nickel. These grains were not present prior to working. In addition,

working and quenching conditions rule out the possibility of formation

between the working period and quenching to room temperature. Thus it

must be concluded that under certain conditions new grains can form dur-

ing hot working. This is an important point and will be considered in

some detail in the discussion (Chapter IV).


Annealing after hot working

The evolution from a strained material to strain-free grains

which occurs during annealing after hot working is the principal concern

of this study. Thus, the few existing investigations of annealing after

hot working are of considerable importance. These studies are discussed

in the following paragraphs. They can be divided conveniently into two

periods with respect to time and general approach to the subject. The

first of these periods begins about 1920 and ends with the second World

War. Most investigations in this period were performed by German workers

who were concerned with establishing the relationships between amount of

working, annealing temperature and the completely annealed grain size

(results were plotted as a type of Czochralski diagram). The second ac-

tive period begins in the late 1950's and is characterized by a more de-

tailed study of the structural evolution during annealing.

The original investigations of annealing after hot working (by

rolling and forging) appear to have been made by Hanemann and Licke (21),

by Hanemann (22), and by Tafel, Hanemann and Schneider (23). Similar in-

vestigations were performed at a later date by Kornfeld (24) and by

Kornfeld and Hartleif (25). In all of these studies the emphasis was on







the recrystallized grain size as a function of the amount and temperature

of working. No attempt was made to determine the kinetics of the evolu-

tion from strained to strain-free material. Hanemann and co-workers con-

cluded that the initial grain size has no influence on the fully annealed

grain size and that the latter is determined only by the temperature and

amount of working. These conclusions were disputed by Kornfeld, and by

Kornfeld and Hartleif who established for an "Armco" type iron forged in

the alpha region that the fully annealed grain size does depend on ini-

tial grain size. The conclusion of Tafel, Hanemann, and Schneider, how-

ever, was found to be valid for working in the gamma field.

More recent investigations have yielded some interesting informa-

tion on the structural changes which occur during annealing after hot

working. These are summarized in the following paragraphs.

The microstructural positions occupied by grains formed during

annealing after hot working were noted by Malyshev et al. (7) in their

investigation of the structural changes in an austenitic steel during hot

rolling. Specimens rolled at various temperatures and then quenched were

partially recrystallized by reheating to a suitable temperature. New

grains in a specimen deformed at room temperature showed a very marked

preference for formation on slip lines. This tendency is much less in

material deformed at 4500C and most new grains were formed at old grain

boundaries. The marked preference exhibited by strain-free grains for

formation along old grain edges and at serrated grain boundaries was also

noted by Rhines et al. (9) and by English and Backofen (26).

Observations of the effect of different variables on the velocity

of formation of strain-free grains have been made by a number of authors.








Leguet et al. (3) found for a 70-30 brass annealed at a constant tempera-

ture that the rate of recrystallization decreases with increasing working

temperature (their specimens were quenched after working and reheated to

the annealing temperature). Rossard and Blain (27) noted that a certain

minimum amount of working was necessary before new grains formed during

annealing. This "threshold" value decreases with increasing annealing

time. These authors also noticed that the annealed grain size decreased

with increasing velocity and degree of working and decreasing temperature

of working. Growth rates were measured in only one study, namely that by

English and Backofen (26). This study is also the only one in which the

structural evolution during annealing after hot working was followed by

measuring the amount of strain-free (recrystallized) material as a func-

tion of annealing time.

It is obvious from the above discussion that little qualitative

and practically no quantitative data are available from previous studies

of the structural evolution during annealing after hot working. Thus,

there is not even a basis for the formulation of general principles such

as have been established for annealing after cold working. The present

study is a systematic attempt to partially remedy this situation.











CHAPTER II


EXPERIMENTAL MATERIAL, APPARATUS AND PROCEDURES


Experimental Material

All tensile bars were machined from 5/8-inch diameter rod obtained

from one heat of Nickel 200. A certified analysis of this heat is in-

cluded as Table 1.


TABLE l.--Certified analysis of Nickel 200,
heat 513A

Element Per Cent

C 0.07
Mn 0.26
Fe 0.04
S 0.005
Si 0.07
Cu 0.01
Ni 99.52



The rod was received in the cold-drawn condition.


Experimental Apparatus

High temperature deformation utilized a jig designed to extend a

standard tensile bar at a controlled rate. A sketch of this jig is in-

cluded as Figure 1. Rate of extension could be varied in a step-wise

manner by adjusting the combination of gear reducers and gears. The jig

was self-contained and designed to sit over a 12-inch diameter salt pot

so that the specimen was immersed completely in the liquid salt.





















































Fig. 1.--A sketch of the high temperature deformation apparatus.

z









Quenching was easily and rapidly performed by two men lifting the jig out

of the salt pot and dropping it into a tank of cold water. Two electri-

cally heated pot furnaces, both equipped with Inconel pots, were used

throughout the testing. The heating media were: (I) Houghton's Liquid

Heat 1145 for the pot in which the deformation was performed, and (2)

Houghton's Liquid Heat 1145 plus 5 to 10 per cent lithium chloride for

the pot in which annealing at 7000C and 6700C was performed. Both pot

furnaces were equipped with suitable temperature controllers. Tempera-

ture fluctuations within the pots were reduced to a minimum by stirring

with variable speed laboratory stirrers.

All measurements and photomicrographs were made on a Bausch and

Lomb Research Model Metallograph.


Experimental Procedures

Preparation of tensile bars

The as-received Nickel 200 rod was cut into ll-inch lengths and

annealed for 18 minutes at 7500C 1C in Liquid Heat 1145. This treat-

ment resulted in a completely recrystallized structure. The annealed,

5/8-inch diameter bars were cold swaged in two stages to a nominal diam-

eter of 1/2 inch. Actual reductions in area varied from 34 to 36 per

cent. Tensile bars similar to that illustrated by Figure 2 were machined

from the swaged bars. Each length provided 5 tensile bars and the same

number of 1/16-inch thick disks. These disks received the same subse-

quent thermal treatments as the tensile bars (one disk accompanying each

bar) and were useful for control and comparative purposes.















3"





-.-4 ---





Fig. 2.--A sketch of the tensile bar used for the hot working and annealing
experiments.








After machining, the gauge section of all tensile bars was pol-

ished in order to remove the layer of badly distorted material produced

by machining. This treatment prevented the formation of a fine-grained

"skin" during subsequent annealing. The complete procedure consisted of

grinding through 240-, 320-, 400-, and 600-grit Silicon Carbide Metallo-

graphic Papers and electropolishing the gauge section. The 1/2-inch di-

ameter disks were similarly treated. Electropolishing was performed in a

solution containing 144 ml C2H50H, 32 ml H20, 16 ml n-butyl alcohol, 45 g

ZnCI2, and 10 g AICI3 6H20. Polishing was accomplished satisfactorily

at voltages from 14 to 16 volts, and at temperatures from -10C to -250C

utilizing a stainless steel cathode and a polishing time of approximately

one hour. After electropolishing, the bars were given a final anneal in

Liquid Heat 1145 at 7500C 10C for 25 minutes. The final anneal re-

sulted in a fairly equiaxed structure, illustrated by Figure 3, with an

NL of 45/mm. The gauge length and gauge diameter of all bars were meas-

ured on an optical comparator.


Extension of tensile bars

The same procedure was followed in extending all tensile bars. A

bar was placed in the grips of the deformation apparatus and all slack

taken up manually. One of the 1/2-inch diameter disks was wired on the

upper grip so that it hung adjacent to the gauge section of the tensile

bar. The jig was next placed in the liquid salt and the whole apparatus

annealed for 20 minutes. During this time the temperature of the pot was

adjusted to 7490C 10C. At the end of the holding period, the jig was

switched on for 25 seconds (a time calculated to give a total extension












































Fig. 3.--A photomicrograph of the structure
which resulted from the final 25-minute anneal at
7500C. 400x.









of about 31 per cent to all test bars) and then switched off if annealing

was to be performed at 7500C. If annealing was to be performed at 7000C

or 6700C, the jig motor was shut off as the jig was lifted for transfer

to the second pot. Total transfer time was approximately 3 seconds. A

simple experiment with a test bar exactly the same as those used for the

actual tests showed that 6 seconds were required for the surface of the

gauge section to cool from 7500C to 7000C. At the end of the annealing

period, the jig was water quenched. Approximately one second was neces-

sary to transfer the jig from the salt pot to the quench bath. After

quenching, the tensile bar and the slug were removed from the jig and the

gauge section of the bar remeasured on the optical comparator. Total ex-

tensions were calculated from the initial and final measurements.

Temperature control for the 7500C anneals was fairly simple and

in all cases the temperature was held between 7480C and 7500C. Control

was not so simple for the lower temperature anneals; however, all runs

fell within the following limits: 6980C to 7020C for nominal 7000C an-

neals and 6640C to 6710C for the nominal 6700C anneals.


Metallography

A portion of the gauge length which had experienced a reduction

in area of approximately 24 per cent was located in each tensile bar and

a 3/8-inch to 3/4-inch section removed with a jeweler's saw. This piece

was mounted in Bakelite, rough ground to approximately mid-diameter, and

ground through 240-, 320-, 400-, and 600-grit Silicon Carbide Metallo-

graphic Papers. Initial polishing was performed with 6-micron diamond

paste on a Nylon cloth and 1-micron diamond paste on Microcloth. The










final mechanical polish utilized a Syntron vibratory polisher. The abra-

sive was Linde "B"' on Microcloth and the polishing time was 40 minutes.

In order to remove all traces of distorted metal, the specimens

were electropolished in the same solution used to polish the tensile bars

before the final anneal. Polishing conditions, however, were much more

critical. A well-aged solution with a deep green color was used. The

temperature of the polishing bath was maintained between -300C and -350C

and the specimen allowed to reach this temperature before polishing was

begun. The most satisfactory open circuit voltage was found to be 35

volts and the best polishing time 40 seconds. A stainless steel cathode

was satisfactory. No agitation was necessary. At the end of the polish-

ing period, the specimen was removed from the bath with the current on,

washed under warm, running water, and blown dry.

Correct etching was of extreme importance and was performed as

described below. A solution containing 45 ml H20, 47 ml concentrated

HNO3 and 8 ml HF (48-51 per cent HF) was prepared. To 3 ml concentrated

HCI in a polyethylene graduate was added 17 ml of the above solution and

the mixture was heated in a water bath until light yellow. The solution

then was poured into a polyethylene beaker and used to saturate a cotton

swab on the end of a pair of stainless steel tongs. In a few seconds, a

reaction with the tongs began and the cotton swab gradually acquired a

dark green color. When a large portion of the cotton had become stained,

the swab was swirled around in the solution remaining in the polyethylene

beaker for a few seconds, squeezed as dry as possible and discarded. The

green solution in the beaker was allowed to cool to 250C and used as an

immersion etch. Etching times were between 8 and 12 seconds. The









specimen was held face down in the solution and agitated very slightly.

At the end of the etching period, the specimen was removed from the etch

and washed thoroughly in warm, running water.

The above etching procedure was developed during the investiga-

tion and is a refinement of the procedure used by Reed-Hill et al. (28).

It produced a surface highly sensitive to polarized light and one which

can be easily examined at magnifications as high as or higher than 1000X.

Many metallic surfaces prepared for examination under polarized light

cannot be viewed at magnifications over a few hundred times. The success

of the present procedure lies in the production by the etch of a very

fine pseudo-crystallographic grooving (28). The appearance of the

grooves as revealed by the electron microscope is illustrated by Figure 4

taken from a chromium shadowed formvar replica of a surface etched as de-

scribed above.

Although all groove axes within a particular grain are oriented

in a unique direction, this direction is not truly crystallographic and

hence cannot be used in precise orientation determinations. However, the

grooves do reflect accurately the degree of lattice strain present in in-

dividual grains. If the grain is undistorted, then the grooves produced

by the etch will all be straight and all oriented in the same manner with

respect to the surface of the specimen. Examination with polarized light

will result in all of the grain reaching a particular degree of extinc-

tion at the same position of the microscope stage. There will be no var-

iation in shading within a grain unless caused by a twin or by a polish-

ing or etching artifact. On the other hand, if the grain is distorted

and the lattice planes bent, the grooves produced by etching will also be













































Fig. 4.--Electron photomicrograph illustrat-
ing the grooved surface produced on a specimen pol-
ished and etched as described in the text. 13,000X.









bent and possibly will not all be oriented in the same manner with re-

spect to the surface of the specimen. Thus, various parts of the grain,

when examined under polarized light, will reach different degrees of ex-

tinction at a particular microscope stage position and variations in

shading will appear. The type of extinction noted under polarized light

is therefore a rather sensitive indication of the lattice strain present

in a particular grain. Undistorted or recrystallized grains thus can be

unequivocally separated from distorted or unrecrystallized grains. It is

also possible to reveal all grain and twin boundaries.

The above procedure, however, has a number of disadvantages:

1. All stages of specimen preparation must be carefully
performed.

2. A finite number of grains will be oriented such that
no grooves will form on etching. Thus, no extinction
is possible under polarized light.

3. A minimum amount of strain is necessary to produce
enough lattice bending to be visible under polarized
light. Specimens extended as little as 4 per cent,
however, have shown lattice bending and the threshold
value for the specimen as a whole must be less than
this.


Quantitative metallography

Most of the quantitative data obtained resulted from two types of

measurements: (1) point counting, and (2) intercept counting. Both pro-

cedures are well established. The papers by Hilliard and Cahn (29) and by

Smith and Guttman (30) may be consulted for further details. In addition,

one type of measurement involving number per unit area was performed.

All measurements, except those of caliper diameter, were performed at a

magnification of 1025X.










Point counting.--Point counting is most easily performed by

superimposing a uniform array of points on the microstructure and count-

ing the number of points which fall within a certain structural feature.

The ratio of the number of points falling on the feature of interest to

the total number of points applied is defined as Pp* and is equal to VV,

the volume fraction occupied by the feature of interest.

In the present investigation a 7 x 7 grid was introduced into the

microscope eyepiece. This grid had the advantage that it could be used

as a 25-point, 16-point, 9-point, 4-point or even a I-point grid, depend-

ing on the structure being measured. New areas were brought into the

field of view simply by moving the microscope stage a predetermined

amount. An estimate of the number of points which must be counted for a

predetermined precision can be made from the expression given by Hilliard

and Cahn (29): (Ov/VyV)2 1/Np where OV is the standard deviation

for the volume fraction of the feature of interest, VV is the volume frac-

tion of this feature present, and Np is the total number of points which

fall on this feature. It is assumed that: (1) the feature of interest oc-

curs as discrete particles randomly distributed in three dimension, and

(2) the point grid is so coarse that the distance between points is

larger than the intercept length for the feature of interest. This ex-

pression is then, strictly speaking, only valid for small and for large

amounts of strain-free material. For intermediate amounts the empirical

expression (6Vy/VV)2 = (I-Vv)/Np given by Hilliard and Cahn can be used.


*All symbols have been defined in the Table of Symbols which is
located in front of the text.









Both of these equations also can be used to calculate the precision ob-

tained from the number of classified points.

Intercept countinq.--Intercept counts were used to determine the

surface area per unit volume of various features through the expression

2NL = SV. In this expression NL is the number of intercepts per unit

length made by a test line with the feature of interest and SV is the

surface area per unit volume possessed by the feature of interest. The

eyepiece grid and movement from area to area were the same as described

above. The grid was rotated 90 between areas in order to avoid an orien-

tation dependence in the results due to the position of the test line

with respect to the tensile axis of the specimen. A total of 20 areas

were counted as a group. This is equivalent to the superposition of a

uniform array of lines on the gross area examined. Enough groups of 20

areas were measured that the standard error of the average number of in-

tercepts per unit length of test line was usually less than 10 per cent

of the average and quite often in the neighborhood of 5 per cent. A sec-

tion perpendicular to the tensile axis of a specimen with VV = 0.94 was

also examined. A measurement of the total grain boundary area for this

section yielded the same result as obtained from a section parallel to

the tensile axis. This result and metallographic observations made on the

same specimen proved that the new grains are equiaxed. Other authors

have found that the volume fraction new grains is independent of the ori-

entation of the metallographic surface (31, 32).

Three basic types of intercept counts were made:

1. Total number of intercepts made with all grain and twin
boundaries--(NL)total = 1/2(S) total'










2. The number of intercepts made with grain and twin
boundaries having strained material on at least one
side--(NL)old = 1/2(SV)old.

3. The number of intercepts made with grain and twin
boundaries having strain-free material on at least
one side--(NL)new = 1/2(Sv)new.

All three types are illustrated by Figure 5. The line drawn on the print

intercepts boundaries with strained material on at least one side at

points marked (2) and boundaries with strain-free material on at least

one side at points marked (3). The total boundary area is obtained by

counting all the intersections. Note that in all cases both grain and

twin boundaries were counted as equivalent. The reasons for this proce-

dure will be discussed later.

Calculation of NV, the number of strain-free grains per unit vol-

ume, necessitated counting the number of grain boundary intercepts care-

fully excluding all twin boundaries. This measurement was performed ex-

actly as were the other types of intercept measurements. Difficulty in

separating grain from twin boundaries, however, resulted in it being more

difficult to perform and subject to a greater inaccuracy than the other

intercept measurements.

Determination of number per unit area.--The number of new grains

per unit area, NA, was measured. This involved only a straightforward

counting of the number of new grains in a certain area of the eyepiece

grid. Again, enough areas were counted that the standard error of the

mean was usually between 5 per cent and 10 per cent of the mean value.

The measurement was subject to errors from two sources:

I. At very short annealing times the area of intersection
on the metallographic surface with a particular new
grain may be below the smallest size recognizable as







































Fig. 5.--A photomicrograph which illustrates
the three basic types of intercept counts performed
in this study. Boundaries with strained material on
at least one side are marked (2) and boundaries with
strain-free material on at least one side are marked
(3). Polarized light. 400X.










a new grain. With the aid of an estimate of the small-
est area visible (around a diameter of two microns or
possibly somewhat less) and the assumption that all
new grains grow initially as spheres, one can calculate
the probability of intersecting a sphere of a certain
size and revealing a visible section. With the aid of
the experimental growth rates, and assuming a suitable
minimum probability, one can then calculate the time
necessary for a new grain which originated at zero an-
nealing time to reach visible size. These times were
found to be less than the shortest annealing times at
all three annealing temperatures.

2. All grains which appeared inside a particular area in
the eyepiece were counted, even if the largest part of
the grain was outsidethe measured area. Strictly
speaking, those grains which appeared both in and out
of the measured area should have been weighed by a
factor of one-half. Errors from this source were
later realized to be considerable. Consequently, the
data were adjusted with the aid of empirical correction
factors. These were calculated for a number of speci-
mens by measuring NA with all grains having a weighing
factor of one and then remeasuring the same area with
the grains which extended over the edge of the area be-
ing given a weighing factor of one-half. The ratio of
the corrected NA to the uncorrected NA was then plotted
versus VV. Measurements from specimens at all three
annealing temperatures (Figure 6) indicated that the
ratio was a function of VV only and not a function of
temperature. The plot of Figure 6 was used to correct
all the measured values of NA.

A few determinations were made of the length of grain edge per

unit volume. This involved measuring the number of triple points per

unit area. The length of edge was then calculated from the expression

(NA)T = 1/2LV where (NA)T is the number of triple points per unit area

and LV is the length of grain edge per unit volume. Although this meas-

urement was the most difficult to perform, duplicate determinations

agreed to within 10 per cent of the average.

Miscellaneous measurements.--The maximum intercept length of the

largest unimpinged grain was measured where possible. For the purpose of







1.0



O






oo
So.9-
0












0 0. I 0.2 0.3 0.1 0.5 0.6 0.7 0.8 0.9 1.0
Vv

Fig. 6.--A plot of (NA)corrected/NA versus VV for specimens from all three annealing tempera-
tures. Specimen numbers are indicated beside the experimental points.









this measurement, maximum intercept was defined as the longest dimension

within an unimpinged strain-free grain which would be found on the metal-

lographic surface. The measurement was performed at a somewhat lower

magnification than the other measurements described above. A filar eye-

piece was used and the metallographic surface scanned enough times that

the author was fairly certain that the largest revealed grain was

measured.

Calibration of optics.--A stage micrometer was used to calibrate

the eyepiece grid for the particular magnification used. The error in

the calibration was estimated as approximately 0.5 per cent.












CHAPTER III


EXPERIMENTAL RESULTS


Metalloqraphic Observations

General observations

A list of all worked specimens has been included as Table 2. In

addition, this table lists for each specimen: (1) values for total ex-

tension calculated from the measured length change, and (2) the reduction

in area experienced by the section of each specimen prepared for metallo-

graphic examination.

Photomicrographs of all specimens were obtained. These are in-

cluded as Appendix B. In all photomicrographs the tensile axis is paral-

lel to the long dimension of the photographic print. Four photomicro-

graphs were abstracted from Appendix B and are included in this section

as Figure 7. Also included as Figure 7 (a) is a photomicrograph of the

structure immediately before deformation. These five photomicrographs

illustrate the most important metallographic observations. These obser-

vations are discussed in the following paragraphs.

Grain boundary serrations are very marked in the as-deformed

microstructure, Figure 7 (b). These serrations are evidently character-

istic of hot-worked structures as they also have been observed in alumi-

num, nichrome, an austenitic stainless steel, zirconium, magnesium, and

uranium.






TABLE 2.--List of all specimens worked (at 7500C) and annealed (at 7500C, 7000C and 6700C) with measured extensions
and reductions in area (sections mounted for metallographic examination)


Annealing Temperature


Specimen
Number

2-1

2-2

3-1

11-4

3-4

1 1-1

1-3

2-3

1-2

2-4

1-1

11-3

11-5

7-3


6700C
Over-all Reduction
Specimen Extension in Area
Number (Per Cent) (Per Cent)


750"C
Over-all
Extension
(Per Cent)

29

30

30

31

29

30

30

30

29

31

29

31

31

30


Reduction
in Area
(Per Cent)

25

23

22

24

24

24

22

22

25

19

25

23

24

26


700"C
Over-all Reduction
Specimen Extension in Area
Number (Per Cent) (Per Cent)

2-1 29 25

7-5 29 24

6-2 28 26

6-4 32 23

8-2 30 23

7-1 33 23

8-4 30 25

7-2 31 27

8-5 30 25

8-3 29 25

8-1 31 27


25

24

25

24

26

24

27

26

26


2-1

9-3

12-4

10-2

9-4

10-4

10-3

12-1

12-2


29

30

32

30

31

31

31

31

31




























(a) Specimen number 2-1T V = 100


(b) Specimen number 2-1 VV = 0.006




Fig. 7.--Selected photomicrographs from the
group of specimens worked at 7500C and annealed at
7500C (a) immediately before deformation, (b) 0 seconds
anneal, (c) 45 seconds anneal, (d) 120 seconds anneal,
(e) 720 seconds anneal. Polarized light. 400X.






























(c) Specimen number 11-4


(d) Specimen number 2-3


Fig. 7.--Continued


VV = 0.053


Vy : 0.415







































(e) Specimen number 11-5


Fig. 7.--Continued


vv = 0.991









The large amount of banding and shading present in the as-deformed

microstructure, Figure 7 (b), was never observed in undeformed grains and

is indicative of lattice bending. Since deformation was performed at an

elevated temperature, one might expect rapid dislocation climb and the

formation of a well-defined subgrain network. Only a few grains, how-

ever, were observed to possess a network of subgrain boundaries similar

to that often observed in aluminum. One of these grains is located to

the right of center in Figure 7 (c).

A comparison of the stacking-fault energies for aluminum and

nickel led to the conclusion that subgrains would probably not be as well

developed in nickel as in aluminum. This conclusion follows from the

fact that the presently accepted value for the stacking-fault energy of

nickel, 150 ergs/cm2 (33) is somewhat less than that for aluminum, 225

ergs/cm2 (34). A high stacking-fault energy is associated with a small

separation between the two partial dislocations produced by the disloca-

tion reaction 2 [T2 I [T2T] + 2 [31] an energetically feasible

reaction. The small separation between partial in turn means that the

dislocation can climb much more easily than one composed of two widely

separated partial in a material of low stacking-fault energy. Since

climb is necessary for the formation of a well-developed subgrain struc-

ture, the development of substructure depends greatly on the stacking-

fault energy. On the other hand, one should not overlook the possibility

that subgrains are not observed in some grains simply because the ease of

subgrain formation varies from grain to grain due mainly to orientation

effects.









Ormerod and Tegart (16) have reported that subgrains formed in

nickel during hot torsion at 6000C are small with diffuse boundaries and

contain many dislocations in their interiors. An increase in the defor-

mation temperature to about 8500C resulted in a considerable increase in

subgrain size, an increased sharpness of the subgrain boundaries and a

decrease in the number of dislocations in the interior of the grains.

Thus, one might expect that deformation at 7500C would result in a fairly

well-defined subgrain network in almost all grains.

With increasing annealing time, more and more of the structure

became strain-free by the initiation and growth of regular, equiaxed

grains. The number of grains with serrated boundaries and shading de-

creased, finally to none, Figure 7 (d) and 7 (e).


Observations pertaining directly to
the initiation and early stages of
growth of strain-free grains

Note in Figure 7 (b) the number of very small grains which are

situated along the grain boundaries and at triple points (along grain

edges in three dimensions). Close examination showed most of these to be

strain free. A somewhat more quantitative measure of the type of posi-

tions occupied by the strain-free grains was obtained by recording the

number of strain-free grains which appeared in grain interiors, along

grain boundaries and at triple points (grain edges in three dimensions)

for a number of random areas in a series of specimens annealed at the

same temperature. These data appear in Table 3. For annealing times

longer than 30 seconds, an appreciable fraction of the new grains had

grown so large that classification was impossible.













TABLE 3.--Microstructural positions occupied by strain-free grains at various annealing times
for specimens worked at 7500C and annealed at 7500C

Annealing Fraction of Grains Counted Fraction
Specimen Time at triple in grain in grain Whose Position
Number (Seconds) points boundaries interiors is Indeterminate

2-1 0 0.42 0.42 0.16 0

2-2 15 0.49 0.38 0.10 0.03

3-1 30 0.53 0.30 0.11 0.06









With increasing annealing time, the data apparently show a slight

increase in the fraction of new grains which appeared at triple points,

and slight decreases in the fractions which appeared along grain bounda-

ries and in grain interiors. The changes were small.

The characteristic positions and appearance of the small, strain-

free grains were documented by a series of photomicrographs taken at

I00X. These are included as Figure 8. Note the following features:

1. Although a number of "colonies" containing two, three
or more new grains were observed, there was a larger
number of grains apparently growing completely divorced
from other new grains, Figure 8 (a), (c), and (d).

2. Strain-free grains in some cases appeared to grow with
equal ease into the strained grains on both sides of
the boundary. Figure 8 (a), (c), and (e). In most
cases, however, there appeared to be a preferential
growth into one of the strained grains.

3. Small, strain-free grains initially had a rather ir-
regular boundary, but exhibited roughly circular
cross-sections. With increasing annealing times, they
acquired more regular boundaries, compare Figure 8 (a)
and (c) with Figure 8 (e). There is one aspect of the
boundaries possessed by the strain-free grains indicated
in Figure 8 (a) and (b) (in particular) which should be
given close attention. This aspect is the "scalloped"
appearance of the boundaries, note especially the middle
grain in Figure 8 (b). It is believed that this particu-
lar feature provides considerable insight into the mech-
anism by which strain-free grains originate and grow be-
fore impingement. This idea will be developed in a
subsequent chapter.

4. A number of the strain-free grains appeared to have
formed in grain boundary serrations, Figure 8 (f),
(g), and (h).


Volume Fraction Strain-free Material

Experimental values for the volume fraction of strain-free mate-

rial were collected into Table 4. These values also were plotted versus





























(a) Annealing temperature--7500C; Annealing time--0 seconds. An approxi-
mately equiaxed, strain-free grain is growing at apparently almost
equal velocities into both grains sharing the boundary in which it
originated. Mean grain diameter is about 3 microns.




















(b) Annealing temperature--7500C; Annealing time--0 seconds. Indicated is
a group of contiguous, strain-free grains, one of which is growing
along a grain edge and the other two in a grain boundary.


Fig. 8.--Photomicrographs chosen to illustrate the various posi-
tions occupied by small, strain-free grains. Polarized light. 100X.





























(c) Annealing temperature--7500C; Annealing time--0 seconds. A group of
contiguous strain-free grains is growing at or near a grain boundary.
One of the group is apparently divorced from the boundary. Further
along the same boundary is a single, somewhat larger strain-free
grain similar to that in Figure 8 (a). Note the irregular boundary
of both single grains.



















(d) Annealing temperature--7500C; Annealing time--15 seconds. A rather
large, elliptical strain-free grain is growing in a grain boundary.
Note that this grain possesses a fairly regular boundary.


Fig. 8.--Continued





























(e) Annealing temperature--7500C; Annealing time--90 seconds. At lower
center of the photo note the rather large, strain-free grain which
has apparently grown to about an equal extent into both grains shar-
ing the boundary. Compare this grain with the somewhat smaller
grain in upper right of center which has grown preferentially into
one of the strained grains.


















(f) Annealing temperature--7500C; Annealing time--15 seconds. Note the
rather large strain-free grain slightly to the left of center. It
apparently occupies two serrations in the boundary between the strained
grains. One of the strain-free grains growing in the boundary slightly
to the right of center apparently has grown preferentially into the
left-hand strained grain and the second new grain into the right-hand
strained grain.

Fig. 8.--Continued























(g) Annealing temperature--7500C; Annealing time--60 seconds. The two
strain-free grains growing along the upper, serrated boundary appa-
rently have experienced a preferred growth into the lower grain.
The strain-free grain occupying the lower boundary has evidently
grown into both strained grains.















(h) Annealing temperature--7000C; Annealing time--240 seconds. The group
of three strain-free grains have apparently formed in serrations and
are growing preferentially into the right-hand grain.


Fig. 8.--Continued


V4













TABLE 4.--Volume fraction strain-free material for specimens erdat7510


7500c
Annealing
Specimen Time Volume
Number (seconds) Fraction, VV VV*


2-1

2-2

3-1

11-4

3-4

11-1

1-3

2-3

1-2

2-4

1-1

11-3

11-5

7-3


0.006

0.015

0.031

0.053

0.081

0. 16

0.225

0.415

0.70

0.94

0.980

0.984

0.991

0.999


0.002

0.005

0.005

0.005

0.008

0.01

0.015

0.015

0.01

0.01

0.004

0.001

0.003

0.001


Annea i nq Temp!rtur
7000C
Annealing
Specimen Time o1lu
Number (seconds) Fration, L_

2-1 0 1,b

7-5 60 0,01

6-2 120 0.031

6-4 240 01.A

8-2 360 lll0

7-1 480 O.JI

8-4 600 0,

7-2 720 1,R

8-5 960 0.;8

8-3 1440 0.90

8-1 1920 0.986


*Calculated from
VV (see reference 29).


the expression VV2 = Vv2 for 0.10 < VV 1 0.90 anlfrathe
Np














worked at 750C and annealed at 7500C, 7000C and 6700C


erature


Volume
*action, Vy VV^

0.006 0.002

0.014 0.004

0.031 0.005

0.047 0.006

0.140 0.008

0.213 0.010

0.48 0.01

0.62 0.02

0.78 0.01

0.90 0.01

0.986 0.004


670-C
Anneali ng
Specimen Time Volume -
Number (seconds) Fraction, VV Vy

2-1 0 0.006 0.002

9-3 480 0.029 0.003

12-4 960 0.089 0.008

10-2 1440 0.174 0.011

9-4 1920 0.273 0.012

10-4 2880 0.465 0.015

10-3 3840 0.745 0.015

12-1 4800 0.85 0.01

12-2 5760 0.90 0.01


land from the expression 2 = -K)V or all other values of
-po for all other values of


-.A









annealing time for each annealing temperature in Figures 9, 10, and 11.

All three sets of data could be represented by sigmoidal curves. In only

one or two cases were the actual data points more than V from these

curves. The curves differ from those commonly obtained in studies of re-

crystallization after cold deformation in two important respects:

I. A small fraction of strain-free material was present
immediately after working. This material may have
resulted either from small areas which experienced
growth during working instead of becoming deformed,
or from strain-free areas which originated and grew
during the working process. This small amount of
strain-free material present at the beginning of the
annealing period removed all possibility of an incu-
bation period such as is commonly observed in studies
of annealing after cold working.

2. A small fraction of strained material persisted to
very long annealing times. This is illustrated by
Figure 9 for specimens annealed at 7500C. This
phenomenon also has been observed during a study of
the recrystallization of high-purity iron (35). Other
authors also have noted small islands of unrecry-
stallized material in a recrystallized matrix (36).
The latter study showed that these areas were either
very close in orientation or twin-related to the sur-
rounding recrystallized material.


Number of Strain-free Grains Per Unit
Area and Per Unit Volume

DeHoff (37) has derived an expression relating the three experi-

metally measurable quantities VV, NA, and (NL)NE to the number of parti-

cles, or grains, per unit volume. The exact relationship is:

V (NA)3 K23
NV = VV(NA) K2 where Kl, K2 and K are shape factors and (NL)NE
NL)NE3 8K13K3

is the number of grain boundary intersections per unit length of test

line. Assuming that the strain-free grains were spheres, a rather good

assumption for short annealing times, the ratio of shape factors was












0.8


0.6


o0


I I I I I 1r I I s


0 50 100 150 200 250 300) '300 600 900 1200 1500
ANNEALING TIME (SECONDS

Fig. 9.--Volume fraction strain-free material versus annealing time for specimens worked at
7500C and annealed at 7500C.


I







1.0






?0.8


-J


w 0.6


I-
w

Lo.


z 0.4
o





4 0.2
0


ANNEALING TIME (SECONDS)

Fig. O0.--Volume fraction strain-free material versus annealing time for specimens worked at
7500C and annealed at 7000C.











z0.8 -




0.6 -



I- '
o0.4




0.2





0 800 1600 2400 3200 4000 4800 5600 640(
ANNEALING TIME (SECONDS)
Fig. ll.--Volume fraction strain-free material versus annealing time for specimens worked at
7500C and annealed at 6700C.






47

found to be 7.39. The major assumption of the derivation which resulted

in the above equation was that the distribution of particle sizes is log

normal. This assumption was tested by measuring over 400 chord lengths

and calculating the actual particle size distribution according to the

method of Spektor as described by Underwood (38). Procedure, calcula-

tions and results are described in Appendix C. It is sufficient to state

here that the particle size distribution was close to log normal.

Corrected values for the number of strain-free grains per unit

area are included in Table 5. These values, in conjunction with the ap-

propriate values for VV and (NL)NE, were used to calculate the number of

strain-free grains per unit volume. Table 6 contains the experimental

values of (NL)NE.

Calculated values for the number of strain-free grains per unit

volume are included in Table 5 and plotted in Figure 12. The data were

subject to errors from several sources. There were not only the usual

errors of a statistical nature but also those which stem from: (I) the

assumptions used to derive the relationship between NV and the measurable

quantities, and (2) those inherent in the approximate correction applied

to the original experimental data. A rough calculation involving esti-

mates of the errors from the above sources indicated that the calculated

values of NV were most probably within 0.5 x 105/mm of the true value.

These limits are indicated on the plots of Figure 12. In all but two

cases the experimental points fall within the probable error of the

measurement.

The most important thing to note about Figure 12 is that there

was no tendency at any temperature for the number of new grains per unit













TABLE 5.--Number of strain-free grains per unit area and per unit volume fcPiPS
7000C and 6700C

Annealing Temperature
7500C 7000C
Annealing Annealing
Specimen Time NV/m 3 Specimen Time
Number (seconds) NA/mm2 x 10-5 Number (seconds) NA/mm2 05

2-1 0 425 1.3 2-1 0 425 1,

2-2 15 490 1.4 7-5 60 460 .,1

3-1 30 480 1.15 6-2 120 475

11-4 45 485 1.0 6-4 240 570 la

3-4 60 475 1.05 8-2 360 595 1.

11-1 75 630 0.8 7-1 480 655 01.

1-3 90 710 0.8 8-4 600 790 0,

2-3 120 800 0.7 7-2 720 875 0,8

1-2 180 890 1.0 8-5 960 885 1

2-4 240 925 1.2 8-3 1440 900 1.2

1-1 300 880 1.9 8-1 1920 920 1,

11-3 360 795 1.9

11-5 720 740 1.5

7-3 1440 740 1.2














r specimens worked at 7500C and annealed at 7500C,



6700C
Annealing
NV/mm3 Specimen Time NV/mm3
x 10-5 Number (seconds) NA/mm2 x 10-5

1.3 2-1 0 425 1.3

1.15 9-3 480 550 1.1

1.4 12-4 960 600 0.8

1.25 10-2 1440 590 0.75

1.0 9-4 1920 580 0.60

0.7 10-4 2880 595 0.50

0.6 10-3 3840 670 0.60

0.8 12-1 4800 740 0.85

1.0 12-2 5760 690 1.3















TABLE 6.--Grain boundary intercepts (excluding twin boundary intercepts) f
specimens worked at 7500C and annealed at 7500C, 700't

Annealing Temperature
7500C 7000C
Annealing Annealing
Specimen Time (NL)NE/ Specimen Time (NL)NE/
Number (seconds) mm Number (seconds) mm


2-1

2-2

3-1

11-4

3-4

11-1

1-3

2-3

1-2

2-4

I-I

11-3

11-5

7-3


0

15

30

45

60

75

90

120

180

240

300

360

720

1440


2-1

7-5

6-2

6-4

8-2

7-1

8-4

7-2

8-5

8-3

8-1


0

60

120

240

360

480

600

720

960

1440

1920















.rcq for strain-free grains (NL)NE, for
iO,SC and 6700C


6700C
Annealing
S Specimen Time (NL)NE/
Number (seconds) mm

8 2-1 0 2.8

9-3 480 6.2

S 12-4 960 11.9

10-2 1440 15.3

9-4 1920 18.9

S 10-4 2880 25.1

10-3 3840 30.7

12-1 4800 31.5

S12-2 5760 29.2


~






7500C
2.0-




1.I ia /







2.0 7000
0.5-








0 400 800 1200 1600 2000
1100 1500







ANNEALING TIME (SECONDS)








2.0 700
So.> -









0 1 2000 0 00 4000 5000 6000
ANNEALING TIME (SECONDS)







Fig. 12.--Number of strain-free grains per unit volume versus
annealing time for specimens worked at 7500C and annealed at 7500C,
7000C and 6706C.
/T77I. -7'r7
:>o. ]SS7 ///!SsZSS!








700C and 6700C.









volume to increase with increasing annealing time until over 40 per cent

of the structure was strain free. The decrease noted in the number of

strain-free grains per unit volume for short annealing times at all tem-

peratures is most likely due to the selective absorption of some grains

by their neighbors, which neighbors possess a considerable growth advan-

tage. For instance, it is unlikely that all three grains of the group

indicated in Figure 8 (b) will survive and grow. At least one will prob-

ably disappear. Since impingement of grains growing in the same boundary

occurs very early, one could expect a considerable number of the strain-

free grains originally present to disappear by this mechanism. The in-

crease in the number of strain-free grains per unit volume which begins

at moderate annealing times for all temperatures is not so readily ra-

tionalized. There are two other changes which occur at the same anneal-

ing times: (1) experimental values of (SV)o-N begin to decrease, and (2)

the slope of the VV versus annealing time plots begins to decrease. Both

of these phenomena are probably associated with the beginning of rapid

impingement of grains which originated in different boundaries or along

different edges. It is at this point that the assumption of spherical,

strain-free grains could be expected to result in a serious error.

A comparison of all three plots revealed a slight tendency for

the number of new grains per unit volume to decrease with decreasing an-

nealing temperature. The average values indicated in Figure 12 are as

follows: 1.2 x 105/mm3 at 7500C, 1.05 x 105/mm3 at 7000C and 0.87 x

105/mm3 at 6700C. However, an analysis based on Student's "t" test indi-

cated that the three averages are not significantly different.









Growth Rates

The two methods used to calculate growth rates of the strain-free

grains yielded quite different results. These are summarized in the fol-

lowing table.


TABLE 7.--Growth rates for annealing temperatures of 7500C,
7000C and 6700C

Growth Rates, G(mm/sec)
Calculated from
the Expression
Annealing Calculated from Maximum G (SV)O- N
Temp. (C) Intercept Data dVV/dt(26)*

750 1.0 x 10-3 1.4 x 10-4

700 2.3 x 10-4 2.6 x 10-5

670 6.1 x 10-5 6.4 x 10-6


*These values are averages of the data given in Table 9.


The actual measurements of maximum intercept appear in Table 8

and are plotted versus annealing time in Figure 13. Values listed above

are the slopes of these curves.

Data necessary for the calculation of growth rates from the ex-

pression G (SV)0-N = dVV/dt are readily available. Slopes measured

from the curves of Figures 9, 10 and 1I at the appropriate times gave di-

rectly values for dVv/dt. Table 11 contains values for (SV)o-N calcu-

lated from the expression (SV)0-N = (SV)old + (SV)new (SV)total as ex-

plained in a subsequent section. These values are plotted in Figures 14,

15 and 16. Values of (SV)o-N for the calculation of growth rates were

obtained from the smooth curve drawn through the experimental points.

The growth rates thus calculated have been collected into Table 9.





















TABLE 8.--Maximum intercept of largest unimpinged grain for specimens wo;:liflan
7000C and 6700C

Annealing Temperature
7500C 7000C
Annealing Annealing
Specimen Time Diameter Specimen Time Diameter idm
Number (seconds) (x 10 mm) Number (seconds) (x 102 mm) IfA,

2-1 0 1.2 2-1 0 1.2 H

2-2 15 2.2 7-5 60 2.4 H

3-1 30 4.2 6-2 120 3.7 Il

11-4 45 6.2 6-4 240 6.5 H

3-4 60 7.1 8-2 360 9.4

11-1 75 8.6





53
















r)rked at 7500C and annealed at 7500C,


6700o
Annealing
Time
(seconds)


Diameter
(x 102 mm)

1.2

3.9

7.2

10.0


Specimen
Number

2-1

9-3

12-4

10-2








10

7500C






2O

0 I I i
0 16 32 8 4 8
ANNEALING TIME (SECONDS)


10 -

S8 7000C





2

0
u 0 0 160 240 320 00
ANNEALING TIME (SECONDS)


10 -

v 8 6700C

S6



2

0
0 250 500 750 1000 1250 1500
ANNEALING TIME (SECONDS)

Fig. 13.--Maximum intercept of largest unimpinged grain
versus annealing time for specimens worked at 7500C and annealed
at 750C, 7000C and 670C.























16




8-




I I I I I I I I I I
0 40 80 120 160 200 240 280 320 360
ANNEALING TIME (SECONDS)
Fig. 14.--Surface area per unit volume separating strain-free from strained material (the
migrating interface area) versus annealing time for specimens worked at 7500C and annealed at 7500C.












32




24




16









0I I I I I I4
S 240 480 720 960 1200 1440 1680 1920
ANNEALING TIME (SECONDS)

Fig. 15.--Surface area per unit volume separating strain-free from strained material (the
migrating interface area) versus annealing time for specimens worked at 7500C and annealed at 7000C.











32



O
24




16




8




I I y 2 D 1 4 b
ANNEALING TIME (SECONDS)
Fig. 16.--Surface area per unit volume separating strain-free from strained material (the
migrating interface area) versus annealing time for specimens worked at 7500C and annealed at 6700C.














TABLE 9.--Growth rates calculated from the expression G (SY)oN = dVV/d i
and annealed at 7500C, 7000C and 6700C


7500C
Annealing
Specimen Time G x 10
Number (seconds) (mm/sec)

2-1 0

2-2 15 0.9

3-1 30 1.2

11-4 45 1.2

3-4 60 1.3

11-1 75 1.4

1-3 90 1.5

2-3 120 1.5

1-2 180 2.2

2-4 240 1.7

1-1 300

11-3 360

11-5 720

7-3 1440


Annealing Temperature
7000C
Annealing
Specimen Time G x 105
Number (seconds) (mm/sec)

2-1 0

7-5 60 2.1

6-2 120 2.0

6-4 240 2.4

8-2 360 2.8

7-1 480 4.0

8-4 600 4.2

7-2 720 2.9

8-5 960 1.4

8-3 1440 1.6

8-1 1920


II















$dt for specimens worked at 7500C



6700C
Annea i ng
SSpecimen Time G x 106
S Number (seconds) (mm/sec)

2-1 0

9-3 480 5.8

12-4 969 9.9

10-2 1440 7.8

9-4 1920 6.6

10-4 2880 7.2

10-3 3840 7.2

12-1 4800 3.5

12-2 5760 3.3









Neglecting the values calculated for zero time and those calculated for

long annealing times, one notes that the calculated values for a particu-

lar temperature vary (with one exception) only by a factor of between

two and three. In the absence of any systematic variation, one can as-

sume that the data indicated a constant growth rate for each temperature.

The calculation of growth rates from area or length measurements

performed on a metallographic surface has a long history. Measurements

of this type were made as early as 1930 (39) and as recently as 1964 (35).

Although the descriptions of the actual procedures are often less than

precise, it can be inferred that either a maximum revealed diameter or

area was measured, usually the latter. The objections to these proce-

dures are widely realized, but should probably be repeated.

One must first consider the probability that a random plane will

intersect the largest strain-free grain to reveal a maximum area. This

probability is, of course, close to zero. If this unlikely event were to

occur in each of a series of specimens, one must still face the problem

that growth rates have been shown to vary widely from grain to grain.

The result, therefore, is the growth rate of a grain which may be neither

the first formed nor the fastest growing. The only rational appears to

be that results plotted versus annealing time yield a monotonic curve,

usually linear.

In the present study initiation of new grains was complete at

zero time. Growth rates calculated from maximum intercept measurements

performed should therefore approach those of the fastest growing grain,

subject to the probability considerations outlined above. In this re-

spect, it should be noted that measurement of a maximum intercept will










approach more closely the maximum growth rate than maximum area measure-

ments. This is so since there are an infinite number of planes which

contain the maximum intercept, but only one which contains the plane of

maximum area.

The major reason for performing the maximum intercept measurement

was to provide comparisons with the growth rates calculated from the ex-

pression G (SV)0-N = dVV/dt. This method is free of the above objec-

tions and yields an average rate for all interfaces between the strained

material and strain-free grains. The results are therefore much more

satisfactory and satisfying than those from the maximum intercept

measurements


Surface Area Measurements

Three basic surface area measurements were made on all specimens.

They were:

I. Total surface area per unit volume, (SV)total'

2. Surface area per unit volume possessed by the new,
unstrained grains, (SV)n i.e., the grain boundary
area which had undeformed material on at least one
side of the boundary.

3. Surface area per unit volume possessed by the old,
strained grains, (SV)old, i.e., the grain boundary
area which had deformed material on at least one
side of the boundary.

These measurements were described in greater detail in a previous section.

Since subgrain boundaries were not revealed by the etching procedure used,

measurements could include only grain and twin boundaries. Data obtained

are included as Table 10. Values for (SV)total have been plotted versus

annealing time for each annealing temperature, Figures 17, 18, and 19. In














TABLE 10.--Experimental measurements of surface area per unit volume withitin
strained material on at least one side of the boundary, (SV)old and the tlls
55K


7500C
Annealing
Specimen Time (Sv)new (Sv)old (SV)total
Number (seconds) /mm /mm /mm

2-1 0 5.5 99 99

2-2 15 8.5 103 103

3-1 30 11.5 98 98

11-4 45 20.5 103 104

3-4 60 20.5 104 104

11-1 75 39.5 98 110

1-3 90 50 95 107

2-3 120 68 72 108

1-2 180 95 29.5 101

2-4 240 101 8.8 101

1-1 300 92 6.6 92

11-3 360 89 2.2 89

11-5 720 86 0.05 86

7-3 1440 84 0.15 84


700'(
Annealing
Specimen Time iija
Number (seconds) In

2-1 0 ,5

7-5 60 8,5

6-2 120 11

6-4 240 16

8-2 360 1i.

7-1 480 41

8-4 600 78

7-2 720 I

8-5 960 5

8-3 1440 so

8-1 1920 92












4 strain-free material on at least one side of the bound, (SV)new, with
hotal surface area, (Sv)total, for specimens worked at 790 C and annealed at
7500C, 7000C and 6700C


Annealing Temperature
it
(SV)new (SV)old (Sv)total
/mm /mm /mm
5.5 99 99
8.5 108 108
11 106 106
16 104 104
31.5 96 106
43 94 105
78 67 109
84 46.6 100
93 29.8 101
90 16.2 93
92 4.2 92


670uC
Annealing
Specimen Time (SV)new (SV)old (Sv total
Number (seconds) /Am /mm /mm
2-1 0 5.5 99 99
9-3 480 12.5 98 99
12-4 960 26 99 104
10-2 1440 35 90 100
9-4 1920 44.5 84 102
10-4 2880 65.5 73 102
10-3 3840 84 37 94
12-1 4800 89 21 91
12-2 5760 87 15.5 89





1
























8-




20-




0 50 O00 150 200 250 30 L '300 600 900 1200 1500
ANNEALING TIME (SECONDS)
Fig. 17.--Total boundary area per unit volume, (SV)total, versus annealing time for specimens
worked at 7500C and annealed at 7500C.








160 to 300




140 \



120





0oo




80




20 -




0240 00 720 960 1200 4 150 16O 1920
ANNEALING TIME (SECONDS)

Fig. 18.--Total boundary area per unit volume, (S) total, versus annealing time for the specimens
worked at 7500C and annealed at 7000C.








160 to 300




\
\

140 \


.100
Jio

,'


NT


l I I
0 800 1600


I I I 1
2400 3200 4000
ANNEALING TIME (SECONDS)


jOO b 56o0


Fig. 19.--Total boundary area per unit volume, (SV)total, versus annealing time for the
specimens worked at 7500C and annealed at 6700C.









all of the above data no effort was made to separate twin boundaries from

grain boundaries. Thus, all surface area values represent the sum of the

grain boundary area and the twin boundary area. Twin boundaries not only

form a part of the total boundary network but also one could argue that

since twin boundaries evidently serrate and distort as readily as grain

boundaries during working there is no real difference between them. They,

thus, may be considered as high-angle boundaries.

Experimental measurements of (SV)old, (Sv)new and (SV)total per-
mitted the calculation of three more significant types of surface area:

I. (SV)0-0, the grain boundary area per unit volume
separating deformed grains.

2. (SV)N-NI the grain boundary area per unit volume
separating strain-free grains.

3. (SV)0 the grain boundary area per unit volume
with deformed material on only one side of the
boundary.

It is obvious from the above definitions that:

(SV total = (SV)0-0 + (SV)N-N + (SV)-N

(SV)old = (S0-0 + (SV0-N

(SV)new = (S)N-N + (SV0-N

From these three expressions, one finds that:

(SV)N-N = (S) total (SV)old

(SV)0-0 = (SV)total (SV)new

(Sv)o-N = (SV)old + (SV)new (SV)total

Values of (SV)0_0, (SV)N-N, and (SV)O-N calculated from the above equa-
tions are included in Table 11. Values obtained for all three types of















TABLE lI.--Calculated values of
on both sides of the boundary,


surface area per
(Sv)o-o; and (3)
migrating


unit volume with: (1) sip
strained material on one i
interface area) for speca


7500C
Annealing
Time (Sv)N-N
(seconds) /mm

0 0.0

15 0.0

30 0.0

45 1.0

60 -1.0

75 12

90 12

120 36

180 71.5

240 92

300 85.5

360 87

720 86

1440 83.5

86


(Sv)o_0-0
/mm

93.5

94.5

86.5

86.5

83.5

70.5

57

40

6

0.0

0.0

0.0

0.0

0.0


(SV) -N
/mm

5.5

8.5

11.5

19.5

21

26.5

38

32

23.5

9

6.5

2

0. I

0.3


Anl'

Annealing
Specimen Time
Number (seconds)

2-1 0

7-5 60

6-2 120

6-4 240

8-2 360

7-1 480

8-4 600

7-2 720

8-5 960

8-3 1440

8-1 1920


*This specimen had the same thermal history


Specimen
Number

2-1

2-2

3-1

11-4

3-4

11-1

1-3

2-3

1-2

2-4

1-1

11-3

11-5

7-3

2-1T


as specimen 2-1, but vii,














train-free material on both sides of the boundary, (SV)N-N; (2) strained material
side of the boundary and strain-free material on the other side, (SV)o-N (the
imens worked at 7500C and annealed at 7500C, 7000C and 6700C

lealinq Temperature
7000C 6700C
Annealing
(SV)N-N (Sv0-0 (SV)O-N Specimen Time (SV)N-N (S)0-0 (SV)O-N
/mn /mm /mm Number (seconds) /mm /mm /mm

0.0 93.5 5.5 2-1 0 0 93.5 5.5

0.0 99.5 8.5 9-3 480 1.0 86.5 12

0.0 95 11 12-4 960 5 78 21

0.0 89 16 10-2 1440 10 65 25

10 74.5 21.5 9-4 1920 18 57.5 26.5

11 62 32 10-4 2880 30 38 35.5

42 32 35 10-3 3840 57 10 27

53.5 16 30.5 12-1 4800 70 2 19

73 8 22 12-2 5760 73.5 2 13.5

77 3 13

88 0.0 4


vas not worked.






67
boundary area have been plotted versus annealing time: (Sv)o-N in

Figures 14, 15 and 16; (Sv)0-0 in Figures 20, 21 and 22; and (SV)N-N in

Figures 23, 24 and 25.



































I I I I


60


40 I


20 -


0 40 80 120 160 200 240 280 320 36
ANNEALING TIME (SECONDS)

Fig. 20.--Boundary area per unit volume with strained material on both sides of
boundary, (SV)0-0, versus annealing time for specimens worked at 7500C and annealed at
750C.


I I ,

























O
40 -





2C -
0




240 480 720 960 1200 1440 1680 1920
ANNEALING TIME (SECONDS)

Fig. 21.--Boundary area per unit volume with strained material on both sides of boundary,
(Sy)0-0, versus annealing time for specimens worked at 7500C and annealed at 7000C. a
%0





















0

O



20





0 800 1600 2400 3200 4000 4800 5600 6400
ANNEALING TIME (SECONDS)
Fig. 22.--Boundary area per unit volume with strained material on both sides of the boundary,
(SV)O-0. versus annealing time for specimens worked at 7500C and annealed at 6700C.




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