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 metal lographic measurements .

The author would 1 i ke-.fts, 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 . Jenki ns .

If

TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS i i

LIST OF TABLES V

LIST OF FIGURES MM

KEY TO SYMBOLS xiv

ABSTRACT xvi i

Chapter

I INTRODUCTION 1

Purpose of the Study and Definition of

Hot Working 3

Previous Studies 4

Hot working 4

Annealing after hot working 8

II EXPERIMENTAL MATERIAL, APPARATUS AND

PROCEDURES II

Experimental Material 11

Experimental Apparatus 11

Experimental Procedures 13

Preparation of tensile bars 13

Extension of tensile bars 15

Metallography 17

Quantitative metallography 21

III EXPERIMENTAL RESULTS 29

Metal lographic Observations 29

General observations 29

Observations pertaining directly to
the initiation and early stages

of growth of strain-free grains 35

Volume Fraction Strain-free Material 37

Number of Strain-free Grains Per Unit

Area and Per Unit Volume 43

Growth Rates 52

Surface Area Measurements 60

TABLE OF CONTENTS--Continued

Page

IV DISCUSSION T*

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 '07

Summary '22

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 1*6

V CONCLUSIONS 1*3

APPENDICES 1*5

LIST OF REFERENCES '79

i v

LIST OF TABLES

Table Page

1 Certified analysis of Nickel 200, heat 513A II

2 List of all specimens worked (at 750°C) and annealed
fet 750°C, 700°C and 670°C) wi th measured extensions
and reductions in area (sections mounted for

metal log raphic examination) 30

3 Microstructural positions occupied by strain-free
grains at various annealing times for specimens

worked at 750°C and annealed at 750°C 36

h Volume fraction strain-free material for specimens
worked at 750°C and annealed at 750°C, 700°C and
670°C ^2

5 Number of strain-free grains per unit area and per
unit volume for specimens worked at 750°C and

annealed at 750°C , 700°C and 670°C WI

6 Grain boundary intercepts (excluding twin boundary
intercepts) for strain-free grains, (Nl) hje, for
specimens worked at 750°C and annealed at 750°C,

700°C and 670°C ^9

7 Growth rates for annealing temperatures of 750°C,

700°C and 670°C . . . 52

8 Maximum intercept of largest unimpinged grain for
specimens worked at 750°C and annealed at 750°C,

700°C and 670°C 53

9 Growth rates calculated from the expression
G • (Sy)Q-N = dVy/dt for specimens worked at

750°C, 700°c and 670°C 58

10 Experimental measurements of surface area per

unit volume with strain-free material on at least

one side of the boundary, (Sv)new. witn strained

material on at least one side of the boundary,

(Sv)o]d, and the total surface area, (S\/)totai>

for specimens worked at 750°C and annealed a?

750°C, 700°C and 670°C 61

LIST OF TABLES --Continued

Table Pa9e

11 Calculated values of surface area per unit volume
with: (1) strain-free material on both sides of
the boundary, (SV)N.N; (2) strained material on
both sides of the boundary, (Sw)q_0; 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 750°C and annealed at 750°C, 700°C and

670°C 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.) . Nickel

200. Hot -working temperature = 705°C 77

13 Experimental values of Vv compared to those
calculated from the expressions Vv ■ 1 -exp-
^LvG2t2 (upper limit) and Vv ■ 1 -exp-

(?r LvGzt2)/3 (lower limit) for specimens

worked at 705°C and annealed at 750°C, 700°C

and 670°C no

]k 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 (t0 A 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 '33

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 '37

LIST OF TABLES— Continued

Table 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 1^*1

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

of hot working 1*7

21 Measured chord lengths and calculated values
for the number of grains per mtH 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

750°C. 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 (l) . Polarized light. 400X 25

6 A plot of (NAJcorrected/Na versus Vy 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 750°C and annealed at 750°C
(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 750°C

and annealed at 750°C 44

LIST OF FIGURES— Continued

Figure Page

10 Volume fraction strain-free material versus
annealing time for specimens worked at 750°C

and annealed at 700°C 45

11 Volume fraction strain-free material versus
annealing time for specimens worked at 750°C

and annealed at 670°C 46

12 Number of strain-free grains per unit volume
versus annealing time for specimens worked at

750°C and annealed at 750°C, 700°C and 670°C 50

13 Maximum intercept of largest unimpinged grain
versus annealing time for specimens worked at

750°C and annealed at 750°C, 700°C and 670°C 5**

14 Surface area per unit volume separating strain-
free from strained material (the migrating
interface area) versus annealing time for

specimens worked at 750°C and annealed at 750°C 55

15 Surface area per unit volume separating strain-
free from strained material (the migrating
interface area) versus annealing time for

specimens worked at 750°C and annealed at 700°C 56

16 Surface area per unit volume separating strain-
free from strained material (the migrating
interface area) versus annealing time for

specimens worked at 750°C and annealed at 670°C 57

17 Total boundary area per unit volume, (SyKotal'
versus annealing time for specimens worked at

750°C and annealed at 750°C 62

18 Total boundary area per unit volume, (Sy) ,,
versus annealing time for the specimens worked

at 750°C and annealed at 700°C 63

19 Total boundary area per unit volume, (Sv^total'
versus annealing time for the specimens worked

at 750°C and annealed at 670°C 64

20 Boundary area per unit volume with strained
material on both sides of boundary, (S^)q_q,
versus annealing time for specimens worked at

750°C and annealed at 750°C 68

LIST OF FIGURES— Continued

Figure Page

21 Boundary area per unit volume with strained
material on both sides of boundary, (Sv)n-n'
versus annealing time for specimens worked at

750°c and annealed at 700°C 69

22 Boundary area per unit volume with strained
material on both sides of the boundary,
(Sy)g_n, versus annealing time for specimens

worked at 750°C and annealed at 670°C 70

23 Boundary area per unit volume with strain-
free material on both sides of the boundary,
(Sw)m.(j, versus annealing time for specimens

worked at 750°C and annealed at 750°C 71

2k Boundary area per unit volume with strain-
free material on both sides of the boundary,
(Su)u.u, versus annealing time for specimens
worked at 750°C and annealed at 700°C 72

25 Boundary area per unit volume with strain-
free material on both sides of the boundary,
(Sw)u.Mj versus annealing time for specimens

worked at 750°C and annealed at 670°C 73

26 A plot of measured total extension versus
calculated e for Nickel 200. Specimens

extended at 705°C and 0.009/minute 78

27 A plot of the ratio of the calculated eg 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 1 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 (k, 46) 85

LIST OF FIGURES --Continued

Figure Page

30 A plot of ln(l/l-Vy) versus annealing time for
specimens worked at 750°C and annealed at 750°C,

700°C and 670°C 3h

31 An electron photomicrograph of a presumably
strain-free grain with a scalloped boundary

growing at an old grain boundary. 10.000X 96

32 A photomicrograph illustrating the growth of
a strain-free grain from a strained grain
apparently of nearly the same orientation.

Polarized light. I000X 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 l/tc versus l/T(°K) for Vv = 0.05 104

35 A plot of experimental growth rates (calculated

from G-(SV)0.N = dVv/dt versus 1/T(°K)) 105

36 A plot of calculated and experimental values
of Vw versus annealing time for specimens
worked at 750°C and annealed at 750°C. Solid
lines indicate calculated limits of circled

points experimental values Ill

37 A plot of calculated and experimental values

of Vw versus annealing time for specimens worked

at 750°C and annealed at 700°C . Solid lines

indicate calculated limits and circled points

experimental values 112

38 A plot of calculated and experimental values
of Vy versus annealing time for specimens
worked at 750°C and annealed at 670°C . Solid
lines indicate calculated limits and circled

points experimental values 113

39 A plot of (Sv)n -N versus ^V which includes all
values obtained from specimens annealed at

750°C, 700°C and 670°C 115

LIST OF FIGURES— Continued

Figure Page

40 A plot of (Sy)g_M versus Vv for hot -worked
silicon iron deformed to a strain of 0.45
at 8)2°C and annealed at 8I2°C. The data
were taken from the study by English and

Backofen 116

41 A plot of (Sy)o-o versus Vy which includes
all values obtained from specimens annealed

at 750°C, 700°C and 670°C 118

42 A plot of diamond pyramid hardness versus
annealing time for specimens extended 38

per cent at 755°C and annealed at 755°C 119

43 A plot of (Sy) N_», versus Vy which includes
all values obtained from specimens annealed

at 750°C, 700°C and 670°C 121

44 Photomicrographs obtained from partially
annealed specimens (worked and annealed at
705°C) having initial NL's of (a) 18/mm, and
(b) 4l/mm. Note the number of strain-free
grains which have formed at old grain edges

(triple points in two dimensions). 200X 130

45 A photomicrograph obtained from a specimen
of Nickel 200 worked at 855°C 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 132

46 A photomicrograph obtained from a specimen of
Nickel 200 worked at a rate of 0.009/mi nute 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 135

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) 139

48 Photomicrographs of specimens worked at 750°C
and annealed at 750°C . Annealing times are

indicated. Polarized light. 400X 150

LIST OF FIGURES— Continued

Figure Page

49 Photomicrographs of specimens worked at 750°C
and annealed at 700°C . Annealing times are

indicated. Polarized light. 400X 157

50 Photomicrographs of specimens worked at 750°C
and annealed at 670°C . 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

9

nk-l

"k

the average longitudinal strain in the grains calculated
from the equation given by Rachinger C+3)

G the growth rate calculated from the equation G • (Sy)rj-N

dVv/dt

k a constant

k a particular size class in Spektor's equation

K| a geometrical constant

K2 a geometrical constant

K^ a geometrical constant

Lu the length of grain edge per unit volume possessed by

strain-free grains—the nucleating edge

n a constant in the equation Vy " 1 -exp-ktn indicative of

the microstructural position at which new grains form

the number of chords per unit length of line in the kth
si ze class

the number of chords per unit length of line in the size
class k+1

&* the number of strain-free grains per unit area of

metal log raphic surface

(N^)-r the number of triple points per unit area which are at

least partially surrounded by strain-free grains

N|_ the number of intercepts per unit length of random line

made with a particular structural feature

(N[_)i the number of boundary intercepts per unit length of line

oriented parallel to the tensile axis

(nlW

(NL)new

(\)old

(NL)T

<NL>total

Np

NV

<Nv>k*

PP

Qg

It

R

sv

(Sv)new

(Sv)n-N

(Sv)old

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

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

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

the number of boundary intercepts per unit length of line
oriented perpendicular to the tensile axis

the total number of boundary intercepts per unit length of
random 1 i ne

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

the number of strain-free grains per unit volume

the number of particles per unit volume with mean diameter

ka

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

The "activation energy" for grain boundary migration cal-
culated from growth rates obtained from the equation
G • (Sv)fJ-N = dVu/dt

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

the gas constant

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

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

the boundary area per unit volume with stain-free grains
on both sides of the boundary

the boundary area per unit volume with strained material
on at least one side of the boundary

^V^O-N tne boundary area per unit volume separating strained

material and strain-free grains — the migrating interface

^V^O-0 tne boundary area per unit volume with strained material

on both sides of the boundary

V total the total boundary area per unit volume

t t i me

T temperature

tc the annealing time at which any specified fraction of the

structure is strain-free

tg_j 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

Vy the standard error of the volume fraction strain-free

grai ns

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. Metal lographic observations and
quantitative metal lographi c measurements were used to characterize the
structures formed during both processes. Quantitative metal lographic
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 (k) 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: (1) 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 stacki ng-faul t energy depended
upon the working conditions.

A study of specimens annealed at 750. 700, and 670°C after work-
ing at 750 C 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 snaring the edge or boundary
at which it is growing.

k. 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.

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 . (I)* noted that hot-rolled nickel (800°C followed by a
water quench) exhibited a stress-rupture life 25 times that of a similar,
unworked specimen quenched from 800°C . 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 .

1

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 agai n shows I i ttle 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 also they 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

crystal lographic 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
usual ly 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
recrystal 1 i zation of OFHC copper in as little as one-fifth of a second
after a moderate reduction by rolling at 700° 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 af tef worki ng , 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 1 i nes. — Slip lines are the manifestation on an external sur-
face of dislocation movement on a definite crystal lographi c plane and in
a specific direction. Observations made (under the optical microscope)
on high temperature slip in copper (3, k) , 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 serrati ons . --G rai n 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), ni ckel -al umi num 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 unresol vabl e. Above a considerably higher temperature they are
destroyed by recrystal 1 i zat ion along old grain boundaries (1). 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 Mwavey" or scalloped appearance
(9). An increase in grain size results in less prominent serrations (10).

Subqrai ns . --Subgrai ns 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-faul t energy of the material but also on the working
conditions. Materials of low stacking-faul t 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-faul t 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 stacki ng-faul t 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 worki nq. --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 Lucke (21),
by Hanemann (22), and by Tafel , Hanemann and Schneider (23). Similar in-
vestigations were performed at a later date by Kornfeld (2k) and by
Kornfeld and Hartleif (25). In all of these studies the emphasis was on

the recrystal I i zed 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 mi crostructural 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 recrystal 1 i zed 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 450°C 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.

10

Leguet et al , (3) found for a 70-30 brass annealed at a constant tempera-
ture that the rate of recrystal 1 ization 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 (recrystal 1 i zed) 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 genera] principles such
as have been established for annealing after cold working. The present
study is a systematic attempt to partially remedy this situation.

CHAPTER I I

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

El ement

C
Mn

Fe
S

Si
Cu

Ni

Per

Cent

0

.07

0

.26

0

.ok

0

.005

0

.07

0

.01

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.

11

12

13

Quenching was easily and rapidly performed by two men lifting the j i g 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: (1) Houghton's Liquid
Heat 11^5 for the pot in which the deformation was performed, and (2)
Houghton's Liquid Heat 11^5 plus 5 to 10 per cent lithium chloride for
the pot in which annealing at 700 C and 670°C 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 Metal lograph.

Experimental Procedures
Preparation of tensile bars

The as-received Nickel 200 rod was cut into 11-inch lengths and
annealed for 18 minutes at 750°C ± 1°C in Liquid Heat 1145. This treat-
ment resulted in a completely recrystal 1 i zed 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 3^ 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.

--r

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15

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-gri t Silicon Carbide Metallo-
graphic Papers and electropol ishi ng the gauge section. The 1/2-inch di-
ameter disks were similarly treated. Electropol i shi ng was performed in a
solution containing 144 ml C^hVOH, 32 ml 11,0, 16 ml n-butyl alcohol, 45 g
ZnCl2. ancl ,u 9 AlClj • 6H20. Polishing was accomplished satisfactorily
at voltages from 14 to 16 volts, and at temperatures from - 1 0°C to -25°C
utilizing a stainless steel cathode and a polishing time of approximately
one hour. After electropol i shi ng, the bars were given a final anneal in
Liquid Heat 1145 at 750°C ± 1°C for 25 minutes. The final anneal re-
sulted in a fairly equiaxed structure, illustrated by Figure 3, with an
N|_ of 45/11™. 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 749°C ± 1°C. At the end of the holding period, the jig was
switched on for 25 seconds (a time calculated to give a total extension

16

Fig. 3. — A photomicrograph of the structure
which resulted from the final 25-minute anneal at
750°C. 400X.

17

of about 31 per cent to all test bars) and then switched off if annealing
was to be performed at 750°C. If annealing was to be performed at 700°C
or 670°C, 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 750°C to 700°C. 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 750°C anneals was fairly simple and
in all cases the temperature was held between 7^8°C and 750°C. Control
was not so simple for the lower temperature anneals; however, all runs
fell within the following limits: 698°C to 702°C for nominal 700°C an-
neals and 664°C to 671°C for the nominal 670°C anneals.

Metal loqraphy

A portion of the gauge length which had experienced a reduction
in area of approximately 2k per cent was located in each tensile bar and
a 3/8-inch to 3A-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-gri t Silicon Carbide Metal lo-
graphic Papers. Initial polishing was performed with 6-mi cron diamond
paste on a Nylon cloth and 1-micron diamond paste on Microcloth. The

18

final mechanical polish utilized a Syntron vibratory polisher. The abra-
sive was Linde "B" on Microcloth and the polishing time was kO minutes.
In order to remove all traces of distorted metal, the specimens
were electropol i shed 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 -30°C and -35°C
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 kO 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 kS ml H20, hi ml concentrated
HNO3 and 8 ml HF (48-51 per cent HF) was prepared. To 3 ml concentrated
HC1 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 25°C and used as an
immersion etch. Etching times were between 8 and 12 seconds. The

19

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-crystal lographic grooving (28). The appearance of the
grooves as revealed by the electron microscope is illustrated by Figure k
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 crystal lographic 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

20

Fig. 't. --Electron photomicrograph illustrat-
ing the grooved surface produced on a specimen pol-
ished and etched as described in the text. 13,000X.

21

bent and possi bly wi 1 1 not al 1 be oriented i n the same manner wi th 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 recrystal 1 i zed grains thus can be
unequivocally separated from distorted or unrecrys tal 1 i zed 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 k 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 Hilliardand 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.

22

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 1-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): C^Vy/Vy)2 : 1/Np where <^VV 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 C^l/y/Vy)2 = (1-Vv)/Np given by Hilliard and Cahn can be used.

*A11 symbols have been defined in the Table of Symbols which is
located in front of the text.

23

Both of these equations also can be used to calculate the precision ob-
tained from the number of classified points.

I ntercept counting. — Intercept counts were used to determine the
surface area per unit volume of various features through the expression
2N|_ = Sy. In this expression N|_ is the number of intercepts per unit
length made by a test line with the feature of interest and Sw 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 9° 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 1 i ne 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 metal lographi c 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 metal lographi c surface (31, 32).

Three basic types of intercept counts were made:

1. Total number of intercepts made with all grain and twin
boundaries-(NL)tota, = 1/2 (S„) tota] .

Ik

2. The number of intercepts made with grain and twin
boundaries having strained material on at least one
side-(NL)0|d = l/2(Sv)Q|d.

3- The number of intercepts made with grain and twin
boundaries having strain-free material on at least
one side--(NL)new = l/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 Ny, 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, N^, 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:

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

25

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
Q). Polarized light. 400X .

26

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 N/\ 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 N/\ 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 Vy only and not a function of
temperature. The plot of Figure 6 was used to correct
all the measured values of N^.

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
(Nfl'T : l/2Ly where {H^)j is the number of triple points per unit area
and Ly 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

27

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28

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 metal lographi c 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 I I I

EXPERIMENTAL RESULTS

Metal loqraphi c 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 metal lographic 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
urani urn.

29

30

TABLE 2. --Li st of all specimens worked (at 750°C) and annealed (at 750°C, 700°C and 670°C) with measured extensions
and reductions in area (sections mounted for meta 1 lographi c examination)

Annea 1 i ng Temps

srature

750°C

700°C

670°C

Specimen
Number

Over-al 1
Extensi on
(Per Cent)

Reduc t i on

i n Area
(Per Cent)

Speci men
Number

Over-al 1
Extension
(Per Cent)

Reduc ti on

i n Area
(Per Cent)

Spec i men
Number

Over-al 1
Extensi on
(Per Cent)

Reduction

i n Area
(Per Cent)

2-1

29

25

2-1

29

25

2-1

29

25

2-2

30

23

7-5

29

2k

9-3

30

2k

3-1

30

22

6-2

28

26

12-4

32

25

11 -it

31

2k

6-4

32

23

10-2

30

2k

3-k

29

2k

8-2

30

23

3-k

31

26

11-1

30

2k

7-1

33

23

)0-k

31

2k

1-3

30

22

8-k

30

25

10-3

31

27

2-3

30

22

7-2

31

27

12-1

31

26

1-2

29

25

8-5

30

25

12-2

31

26

2-k

31

19

8-3

29

25

1-1

29

25

8-1

31

27

11-3

31

23

11-5

31

2k

7-3

30

26

31

(b) Specimen number 2-1

Fig. 7. --Selected photomicrographs from the
group of specimens worked at 750°C and annealed at
750°C (a) immediately before deformation, (b) 0 seconds
anneal, (c) 45 seconds anneal, (d) 120 seconds anneal,
(e) 720 seconds anneal. Polarized light. 400X.

32

(c) Specimen number 11 -k

Vv = 0.053

(d) Specimen number 2-3

Vv = 0.415

Fig. 7. — Cont i nued

33

(e) Specimen number 11-5

Vu = 0.991

Fig. 7. — Conti nued

34

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 stacki ng-faul t 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-faul t energy of
nickel, 150 ergs/cm (33) is somewhat less than that for aluminum, 225
ergs/cmz (3^) • A high stacking-faul t energy is associated with a small
separation between the two partial dislocations produced by the disloca-
tion reaction | [Tio] -^» | [T2T] + | [*2|T] , an energetically feasible
reaction. The small separation between partials in turn means that the
dislocation can climb much more easily than one composed of two widely
separated partials in a material of low stacking-faul t energy. Since
climb is necessary for the formation of a wel 1 -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.

35

Ormerod and Tegart (16) have reported that subgrains formed in
nickel during hot torsion at 600°C are small with diffuse boundaries and
contain many dislocations in their interiors. An increase in the defor-
mation temperature to about 850°C 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 750°C 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.

36

<Si

a>

e

C -M

E

O <D

— c

4-J

c *■» .—

0 — E

CJI

•- I/l L

c-\

\D

c

+-> o a>

O

O

O Q_ -M

(U CD

o

o

O

ro

1- ID "D

CD

U_ l/l C

C

o —

c

JZ

to

3 VI

</>

D

O

>- o

(DO

> o

LT\

l/l

■m p^

C 1-

ro

— o

+J

(0 —

^D

o

l/l (0

c

en <D

— TJ

o

o

O

to tu

"O

c c

tu

en <u

4-J

CD

c

<d c

D

<u c

o

l- 15

<_>

i -a

I/)

l/l

c c

— (0

f0

c

C 0)

TO

flj 1-

CM

CO

O

i- O

!_

L_ fD

J"

m

CI

4-JO

CJ

en -a

IT) O

c

O

o

O

LA

4-

C D

>«r-.

0

— O

.Q

n

c

"O 0)

o

a>

— "O

Q. OJ

o

3 ^

(0

O i-

1_

<D

u o

la-

0 2

Q. l/l

.— 4-J

<N

en

c-t

l/l t/1

1- C

J-

J-

LT\

c c

o a)

o

o

o

O

— E

-m a.

-t-i ._

«J

.- u

in tu

0 Q-

Q_ l/>

— !_

fD O

1_ i+-

cn s-^.

D

C i/l

-t-J

— "U

o

— <D C

D

03 E O

o

LTi

o

u

Q> — O

CV-!

C 1— 0)

l/l

C C/)

o

< '-*

u

1

on

<L> 1-

LU

E <D

_l

— .Q

cvj

CD

U E

1

1

1

<

0) D

CN

OJ

C"\

1-

Q. -Z.

t/>

37

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
1000X. 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.

k. 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 k. These values also were plotted versus

38

(a) Annealing temperature — 750°C; 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--750°C; 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. I000X.

39

(c) Annealing temperature — 750°C; 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 — 750°C; 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. --Cont i nued

40

(e) Annealing temperature — 750°C; 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 — 750°C; 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. — Conti nued

41

(g) Annealing temperature--750°C; 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— 700°C; 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. — Conti nued

42

TABLE 4. — Volume fraction strain-free materia) for specimens worked at 750°C and annealed at 750°C, 700°C and 670°C

Annea 1 i r

!S_

Temp

erature

750°

700°C

670

JC

Speci men
Number

Annea 1 i
Ti me
(seconc

ng
s)

Vo 1 ume
Fraction,

cr ...

Speci men
Number

Annea 1 i ng

Ti me
(seconds)

Vol ume
Fraction,

VV

vv

Specimen
Number

Annea 1 i
Time
(seconc

"9
s)

Vol ume
Fracti on,

0.002

2-1

0

0.006

0.002

2-1

0

0.006

0.002

2-1

0

0.006

2-2

15

0.015

0.005

7-5

60

0.014

0.004

9-3

480

0.029

0.003

3-1

30

0.031

0.005

6-2

120

0.031

0.005

12-4

960

0.089

0.008

11-4

45

0.053

0.005

6-4

240

0.047

0.006

10-2

1440

0.174

0.01 1

3-4

60

0.081

0.008

8-2

360

0. 140

0.008

9-4

1920

0.273

0.012

11-1

75

0.16

0.01

7-1

480

0.213

0.010

10-4

2880

0.465

0.015

1-3

90

0.225

0.015

8-4

600

0.48

0.01

10-3

3840

0.745

0.015

2-3

120

0.415

0.015

7-2

720

0.62

0.02

12-1

4800

0.85

0.01

1-2

180

0.70

0.01

8-5

960

0.78

0.01

12-2

5760

0.90

0.01

2-4

240

0.94

0.01

8-3

1440

0.90

0.01

1-1

300

0.980

0.004

8-1

1920

0.986

0.004

11-3

360

0.984

0.001

11-5

720

0.991

0.003

7-3

1440

0.999

0.001

Vy (see

-'-'Calculated f
reference 29)

'om

the exp

a" 9

-ess ion Vy

= VV2 for 0
Np

10* vv £

0

.90

and from

the

expression

<r, 2 = (i

VV

-KV)VV2
Np

for

al 1 other

values of

*3

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 750°C. This
phenomenon also has been observed during a study of
the recrystal I ization of high-purity iron (35). Other
authors also have noted small islands of unrecry-
stallized material in a recrystal 1 i zed matrix (36).
The latter study showed that these areas were either
very close in orientation or twin-related to the sur-
rounding recrystal 1 i zed 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 Vy, NA> and (NL)NE to the number of parti-
cles, or grains, per unit volume. The exact relationship is:

VV(NA)3 K 3
V = (n ) 3 ' — S — where Kj , K2 and K are shape factors and (N|_)NE
1- NE °K] ^3

is the number of qrai n 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

Q

(fy\) 1VIU3J.VW 33MJ-NIVX1S N0U3VWJ 3WmOA

Mi

o

a

*->

—

ro

1

o

s

s

c

1

'u
j
a.

o

o

vt

cr>

0

<4-

o

I

o

•J3

ftl

c

"J

O

<U

O

E

m

c

^ i/>

*u

V-

at

tfl

o o

3

c-» U

Ul

til

u

I/)

i

•**

>

Ui

_

o r:

<u

IA —

CM l~

0)

CJ

-

Z
-J

S

<

0)

UJ

0)

,

o z

l_

o z

M-

TM <

1

c

~

L

o

wi

l/\

c
O

u ■

to (.1
*- 0
*- o

o

in

o

0) h*

E
— to

o

> -a

>7

o

a\ a>

c

. ■ c

en <D

i i

e

i i y

0

U

1SI

o

o

o

o

IT*

"I0A

r*.

A5

(AA) 1VIM3J.VW 33bJ-NIVMiS NOUDVMJ 3WfnO/\

46

(AA) IVIHBiVH 33MJ-NIVU1S NO I13VMJ BWmtM

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 (N|_)N£.

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: (1) the
assumptions used to derive the relationship between Nw 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 Ny were most probably within ± 0.5 x 10^/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

48

TABLE 5 --Number of strain-free grains per unit area and per unit volume for specimens worked at 750°C and annealed at 750°C,

700°C and 670°C

Anneal i nq

Temperature

75u°C

700°C

670°C

Speci men
Number

Annea 1 i ng

Ti me
(seconds)

Vmm2

Nu/ 3
» mm

x 10"5

Speci men
Number

Annea 1 i
Ti me
(second

ng
s)

NA/mm2

vmm3

x 10-5

Speci men
Number

Annea 1 i ng

Time
(seconds)

^mm2

Mmm3

v mm

x 10-5

2-1

0

425

1.3

2-1

0

425

1.3

2-1

0

425

1.3

2-2

15

490

1.4

7-5

60

460

1.15

9-3

480

550

1. 1

3-1

30

480

1.15

6-2

120

475

1.4

12-4

960

600

0.8

11 -it

45

485

1 .0

6-4

240

570

1.25

10-2

1440

590

0.75

3-4

60

475

1.05

8-2

360

595

1.0

9-4

1920

580

0.60

11-1

75

630

0.8

7-1

480

655

0.7

10-4

2880

595

0.50

1-3

90

710

0.8

8-4

600

790

0.6

10-3

3840

670

0.60

2-3

120

800

0.7

7-2

720

875

0.8

12-1

4800

740

0.85

1-2

180

890

1.0

8-5

960

885

1.0

12-2

5760

690

1.3

2-4

240

925

1.2

8-3

1440

900

1.2

1-1

300

880

1.9

8-1

1920

920

1.2

11-3

360

795

1.9

11-5

720

740

1.5

7-3

1440

740

1.2

49

TABLE 6. --Grain boundary intercepts (excluding twin boundary i ntercepts) for strain-free grains (NL)NE> for
specimens worked at 75n°C and annealed at 750°C, 700°C and 670°C

Anneal i ng Tempe

rature

750°C

700°C

670°C

Speci men
Number

Anneal i ng

Ti me
(seconds)

<nlV/

mm

Speci men
Number

Anneal i ng

Ti me
(seconds)

mm

Speci men
Number

Anneal i ng

Ti me
(seconds)

<nlW

mm

2-1

0

2.8

2-1

0

2.8

2-1

0

2.8

2-2

15

4.3

7-5

60

4.2

9-3

480

6.2

3-1

30

5.8

6-2

120

5-4

12-4

960

11.9

11-4

45

7.7

6-4

240

7.9

10-2

1440

15.3

3-4

60

8.4

8-2

360

13.1

9-4

1920

18.9

11-1

75

15-3

7-1

480

18.6

10-4

2880

25-1

1-3

90

19.6

8-4

600

31.2

10-3

3840

30.7

2-3

120

28.0

7-2

720

33-5

12-1

4800

31-5

1-2

180

33.4

8-5

960

34.1

12-2

5760

29.2

2-4

240

34.0

8-3

1440

30.6

1-1

300

29.6

8-1

1920

31.7

11-3

360

26.7

11-5

720

27.0

7-3

1440

27.8

50

2.0

750°C

L— Hi

'700 I

100

200 300
ANNEALING TIME (SECONDS)

100 1500

U 1.0

700°C

UOO 800 1200 1600 2000
ANNEALING TIME (SECONOS)

1000

2000 3000 1»000

ANNEALING TIME (SECONDS)

5000

6000

Fig. 12. — Number of strain-free grains per unit volume versus
annealing time for specimens worked at 750°C and annealed at 750°C,
700°C and 670°C.

51

volume to increase with increasing annealing time until over kO 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
i ndi cated in Fi gure 8 (b) will survi ve and grow. At least one wi 1 1 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 (S ) q_^ begin to decrease, and (2)
the slope of the Vy 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 wi th decreasing an-
nealing temperature. The average values indicated in Figure 12 are as
follows: 1.2 x 105/mm3 at 750°C, 1-05 X lO^/mm3 at 700oc and 0q7 x
lO^/mrrv at 670°C. However, an analysis based on Student's "t" test indi-
cated that the three averages are not significantly different.

52

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 750°C,
700°C and 670°C

Growth Rates, G(mm/secJ~

Calculated from
the Expression
Annealing Calculated from Maximum G • (Su)p m =

Temp. (°C) Intercept Data dVy/d t (26)*

750 1.0 x 10"3 |.» x lO-**

700 2.3 x lO"** 2.6 x 10"5

670 6.1 x 10"5 G.k 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 • (Sy)g.fj = dVy/dt are readily available. Slopes measured
from the curves of Figures 9, 10 and 11 at the appropriate times gave di-
rectly values for dVy/dt. Table 11 contains values for (Sv)g.N calcu-
lated from the expression (SV)0.N = (S„)o]d + (Sy)new - (Sv)total aS eX~
plained in a subsequent section. These values are plotted in Figures 14,
15 and 16. Values of (Sv)q_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.

53

TABLE 8. — Maximum intercept of largest unimpinged grain for specimens worked at 750°C and annealed at 750°C,

700°C and 670°C

Annealing Temperature

750°C 700°C 67QQC

Annealing Annealing Annealing

Specimen Time Diameter Specimen Time Diameter Specimen Time Diameter

Number (seconds) (x 10 mm) Number (seconds) (x 1 02 mm) Number (seconds) (x 1 02 mm)

2-1

0

1.2

2-2

15

2.2

3-1

30

4.2

11-4

45

6.2

3-4

60

7.1

11-1

75

8.6

2-1

0

1.2

2-1

0

1.2

7-5

60

2.4

9-3

480

3.9

6-2

120

3.7

12-4

960

7.2

6-4

240

6.5

10-2

1440

10.0

8-2

360

9.4

10

8

—

750°C

6

—

O^-""

<4

2

-*^si

0

1

1

1

I

1 1

1

J

1

16

32

<»8

6U

6o

ANNEALING TIME (SECONDS)

— 10

"So r&ij 2i»o

ANNEALING TIME (SECONDS)

320

250

500 750 1000
ANNEALING TIME (SECONDS)

1250

1500

Fig. 13. — Maximum intercept of largest unimplnged grain
versus annealing time for specimens worked at 750°C and annealed
at 750°C, 700°C and 670°C.

55

<u o

JB

O

m

s-'

r^

—

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«0

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»

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E O

O in

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[NJ o

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•- u

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1-

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vD O

V V

— z

E E

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3 —

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I o

• ™

V

uwi/N-O/Aj)

56

o

o o

JZ o

.- c

IB <TJ

E
CTl —

V)

o

Q>

u

DO

u

(U

3F

>

o

n

<o

<u

u/N-0(As)

57

,x

U (
4JVO

UJ

.- a>

3 z

*j a

O —

ID (/)

N K

^

ID l_

13

a o

Z

<u «•

58

TABLE 9. --Growth rates calculated from the expression G • (Sv)0_N = dVV/dt for sPecimens worked at 750°C

and annealed at 750°C, 700°C and 670°C

Annea

i nq Temperature

750°C

700°C

670°C

Specimen
Number

Anneal i
Ti me
(second

s)

G
(

x K/*
urn/sec)

Speci men
Number

Anneal i ng

Time
(seconds)

G x 105
(mm/sec)

Speci men
Number

Annea 1 i
Ti me
(second

^g
0

G x 106
(mm/sec)

2-1

0

-

2-1

0

-

2-1

0

-

2-2

15

0.9

7-5

60

2.1

9-3

480

5.8

3-1

30

1.2

6-2

120

2.0

12-4

960

9.9

11-4

45

1 .2

6-4

240

2.4

10-2

1440

7.8

3-4

60

1.3

8-2

360

2.8

9-4

1920

6.6

11-1

75

1.4

7-1

480

4.0

10-4

2880

7-2

1-3

90

1.5

8-4

600

4.2

10-3

3840

7.2

2-3

120

1.5

7-2

720

2.9

12-1

4800

3.5

1-2

180

2.2

8-5

960

1.4

12-2

5760

3.3

2-4

240

1.7

8-3

1440

1.6

1-1

300

-

8-1

1920

-

11-3

360

-

11-5

720

-

7-3

1440

-

59
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 metal lographi c 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,
usual ly 1 i near.

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

60

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 • (SyjQ,^ = dV„/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:

1. Total surface area per unit volume, (Sy) to ta ^ -

2. Surface area per unit volume possessed by the new,
unstrained grains, (Sy) , 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, (Sy)0id, 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 (s\p total nave been pl°tted versus

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

61

TABLE 10. --Experimental measurements of surface area per unit volume with strain-free material on at least one side of the bounds™ K 1 ■ ^
strained material on at least one side of the boundary, (Sv)old and the total surface area, (§v)total. for specimens worked at 75<& and annealed at

750°C, 700°r. anH £7nOr. annealed at

750°C, 700°C and 670°C

750°C

Annea
700UC

1 i nq Tempi

srature

670'

>L

Speci men
Number

Anneal i
Ti me
(seconc

"9

Is)

' v' new

/mm

(Void

/mm

(V total

/mm

Specimen
Number

Anneal i
Ti me
(seconc

"9

Is)

(Vnew
/mm

(Void
/mm

(V total

/mm

Speci men
Number

Annea 1 i
Ti me

ng
10

(Vnew

(Void

(V total

2-1

0

5.5

99

99

2-1

0

5-5

99

99

2-1

0

5.5

99

99

2-2

15

8.5

103

103

7-5

60

8.5

108

108

9-3

480

12.5

98

99

3-1

30

11.5

98

98

6-2

120

11

106

106

12-4

960

26

99

104

11-4

45

20.5

103

104

6-4

240

16

104

104

10-2

1440

35

90

100

3-4

60

20.5

104

104

8-2

360

31.5

96

106

9-4

1920

44.5

84

102

11-1

75

39.5

98

110

7-1

480

43

94

105

10-4

2880

65.5

73

102

1-3

90

50

95

107

8-4

600

78

67

109

10-3

3840

84

37

94

2-3

120

68

72

108

7-2

720

84

46.6

100

12-1

4800

89

21

91

1-2

180

95

29.5

101

8-5

960

93

29.8

101

12-2

5760

87

15-5

89

2-4

240

101

8.8

101

8-3

1440

90

16.2

93

1-1

300

92

6.6

92

8-1

1920

92

4.2

92

11-3

360

89

2.2

89

11-5

720

86

0.05

86

7-3

1440

84

0.15

84

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65

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)o]d, (Sv)new and (Sv)totaI per-
mitted the calculation of three more significant types of surface area:

'• (Sv^O-O' tne 9ra'n boundary area per unit volume
separating deformed grains.

2. (Sy).|_i|> tne grain boundary area per unit volume
separating strain-free grains.

3- f^V^o-N' tne 9ra'n 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 = (Vo-0 + (SvVn + ^v'o-N

(Sv'old " 'Vo-0 + (Vo-N

(Vnew = (Vn-N + (SvVn
From these three expressions, one finds that:

(Vn-N = (V total ■ (Vold

(SV>o-0= (V total " <Vn«
(SV)0-N= (Sv)old+ (5v)new - (Sv)tQta,

Values of (sy)0_Q, (s\pN-N' and (SV^0-N ca'cu'ated from the above equa-
tions are included in Table 11. Values obtained for all three types of

66

TABLE 1 1 .--Calculated values of surface area per unit volume with: (1) strain-free material on both sides of the boundary (S„)», ,• (2) str*inPH material
on both sides of the boundary, {Sy) 0_0; and (3) strained material on one side of the boundary and strain-free material on the other side (S ) (the

migrating interface area) for specimens worked at 750°C and annealed at 750°C, 700°C and 670°C V °"N

Annealing temperature

750°C 700°C 670°T

Annealing Annealing Anneal i no

Specimen Time (SV)N.N lsv)0-o <Vo-N Specimen Time (SV)N_N (Sv)0.0 (SV)0_N Specimen Time (SV)N_N (Sv)0.0 (Sy)0.N

Number (seconds) /mm /mm /mm Number (seconds) /mm /mm /mm Number (seconds) /mm /mm /mm

2-1 0 0.0 93.5 5.5 2-1 0 0.0 93.5 5-5 2-1 0 0 93.5 5.5

2-2 '5 0.0 94.5 8.5 7-5 60 0.0 99.5 8.5 9-3 480 1.0 86.5 12

3-1 30 0.0 86.5 11.5 6-2 120 0.0 95 11 12-4 96O 5 78 21

11-4 45 1.0 86.5 19.5 6-4 240

3-4 60 -1.0 83.5 21 8-2 36O 10 74.5 21.5 9-4 1920

11-1 75 12 70.5 26.5 7-1 480 11 62 32 10-4 2880 30 38

(sv)n-n

/mm

(svVo

/mm

(sV^0-N

/mm

0.0

93.5

5-5

0.0

94.5

8.5

0.0

86.5

11.5

1.0

86.5

19.5

-1.0

83.5

21

12

70.5

26.5

12

57

38

36

40

32

71.5

6

23.5

92

0.0

9

85.5

0.0

6.5

87

0.0

2

86

0.0

0.1

83.5

0.0

0.3

1-3 90 12 57 38 8-4 600

2'3 '20 36 40 32 7-2 720 53-5 16 30. 5 12-1 4800

1-2 180 71.5 6 23.5 8-5 960

2-4 240 92 0.0 9 8-3 1440

1-1 300 85.5 0.0 6.5 8-1 1920

11-3 360

11-5 720

7-3 1440

2- IT *

0.0

93-5

5-5

0.0

99.5

8.5

0.0

95

11

0.0

89

16

10

74.5

21.5

11

62

32

42

32

35

53.5

16

30.5

73

8

22

77

3

13

88

0.0

4

10-2 1440 10 65 25

57.5 26.5

35-5

10-3 3840 57 10 27

70 2 19

12-2 5760 73-5 2 13.5

-•This specimen had the same thermal history as specimen 2-1, but was not worked.

67
boundary area have been plotted versus annealing time: (Sv)0-n ' n

Figures 14, 15 and 16; (Sy)0_0 in Figures 20, 21 and 22; and (SV)N.N in

Figures 23, 2k and 25.

68

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(nS)

CHAPTER IV

DISCUSSION

The purpose of this chapter is to present a coherent description
and characterization, based upon experimental data and observations, of
the evolution from as-hot -worked material to a structure essentially free
of distortions not associated with the grain boundary network.

Experimental results and observations from this investigation, as
well as those from preliminary work and other investigations, will be
presented from a particular viewpoint. Basically, this viewpoint is that
the driving force provided by surface energy is of primary importance
both during hot working and during annealing subsequent to hot working.
The fundamental idea is not new. In 1951 C. Smith suggested an analogy
between recrystal 1 i zation and ordinary grain growth which was formulated
on the same basis (40) . The essence of Smith's proposal is that high-
angle boundaries possessed by strain-free grains move through a matrix
containing small, we 1 1 -developed subgrains. The driving force for migra-
tion is simply the energy associated with the subgrain boundaries. This
idea apparently has received little additional attention, possibly be-
cause of results obtained by the techniques of transmission electron
microscopy. These results indicated that well-defined subgrains usually
are not formed during cold working (41, kZ) , and that subgrain formation
and recrystal 1 i zation during annealing after cold working can be concur-
rent rather than totally sequential C+2) .

Ik

75

Hot working, however, presents a different situation. There is
considerable evidence that well-defined subgrains will form even during
relatively rapid hot working in materials of moderate and high stacking-
fault energy, e.g., in copper, nickel and aluminum (16). This observa-
tion, as well as others to be mentioned later, suggest that a considera-
tion of surface energy will result in a clearer and more concise exposi-
tion of the phenomena which occur during and after hot working than would
otherwise be possible.

For clarity, the remainder of this chapter is divided into three
sections. The first of these will consider the working process itself
and will discuss the various microstructural aspects of hot-worked mate-
rials. The second section is concerned with the evolution of strain-free
grains during the annealing period. The third section is a discussion of
the agreement obtained between predicted effects of the experimental
variables and the results from other studies of annealing after hot
working.

Aspects of the Hot-worked Structure

This section will characterize the hot-working process through a
consideration of the microstructural changes which are known to occur
during it. The most important of these changes are:

1. The grain boundary network* experiences distortions.

"A network in general is a configuration composed of nodes con-
nected by branches. In the present discussion grains are thought of as
nodes and grain boundaries as branches. A topological ly equivalent net-
work may be constructed from triple lines formed by the intersection of
three grain boundaries (branches) and the quadruple points formed by the
intersection of four triple lines (nodes).

76

2. Lattice bending and twisting not associated with
grain or subgrain boundaries appear as soon as
working begins.

3- A subgrain boundary network begins to form very early
in the working process.

k. Grain boundary serrations are formed and develop under
the influence of the deformation and the driving force
due to surface tension.

5. New grains are initiated and grow during the working
process.

These changes will be considered in the following subsections.

Distortion of the grain boundary network

The microstructural result of distortions involving the grain
boundary network is grain elongation. Note that no changes in the total
number of triple lines and quadruple points, in the number of boundaries
which meet at a triple line, or in the number of triple lines which meet
at a quadruple point result from these distortions. During working, how-
ever, movement away from the equilibrium distribution of angles (as re-
quired by surface tension) will occur at both triple lines and quadruple
points.

Perhaps the simplest way to express grain elongation is as a
grain boundary anisotropy computed from the ratio of the number of grain
boundary intercepts perpendicular to the stress axis, (NL)T, and the num-
ber parallel to the stress axis, (NL)L. This ratio can then be used to
calculate an apparent total strain in the grains, e_, by inserting it
into an expression derived for tensile deformation by Rachinger (43).
This expression is:

eg = [(NL)T/(NL)L]2/3-l

77

A derivation of this expression based on that given by Rachinger has been
included as Appendix D.

Some quantitative measures of the changes in grain boundary ani-
sotropy as they depend upon the working conditions are available from
work by Rhines, et al ■ (9) on Nickel 200. This information appears in
Figures 26 and 27 and in Table 12.

TABLE 12. — Influence of rate of extension on the apparent total strain in
the grains calculated from the expression: eg = [ (NL)T/(NL),f'3_| _
Nickel 200. Hot-working temperature • 705°C

Rate of
Extension (/min.)

Measured
Extension (%)

0.75
0.07
0.009
0.0009

35
31
26
31

eq(%)

32

16

2

0

Data included as Table 12 show a predictable trend in the calcu-
lated values of e as a function of rate of extension; i.e., for an es-
sentially constant total extension e„ decreases with decreasing rate of
extension. This dependence could be rationalized on the basis of the
time available for surface tension forces to affect a return to the re-
quired angular distribution. Microstructural , hardness, and boundary
area data available for the same specimens, however, indicate that this
viewpoint is an oversimplification. These data show that all values of
eg listed in Table 12 are complicated by the formation of new grains dur-
ing the working period. In fact, the results included as Table 12 can be

78

20 r-

20 30
MEASURED EXTENSION (%)

40

J
50

Fig. 26. --A plot of measured total extension versus
calculated e for Nickel 200. Specimens extended at 705°C and
0.009/minuteT

79

1 .Oi —

o 0.6
H

z

LU

g0.6
a

3 o.i.

V)

S

700

7<40

780 820

TEMPERATURE (°C)

860

900

Fig. 27. --A plot of the ratio of the calculated eg to the
measured total extension versus hot-working temperature. Nickel
200. Rate of extension ■ 0.75/minute. Total extension
per cent.

37

80

explained qualitatively on this basis. The data plotted as Figure 26
also may be rationalized on the same basis. That is, the departure of
the calculated values of grain elongation, eg, from those expected on
the basis of the total extension is due to the initiation and growth of
new grains during the working period. This point will be covered in more
detail in the subsection on strain-free grains later in this section.

Data plotted as Figure 27 indicate that, under the experimental
conditions utilized, at about 950°C the amount of grain elongation due to
the working approaches zero or some small value. On the other hand,
below about 700°C, the grain elongation is essentially the same as the
total extension experienced by the specimen. Within the temperature re-
gion between 700°C and 950°C, however, the measured degree of grain elon-
gation depends, for a constant rate and amount of elongation, on the hot-
working temperature. Microscopic observations indicate that this result
cannot be completely explained on the basis of the initiation and growth
of new grains during working. At the highest temperatures another mecha-
nism, possibly readjustment under the influence of the forces resulting
from an imbalance of surface tensions, is operative.

One should not be misled into believing that equi axedness, per se,
constitutes an annealed state. Microstructures and hardness values yield
ample evidence to the contrary. The hardness of a specimen deformed at
900°C is still roughly halfway between that of the completely annealed
material and that of a specimen deformed the same amount at 750°C. Work-
ing at 950°C would be expected, therefore, to yield a material considera-
bly harder than the annealed specimens. The microstructural differences
in the two structures are the subjects of the following subsections.

81

Dislocations not associated with
a boundary network

In the category of dislocations not associated with a boundary
network are included all those dislocations which are present in the
structure after working but which are not part of an organized boundary
network. The number and distribution of these dislocations have been
found to be a function not only of the stacking-fault energy of the mate-
rial, but also of the working conditions.

Hot torsion experiments performed by Ormerod and Tegart (16)
showed clearly that the number of dislocations of the type referred to
above decreases with increasing stacking-fault energy. This study also
showed that with increasing temperature of working the dislocations not
associated with a boundary become fewer in number and tend to arrange
themselves into a poorly defined cell structure.

Since all arrangements are formed under the simultaneous influ-
ence of mechanical and thermal driving forces, one would expect them to
exhibit considerable stability, with respect to similar arrangements,
against dissolution or even marked alteration due to thermal energy
alone. That is, the cell structure and other arrangements of disloca-
tions which obtain at the cessation of working should not possess any
marked energetic advantage over similar arrangements. Thus, they would
persist until removed by a migrating high-angle boundary with an attend-
ant decrease in the total energy of the system.

Data included as Table k as well as photomicrographs obtained
from specimens annealed long times at 750 C (Figure 48, Appendix B)
clearly show that a small fraction of the worked material does persist to

82

long annealing times. Even at these long times, the distortion within
the worked grains is easily noticed and quite often does not appear to
be associated with subgrain boundaries. That is, a study under polarized
light of the extinctions experienced by these grains leads to the conclu-
sion that in many cases the residual distortion is not present in the
form of subgrain boundaries, but as a bending or twisting of the crystal
lattice due to sessile dislocations and restraints imposed by surrounding
grains.

Formation of a subgrain boundary network

Subgrain formation during creep and during annealing after cold
working has been the subject of numerous investigations since about 1950.
Subgrain formation during hot working, however, has not been thoroughly
studied.

As a first approximation, one can envision a network of subgrain
boundaries forming during hot working by the migration of dislocations
within each grain into ordered arrangements which become connected to
form a network. With continued working the subgrain boundaries and hence
the network become better defined. In addition, the degree of misorien-
tation between subgrains increases. The subgrain boundary network inter-
sects the grain boundary network and the two much be considered together.
A schematic diagram of the evolution described above is included as
Figure 28. Excellent examples of the evolution of subgrain boundary net-
works during high temperature deformation are given by Busboom et al .
(44) and by Yim and Grant (45).

The techniques of transmission electron microscopy applied to hot
worked (in torsion) copper, nickel, and aluminum leave no doubt that

83

3 (J
O Q)

jQ i~

O -C

1- -D

8 J

84

well-defined subgrains are formed during working (16). Although no quan-
titative data were obtained from this investigation, it was shown for an
increasing temperature of working that the subgrain boundary network be-
comes better defined and that the individual subgrains increase in size.
Quantitative data on the effects of working temperature (deformation in
tension and by rolling and forging) on subgrain size from the investiga-
tions of Warrington (hd) and Dillamore and Roberts (k) are included as
Figure 29. This figure shows very clearly that subgrain size increases
with increasing working temperature. Unfortunately, the data obtained
by the various working procedures cannot be directly compared. The trend
for a decrease in subgrain size with increasing rate of working is, how-
ever, undoubtedly correct.

The etching technique used in this investigation (along with most
others which permit examination under polarized light) does not reveal
subgrain boundaries as well as one might desire. However, there is ample
evidence in the photomicrographs presented in Figures kH, k9, and 50
(Appendix B) that in many grains a subgrain boundary network has devel-
oped to a considerable degree. Close study of specimens within the series
annealed at 750°C (Figure k8, Appendix B) also indicates that this net-
work does not, to a detectable degree, become better developed during the
annealing period. It is also apparent that not only subgrain development
but also subgrain size varies considerably from grain to grain.

Although it was not possible to obtain measurements of the amount
of subgrain boundary area, a crude estimate of the amount at zero anneal-
ing time was obtained in the following manner:

85

f 2

1/1 U -—.

j- ro fsi —

rn

V

a>

U

i_

1

rj

n

*j

■

m

u

c

U

Q..*

E

u

2 g

86

1. The assumption was made that the increase in hard-
ness of the as-hot -worked material over a similar,
completely annealed specimen with the same total of
grain plus twin boundary area was due completely to
subgrain boundaries. Of course, this condition can
be only approached.

2. The hardness of a number of fully annealed specimens
containing different amounts of grain plus twin bound-
ary area was obtained. A plot of hardness versus
boundary area proved to be a straight line. Extrapo-
lation of this line yielded a hardness at zero bound-
ary area.

3. The hardness at zero boundary area subtracted from
the as-hot-worked hardness gave the total boundary
hardening. From this value was subtracted an amount
corresponding to the total measured grain plus twin
boundary area. The remainder is the hardness due to
subgrain boundaries.

k. With the aid of a reasonable assumption for the rela-
tive effect of grain and subgrain boundaries on hard-
ness, the amount of subgrain boundary was calculated.

The final result was a subgrain boundary area of approximately 200/cnm.

This value is indicated on Figures 17, 18, and 19. From this information

it was estimated that the maximum average subgrain size was 10 microns

and the most probable average value between 2 and 5 microns. The latter

values agree fairly well with the estimate of approximately one micron

obtained from the work of Yim and Grant (45).

Serrated boundaries

Although serrated boundaries have been noted in a wide variety of
hot-worked materials and in a number of creep studies, the manner in
which they are formed and develop is far from clear. Many observations
suggest, however, that serrations are the result of the formation of slip
bands. Their shape may be modified subsequently or concurrently by
boundary migration due to surface tension forces.

87

Metal lographic observations have indicated that serrated bound-
aries exhibit the following characteristics:

1. Serrated boundaries are observed only within a temper-
ature range characteristic of the material. Working
at too low a temperature does not result in serrated
boundaries and working at too high a temperature re-
sults in the initiation and growth of new (and possibly
strain-free) grains along old grain edges and boundaries.

2. Within the temperature range of their existence, the
shape of the serrations is a function of the working
conditions. At low temperatures "or high rates of ex-
tension, serrations tend to be straight-sided, but
with increasing temperature or decreasing rate of ex-
tension they tend to be wavey or scalloped.

3. Serrations become more widely separated as the working
temperature is increased.

k. Serrations have been observed to be associated with
subgrain boundaries in creep studies involving mate-
rials as different as aluminum (k7, k8) , silicon-
iron (49) and magnesium (11, 12).

Specific observations which suggest that the initial formation of
serrated boundaries is a result of slip band formation during hot work-
ing were made by Siutkina and Yakovleva (6), by Wyon and Crussard (50)
and by Chang and Grant (48). In all three papers the formation of serra-
tions was attributed to the intersection of grain boundaries by slip
bands. The investigation by Siutkina and Yakovleva involved the tensile
deformation of 99.99 per cent nickel between 500°C and 700°C and at a
rate of 0.12/minute. Wyon and Crussard and Chang and Grant, on the other
hand, investigated the creep behavior of 99.99 per cent aluminum. In ad-
dition, Forsyth (51, 52) has noted the formation of serrated boundaries
in fatigued high-purity aluminum. This author attributed the formation
of serrations to boundary migration at positions where slip striations
intersected a grain boundary. All of the above evidence indicates that

88

it is quite possible at high temperatures for a large amount of slip
within a narrow band of material to result in visible perturbations of
the grain boundary. These perturbations originally would take the form
of a shear across the grain boundary where it is intersected by the slip
band.

At high temperatures and lower rates of deformation, the straight-
sided nature of the serrations gives way to a wavey or scalloped form.
There are two reasons for this change. The first is the fact that grain
boundaries tend to assume a position of minimum energy, i.e., surface
tension forces tend to minimize the total boundary area. If the tempera-
ture is high enough or the time long enough, then straight-sided serra-
tions are replaced by a more rounded, wavey shape which represents a
smaller amount of boundary area and hence a lower total energy.

The second reason for the change in shape is the formation and
development of a network composed of subgrain boundary and serrated
boundary. As the subgrain boundaries become better developed during
working, surface tension forces associated with the quadruple points of
intersection with serrated grain boundary become appreciable. The ad-
justments dictated by these forces will alter the shape of the serrations
in the direction of their becoming scalloped, or cusp shaped, with the
subgrain boundary at the apex of the cusp. The dihedral angle formed by
the serrated grain boundary and the subgrain boundary depends upon the
relative energies of the several boundaries that meet at the quadruple
point. Since the energy (angle) of the subgrain boundary will increase
as long as the material is being deformed, or until the boundary obtains
the maximum possible energy, the equilibrium dihedral angle must

89

constantly change. To the extent that this factor is determining, the
shape of the grain boundary serration must constantly change.

A number of authors have noted that cusp-shaped serrations quite
often are intersected at the apex of the cusp by a subgrain boundary.
Photomicrographs illustrating this phenomenon are included in the papers
by Chang and Grant (48), Namdar (k9) , and Suiter and Wood (12)

Strain-free grains*

This investigation and similar work preliminary to it (performed
by the author) have established that, under the experimental conditions
utilized, some strain-free grains exist in Nickel 200 at the completion
of hot working. It is obvious from a comparison of the structures imme-
diately before and immediately after working (Figure 7 (a) and (b)) that
these grains originated during the working period. The manner in which
they are formed is qualitatively evident from metal lographi c observations
which permit the conclusion that they originate as a result of boundary
migrations caused by a tendency for the system to minimize its boundary
energy .

Boundary migration will occur naturally at positions of maximum
energy gradient, or in other words, in regions of maximum local differ-
ence in density of quadruple points. Upon this basis two types of posi-
tions would be preferred as growth sites: (1) old grain boundaries
(interfaces) and (2) old grain edges (triple lines). Of these, grain
edges are the most energetically feasible since they are intersected by

*As previously mentioned, these grains are distinguished by the
fact that they contain less than a detectable amount of deformation.

90

three sets of subgrain boundaries, each with a different average spacing.
Another factor which may be of importance is the fact that the intersec-
tion of one subgrain boundary with a triple line will form a new quad-
ruple point, while at least two subgrain boundaries must intersect a
grain boundary in order to form one new quadruple point.

One would expect a section of old high-angle boundary to move
into that region containing the smallest subgrains, the highest energy
subgrain boundaries, or both. This movement will generate new* grains
which may be expected to grow at least to impingement with each other.
In other words, high-angle boundaries are increasing in area at the ex-
pense of subgrain boundaries. The major restriction to growth is that
the decrease in free energy due to the destruction of subgrain boundary
area must be larger than the increase in free energy due to the creation
of high-angle boundary.

The initiation of new grains during working is a dynamic process
which depends for its inception upon the development of a subgrain bound-
ary network beyond a certain degree. Once this degree has been reached
locally and a difference in density of subgrain boundary network quad-
ruple points exists in the same region new grains will be initiated by
the boundary migration process described above. As new grains grow they
too will begin to accept deformation and to form a subgrain boundary net-
work. Since continued growth by boundary migration depends on the exist-
ence of a gradient in quadruple point density across the migrating bound-
ary, the formation and development of a subgrain boundary network within

'The adjective strain-free henceforth will be used to describe
only those grains which contain less than a detectable amount of
deformation.

91

the growing grain will impede growth or stop it completely. The develop-
ment of a subgrain boundary network beyond a certain degree in the "grow-
ing grain" may also eventually result in the formation of new grains at
its edges and boundaries.

Application of the above description to an actual structure which
has experienced more than the degree of working necessary to begin the
formation of new grains would lead one to expect the following:

1. The structure will contain original grains with vari-
ous degrees of subgrain boundary network development
and grain elongation depending upon the amount of de-
formation experienced by each grain.

2. A fraction of the structure will be composed of grains
which originated and grow various amounts during work-
ing. Some of these grains may have developed a sub-
grain boundary network which has impeded or stopped
growth, and may even have begun to form more new grains
at edges and boundaries. Other grains in this class
either will not have grown appreciably and will not
have experienced much deformation or possibly just not
have experienced a detectable degree of deformation and
therefore will appear to be strain free.

The rate of working plays a very important role in the formation

of a hot-worked structure. Very fast rates will not permit the formation

of a subgrain boundary network and new grains during deformation. Thus,

the as-worked structure will contain a more or less uniform dislocation

cell structure throughout. This structure will closely resemble those

arrangements found in cold-worked materials. Slower rates of working

will result in the formation of a subgrain boundary network and new

grains. The extent to which both develop increases with decreasing rate

(for a constant total extention). For high total extensions at very slow

rates all the original grains are replaced by those which continually

92

formed and grew during working. Some of these may contain a well-
developed subgrain boundary network.

The process of new grain formation outlined above should impart a
number of observable characteristics to the over-all structural evolution
both during and after working. These characteristics will be outlined in
the following subsections. Also included in the appropriate subsections
are observations which pertain to the characteristic being discussed.

The initiation of new grains during working. — All grains which
eventually comprise the fully annealed structure originated at some time
during the working process. Thus, all are descended either from grains
formed well within the working period and which maintained some growth
advantage until the end of working or from grains which obtained a growth
advantage during the very last stages of working. This conclusion fol-
lows directly from the suggestion that new grains are formed in regions
containing we 1 1 -developed subgrains and from the fact that the subgrain
boundary network does not change noticeably after hot working (during
annealing). Evidence for the correctness of this conclusion will be con-
sidered in the second section of this chapter.

The microstructural positions at which new grains form. —New
grains should be preferentially associated with old grain edges and to a
lesser degree with old grain boundaries. It is at these positions that
the gradient in the density of quadruple points, and hence the driving
force, is greatest. Thus, at all but the slower rates of working the
number of potential new grains should be a function of the amount of old
grain boundary and/or old grain edge possessed by the structure.

93

Microscopic observations (see especially Figure 8 and the data in
Table 3) indicate clearly that the large majority of strain-free grains
are indeed associated with (at least initially) either old grain bounda-
ries or old grain edges. An indication that most of the strain-free
grains with a growth potential are associated with old grain edges not
only initially but throughout the annealing period was obtained by re-
plotting the data contained in Figures 9, 10, and 11 with In ln(l/l-Vv)
as the ordinate and In t as the abscissa. Plots of this type for all
three annealing temperatures are contained in Figure 30. Slopes of the
three major lines are l.k, 2.1, and 1.9 for annealing temperatures of
750°C, 700°C, and 670°C, respectively. The fact that the slopes are
close to two is a strong indication that the strain-free grains which
contribute to the increase in amount of strain-free material during an-
nealing are associated with the edges of old grains. The reason for this
interpretation lies in the position assumption made in the derivation
which relates Vy to the annealing time. This derivation, due to Cahn
(53), results in an equation of the form Vu = 1 -e"kt if the assumption
is made that the strain-free grains are initiated and grow at old grain
edges. The fact that the process under consideration fulfills all other
conditions of the derivation allows one to draw the above conclusion.
This point will be discussed in more detail in the second section of this
chapter.

The shape of the strain-free grains. — Prior to impingement with
other strain-free grains, the growing grains should have scalloped bound-
aries indicative of nonequi 1 i bri urn quadruple point angles. This form re-
flects the necessity that all sections of the boundary possessed by a
growing grain move towards their centers of curvature.

9«»

10

1.0 -

f

0.1 -

o.oV

10

O ioo

TIME (SECONDS)

1,000

10,000

Fig. 30. — A plot of ln(l/|-v,,) versus annealing time for speci-
mens worked at 750°C and annealed at 750°C, 700°C and 670°C.

95

The shape of these boundaries is particularly well illustrated by
the circled strain-free grain in Figure 8 (b) and to a lesser degree by
the circled strain-free grain in 8 (a). An electron photomicrograph, ob-
tained from the same specimen that provided Figure 8 (a) and (b) , which
shows a similarly shaped grain believed to be strain free, is included as
Figure 31. Each cusp in the boundary of the grain circled in Figure 31
is believed to represent an intersection of the migrating high-angle
boundary with a subgrain boundary. In fact, the cusp in the center of
the figure apparently shows such an intersection. The shape of the scal-
loped boundary is thus dictated by the tendency to maintain a balance be-
tween the surface energies of the boundaries involved.

The orientation relationship between the strain-free grains and
the surrounding strained grains. — It can be concluded that a considerable
number of the strain-free grains should have an orientation very close to
that of one of the surrounding strained grains. This conclusion follows
directly from the supposition that new grains originate by migration of a
section of pre-existing high-angle boundary into the neighboring grain
which contains the greatest density of subgrain boundary network guadruple
points (smallest subgrains). Migration is away from a grain containing
relatively large subgrains and one would expect the atoms which migrate
across the boundary (and result in movement of the boundary) to assume an
orientation close to that of the large subgrains. A photomicrograph,
which shows a strained grain and a strain-free grain which apparently ex-
hibit the expected orientation relationship, is included as Figure 32.
The strain-free grain lies completely within the circled area and is

96

Fig. 3' .--An electron photomicrograph of a presumably
strain-free grain with a scalloped boundary growing at an old
grain boundary . 10.000X.

97

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

98

apparently growing from the large, dark, strained grain of nearly the
same orientation.

It is not possible, however, to obtain unequivocal photographic
evidence for the conclusion that the growing, strain-free grains have an
orientation close to that of one of the surrounding strained grains. Al-
though the etch tends to form grooves with walls composed of {lod} planes,
the observed deviations from this simple relationship are large enough to
mask appreciable orientation differences between the two grains (28).

Directional inhibition in the growth of strain-free grains. — The
growth of strain-free grains should be inhibited in certain directions.
This prediction follows from the supposition that growth is preferen-
tially in the direction of the greatest driving force, i.e., the largest
difference in density of quadruple points. Direct confirmation of this
prediction was obtained from the photomicrographs which appear as Figure
8. In many cases it is quite obvious that the strain-free grains are
growing preferentially into one of the strained grains which share a
boundary. Figure 8 (e) , (g) , and (h) are good examples of this
phenomenon.

The growth rate of the strain-free grains. — Each new grain is
considered to be growing essentially into one old grain which usually
possesses a nearly constant density of quadruple points. Since the driv-
ing force during the annealing period is essentially constant (except for
very short annealing times) the growth rate should also be essentially
constant. Note, however, that it is possible to have a considerable vari-
ation in growth rates among the various growing grains. This variation

99

is a reflection of the great differences in subgrain size observed from
grain to grain within a particular specimen.

Changes in the number of strain-free grains during the annealing
Period. — The number of strain-free grains but not their total volume
should decrease during the annealing period. This conclusion follows
from a consideration of the fact that if strain-free grains all have
their origin at old grain boundaries or old grain edges, then impingement
must occur very early in the annealing process. It is to be expected
that some of the impinged grains will possess a growth advantage over the
strain-free grains with which they are in contact. As a result of this
advantage some strain-free grains will eventually disappear. A good ex-
ample of an impinged group of small, strain-free grains is the three
grains circled in Figure 8 (b) . Data presented as Figure 12 for all
three annealing temperatures indicates that the number of strain-free
grains does actually experience an initial decrease with increasing an-
nealing time. This observation will be discussed further in a subsequent
section.

Summary

The structure which obtains at the completion of hot working de-
pends not only on the conditions of working but also on the stacking-
fault energy of the material. If discussion is limited to materials of
high and moderate stacki ng-faul t energy, e.g., aluminum, nickel, and cop-
per, then the structural evolution during hot working can be described in
terms of concepts introduced earlier in this chapter.

Working at any rate and in any amount results in the introduction
into the structure of dislocations which at high temperatures may

100

manifest themselves in a number of ways. The most important of these are
as grain elongation, as sessile dislocations and a poorly developed cell
structure, and as a subgrain boundary network. These structural features
in turn result in the appearance of grain boundary serrations and new
grains. Variations in the relative proportions of the dislocations which
appear as subgrain boundaries and as sessile dislocation or similar ar-
rangements as a function of rate and amount of working are shown schemati-
cally by Figure 33. Note that at very slow rates of working essentially
all dislocations will be associated with the subgrain boundaries while at
very fast rates practically no subgrain boundaries will be formed.

All of the above manifestations, since they result from a dynamic
process (hot working), are not only sensitive to the working conditions
but also capable of continual change during the working period. Thus,
serrated boundaries may be straight sided at high rates and low tempera-
tures of working, while at high temperatures and slow rates they tend to
be wavey or scalloped. The latter shape is due largely to the develop-
ment of a subgrain boundary network and therefore is a function of the
degree to which this network has developed.

The development of a subgrain boundary network also plays an im-
portant role in the initiation and growth of new grains during working.
New grains are initiated only after the subgrain boundary has formed a
connected network which in turn has produced local differences in the
density of quadruple points across a section of pre-existing boundary.
It is this density difference which provides the driving force for the
growth of new grains by migration of the pre-existing boundary. Old
grain boundaries and edges are seen to be preferred sites for the

'**;

101

go

— c

TJ O

— *>

*-> O

O *J

■M l/>

E v>
m —

i- E

102

initiation and growth of new grains. The growth rate is proportional to
the local difference in density of quadruple points. Since new grains
are formed during working, they in turn may be subject to deformation.
Thus, the formation of new grains is a dynamic process and several gener-
ations of new grains may be present in a particular structure.

At the cessation of working, then, there exists in the structure
a large number of new grains which were formed and grew during working.
Some of these may be essentially strain-free and capable of further growth
during the annealing period, while others will have developed a subgrain
boundary network which destroyed their growth advantage.

Anneal inc. after Hot Working
In the previous section the principal microstructural aspects of
the hot-worked structure were discussed. This section, then, will be
concerned with the microstructural changes which occur during the anneal-
ing period after hot working. Data which re-enforce the conclusion that
all strain-free grains which appear in the fully annealed structure have
their origin during the working period will be considered first. Growth
of strain-free grains and the effects of temperature upon growth will be
discussed in the final subsection.

The initiation of strain-free grains
during working and their growth dur-
i nq anneal i nq

This investigation has established that the new grains formed

during hot working which are identifiable as strain-free upon completion

of working are at least as numerous as the strain-free grains present at

most (later) annealing times. This is apparent from Figure 12. It is

103

tempting to conclude from this fact that there is no initiation of
strain-free grains during the annealing period; however, it is not possi-
ble to provide a direct proof for this supposition. Although the number
of strain-free grains decreases early in the annealing period there is no
direct proof that the extent of this decrease is not greater than that
actually measured. The difference between the true and apparent de-
creases, if such a difference exists, would result from the initiation of
strain-free grains during the annealing period.

The strongest argument against the initiation of strain-free
grains during the annealing period was obtained from "activation ener-
gies"'' calculated from the expressions l/tc s Ae~°-T/RT and G = Be_QG/RT
(5*+) , where tc is the time at which a certain fraction of the structure
is strain free, 0_j and Qq are "activation energies," and A and B are
constants. The former equation yields an "activation energy" for the
evolution from strained to strain-free material and the latter equation
yields an "activation energy" for boundary migration. Graphs of In l/tc
and In G versus 1/T(°K) therefore should be straight lines with slopes
OVR. Plots of this type are included as Figures ik (for tc at Vy = 0.05)
and 35. Calculated "activation energies" are 29,000 cal/mole for Qj (at
Vv z 0.05) and 32,000 cal/mole for Qg . Values obtained for 0_T at Vv =
0.45 and Vv ■ 0.60 were very close to that obtained at Vv = 0.05. If the
initiation of strain-free grains (or any other process in addition to
boundary migration) were occurring during annealing, then the "activation

"The term "activation energy" will be used throughout this sec-
tion to describe the temperature dependence of the process under consid-
eration. No specific mechanism is implied.

0.97 0.99 1. 01 1.03 1.05 1.07
I000/t(°k)

Fig. 3i).--A plot of l/t versus l/T(°K) for Vy ■ 0.05.

0.97

0.99

1.01 1.03
I000/T(°K)

1.05

1.07

Fig. 35.--A plot of experimental growth rates (calculated
from G-(SV)0N : dVv/dt) versus l/T(OK)) .

106

energy" for the over-all reaction (QT) would include a term characteris-
tic of the additional process and Qj would be greater than Qq. The fact
that all three values of QT are essentially the same and only slightly
less than the value obtained for Qq is strong evidence that neither the
initiation of strain-free grains nor any process except boundary migra-
tion occurs during annealing. Recall that arguments presented in the
first section of this chapter also resulted in the conclusion that no
strain-free grains are initiated during the annealing period. Some of
the preliminary work lends support to the conclusion that the complexity
of the annealing process does not change over the range of temperatures
investigated. This work involved the measurement of hardness as a func-
tion of annealing time for specimens deformed and annealed at 705, 755,
and 805°C . Calculation of residual hardness due to the working for all
specimens regardless of annealing time or temperature resulted in values
which were a function of the volume fraction strain-free grains but not a
function of the annealing temperature. It is unlikely that this result
would be obtained if different processes were contributing to the changes
in hardness at different annealing temperatures.

The above observations and arguments perhaps are reconciled best
by the following description:

1. All grains which exist in the annealed structure had
their origin sometime during working.

2. Some of the new grains grow during working (without
accepting appreciable deformation) to a size such
that at the completion of the process they will be
recognized as strain free by the experimental
procedures .

3- At each successive annealing period, the number of
strain-free grains actually observed is the sum of

107

those which survive that particular annealing period
and those which grow to a detectable size during this
period minus those grains of visible size which were
destroyed by aggressively growing grains.

The growth of strain-free grains
and the effects of temperature
upon growth

Experimental "activation energies" compared to those obtained for
other processes. — It is interesting to note that the "activation energy"
for boundary migration calculated from data obtained in this study agrees
well with the two values of the activation energy for grain boundary
self-diffusion in nickel which have appeared in the literature. These
values are 26,000 ± 1 500 cal/mole from the study of Upthegrove and
Sinnott (55) and 30,400 ± 2000 cal/mole from the work of Shinyayev (56).
The experimental value of the activation energy for boundary migration
falls very close to the latter of these two values. This is an indica-
tion that both processes proceed by the same mechanism. It is also in-
teresting that Detert and Dressier (57) recently have determined the ac-
tivation energy for boundary migration during the annealing of cold-
worked nickel to be from 28,000 to 30,000 cal/mole.

The relation between volume fraction strain-free grains and an-
nealing time. — A relation between the volume fraction strain-free grains
and the annealing time has been derived by Cahn (53) on the bases that
all initiation of strain-free grains is complete at essentially zero an-
nealing time, that the linear growth rate is constant, and that grain
edges are the preferred sites for the initiation of strain-free grains.
This derivation also includes the assumptions that: (1) strain-free
grains grow with equal ease into all the strained grains which share the

108

grain edge (triple line), and (2) impingement occurs first with grains
growing at the same edge and then with grains from other edges. The re-
sulting equation is Vv = 1 -exp-/F LvG2t2, where Lv is the length of "nu-
cleating edge" per unit volume.

The assumption that strain-free grains grow with equal east into
all the strained grains which share the grain edge (triple line) at which
they have formed is of questionable validity. Inspection of the photo-
micrographs contained in Figure 8, especially Figure 8 (b), (e) , and (h),
indicate that strain-free grains quite often grow preferentially into
only one of the strained grains. This behavior was predicted from the
mechanism for formation of strain-free grains presented in the first sec-
tion of this chapter. The equation relating Vy and the annealing time
therefore must be re-derived to correct for this possibility. The cor-
rection is based on the assumption that a strain-free grain growing at a
grain edge will grow preferentially into one of the strained grains shar-
ing the edge. In addition, it is assumed that only three strained grains
share an edge and that they meet to form 120° angles between each of the
three boundaries positioned around the grain edge. The equation which
results from these assumptions is: Vv = 1 -exp-(7rLvGZt2)/3. The deriva-
tion of this modification is included as Appendix E.

Use of the above equation involves obtaining the amount of "nu-
cleating" grain edge, i.e., the length of grain edge at which strain-free
grains have formed at essentially zero annealing time. This length was
obtained by measuring the number of triple points, (NA)T, (in those speci-
mens annealed the shortest times) at least partially surrounded by strain-
free material per unit area of polished and etched section. Lv may then

109

be calculated from the relationship (N^)-j- : l/2Ly . The value of Ly found
in this manner was 9^5/mm . The probable error of the measurement was
estimated at ±15 per cent of the given value.

Experimental values of Vu should fall somewhere between the lim-
its set by the original equation (Vy 5 1 -exp-TT LyGzt ) and the corrected
equation (Vy = 1 -exp-/7LyG t2/3) • Values of Vv calculated from these two
equations are included as Table 13 and plotted as Figures 36. 37. and 38.
Also included in Table 13 and Figures 36, 37, and 38 are experimental
values of V.. which have been corrected for the amount of strain-free ma-
terial present at zero annealing time.

The fact that the experimental points lie between the calculated
limits could be predicted on the basis that some of the strain-free ma-
terial is associated with strain-free grains which form at old grain
boundaries as distinguished from those which form at old grain edges.
The volume of a strain-free grain growing at a grain edge will increase
as t while the volume of a grain growing in an old grain boundary in-
creases only as t (assuming impingement has already occurred with other
grains which originated at the same boundary or edge). That some of
the strained material did become strain free due to the growth of new
grains which originated at old grain boundaries is obvious from the po-
sitions occupied by strain-free grains recorded in the previous chapter
(Table 3) and from the photomicrographs of Figure 8.

Changes in the various types of boundary area during annealing. —
A complete description of a partially strain-free (annealed) structure
with respect to boundary area requires the use of three types of bound-
ary. They are: (S\p0-N — the boundary area separating strained material

o

CN O

■w O

CM LA

C3 r^

>

_J -M

fe "

i -o

CL OJ

X "■

0) 03

1 0)

— c

3

II (0

>-o

> c

nj

i/i

C (_)

oo

— o

l/l LA

ui r-

<u

!- -M

a fo

X

a T3

<y

<U J^

-c &.

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s

E

O in

L. C

<+- <L>

E

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a) a

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a

3 O

O l- O

a

— O r-v

b

<U H- vO

OJ

o

ac

^. "D

g c

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OJ c

ui .- f0

h- r

O E

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CT

+J — o

E

o

O i- o

■w <d r--

(0

3

a>

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c

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c

i_ — *

i

a. m

<

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o ^

OCNJ

=<M

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>

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°fc

01 « — *

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4J

L

C >

0

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c

E

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r

L. C

a) 1

a.

x-—

LlI -M

1 —

i E

rA —

l-

LU 0)

_I Q.

CO Q-

< 3

t- ■*-'•

110

J*

en
oo

— CNJ

OA _

— CM

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rA — la

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LA -*

h*. LA
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Ill

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a

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4- o

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r-.

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— <o

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T3

01

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r:

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o

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T3
<U

112

in

o »

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o

a ft

c
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w~ a.

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HI

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E 41

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— o

3 f».

°\

"

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3

0

— *-»

ro fp
O

0 —

\ o

M

O
rM

. 37.— A plot
50°C and annea
values .

o> n*

It 4J flj

1

1 1 1 I 1

1

tO 4-1

1 1

1 1

a

"S I

o

CO UD dt

<N

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n

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8

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.?

v>

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z

to

o

ui o

u

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a

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to
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a) u

to o

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TO

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— c

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< ^

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TO *->

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"S i

o

and strain-free grains, (Sv)0.g--the boundary area with strained material
on both sides, and (Sy)jj_N — the boundary area with strain-free grains on
both sides. These three types will be considered in the remainder of
this section.

During annealing after hot working, rapid increases occur in (Sy)g_N
due to the growth of strain-free grains. These increases begin immedi-
ately with annealing and persist until impingement between strain-free
grains which originated at different boundaries or edges becomes impor-
tant. As indicated by Figure 39, (SV)Q_N increases with increasing Vv
from some low value to a maximum and then decreases to zero. The values
of (Sy)g_fg are independent of the annealing temperature.

The values of (Sy)g„ which appear in Figure 39 can be compared
with similar data obtained by English and Backofen (26) during their
study of the annealing of hot-worked silicon iron. The data presented by
these authors is fairly complete for only one temperature (812°C) and one
amount of strain (0.45). This single set has been plotted as Figure 40.
Note the very close resemblance in shape between this plot and that of
Figure 39. In fact, almost complete correspondence can be obtained by
contracting the ordinate of Figure kO by an appropriate amount. This
correspondence suggests that the evolution of structure in the two cases
is similar, at least with respect to the positions at which strain-free
grains are formed. It is interesting to note that English and Backofen
did find preferential formation of strain-free grains at old grain edge.

There are two processes which may contribute to the observed de-
creases in (Sv)0_0. The most important of these is a result of the tend-
ency for strain-free grains to form at old boundaries and edges. Thus,

115

60 r-

kO -

— 20 —

-

—

O

o"^--

» °

{§

35 O

1

1 1

®0\

1 , 1 . &

0.2

O.lt

0.6

0.8

1.0

Fig. 39. --A plot of ($v)0_N versus Vv which includes all
values obtained from specimens annealed at 750°C, 700°C and 670°C.

116

6t-

I* -

_

0

/"©

-

C^

o

/

\
\

\
\
\

1

\

r

"

1 , 1

1

1

\
\

, \

0.2

O.it

0.6

0.8

1.0

Fig. 40.— A plot of (SV)0_N versus Vv for hot-worked
silicon iron deformed to a strain of 0.<t5 at 8I2°C and annealed
at 8I2°C. The data were taken from the study by English and
Backofen (26).

H7

boundary of the type (Sv)0.0 will be replaced by that designated as
(sv'o-N- Deci"eases may also occur in (Sw)n_0 as a result of ordinary
grain growth. Due to the serrated nature of the old boundaries and their
consequent relative immobility (resulting mainly from the "pinning" ef-
fect of subgrain boundaries) it is probable that only small decreases in
'SV^0-0 result from this source. The values of (Sv)n_n plotted in Figure
41 as a function of Vv, however, must be considered to represent remain-
ders after decrements from the above two processes. These values are
also independent of the annealing temperature.

It should be noted that boundary area of the type recorded as
(Sv)[)-0 contributes only a fraction of the total pre-existing boundary
area which is destroyed during annealing. Roughly two-thirds of the
total amount (estimate taken from the first section of this chapter) is
believed to be subgrain boundary area which cannot be revealed to a meas-
urable degree by the procedures utilized. This fraction provides a major
portion of the driving force for the evolution from strained material to
a strain-free structure. The proposed decreases in total boundary area
(including subgrain boundary area) as a function of annealing time are
indicated in Figures 17, 18 and 19 as dotted lines. The decrease is ap-
proximately exponential. Some support for this proposal was found in the
prel imi nary work. Diamond pyramid hardness values from a series of
specimens annealed at 755 ± 3°C after 38 per cent extension at 755°C ± 3°C
are plotted as Figure k2. The curve is roughly exponential in shape.
Assuming that the decreases in hardness are reflecting only decreases in
the amount of boundary area present, then the roughly exponential decrease
in hardness with annealing time implies a similar decrease in the amount

118

100

J5 20

0.2

0.1*

0.6

0.8

1.0

Fig. 1*\.~A plot of (S^Q-. versus V.. whi
values obtained from specimens annealed at 750°C,

ch i ncludes al I
700°c and 670°C.

119

180 I —

1 20

TIME (SECONDS)

Fig. k2. — A plot of diamond pyramid hardness versus annealing time
for specimens extended 38 per cent at 755°C and annealed at 755°C.

120

of boundary area which contributes to the hardness. This in turn implies
a process obeying first order kinetics. That is, the rate of decrease in
boundary area of the type (Sv)q_q is proportional to the amount of this
type of boundary present, or -d(Sv)Q_,,/dt « k(Sy)0„.

When strain-free grains originating at the same boundary or edge
begin to impinge on each other, boundary of the type measured as (Sy)M.fj
is formed. This process occurs very early in the annealing period, but
the amount of boundary formed (of the type (Sy)u M) is small at first.
Throughout the range 0.1 ^ V„:< 0.95, however, the plot of (Sw)N_N versus
Vy which appears as Figure k3 has a constant slope independent of the an-
nealing temperature. Above Vy s 0.95, the slope of the curve rapidly ap-
proaches zero, as it must, prior to the large scale destruction of bound-
ary of the type (Sy)u_ w by grain growth.

Throughout the period of annealing after impingement, boundary of
the type measured as (Sy)fj.fj will experience rearrangements due to sur-
face tension forces. These rearrangements result in shape changes in the
grain boundary network and will tend to decrease the amount of this type
of boundary present. However, they will not, per se, result i n an in-
crease in grain size. Towards the end of the annealing period the grain
size will begin to increase due to the imbalance of surface tension
forces. This increase will result in decreases in (Sw) fj_m - Data from
the long annealing times at 750°C, however, lead to the conclusion that
decreases in (S\/)(j_n due to grain growth are small.

It is significant that the values of (Sy)Q_m, (Sy)g_g, and
(5v)|l|_N are functions of V.. only and independent of the annealing temper-
ature (see Figures 39, k\ , and ^3) . This result indicates that the

121

100 r-

> i»0 -

o.k

0.6

0.8

1.0

values

Fig. ^3.--A plot of (SV)N_N versus Vy which includes all
obtained from specimens annealed at 750°C, 700°C and 670°

670°C.

122

evolution from strained material to a strain-free structure occurs by the
same phenomenon or process within the temperature range from 670°C to
750°C .

Summary

A study of the evolution from strained material to strain-free
grains during annealing after hot working provided confirmation for many
of the characteristics of the process deduced in the first section of
this chapter. Confirmation was obtained from "act i vat ion energies," from
values of volume fraction strain-free grains versus annealing time, and
from hardness values for the following characteristics: (1) all strain-
free grains present during the annealing period are initiated during
working, (2) strain-free grains are initiated at old grain edges and pos-
sibly at old grain boundaries, (3) the growth of strain-free grains is
inhibited in certain directions, and (h) the only process which occurs
during annealing is an increase in amount of strain-free material by
boundary migration. These characteristics coupled with the experimentally
determined constant growth rate and the assumption that strain-free
grains impinge first upon others growing at the same edge (or boundary)
and only later upon those growing at different edges (or boundaries) per-
mit the conclusion that a modification of the relation derived by Cahn
(53) between volume fraction new grains and annealing time will describe
the actual process.

Measurements of boundary area of the type (Sv)n N plotted versus
Vv yielded the same shape curve as did similar data obtained by English
and Backofen (26) from the annealing of hot-worked silicon iron. This

123

and other observations suggest that the process proposed for the initia-
tion of strain-free grains in hot-worked Nickel 200 may apply to hot-
worked silicon iron. Other boundary area measurements indicated that the
amount of a particular type of boundary present at any time was a re-
sultant of effects due to several processes. Thus, one would expect the
relationship between the amount of any of the various types of boundary
area and annealing time to be even more complex than the relationship be-
tween volume fraction strain-free material and annealing time.

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 Worki ng

A review of the mechanism

Discussion earlier in this chapter developed a mechanism for the
initiation of new grains during working and for their growth into strain-
free grains during annealing, in the following paragraphs, the basic
features of this mechanism will be reviewed.

The initial, undeformed structure is considered to be equiaxed
and to contain only high-angle grain boundaries and twin boundaries. Hot
working introduces into this structure dislocations which under the in-
fluence of the thermal and mechanical driving forces may assume a number
of aspects. If the discussion is restricted to materials of moderate and
high stacki ng-faul t energy, then a large fraction of those dislocations
which remain in the structure are contained in the subgrain boundary net-
work. This network develops continually throughout working (illustrated
schematically by Figure 28). It is this development which plays a major
role in the initiation of new grains.

rah

New grains are considered to be initiated at positions of maximum
energy gradient. In the present case, since most of the energy (disloca-
tions) introduced into the structure during working appears as a subgrain
boundary network, the above criterion reduces to the most favorable posi-
tions being those with the greatest difference in density of boundary
network quadruple points. These positions are associated with old grain
edges and possibly old grain boundaries. They are created by the contin-
ual development of the subgrain boundary network during working. If the
development has exceeded a certain degree locally and a sufficient dif-
ference in density of quadruple points exists, then new grains will be
formed by the migration of a section of high-angle boundary into the re-
gion containing the greatest density of quadruple points.

The process described above is a dynamic one in that new grains
can be initiated any time during working provided that the subgrain
boundary has developed locally into a connected network. Growth of new
grains will proceed vigorously because the density of quadruple points
within the growing grain is zero. Since dislocations are still being in-
troduced into the structure, however, these grains will become deformed
and begin to form subgrain boundary while still growing. Continued de-
velopment of this type of boundary until the formation of a continuous
network will destroy the integrity of the parent grain so that its growth
can proceed no farther. The whole process of initiation, growth, and
deformation may then be repeated.

The structure which obtains on the completion of working depends,
then, on the conditions of working, i.e., the temperature, the rate, and
the extent of deformation. This structure may contain original grains

125

with various degrees of subgrain development. It may also contain grains
that were initiated and grown at various times during the deformation.
These also have subgrains in various stages of maturity depending upon
the degree of deformation experienced since the initiation of each parent
grain. Some of these grains (not having mature subgrain networks) may
remain in active growth into the annealing period.

Predictions based on the proposed
mechanism compared with results
from other studies of hot
working

The proposed mechanism has made possible qualitative predictions
of the effects of the experimental variables upon (1) the type of position
at which strain-free grains form, (2) the linear growth rate, and (3) the
final grain size." These predictions are discussed and the experimental
evidence which applies to each prediction is presented in the following
subsections. The experimental variables which will be treated are the
initial grain size, working temperature, rate of working, extent of work-
ing, and the annealing temperature. The application of the proposed
mechanism is limited to materials of moderate and high stacki ng-faul t
energy because the mechanism is based upon a material which forms a well-
defined subgrain boundary network during hot working.^

"The grain size which exists when the structure first becomes
strain free.

^Note that the structural evolution under consideration must ex-
hibit two characteristics: (1) all strain-free grains are present at es-
sentially zero annealing time, i.e., there is no time dependent nuclea-
tion, and(2) the rate at which the boundary between the strained material
and the strain-free grains moves into the strained material is constant,
i.e., the linear growth rate is constant.

126

Before proceeding with the discussion it is necessary to explain
two of the symbols which will be used to describe the experimental re-
sults. These are the exponent n in the equation Vy = l-exp-ktn and tg c
— the time necessary for 50 per cent of the structure to become strain
free. The value calculated for n is indicative of the type of micro-
structural position at which strain-free grains are formed, i.e., if
n : 1 then strain-free grains are formed at old grain boundaries, if
n = 2 at old grain edge, and i f n = 3 at old grain corners." Values of
tg r permit qualitative comparisons of the growth rates among the various
sets of data, provided n and the initial grain sizes are the same for
each set. This conclusion follows from the equation Vy ■ l-exp-ktn. If
Vv = 0.5, then In 0.5 « ktg ,- and since the constant k contains the
growth rate to the power of n, G3°l/tg r. Since growth rates were di-
rectly determined for the three series comprising the present study and
for one set of preliminary results, comparisons based on values of tQ r
are useful in determining the effects of the experimental variables on the
growth rate in other experiments on Nickel 200.

Data from prior studies which can be used to test the predictions
made in the following subsections have been collected into Table 14. In-
cluded in the table are the initial and final values of Ni along with
values of n and tgj. Tabulated values of N|_ and tg c are fairly precise
(the standard error is estimated at less thanilO per cent of the given
value). Values of n determined from data obtained during the present

*This point is discussed in more detail in the paper by Cahn
(53).

127

TABLE 14. --A listing of initial and final grain sizes, values of n from

the equation Vy = l-exp-ktn, and times necessary for 50 per cent of the

structure to become strain free (t0_5) for all available data on annealing
after hot working of Nickel 200

Total
Extensi

on

Rate of
Temperature (°C) of Worki na

Working Annealing (/min)

NL/mm

n

(%)

Initial

Final

t0.5(sec)

31*

750

670 0.75

45

45/

1.9

3520

31*

750

700 0.75

45

46

2.1

685

11*

750

750 0.75

45

44

2.4

145

36/

705

705 0.75

43

39

1.8

290

37'

705

705 0.75

41

46

2.4

250

37

755

755 0.75

39

34

1.8

100

37

805

805 0.75

31

39

2.0

18

37

855

855 0.75

17

30

1.3

13

24

705

705 0.75

18

18

1.1

24,000

36

705

705 0.75

18

24

1.8

960

47

705

705 0.75

18

26

2.6

600

41

705

705 0.009

40

29

1.3

2500

*Da

ta from

present study.

/At

Vv = °

90.

/Each of these sets of data was obtained from a different heat of
Nickel 200.

128

study have approximately the same precision. All other values of n, how-
ever, have an estimated standard error of 0.4, e.g., 2.4 ± 0.4.

The remainder of this discussion is divided into six subsections.
Each of the first five of these is concerned with the effects resulting
from changes in one of the experimental variables. Contained in each of
these subsections are statements of the predicted effects, an outline of
the arguments which resulted in these predictions, and experimental evi-
dence which is relevant to the effect being discussed. The sixth subsec-
tion is a summary of the predicted and observed effects.

Effects of initial grain size. — Initial grain size is predicted
to have no effect on the type of position at which strain-free grains are
preferentially formed. This prediction is based on the fact that the
formation of strain-free grains at old grain edge or boundary is funda-
mental to the proposed mechanism. As long as the material is polycry-
stalline, sites of these types are available. Values of n included in
Table 15 confirm this prediction. That is, the value of n for an initial

TABLE 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

Total
Extension

m

Temperature (°C) of
Working Anneal i ng

N|_/mm

Initial

Fi nal

n

43

39

1.8

41

46

2.4

18

24

1.8

36*
37*
36

705

705

705

705

"Each of these sets of data was obtained from a different heat of
Nickel 200.

129

NL of 43/mm is the same as for an initial NL of 18/mm. Additional con-
firmation was obtained from the photomicrographs of the series with ini-
tial NL's of 18/mm and 41 /mm. One photomicrograph of a partially annealed
structure from each of these series is included as Figure 44.* In both
structures, but especially in Figure 44 (a), note the formation of strain-
free grains^ at old grain edge (triple points in two dimensions).

It is predicted that changes in initial grain size will not
change the growth rate. This statement is made on the basis that growth
rate depends upon the driving force (density of subgrain boundary network
guadruple points) and the annealing temperature, neither of which is a
function of initial grain size. None of the available data are suitable
for determining the validity of the above conclusion.

If the initial grain size is decreased, then the final grain size
is predicted to decrease. This effect is a result of a change in extent
of old grain edge and boundary with a change in initial grain size. A
change in extent of the old grain edge and boundary changes the number of
possible positions for the formation of strain-free grains and hence the
final grain size. In agreement with the above prediction, values of NL
included in Table 15 show that if the initial NL is decreased from 41/mm
to 18/mm, then the final NL is decreased from 46/mm to 24/mm. A similar

"The two photomicrographs of Figure 44 and those of Figures 45
and 46 were obtained using the Sensitive Tint Plate of the Bausch and
Lomb Research Model Metal lograph.

'strain-free grains are distinguished in this and the two subse-
quent figures (as well as in all photomicrographs obtained using polar-
ized light) by the lack of variations in shading within the grain. For a
more complete explanation of this phenomenon see the section on etching
procedures in Chapter II.

130

Fig. hh. — Photomicrographs obtained from partially an-
nealed specimens (worked and annealed at 705°C) having initial
N.' 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 .

131

relationship was observed by Kornfeld (24) and by Kornfeld and Hartleif
(25) in studies of an Armco Iron hot worked in the « -field.

Effects of working temperature. — At high hot -working temperatures,
strain-free grains will form at the old grain boundary rather than at the
old grain edge. This prediction is made on the basis that at high hot-
working temperatures edge positions are deactivated during the working
period. Deactivation results from the formation at old grain edges of
many rather' large and almost strain-free grains during the working period.
These grains will usually contain a subgrain boundary network which is
well enough developed to eliminate their growth advantage, but not devel-
oped enough to allow their participation in the initiation of new grains.
Thus, only boundary positions remain able to participate in the formation
of strain-free grains during annealing. A photomicrograph which re-
enforces this reasoning is included as Figure hS. It was obtained from
a specimen which had been worked at 855°C and then quenched (no anneal).
Note the number of old grain triple points (edge in three dimensions)
which are occupied by large, nearly strain-free grains. The data con-
tained in Table 16 provide confirmation of the above prediction. For
working temperatures up to and including 805°C, n is approximately two
(indicating preferential formation of strain-free grains at old grain
edge); however, for a working temperature of 855°C n is close to one (in-
dicating preferential formation of strain-free grains at old grain
boundary) .

An increase in working temperature will decrease the growth rate.
The basis for this prediction is the well-established increase in sub-
grain size with increasing working temperature. An increase in subgrain

132

Fig. k$ . --A photomicrograph obtained from a specimen of
Nickel 200 worked at 855°C 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.

133

TABLE 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

Total

Extension

Temperature (°C) of
Working Annealing

Ni_/mm

n

(30

Ini t

al

Final

t0,5(sec)

31

750

700

45

46

-

685

36

705

705

43

39

1.8

290

37

705

705

k\

46

2.k

250

37

755

755

-

-

1.8

-

37

805

805

-

-

2.0

-

37

855

855

-

-

1.3

-

size decreases the density of subgrain boundary network quadruple points
and hence the driving force for the growth of strain-free grains will
also decrease. Although no direct information on the variation of growth
rate with working temperature is available, it is possible to infer from
the values of tgj in Table 16 that the growth rate does indeed decrease
with increasing working temperature. Note that working at 750°C and an-
nealing at 700°C resulted in tQ e = 685 seconds, while working and an-
nealing at 705°C resulted i n t0 c = 290 to 250 seconds. Since it is un-
likely that the small variations in total extension (31 versus 36 per
cent) could account for this difference, growth rates in the two cases
must be different.

The proposed mechanism predicts an increase in final grain size
with an increase in working temperature. The basis for this prediction is
that the increase in subgrain size due to an increase in working tempera-
ture will result in the formation of fewer strain-free grains. However,

134

data included in Table 16 do not show a marked change in final grain size
with a change in working temperature. On the other hand, Rossard and
Blain (27) have reported that the final grain size of an annealed hot-
worked ferritic stainless steel decreases with decreasing temperature of
working. Note that this material would be expected to form wel 1 -defined
subgrains during hot working.

Effects of rate of working. — At low rates of working, strain-free
grains will form at old grain boundaries rather than at old grain edges.
The argument which resulted in this prediction is similar to that pre-
sented for the effect of temperature in the previous subsection; namely,
the formation at old grain edges during working of new grains which do
not preserve a growth advantage into the annealing period essentially de-
activates the edge positions. Some confirmation of this reasoning is
available from the photomicrograph included as Figure 46. This photo-
graph was obtained from a specimen quenched immediately after working (at
705 C and at a rate of 0.009/mi nute) . Note the large number of triple
points (edges) occupied by almost strain-free grains which formed during
working. It is suggested that these grains neither participate in the
formation of new grains nor grow during the annealing period. Thus, only
boundary positions are available to contribute to the growth of strain-
free grains during the annealing period. Values of n included in Table
17 confirm the above prediction. For a rate of 0.75/minute, these values
range from 1.8 to 2.6," while for a rate of 0.009/minute n is 1.3.

"Data for the large-grained material are included since it was
previously shown that grain size does not have an appreciable effect on
the type of position at which strain-free grains are formed.

135

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

136

TABLE 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

Total

Rate of

Extension

Temperature (°C) of
Worki nq Anneal inq

Worki ng
(/mi n)

NL/mir

!

a)

Fins

1

Initial

n

36

705

705

0.75

43

39

1.8

37

705

705

0.75

. 41

46

2.4

42

705

705

0.75

18

26

2.6

41

705

705

0.009

40

29

1.3

A decrease in the rate of working will result in a decrease in
growth rate. This effect is predicted on the same basis as the effect of
increasing working temperature discussed in the previous subsection. No
data are available with which to test this prediction.

A decrease in rate of working will result in an increase in final
grain size. This prediction also follows from the fact that subgrain
size increases with decreasing rate of working. The increase in subgrain
size results in a decrease in the number of strain-free grains formed and
hence in an increase in final size. This effect is illustrated by the
data in Table 17 which show that, for the same initial grain size, a rate
of 0.75/minute resulted in a final N[_ of 46/mm while a rate of
0.009/minute resulted in a final N|_ of 29/mm. A similar observation was
reported by Rossard and Blain (27) in their study of a ferritic stainless
steel .

Effects of extent of working. — The proposed mechanism predicts
that if the extent of working is below a certain value, then a connected
network of subgrain boundaries does not exist and no strain-free grains

137

will be formed during annealing. Experiments performed prior to the main
study confirmed that a minimum amount of working is necessary before
strain-free grains will form during annealing. These experiments in-
volved working large-grained (NL = 18/ mm) specimens of Nickel 200 to
total extensions of 6, 12, 2k, 36, and k2 per cent at 705°C and then an-
nealing at 705°C. Specimens extended at least 2k per cent underwent a
structural evolution during annealing, those extended 12 per cent expe-
rienced no noticeable microstructural change in annealing times up to ap-
proximately 12,000 seconds. Rossard and Blain (27) also have noted that
a certain minimum amount of working is necessary before "recrystal 1 iza-
tion" occurs during the annealing of a hot-worked ferritic stainless
steel .

It is also predicted on the basis of the proposed mechanism that
the extent of working will have no effect on the type of position at
which strain-free grains are formed, provided the extent of working has
been great enough to permit a structural evolution during annealing.
However, data included in Table 18 do not support this prediction. Note

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

Total "
Extension Temperature (°C) of NL/mm
L%) Working Annealing Initial Final

2i* 705 705 18 18

36 705 705 18 2k

1.1
1.8
42 705 705 18 26 2.6

138

that the value of n drops from 1.8 for a total extension of 36 per cent
to 1.1 for a total extension of 2k per cent. Thus it appears that strain-
free grains form at old grain boundaries at low total extension, but at
old grain edges at moderate total extensions.

A decrease in the extent of working will decrease the growth rate.
This prediction is based on the observations that the subgrain boundaries
are less well developed and the subgrains are larger for the lower extents
of working. Both effects will decrease the driving force for the growth
of strain-free grains. No information is available which can be applied
to a test of this prediction.

Decreasing the extent of working will increase the final grain
size. The basis for this prediction is the increase in subgrain size and
the resulting decrease in number of strain-free grains formed with de-
creasing extent of working. Data included in Table 18 show that a speci-
men extended 2k per cent yielded a final NL of 18/mm while a specimen ex-
tended k2 per cent yielded a final NL of 26/mm. This observation is con-
sistent with the early work of Hanemann and Lucke (21) and Hanemann (22).
Data presented by these authors (of which Figure kl is an example) indi-
cate that above a critical extent of working the final grain size de-
creases with increasing extent of working. A similar observation was
made by Rossard and Blain (27) in their study of a hot-worked ferritic
stainless steel .

Effects of annealing temperature.— The effects of annealing tem-
perature on the type of position at which strain-free grains are formed,
on the growth rate, and on the final grain size are part of the founda-
tion of the proposed mechanism. Therefore, these effects are consistent

139

ioooo r

0 10 20 30 40 50 60
AMOUNT OF WORKING (%)

Fig. k7 . --A three-dimensional representation of the
relationship between grain size, working temperature and de-
gree of working for electrolytic copper fully annealed after
working (from reference 21).

140

with this mechanism and are reviewed here only for the sake of complete-
ness. The annealing temperature has no effect on either the type of po-
sition at which strain-free grains are formed or on the final grain size.
Growth rates, however, due to the great increase in atomic mobility with
temperature, are strongly dependent upon the annealing temperature. The
exact dependence is: G = A exp-C^/RT with Qg = 32,000 cal/mole.

Summary. — A summary of the predicted effects of the experimental
variables on the type of position at which strain-free grains are formed,
on the growth rate, and on the final grain sizes is included as Table 19.
Capital letters are used for effects confirmed by experimental results,
lower case letters are used for predicted but unconfirmed effects, and
underlining to indicate either predicted effects not confirmed by the
available results, or effects for which the available data are
contradictory.

Application of the proposed mechanism
to annealing after cold working

The mechanism proposed in this study for the initiation and
growth of strain-free grains depends upon the development of a well-
defined subgrain boundary network during working. Since a well-defined
subgrain boundary network is generally not formed during cold working,
the proposed mechanism would be expected to apply to annealing after cold
working in only three special cases (provided the material is one of high
stacking-faul t energy):

1. The material is of such high purity that subgrain
formation can occur during cold working, e.g., very
high purity aluminum which may have a recrystal 1 i za-
tion temperature as low as -^0°C (58).

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2. The heat generated during working is sufficient to
cause the formation of a subgrain boundary network.

3. Subgrain boundary formation occurs so rapidly that a
network is formed during the time required to heat to
the annealing temperature.

On the above bases, one might expect to find cases in which the proposed
mechanism is operative among studies of annealing after cold work involv-
ing high purity aluminum.

An example of a study of thi s type is the one performed by
Vandermeer and Gordon (31) on the recrystal 1 i zati on of high purity alumi-
num (99-999 to 99.9999A1) alloyed with 0.008 weight per cent copper. Re-
crystallization of this material was described as being edge-nucleated
and growth controlled, i.e., all new grains were formed at essentially
zero annealing time. In addition, growth rates were found to be constant
and plots of In ln()/l-Vw) versus In t yielded slopes of two. These four
conditions are also characteristic of the present study. This corre-
spondence suggests an identity of mechanism.

CHAPTER V

CONCLUSIONS

The principal conclusions of this study appear below.

1. The as-hot-worked structure of Nickel 200 is charac-
terized by the following features:

(a) grain elongation.

(b) dislocations not associated with a boundary
network.

(c) subgrains.

(d) serrated boundaries.

(e) new grains formed during working.

The relative importance and even the appearance
of these features is a function of the working
conditions.

2. The evolution from a strained material to strain-
free grains which occurs in Nickel 200 during anneal-
ing after hot working is governed to a great extent
by the structure which exists at the completion of
working. Of particular importance are the subgrains
and the new grains formed during working.

3- The evolution from a strained material to strain-
free grains which occurs during annealing after
hot working is best described as follows:

(a) All strain-free grains originate at essen-
tially zero annealing time. The number of
these grains decreases slightly at short an-
neal ing times.

(b) Strain-free grains are preferentially formed
at old grain edges and to a lesser degree at
old grain boundaries.

(c) Strain-free grains have a tendency to grow into
only one of the old grains which share an edge
or boundary.

1*3

\kh

(d) The only process which occurs during annealing
is boundary migration.

(e) The linear growth rate of the strain-free grains
calculated from the expression G = (dVw/dt)/
(sv)o-N is cor|stant throughout the annealing
period. The temperature dependence of this
growth rate is given by G = A exp-(WRT with

Qc = 32,000 cal/mole.

4. The initiation of new grains during hot working and
their growth as strain-free grains during annealing
after hot working in Nickel 200 can be rationalized
in terms of a mechanism which may be outlined as
f o 1 1 ows :

(a) Most dislocations introduced into the structure
during hot working form a subgrain boundary net-
work which develops continually throughout
working.

(b) This development results in differences in density
of subgrain boundary network quadruple points
across grain boundaries.

(c) The difference in density of subgrain boundary
network quadruple points creates an energy
gradient. The positions of maximum energy
gradient are associated with grain edge and
grain boundary.

(d) New grains form during working at positions of
maximum energy gradient by migration of a sec-
tion of high-angle boundary into that grain with
the smallest subgrains, the highest angle bound-
aries, or both.

(e) A fraction of the new grains formed during work-
ing will maintain a growth advantage into the
annealing period. These grains then grow by
boundary migration and consume the strained
matrix.

5. The mechanism proposed above allows predictions of the
effects of the experimental variables upon the struc-
tural evolution during annealing. The majority of these
predictions are confirmed by results from other studies
of annealing after hot working.

APPENDICES

APPENDIX A

AN OUTLINE OF PREVIOUS INVESTIGATIONS
OF HOT WORKING

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APPENDIX B

PHOTOMICROGRAPHS OBTAINED FROM SPECIMENS
WORKED DURING THE STUDY

(a) Spec i men number 2- 1

0 seconds

(b) Specimen number 2-2

!5 seconds

Fig. kS. — Photomicrographs of specimens worked
at 750°C and annealed at 750°C. Annealing times are
indicated. Polarized light. ifOOX.

150

151

(d) Specimen number 11-4

kS seconds

Fig. 48 . - -Conti nued

152

(e) Specimen number 3-k

60 seconds

(f) Specimen number 11-1

75 seconds

Fig. k8 . — Continued

153

(g) Specimen number 1-3

90 seconds

(h) Specimen number 2-3

120 seconds

Fig. 48. — Conti nued

15*+

(i) Specimen number 1-2

1 80 seconds

(j) Specimen number 1-k

2*4-0 seconds

Fig. 48. — Conti nued

155

(1) Specimen number 11-3

360 seconds

Fig. k8 . — Conti nued

156

(m) Specimen number 11 — 5 720 seconds

(n) Specimen number 7-3 ]kk0 seconds

Fig. 48. — Continued

157

(b) Specimen number 7-5

60 seconds

Fig. kS. — Photomicrographs of specimens worked
at 750°C and annealed at 700°C. Annealing times are
indicated. Polarized light. A-OOX.

158

(c) Specimen number 6-2

120 seconds

(d) Specimen number 6-4

240 seconds

Fig. 49. — Conti nued

159

(e) Spec! men number 8-2

360 seconds

(f) Specimen number 7-1

480 seconds

Fig. kS . — Continued

160

(g) Specimen number 8~k

600 seconds

(h) Specimen number 7-2

720 seconds

Fig. ^9 . - -Conti nued

161

(i) Specimen number 8-5

960 seconds

(j) Specimen number 8-3

1440 seconds

Fig. 49.--Conti nued

162

(k) Specimen number 8-1

1920 seconds

Fig. 49. — Continued

163

fc. \ ^*5i

p <

%f^

^i ^Fj?

[^ 3

■ '£^m

(a) Specimen number 2-1

0 seconds

(b) Specimen number 9-3

480 seconds

Fig. 50. — Photomicrographs of specimens worked
at 750°C and annealed at 670°C. Annealing times are
indicated. Polarized light. 400X.

164

(c) Specimen number 12-4

960 seconds

(d) Specimen number 10-2

1440 seconds

Fig. 50.- -Conti nued

165

^^^^^H ^B

^^t^^m^\d

^^^LV^' ^

Ty^y**- T\ «.

EL )

KH^^^^

(e) Specimen number 9-4

1920 seconds

(f) Specimen number 10-4

2880 seconds

Fig. 50. — Conti nued

166

(g) Specimen number 10-3

38^+0 seconds

(h) Specimen number 12-!

4800 seconds

Fig. 50. --Conti nued

167

(i) Specimen number 12-2

5760 seconds

Fig. 50' — Conti nued

APPENDIX C

CALCULATION OF GRAIN SIZE DISTRIBUTION BY THE METHOD OF
SPEKTOR AS DESCRIBED BY UNDERWOOD (38)

A total of 428 chord lengths were measured for specimen 11-1.
Measurements were performed with a filar eyepiece on a Bausch and Lomb
Research Model Metal lograph. Total traverse length was 62 mm. The data
obtained and the calculated number of grains appear in Table 21.

TABLE 21. — Measured chord lengths and calculated values for the number of
grains per mnv having a certain average diameter

k

I nterval
Upper

Limits (?)
Lower

1 nterval
Mean

W)

Number of
Chords

Chords
/mm

Grains

/mm-'

1

0

8.74

4.37

160

2.58

133,000

2

8.74

17.48

13.11

107

1.73

22,600

3

17.48

26.22

21 .85

74

1.19

9,300

4

26.22

34.96

30.59

42

0.678

3,800

5

34.96

43.70

39.33

24

0.387

1,800

6

43.70

52.44

48.07

11

0.178

400

7

52. 44

61.18

56.81

8

0.129

530

8

61.18

69.92

65.55

2

O.032

130

The number of grains per mm' in a certain size range can be calculated
from the equation (26):

nk „k+l

(N„). =4 Vi.^_

V ka Tf ^2 2k-l 2k+l

where (N„). 's tne number of grains with mean diameter kA , k is the

interval number, A is the interval length, n. , is the number of chords

k+1
per unit length in the kth size class and n. is the number of chords

per unit length in size class k+1.

169

170

In order to determine if the size distribution was log normal,
the cumulative per cent of the total number of grains with a certain mean
diameter was plotted on a probability scale with the logarithm of the
mean grain diameter as the other coordinate. This plot is included as
Figure 51. The fact that all points, except one, fall reasonably close
to the straight line indicates that the distribution is close to log
normal. The deviation of the point for the smallest grain size is due to
a lack of resolution which transforms the experimental data from a single-
humped skewed distribution into an essentially parabolic distribution.

171

99.99 ©

-

99.9

99.8

99

-

98

-

95

K

LU

fe()

3

2

<80

1-

0

H-70

u_

°60

H

550

o,

>

Ul

^•30

UJ

>20

>-

3

iio

_

3

0

5.0

2,0

1.0

0.5

0.2
0.1

o.o:

0.011 —
0.95

GT

15 1.35 1.55
LOG MEAN DIAMETER (MICRONS)

1.75

Fig. 51. *-A plot of cumulative per cent of total number
of ycalns with * certain mean diameter versus I09 or the mean
dl ameter.

APPENDIX D

A DERIVATION OF THE EXPRESSION eg = [(NL)T/(NL)L] 2/3-\
FOLLOWING THAT ORIGINALLY GIVEN BY RACHINGER (43)

The desired result is an equation relating e , the average longi-
tudinal tensile strain in the grains, to the easily measurable quantities
(N|_)T and (N|_)(_- The derivation is restricted to deformation in tension,
by drawing or by swaging in which it can be assumed that the change in
shape experienced by the "average" grain can be described by only two
parameters. In other words, the change in shape measured in any direc-
tion on a plane perpendicular to the extension axis is the same. In the
present case, the complications which would be introduced by directional
grain growth, recrys tal 1 i zati on, etc., are neglected.

Consider an equiaxed structure with a grain size described by
specifying that a unit length of random line will intersect n grain bound-
aries per unit length. If each grain now experiences a tensile strain of
amount e„, then the number of grain boundary intercepts per unit length
of line parallel to the tensile axis is decreased by a corresponding
amount, or (Ni ) i = n/1 + e . Considering any element of volume origi-
nally a unit cube, one easily calculates that the number of intercepts

perpendicular to the tensile axis is increased by an amount (1 + eg)

1 /?

and therefore (NL)j = n(l + e ) . The above statement becomes obvious

from a study of the diagrams given below.

173

174

T

^L^

Final
Vf = x2(l + eg) = VQ = 1
x = 1/(1+ eg)1/2
Solution of the above expressions involving Ni, N and e for e yields

eg=[(NL)T/(NL)L]2/3-l.
This equation permits a calculation of the average strain experienced by
the grains from measured values of (N.). and (Ni)t.

APPENDIX E

MODIFICATION OF CAHN'S EQUATION (53) FOR THE

VOLUME FRACTION STRAIN-FREE GRAINS VERSUS

ANNEALING TIMES

The original equation was derived on the following bases:

1. A constant linear growth rate.

2. All strain-free grains are initiated at essen-
tially zero annealing time.

3. Strain-free grains are initiated and grow at
old grain edges.

k. The growth of strain-free grains occurs equally
in all directions from the edge at which it
ori gi nated.

5. Impingement of strain-free grains occurs first among
grains originating at the same edge and then with
grains originating at different edges.

These bases are retained in the modification with the exception of number

four which is changed to read: growth of strain-free grains occurs into

the one grain sharing the edge which possesses the greatest density of

quadruple points. The derivation then proceeds as follows:

1. Consider a straight length of edge E of infinite
extent having a specific nucleation
rate le. The arbitrary line F is g c

parallel to E at a distance r.

A new grain which begins to grow at time T from E
will intercept on F a length
W = 2[G2(t-7)2-r2]l/2

at time t.

176

177

2. The extended length fraction (calculated without

regard for impingement) at time t due to strain-free
grains starting to grow in the time between T and
7 + d T is

dZe = 2ledT [G2(t-T)2-r2],/2.

3- Let x : r/Gt and note that t-r/G is the time elapsed
after the growing grain impinges on line F, then

ie -- rl dze = 2ie r'^u-nz-rV^dT

and on performing the substitution and the integra-
tion, one finds that

= I.Gt2[>/r^2 . x2 )og J+_

The volume occupied by new grains originating from
unit length of E is

l-BO .1

o : I 2tfrZdr = 2yG2t2 I x(l-e"Ze)dx

letting r s Gtx. The assumption that the strain-free
grains grow equally in all directions from the edge
at which they originate is introduced in the above
expression. However, if this assumption is replaced
by the one that growth is preferentially into one of
the grains which share the edge, then instead of

V0 = j2?frZdr, one finds that V0*[ (2 If /3)rZdr

0 o

since the grain boundaries which share an edge are
considered to subtend an angle of 120° = 2^/3. The
relation between the extended line fraction and the
actual line fraction, Z = 1 -e e is also introduced
at this point.

5- With the above change, one finds that

V0 = (2*/3)G2t2 ('x(l-e-ze)dx
Jo

6. If the structure contains a randomly distributed
edge length Ly per unit volume, then

(Vv)e = LUV0 = (2?7/3)LvG2t2 f x(l-e-Ze)dx

Jo

178

For large values of le (all strain-free grains
originate at essentially zero annealing time) the
above expression reduces to

(Vv)e ■ (^KvGVf'wU =fLvG2t2
Jo '

0 as L

Making use of the expression between the extended
volume fraction and the actual volume fraction,
»V " 1 -e » V'e one arrives at the expression
Vv = l-exp-('7/3)LvG2t2.

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181

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182

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BIOGRAPHICAL SKETCH

Charles Robert Smeal was born September 27, 1932 in Altoona,
Pennsylvania. He received his primary schooling in the Altoona Public
Schools and graduated from the Altoona Senior High School in June, 1950.
He attended The Pennsylvania State University and graduated in June, 195^
with the degree Bachelor of Science in Metallurgy. For the remainder of
1951* he was a Metallurgist for the Stackpole Carbon Company. In January,
1955 he entered the United States Army. After separation from the army
in October, 1956 he began graduate work at The Pennsylvania State Uni-
versity and received the degree of Master of Science in Metallurgy in
August of 1958. For the next twelve months he was a Research Engineer
for the National Aeronautics and Space Administration at the Lewis
Laboratory in Cleveland, Ohio. In September, 1959 he began studies for
the doctorate at The Pennsylvania State University and in October, i960
transferred to The University of Florida.

Charles Robert Smeal is married to the former Eleanor Marie
Cutri, a graduate of Duke University and of The University of Florida.
He is the father of one child. He is a member of the American Society
for Metals and the American Institute of Mining and Metallurgical
Engineers.

This dissertation was prepared under the direction of the chair-
man of the candidate's supervisory committee and has been approved by
all members of that committee. It was submitted to the Dean of the
College of Engineering and to the Graduate Council, and was approved as
partial fulfillment of the requirements for the degree of Doctor of
Phi losophy.

April Ik, 1965

Dean, College of Engineering

yfv*Dean,' Graduate School j

6^J

Supervisory Committee:

Chai rman

■^iM

it,

■lis

IBIlHiiiiiiiiiiiR,M

3 1262 086663944