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This is to certify that the
thesis entitled
EFFECT OF TEMPERATURE ON THE DEFORMATION BEHAVIOR OF
TWO-PHASE BICRYSTALS OF ALPHA-BETA BRASS

presented by

ALI ASGHAR KHEZRI YAZDAN

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Metallurgy

 

 

&' W' Momma/trim

Major professor

Date January 20, 1976

 

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ABSTRACT
EFFECT OF TEMPERATURE ON THE DEFORMATION

BEHAVIOR OF TWO-PHASE BICRYSTALS OF
ALPHA-BETA BRASS

By
Ali Asghar Khezri Yazdan

Two-phase bicrystals of alpha-beta brass were de-
formed.at various temperatures to investigate the effect
<3f ordering and disordering in beta brass on the overall
deformation behavior of this two-phase alloy. Tensile
testing of these specimens was carried out at various
strain-rates at 700°, 800°, 900° and 1000°F to gain under-
standing of the basic mechanisms involved. Single crystals
of alpha and beta brass, as well as coarse-grained beta
brass, were also deformed at these temperatures at various
strain-rates. The deformation structures were studied by
Optical microscopy.

Deformation of Beta, unlike Alpha, was found to be
highly sensitive to temperature and strain-rate. The
predominant mode of deformation in Beta at temperatures
below TC (ordering temperature) was by grain boundary
sliding and at temperatures above TC it was by slip.
Further, Beta did not exhibit any work-hardening at tempera-

tures above Tc'

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Ali Asghar Khezri Yazdan

Unlike in the room temperature deformation of these
bicrystals, interaction of slip in one phase with the
phase boundary was not an important factor in initiating
deformation in the other phase. Overall deformation of
the bicrystals at these temperatures depended on the de-
formation of the individual phases. Usually, the deforma-
tion of one phase did not influence the deformation of
other phase. The alpha-beta phase boundary did not play
any role in the deformation of these bicrystals.

It was discovered that a uniform deformation of
both the phases present in alpha—beta brass could be
achieved by using low and moderate strain-rates at tempera-
tures below Tc and by using high strain-rates at
temperatures above Tc“ The results are explained by

using simple hypothetical models.

 

 

EFFECT OF TEMPERATURE ON THE DEFORMATION
BEHAVIOR OF TWO-PHASE BICRYSTALS OF
ALPHA-BETA BRASS

By
Ali Asghar Khezri Yazdan

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Metallurgy, Mechanics and
Materials Science

1976

To

My Parents

ii

I won.
a: g: tituae;
1.,

n 218 CORCI'

I‘EZtS. My ap-

 

 

 

ACKNOWLEDGMENT

I would like to express my deepest appreciations
and gratitudes to my major advisor Dr. K.N. Subramanian
for his contributions through his guidance and encourage-
ments. My appreciations are also extended to members of
my thesis committee, Drs. G. Cloud, D. McGrady and W.
Hartman (sitting in for Dr. P. Schroeder) for their
valuable suggestions along with Mr. and Mrs. Siriani for
helping me in editing.

Many thanks to Dr. R. Summitt, chairman of the
Department of Metallurgy, Mechanics and Materials Science
for awarding me with teaching assistantship, Pahlavi
Foundation for providing me with a loan and Utilex, A
Division of Hoover Ball and Bearing in Fowlerville for
hiring me as a consultant during the course of these
studies.

My special love and affections go to my wife
Naheed and my daughter Shabnam.who suffered the most along

with our parents during this work.

iii

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TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

Chapter
I.

II.

III.

INTRODUCTION .

1.1 General .

HISTORICAL REVIEW

2.1 Growth of Crystals

2.2

2.3

2.1.1 Growth of Alpha and Beta Brass
Single Crystals . .

2.1.2 Growth of Bicrystals of Alpha-
Beta Brass .

Deformation of Single Phase Materials

2.2.1 Deformation of Single Crystals :

2.2.2 Deformation of Bicrystals
2.2.2 (8) Deformation Behavior of
Bicrystals of Alpha and
Beta Brasses . .
2.2.3 Deformation Behavior of Poly-
crystals . . .
2.2.3 (a) Deformation Behavior of
Polycrystalline Alpha and
Beta Brass . .
Deformation of Two- Phase Materials
2.3.1 Deformation of Bicrystals of
Two- Phase Materials

2. 3. 2 Deformation of Polycrystals of .

Two- Phase Materials . .
2.3.3 Objectives of the Work .

EXPERIMENTAL PROCEDURES

3.1

3. 2 Growth of Single Crystals of Alpha and.

Preparation of Alpha and Beta Stock .

Beta Brass

iv

Page
vii

ix

DVNU'I U1 U1 U1 H H

H

17

18

22

24
26

28
28
28

:3
N

4.3

 

 

 

 

Chapter

3.3 Growth of Two- Phase Bicrystals of
Alpha- -Beta Brass . . .
3.4 Mechanical Testing of specimens at
Elevated Temperatures

IV. RESULTS AND DISCUSSION

4.1 Deformation Behavior of Bicrystals of
Alpha-Beta Brass in the Temperature
Range at which Beta Exists in the
Ordered State (less than 850°F).

4.1.1 Deformation Studies at 700°F

4.1.2 Deformation Studies at 800°F

4.1.3 Remarks on Specimens Deformed
at Temperatures Below the
Ordering Temperature of Beta
Brass: (less than 850° F) .

4.2 Deformation Behavior of Bicrystals of
Alpha- -Beta Brass in the Temperature
Range at which Beta Exists in the Dis-
ordered State (greater than 850° F) .
4.2.1 Deformation Studies at 900° F .
4.2.2 Deformation Studies at 1000°F .
4.2.3 Remarks on Specimens Deformed

at Temperatures above the
Ordering Temperature of Beta
Brass: (greater than 850°F) .
4.3 Supporting Studies on Single Crystals
of Alpha and on Single and Polycrystals
of Beta Brasses . . .
4.3.1 Deformation Behavior of Alpha
Brass Single Crystals at
Elevated Temperatures

4.3.2 Deformation Behavior of Beta
Brass Single Crystals at
Elevated Temperatures .

4.3.3 Deformation Behavior of Beta
Brass Polycrystals at Elevated
Temperatures . .

4.3.4 Deformation Behavior of Two-
Phase Muntz metal at Elevated
Temperatured

4.4 Factors that Influence Uniform Deforma-
tion of Both the Phases Present in a
Two-Phase Material . . . . .

V. SUMMARY AND CONCLUSIONS

Page

29
37
40

40

40
50

65

71
71
79

85

86

95

98

101

104

104
129

Enter
‘51. SUGGEST
ZIS'.’ vi REFEREI

cart"
:5 l an‘d 5‘

 

 

Chapter Page

VI. SUGGESTED TOPICS FOR FURTHER INVESTIGATION . 132
LIST OF REFERENCES . . . . . . . . . . . . . . . . . 134

APPENDIX 137

vi

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at 10s

Qualit
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Yield
Stress
BFaSs
Tempe:

 

Yield
Stres
Vario.
Yieldl
at Va
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Brass
Peed

 

 

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0.10

 

 

Table

II.

III.

IV.

VI.

VII.

VIII.

IX.

XI.

XII.

LIST OF TABLES

Quantitative Results of Bicrystals Deformed
at 700°F .

Quantitative Results of Bicrystals Deformed
at 800°F .

Qualitative Observations made on Specimens
Deformed at 800°F

Quantitative Results of Bicrystals Deformed
at 900°F .

Qualitative Observations made on Specimens
Deformed at 900°F

Quantitative Results on Specimens Deformed
at 1000°F

Qualitative Observations made on Specimens
Deformed at 1000°F .

Yield Stress (Critical Resolved Shear
Stress) of Single Crystals of Alpha-Beta
Brass at Various Strain-Rates and
Temperatures

Yield Stress (Critical Resolved Shear
Stress) of Single Crystals of Beta Brass at
Various Strain-Rates and Temperatures

Yield Stress of Polycrystals of Beta Brass
at Various Strain-Rates and Temperatures

Yield Stress of 60-40 (Cu—Zn) Commercial
Brass (Muntz metal) at Various Cross-Head
Speeds and Temperatures

Deformation Behavior of Alpha-Beta Brass

Bicrystals Tested at Cross-Head Speed of
0.10 cm/min at Low and High Temperatures

vii

Page

67

69

74

87

89

90

92

96

99

100

106

120

I lh‘
- I
$39;

Data 0
clined
Tezper

uzmar
Defer:
Brass
tures

 

 

 

Table
XIII.

XIV.

Page

Data on the Deformation Behavior of In-
clined Boundary Specimens Tested at Room
Temperatures . . . . . . . . . . . . . . . . 161

Summary of the Observations made on the
Deformation Behavior of Two-Phase Alpha-Beta

Brass Bicrystals Tested at Elevated Tempera-
tures . . . . . . . . . . . . . . . . . . . 127

viii

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U

‘3‘

Ch

 

 

 

Figure

10.

11.

12.

LIST OF FIGURES

Cesium Chloride Structure. (a) A Two-
Dimensional Model, (b) A Three-Dimensional
Model .

Critical Resolved Shear Stress for Beta
Brass Single Crystals

Schematic Diagram of the Crucible Assembly
for Growing Single Crystals of Alpha and
Beta Brass . . .

Schematic Diagram of the Furnace for Growing
Single Crystals of Alpha and Beta Brass .

Schematic Diagram of Apparatus for Joining
Beta Brass to the Single Crystal of Alpha
Brass . . . . . . . . . .

Schematic Diagram of the Apparatus for
Local Annealing .

Schematic Diagram of Ten Units for Automatic
Cyclic Local Annealing Operation

Schematic Diagram of the Apparatus Used for
Elevated Temperatures Test

Interaction of Slip in Alpha with the Alpha-
Beta Phase Boundary in a Specimen Tested at
700°F with a Cross-Head Speed of 0.02 cm/min

Grain Boundary Sliding in a Beta Region away
from the Boundary in a Specimen Tested at
700°F with a Cross-Head Speed of 0.02 cm/min

Development of Small Cracks in Beta at Grain
Boundaries in a Specimen Tested at 700°F
with a Cross-Head Speed of 0.10 cm/min

Multiple Slip in Alpha Near the Phase

Boundary in a Specimen Tested at 700°F with
a Cross-Head Speed of 0.10 cm/min . .

ix

Page

12

15

30

31

33

34

36

39

42

44

46

47

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I
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v

5.

a.

H.

 

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a Cros

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0.02 c

Defort
Orient
Phase
830’?
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(b) F

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Bounda
the Er
at 80C
0.50 c

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Smalle
800°F

 

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Grain
800°F

Crack
Bound
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Figure Page

13. Interaction of Slip in Alpha with the Phase
Boundary in a Specimen Tested at 700°F with
a Cross-Head Speed of 0.10 cm/min . . . . . 48
14. Grain Boundary Sliding in Beta Regions away

from the Phase Boundary in a Specimen
Tested at 800°F with a Cross-Head Speed of

0.02 cm/min . . . . . . . . 51
15. Deformation of Beta by Slip in Favorably-

Oriented Grains in Regions away from the

Phase Boundary in a Specimen Tested at

800°F with a Cross-Head Speed of 0.02 cm/min

(a) Fine Slip in Beta . . . . . . . . . . 52

(b) Rumple Appearance in Beta . . . . . . 53

16. Slip Initiated by Grain Boundary Sliding
in Beta Phase in a Specimen Tested at
800°F with a Cross-Head Speed of 0.02 cm/min 54

17. Deformation of Beta in a Most Favorably-
Oriented Grain by Coarse Slip, when Grain
Boundary Sliding is Unable to Accommodate
the Entire Deformation, in Specimen Tested
at 800°F with a Cross-Head Speed of
0.50 cm/min . . . . . . . . . . . . 55

18. Severe Deformation in Beta near the Tips of
Smaller Grains in a Specimen Tested at
800°F with a Cross-Head Speed of 0.02 cm/min 57

19. Deformation of Regions in Beta near the
Grain Boundary in a Specimen Tested at
800°F with a Cross-Head Speed of 0.02 cm/min 58

20. Cracking Near the Junction of Three Grain
Boundaries in Specimen Tested at 800°F With

a Cross-Head Speed of 0.02 cm/min . . . . . 59

21. Absence of Plastic Deformation in Alpha in
a Specimen Tested at 800°F with a Cross-Head

Speed of 0.02 cm/min . . . . . . . . . . . 60
22. Interaction of Slip in Alpha with the Phase

Boundary in a Specimen Tested at 800°F w1th

a Cross-Head Speed of 0.10 cm/min . . . . . 61

23. Independent Slipping of Alpha and Beta in
the Region near the Phase Boundary in a
Specimen Tested at 800°F with a Cross-Head
Speed 0.10 cm/min . . . . . . . . . . . . . 62

I‘ ‘_'I
‘0
c

L;-
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-

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Defort
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800 F '

Stress
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Stress
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Head S

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900°F-
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Figure Page

24. Grain Boundary Sliding Leading to Severe
Deformation of Beta Grains away from the
Phase Boundary in a Specimen Tested at
800°F with a Cross-Head Speed of 0.10 cm/min 64

25. Stress-Strain Curves for Bicrystals Tested

at 700°F and Strained at Various Cross-Head

Speeds . . . . . . . . . . . . . . . . . . 72
26. Stress-Strain Curves for Bicrystals Tested

at 800°F and Strained at Various Cross-

Head Speeds . . . . . . . . . . . . . . . 73
27. Deformation Behavior near and away from

the Phase Boundary in a Specimen Tested at
900°F with a Cross-Head Speed of 0.02

cm/min
(a) No Observable Plastic Deformation in
Alpha near the Boundary . . . 75
(b) Severe Deformation in Beta away from
the Phase Boundary . . . 75
(c) Macrograph Showing Necking in Beta . 76
28. Severe Deformation in Beta Regiontnear

the Phase Boundary in a Specimen Tested
at 900°F with a Cross-Head Speed of
0.10 cm/min . . . . . . . . . . . . . . . 78

29. Deformation of Alpha in SingleSlip away from
the Phase Boundary in a Specimen Tested
at 900°F and Strained at a Cross—Head
Speed of 0. 50 cm/min .

(a) Macrograph of Slip in Alpha : : I : : 80
(b) Micrograph of Slip in Alpha . . . . 30
(c) Interaction of Single Slip in Alpha
with the Boundary . . . . . . . . . 31
30. Deformation of Both the Phases near the

Phase Boundary in a Specimen Tested at
900°F with a Cross- Head Speed of 0. 50

cm/min . . . . . . . . . . . 82
31. Needle Fracture in Beta Phase . . . . . . 84
32. Stress-Strain Curves for Bicrystals

Tested at Elevated Temperature of 900°F

and Strained at Various Cross-Head Speeds 93
33. Stress- Strain Curves for Bicrystals Tested

at Elevated Temperatures of 1000° F and

Strained at Various Cross- Head Speeds . . 94

xi

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If.
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Yield
Resolx
Alpha
Tezpe:

Yield
CIVSEE
and 8:

Yield
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(b)

 

 

 

Figure

34.

35.

36.

37.

38.

39.

40.

41.

42.
43.

44.

45.

Yield Stress (Solid Line) and Critical
Resolved Shear Stress (Dotted Line) for
Alpha Brass Single Crystals Tested at
Temperatures Ranging from 700°to 1000°F

Yield Stress for Beta Brass Single
Crystals Tested at Elevated Temperatures
and Strained at Various Strain-Rates

Yield Stress for Beta Brass Polycrystals
Tested at Elevated Temperatures and
Strained at Various Strain-Rates

A Simulated Model Illustrating the Inter-
action of Grain Boundary Sliding with Beta
Grain .

Simulated Models Representing the Three

Possible Grain Boundary Orientations in

Bicrystals of Beta Brass .

(a) Grain Boundary is Perpendicular to
the Tensile Axis .

(b) Grain Boundary is Nearly Parallel to
the Tensile Axis . . . .

(c) Grain Boundary Makes 45°with the
Tensile Axis . . . . . . . .

A Dislocation Model for Grain Boundary
Sliding in Single Phase Alpha and Beta
Brasses . . - -

A Simulated Model of Two-Phase Alpha-Beta
Brass Deformed Under Normal Stress .

A Simulated Model of Two-Phase Alpha-Beta
'Muntz metal (60-40 Cu—Zn Brass)

Free Hand Sketch of Alpha-Beta Brass

Single Slip in Alpha in a Specimen Having
60° Inclined Boundary with Tensile Axis

Fine Cross-Slip in Alpha in a Specimen
Having 60° Inclined Boundary with the
Tensile Axis . . . . . . . . .

Cross-Slip in Alpha near the Boundary in a

Specimen Having 60° Inclined Boundary with
the Tensile Axis . .

xii

Page

97

100

105

113

117

117

117

117

118

122

124
125

140

141

145

EL

51

31

5;.

35,

37.

Cross-
in a E
with I

Exten:
Bound;
Bound;

lip :
Bmmd
Mum.

Macro;
Stres.
Bound.

Macro
60° I:
Axis

Exten
Obser

 

 

the

 

 

Figure Page

46. Cross-Slip in Alpha near the Phase Boundary
in a Specimen Having 60°Inc1ined Boundary
with the Tensile Axis . . . . . . . . . . . 143

47. Extensive Cross-Slip in Alpha near the
Boundary in a Specimen Having 60° Inclined

Boundary with the Tensile Axis . . . . . . 144
48. Slip in Beta in a Region away from the Phase

Boundary in a Specimen Having 60° Inclined

Boundary with the Tensile Axis . . . . . . 145

49. Macrograph Showing Slip in Beta at a High
Stress in a Specimen Having 60° Inclined
Boundary with the Tensile Axis . . . . . . 147

EML Macrograph of the Tested Specimen Having
60° Inclined Boundary with the Tensile
Axis . . . . . . . . . . . . . . . . . . . 148

51“ Extensive Deformation in Alpha with no
Observable Deformation in the Beta Region
Adjoining it, in a Specimen Having 45°
Inclined Boundary with the Tensile Axis . . 149

52. Cross-Slip in Alpha Occurring at the Inter-
face Region in a Specimen Having 45°

Inclined Boundary with Tensile Axis . . . . 150
53. Slip in a Beta Grain that was in Contact

‘with the Boundary in a Specimen Having 45°

Inclined Boundary with the Tensile Axis . . 151

54. Interaction of Slip in Alpha with the
Boundary in a Specimen having 45° Inclined
Boundary with the Tensile Axis . . . . . . 152

55. Heavy Deformation in Alpha and Slip in Beta
in a Region away from the Boundary in a
Specimen Having 45° Inclined Boundary with
t e Tensile AxiS. . . . . . . . . . . . . . 153

56. IMacrograph Showing Extensive Slip in Beta
Regions away from the Boundary in a
Specimen Having 45° Inclined Boundary with
the Tensile Axis . . . . . . . 155

57, Interaction of Slip in Alpha with the

Boundary in a Specimen Having 30° Inclined
Boundary with the Tensile Axis . . . . . . 156

xiii

later;
the B:
Inclh

iacro
from
Incli:

Slip :
with l
Inclir

 

Figure

58.

59.

60.

Interaction of Single Slip in Alpha with
the Boundary in a Specimen Having 30°
Inclined Boundary with the Tensile Axis

Macrographs of Slip in Beta in a Region Away
from the Boundary in a Specimen Having 30°
Inclined Boundary with the Tensile Axis

Slip in the Beta Grain that is in Contact
with Alpha in a Specimen Having 30°
Inclined Boundary with the Tensile Axis

xix
XIL

Page

157

158

159

'“1 General

A vas
gractical 3??
phase substan
grapertieS, a
he has to in
bet:er, 30 th
severe them0
:5 such two-p'
steel. and two

:an (brasses

2.:n2ugh thes

+1..
. p
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gh uncle
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CHAPTER I
INTRODUCTION

1.1 General

A vast number of engineering materials used in
practical applications are made of two-phase or multi-
phase substances. These materials, depending on their
properties, are used in making various types of products.
One has to investigate and understand these materials
better, so that they can be used most efficiently under
severe thermoemechanical conditions of service. Examples
of such two-phase materials are, steel, duplex stainless
steel and two-phase alloys of titanium-Aluminum, copper-
zinc (brasses), copper-tin (bronzes) and copper-aluminum.
Although these two-phase materials are widely used, a
thorough understanding of their mechanical behavior is far
from complete.1

In order to understand the basic mechanisms con-
trolling two-phase materials, the number of factors in-
fluencing their deformations should be minimized. Single
crystals constitute ideal models for studying the deforma-
tion behavior of single phase materials. One cannot produce

a single crystal of a two-phase material, since such a

crystal can have only one phase. So, a basic unit for a
1

res-phase mate
:m-phase bicr
fziaehtal uh
phase boundary
asaresult, t
:lase to a bio
abs-under}: in

The in
sauld consis
iiifigle CYYS
chsible to o
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ta WO-phas
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33555, the f
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fish a unit
Hing;

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Bicrystals 0.
W131 ten I

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two-phase material must be a two-phase bicrystal. Such a
two-phase bicrystal will have a phase boundary in the
fundamental unit. The deformation characteristics of the
phase boundary may correspond to that of a grain boundary;
as a result, two-phase bicrystals will be, in reality,
close to a bicrystal of a single phase material, which has
a boundary in the model system.

The fundamental model for a two-phase material
should consist of a single crystal of one phase joined to
a single crystal of another phase. However, it is not
possible to obtain such fundamental units for most of the
two-phase materials. Quite often, both the phases present
in a two-phase material are metallic in nature. One such
material is alpha-beta brass. In the case of alpha-beta
brass, the fundamental unit used for deformation studies
consists of a single crystal of alpha joined to a coarse-
grained polycrystal of beta. Often, only a single grain
of beta will be in contact with the alpha single crystal.

Such a unit can be called a two-phase bicrystal.2

3

Hingwe and Subramanian have developed a technique

fer growing bicrystals of alpha-beta brass. Hingwe4 and

Nilsen5

have studied the mechanical properties of such
bicrystals of alpha-beta brass at room temperature, under
Uniaxial tension, at various strain rates. These studies
onbicrystals of alpha-beta brass were aimed at under-

standing the basic mechanisms involved in the deformation

:f 30°?hase I

2: the abilit
azrsss the Ph
abicrystal w
stress. This
:::s:ar.:s, Cl’
::ie:::ationS.
Peierls-Nabar
:ie ability f
ziritary, and
if the phases
Eel-avior of 3

All 0
'45 alpha-beta

3'58. hateri

 

 

 

of two-phase materials. During elastic deformation,
response of such a bicrystal to an applied stress depends
on the ability of its constituents to transfer strain
across the phase boundary. The two participant phases in
a bicrystal will differ in their responses to an applied
stress. This is a direct result of differences in elastic
constants, crystal structures, relative crystallographic
orientations, etc. The number of available slip systems,
Peierls-Nabarro stresses, work-hardening in each phase,
the ability for the deformation to progress through the
boundary, and the relative crystallographic orientations
of the phases will affect the over-all plastic deformation
behavior of such bicrystals.

All of the mechanical tests performed on bicrystals
of alpha-beta brass have been carried out at room tempera-
ture. Materials such as brasses are often hot-rolled and
extruded during manufacturing processes. In order to
understand the basic mechanisms controlling the deforma-
tion behavior of such materials at elevated temperatures,
umchanical tests have to be carried out on fundamental
units, such as two-phase bicrystals, at various tempera-
tures. Beta brass undergoes a structural change at 850°F
(454°C). The effect of such a structure change on the
high temperature deformation behavior can also be in-

vestigated by using alpha-beta brass bicrystals.

The 1
3f alpha-beta
:: the mechan
:ezperatures .

The ef
iith respect t
Iézperature am
Growth
iSwell as Of t

139 reviewed in

 

The purpose of this study is to grow bicrystals
of alpha-beta brass and to study the effect of temperature
on the mechanical behavior of such specimens at elevated
temperatures.

The effect of the phase boundary orientations
with respect to the tensile axis are studied at room
temperature and are presented in Appendix A.

Growth and mechanical properties of Alpha, Beta
as well as of two-phase bicrystals of alpha-beta brasses

are reviewed in the following chapter.

.1 Growth of CryE
;.:.1 W

Single CY?
gran by the Bridg
:lten brass, whic

e crucible

;;;;;

CHAPTER II
HISTORICAL REVIEW

2.1 Growth of Crystals

2.1.1 Growth of Alpha and Beta Brass Single Crystals

 

Single crystals of alpha and beta brass can be
grown by the Bridgmen technique. In this technique, the
inolten brass, which is contained within a sharp-tipped
graphite crucible, is lowered through a temperature
gradient. Upon cooling, the nucleus is formed at the
sharp tip, and the rest of the crystal grows on it.
‘Maintaining a uniform chemical composition during growth
of an alloy single crystal is extremely difficult, since
segregation contributes to the non-uniformity of composi-
tion. In brasses, the parts solidifying first contain
less zinc than those solidifying later. Non-uniformity in
composition can be minimized by employing very slow crystal
growth-rates. Furthermore, annealing the brass in a
sealed tube at 1450°F (800°C) for 16 hours will completely

remove any segregation.6

2.1.2 Growth of Bicrystals of Alpha-Beta Brass

 

Hingwe and Subramanian3 developed the technique
for growing bicrystals of alpha-beta brass in which beta

brass (48.5 w/o Zn) was melted on a single crystal substrate
5

:‘alzha brass (
*‘srediate zin
ZET£EEI1 alpha at:

Ti:-Dl‘.&$€ tran s i

"9

~ 6 Y‘aSeS L a
F n F'"
:eccte t'l .»

firs: heat- treat

:::::gh a tempe I

raise the size

.32. and beta ;
:ctecone contir
2 the second he
ieated to 1450°l
Zezperature grac
:‘zen cooled to

Site“ Several

C 4::
.,. 3“

of alpha brass (30 w/o Zn). A two-phase foil with an
intermediate zinc composition of 40 w/o Zn was placed
between alpha and beta stock before melting, to reduce the
two—phase transition zone formed between the alpha and
beta phases. Two special heat-treatments were employed

to reduce the two-phase transition zone formed. In the
first heat-treatment, the as-joined crystal was lowered
through a temperature gradient. This operation helped to
reduce the size of the transition zone, and caused the
alpha and beta platelettes present in the transition zone
to become continuous with alpha and beta regions respectively.
In the second heat-treatment, the transition zone was
heated to 1450°F (800°C) in a furnace having a very sharp
temperature gradient for about one hour. The sample was
then cooled to room temperature. This process was re-
peated several times. During the heating cycle, the two-
phase transition zone becomes a single phase beta region,
and diffusion of zinc from regions containing higher zinc
concentration to a lower concentration is made possible.
Beta grain growth also takes place during such a cyclic
local annealing. Repetitive heating and cooling produces
the required bicrystal. Since then, such a unit has been
referred to as the basic model for fundamental studies on

3’4’5 The deforma-

alpha-beta brass by various researchers.
tion behavior of such model systems will invariably be
dependent on the deformation behavior of the individual

phases, and also on the deformation of phase boundary.

.‘ze deformat ion

:eri ewe d in t h e

12 Defomaticn
2,2,1 Deformati
Plastic
sterials when tl
:irection (slip <
reaches a critice
its plastic flo'.
Silved shear stre

.16 cfi

 

The deformation behavior of alpha and beta brasses are

reviewed in the following section.

2.2 Deformation of Single Phase Materials

2.2.1 Deformation of Single Crystals

 

Plastic deformation by slip occurs in crystalline
materials when the shear stress acting along a specific
direction (slip direction) on a specific plane (slip plane)
reaches a critical value. The value of stress at which
this plastic flow occurs is defined as the critical re—

7

solved shear stress. The Schmidt Law relationship for

the critical resolved shear stress 0c is:

o = 0 cos A cos o
c o

where Go is the yield stress in uniaxial loading, A
is the angle between the normal to the slip plane and the
axis of loading, and o is the angle between the slip
direction and the axis of loading. In this expression
(cos A) (cos ¢) is termed the Schmidt factor.

Single crystals of face-centered cubic materials,
[F.C-C] such as copper and alpha brass, exhibit three
stages of work-hardening during deformation. During the
first stage, there is a low work-hardening rate. The
extent of this stage is sensitive to crystal orientation,
purity and temperature of testing. In Stage II there is
much higher rate of work-hardening, which is constant at

moderate temperatures. This stage is independent of

c.752allographic 0
single as well as
iecreasing work he
:3 dynamic recovei
tenservative clir.‘
zezals such disor
strain-hardening
inn.

8

Orowan 1

:7” .
“"encmg the st:

éiven t

crystallographic orientation and other test variables.
Single as well as polycrystals exhibit this stage. The
decreasing work hardening rate in Stage III is attributed
to dynamic recovery of the material due to cross-slip and
conservative climb. Body centered cubic, [B-C-C],
metals such disordered beta brass, display a decreasing
strain-hardening rate over their entire range of deforma-
tion.

Orowan8 has'made observations on the factors in-
fluencing the strain-rate sensitivity of materials and has

given the formula for strain-rate (E) as,

g%=é=pbv

where p is the mobile dislocation line length per unit
volume, b is the Burgers vector of the mobile dislocations,
and v is the average velocity of the dislocations. The
magnitude of each of the factors b, v, and p can vary
with respect to time.

Johnston and Gilman9

suggested that the total
strain was directly related to the density of the mobile
dislocations. They also suggest that dislocations can
'multiply, especially by a cross-glide process. It has
been observed that materials such as beta brass are highly
strain-rate sensitive. With increasing strain-rate, the
ease of movement of mobile dislocations decreases, because

of the more frequent dislocation interactions. After the

mobile dislocations are tangled in some ways, a higher

SIBSlfi reqUiIEd
I: is at this poin
tin can multiply
fixation closely
:ltiplication .

At elevat
the tensile test
:reep. Creep is
3163131 fluctuat
:e resistance f
If 2rI’Stailline 1r
iislocations, tl
tamed by the

32:2 QbSlZacles

31‘
Se.
313;
thE

stress is required for activating new dislocation sources.
It is at this point that the rate at which the disloca-
tion can multiply becomes important, and the rate of de-
formation closely corresponds to the rate of dislocation
multiplication.

At elevated temperatures (if the strain-rate of
the tensile test is small), the specimen can deform by
creep. Creep is a thermally activated process and the
thermal fluctuations aid the applied stress in overcoming
the resistance for plastic flow. Since the deformation
of crystalline materials occurs primarily by the motion of
dislocations, the deformation behavior of crystals is de-
termined by the method by which these dislocations over-
come obstacles.

The deformation behavior of crystalline metals at
high temperature is usually dependent on a diffusion
controlled mechanism.

Examination of polished surfaces of metallic
crystals deformed at high temperatures indicates that slip
occurs in the two forms described below:

(a) Coarse slip bands whose spacing and dis-

placements are of the order of l to lOu

(lu = 10-3mm). These slip bands in nature
are steps in the crystal surface and can be
seen at relatively low magnifications. The
Spacing between coarse slip bands depends on

the stress experienced by the specimen.

(b) F

b
f
P
McLe an

:rystals durin
iezperatures.
35 arrested di
plane. These
vertical Wall
MCLean
rare recovery

:7?!-

...din-hardeni

1.2

m

10

(b) Fine slip lines are those whose spacing will
be of the order of several angstroms. These
fine markings appear in areas between
prominent slip bands.

McLean10

observed polygonization in Aluminum single
crystals during the early stages of deformation at elevated
temperatures. The polygonization process requires climb

of arrested dislocations in a direction normal to the slip
plane. These dislocations subsequently glide and form a
vertical wall which is termed a low angle grain boundary.

McLean11

also reported that above certain tempera-
ture recovery becomes possible and offsets some of the

strain-hardening.

2.2.1.a Deformation Behavior of Single Crystals of Alpha

 

and Beta Brasses

 

The structure of alpha brass is face-centered
cubic, and atoms of zinc occupy randomly some of the
lattice positions of copper atoms. Alpha brass normally
deforms in close packed {111} planes and along <llO>
directions. There are a total of twelve operable slip
systems in alpha brass. Those dislocations with a Burgers
vector that retain the original crystal structure in the
deformed lattice, are referred to as perfect dislocations.
In that case atomic translations in some specific direc-
tion do not restore the crystal to its original structure,
but do leave it in a stable state, thus forming a stack-

ing fault.

Heiderich
Location in F . C . C.

tat partial dis lo:

13 [1‘

1
- n b
. .

.. .hereby lower
The F.C.C
:zits melting p0
trough the fores
passible at eleva
lccations become
:‘zedefomation o

11

Heiderich and Shockley12 have suggested that a dis-
location in F.C.C. crystal structure can dissociate into

two partial dislocations, according to the reaction
% [110] = g [211] +%[1211;

and thereby lower the energy of the system.

The F.C.C. structure of alpha brass is retained up
to its melting point. The process of dislocations cutting
through the forest dislocations present becomes more
possible at elevated temperatures. Since blocked dis-
locations become liberated from their locked positions,
the deformation of alpha brass becomes easy at elevated
temperatures.

The ordered beta below critical temperature (Tc)’
has cesium chloride (Cs Cl) structure. This cesium
chloride structure consists of two interpenetrating simple
cubic unit cells, one of c0pper and the other of zinc, and
is referred to as B-2 type superlattice. Figures 1 (a)
and (b) illustrate such a structure in two and three-
dimensional atomic arrangements. Slip systems in this
structure are of the type {110} <IIl>.

13 when a dislocation,

In B-2 type structures,
whose Burgers vector is a unit lattice vector moves
through an ordered lattice on a slip plane, a disturbance
in the local arrangement of the atoms on this slip plane

is produced. This process creates an antiphase boundary.

A second dislocation of the same Burgers vector is required

Figure l.

12

Cesium Chloride Structure

(60

(b)

A two-dimensional model of Cesium
Chloride structure. 'A"representing

Cs and'B"representing C1 or vice versa.

A three-dimensional model for CsCl type
structure and a representation for beta
brass in superlattice structure (a unit

cell). (J.P. Birth 14).

If! D

 

 

:—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b)
Figure 1

:cpass through P
Elite passage Of
rtiphase boundar
:0 be associated
rescues this high
:5 dislocations i
Tease dislocatior
:a B-2 type cr)
Liz'erent of such
3 a result, the
Pirature, which 1
is extremely difj

tater stress the

l
.IasS'

'3‘53 above T
7» i C
6 average

13

to pass through this plane to reorder the structure.

Since passage of a single unit dislocation produces an
antiphase boundary, it is energetically favorable for it
to be associated with a second unit dislocation, which
removes this high energy antiphase boundary. This pair

of dislocations is called a superlattice dislocation.
These dislocation pairs should move on the same slip plane

13 has observed that, for

in a B-2 type crystal. Brown
movement of such dislocations, a high stress is required.

As a result, the deformation of beta brass at room tem-
perature, which requires motion of superlattice dislocations,
is extremely difficult, and usually requires several times
higher stress than that required for deformation of alpha
brass.

Beta brass exists in a disordered state at tempera-
tures above Tc [850°F or 454°C] and has a B.C.C. structure
on the average. The lattice positions can be occupied by
either copper or zinc. In the B.C.C. structure, the slip
system is of the type {110} <II1>. The dissociation of
perfect dislocations in B.C.C. lattice is not common, and
therefore, screw components are not limited to a particular
slip plane. Since three {110} type planes intersect in a
<1Il> direction, screw dislocations may move in a haphazard
way on those {110} planes depending on the local stress

state.15 For this reason, the slip lines in beta brass

are often wavy and ill-defined.

J.H- ‘
critical 759501
:5 beta brass '
3:99 of the er
a: temperature

:5 decrease in

1.2.2. Deforma
\

A bicry

‘

1
D"

two grains 0
:Zte region of d:
icmdaries resi:
ieformation of a
tie structure of
often referred t

ief - '
Omation of s:

 

l4

J.H. Westbrook16 studied the relation between the
critical resolved shear stress and the test temperature
of beta brass. His results are in Figure 2. The sudden
drop of the critical resolved shear stress for beta brass
at temperatures above TC is accounted for on the basis

of decrease in short-range order.

2.2.2. Deformation of Bicrystals

 

A bicrystal of a single phase material consists
of two grains of the same phase. The grain boundary is
the region of disregistry between these grains. Grain
boundaries resist the motion of dislocations during plastic
deformation of a bicrystal. Due to the irregularities in
the structure of a grain boundary, a grain boundary is
often referred to as a forest of dislocations. During the
deformation of such a bicystal, it appears that some kind
of a slip interaction with the boundary should take place
for the propagation of slip from one grain to the other.
Grain boundaries are effective barriers in blocking dis-

locations. Grain boundaries are found17

to undergo
structural changes sooner than the grains (by phase trans-
formations), and in most cases exhibit a loss of strength

at elevated temperatures.

2.2.2.a. Deformation Behavior of Bicrystals of Alpha

and Beta Brasses

 

During room temperature deformation, a grain

boundary in a bicrystal of Alpha acts as a barrier to the

15

Figure 2. Critical Resolved Shear Stress for Beta Brass

Single Crystals.

After, J.H. Westbrook,l6 Mechanical properties
of intermetallic compounds. A review of the
literature in "Mechanical Properties of Inter-
metallic Compounds", 3. Wiley, N.Y. (I960),

p. 180.

\I‘

 

 

 

 

4b

 

 

 

L D P
1

.
1‘ l‘l

5 l4 3 2

A Eo\mmczu v oa
mwmppm yam m vm>aommm mofipfiwo

900

850

860
Temperature (F)

 

700

Figure 2

tzeraction disloca:
grain deforms first.
trough the boundar;
iriened considerab
slip to propagate tl
E7 the structure of
:2 the temperature.

McLean11 s

 

 

 

:2' grain boundaries
tures. The grain 1
skewed to slide ‘
icindary with an o
:ezsile axiswas OE
Zion and necking I
Chuang an<
relations of beta
‘16 grain boundar

tl.
we r.

C14

3]
ere Elastic

Compatibiiity

L;

23:4
"“1 boundar

, V d
.Ent. ‘

0Llliside 0‘

Saul
Si C _
Omponeht

l6

interaction dislocations. Usually a favorably oriented
grain deforms first. In such a case, deformation progresses
through the boundary after the deforming grain work-
hardened considerably. The resolved shear stress for

slip to propagate through the boundary is greatly enhanced
by the structure of the boundary, which strongly depends

on the temperature.

11 studied some of the mechanical behaviors

McLean
of grain boundaries in Cu-Zn alloys at elevated tempera-
tures. The grain boundaries in alpha bicrystals have been
observed to slide with respect to each other. A grain
boundary with an orientation of 45° with respect to the
tensile axiswas observed to undergo a continuous deforma-
tion and necking took place at this grain boundary.

Chuang and Margolin18 studied the stress-strain
relations of beta brass bicrystals at room temperature.
The grain boundaries in these specimens were parallel to
the compression axis. The isoaxial beta brass bicrystals
used were elastically and plastically incompatible. This
incompatibility led to the formation of a clearly defined
grain boundary deformation zone for strains up to 3.2 per-
cent. Outside of the grain boundary deformation zone,
each component crystal behaved as a single crystal. For
the non-isoaxial bicrystal of beta brass consisting of a
hard and a soft component, it was possible to express the
total applied stress in terms of the sum of the product
of the average stresses and volume fraction of the hard

and soft crystals respectively.

, 19 o‘

Chuang
Brass undergo grai:
53‘C(122°F). Gra
sensitive to the r
bicryStals, which
iefomed to the sh

Grain boun
:eratures above T
35383. Consequent

test all of the

"2'3~ Deformatic
feral

The (16me
”ate:

aim bonndaries 1'
...-n of individual

wanes do not

“”1398, and rt

‘11
“erstOOd.

The effect

 

l7

Chuang19

observed that grain boundaries in beta
brass undergo grain boundary sliding at temperatures above
50°C (122°F). Grain boundaries in beta brass are highly
sensitive to the rate of deformation. The beta brass
bicrystals, which had a large grain boundary surface area,
deformed to the shape of a spear at elevated temperatures.
Grain boundaries in beta brass at elevated tem-
peratures above Tc’ resisted deformation at high strain-

rates. Consequently the grains themselves accommodate

almost all of the strain.

2.2.3. Deformation Behavior of Polycrystals

 

General

The deformation behavior of a polycrystalline
material is more complicated than that of a single crystal.
Grain boundaries impose added constraints to the deforma-
tion of individual grains. Unlike the grains, the grain
boundaries do not have any repeating patterns in their
structures, and their deformation behavior is not clearly
understood.

The effect of temperature on the deformation be-
havior of polycrystals is very significant. In most cases
the result is a drop in the yield stress arising from the
loss of strength in the grains and in the grain boundaries.
In certain cases where the temperature and testing con-
ditions are met, a region in a form of a narrow strip

adjacent to the grain boundaries is deformed. This kind

:5 deformation occuzi
:ezgeratures in coat
:icrocreep. At elei
{rich vacancies mig‘
the: side takes pl

the notion of vacan

 

2963. This is a s

7') P“
--'~.3.a. DEED “blatj
\

a
nd Beta

Karashimaz‘

is flue to stress C
ions against the
Pissibilities tha1
Izrst one postula
13% grains begin

five ten inge
b a Ss ef
h o
“e. .
Two is
Served t1

18

of deformation occurs at low strain rates and at high
temperatures in coarse-grained polycrystals and is called
microcreep. At elevated temperatures, a mechanism by
‘which vacancies migrate from one side of a grain to the
other side takes place. At low strain rates, because of
the motion of vacancies, further plastic deformation pro-

ceeds. This is a stress motivated diffusion process.

2.2.3.a. Deformation Behavior of Polycrystalline Alpha

and Beta Brass
20

 

Karashima studied the deformation behavior of
alpha brass polycrystals. He concluded that the process

of deformation propagation in polycrystalline aggregates

is due to stress concentrations from piling up of disloca-
tions against the grain boundaries. There were two
possibilities that could account for this process. The
first one postulates that Frank-Read sources in neighbor-
ing grains begin to operate as a result of stress concentra-

21

tions; the second one suggests that dislocations are

emitted from grain boundaries.22
Observations made on deformed samples of alpha
brass polycrystals showthat23 dislocations piled up
against grain boundaries at small strains and slip lines
are continuous across the boundaries.
Greninger24 made observations on polycrystals of
beta brass deformed slightly in a vise at room tempera-

ture. Two distinct structural characteristics were

observed on the polished surfaces:

(1) Sets Of
ferred
(2) a CO“
illumi?
dark b
grain.
tion b
fieit'aer slip lines
grain boundary Wit}
:5: be related in
grains and the sup
Denture. Slip
;ro:inent than tho
Grain boun

tome r
s.rength o

 

l9

(1) Sets of parallel fine hairlike lines, re-

ferred to as slip bands, and

(2) a corrugated relief, which under oblique

illumination appeared as a coarse light and
dark banding effect to the surface of a
grain. These were referred to as "deforma-
tion bands".
Neither slip lines nor deformation bands continued over a
grain boundary without changing direction; hence, both
‘must be related in some way to the orientation of the
grains and the superlattice structure of Beta at room
temperature, Slip lines in beta brass are decidedly less
prominent than those in alpha brass.

Grain boundaries in beta brass polycrystals add
to the strength of the aggregate structure. Beta brass
yields at a fairly high stress. The difficulty involved
in the deformation of beta brass is because of the motion
of the superlattice dislocations. Deformation of beta
brass at a high strain rate results in transcrystalline
fracture.

The high temperature tensile deformation of 70-30
(Eu-Zn) polycrystals of alpha brass was studied by Asano

and co-workers.25

The yield stress of the alpha brass
polycrystals was determined through a range of tempera-
tures. There was found a marked drop of yield stress as

the temperature was increased. Microcreep mechanisms

are accounted for
fielding along wit
at elevated temper
The deforr
2;:modated in tl
sliding below T .
c
gains react to t'r
deformation. '.
ticn close to 45°
1311018 deformatic
:31 surface Of 1
.'. ‘1‘
~--te case of co.-
‘scmation can b.

.5“,
ventures be 10‘

.n-E tensile aXi S

an
68 that WeIe
slid

  
   

from the s t

551a $- .
“ms were

u. 8h the anti

20

were accounted forand.in part responsible for the abnormal
yielding along with the dragging motion of dislocations
at elevated temperatures.

The deformation of beta brass is more or less
accommodated in the grain boundaries by grain boundary
sliding bEIOW' Tc' As the temperature increases, the
grains react to the supplied energy and ultimately under-
go deformation. Those grain boundaries, with an orienta-
tion close to 45° with the tensile axis, undergo a con-

26 the

tinuous deformation. Depending on the strain rate,
final surface of the deformed specimen becomes shiny and
in the case of coarse-grained beta brass, grain boundary
deformation can be observed with the naked eye.

The deformation of coarse-grained beta brass at
temperatures below TC was studied by Chunke.27 His
work also showed that the grain boundary orientation with
the tensile axis was extremely important in determining
the deformation behavior. Specimens having grain bound-
aries that were oriented at about 45° to the tensile axis
slid from the start, and continued deforming uniformly;
beta grains were intact and did not deform plastically
through the entire deformation. Grain boundaries, with
orientations perpendicular or parallel to the tensile
axis, underwent very little grain boundary sliding and
fractured right after the yield point.

28

Based on the observations made by Chung on the

fractured surfaces, it was suggested that the failure was

':.e:ause of a hi8h
:cmdaries.
Uniform d
:Eserved at tempe
razes. Deformati
Strain-rate sensi
Fine-grained spe<
sezsitivity at t4

::a:se-grained b.

433- Deformatio
\

:fleral

SO far '

stare phase mat

a
‘An.

21

because of a high stress concentration at the grain
boundaries.

Uniform deformation in beta brass polycrystals was
observed at temperatures above TC at intermediate strain-
rates. Deformation by grain boundary sliding was more
strain-rate sensitive than deformation of individual grains.
Fine-grained specimens exhibited a higher strain-rate
sensitivity at temperatures just above TC compared to

coarse-grained beta brass.

2.3. Deformation of Two-Phase Materials

 

General

So far, this review has dealt with deformation of
single phase materials. A more complicated deformation
behavior is observed in two-phase materials. Two-phase
materials contain phase boundaries rather than grain
boundaries. The deformation behavior of such two-phase
materials that have phase boundaries is not well under-
stood.

29’30’31 have de-

Marcinskowski and co-workers
veloped some theories with reSpect to the deformation be-
havior of internal boundaries. Grain boundary disloca-
tion is discussed in terms of disturbances created at a
boundary, when a glide dislocation crosses a grain boundary.
The nature of the grain boundary dislocation can be de-

termined from a knowledge of the orientation relationships

between slip systems adjacent to the boundary. In fact,

:13 Burgers vec
r331 all of the

3.; a single ex;

-§

stare bl is t
”:cuzzdary, S1 E
aijacent phaSEE
iirectional cos
showed that the
are altered as
shear also lea\
153% range stre
zzcleation of <

rdSES, The ma

22

the Burgers vectors of all of the dislocations associated
with all of the internal boundaries, can be represented

by a single expression:

where b1 is the effective Burgers vector in the grain
boundary, b1 and b2 are the Burgers vectors of the
adjacent phases, and a is an entry in the matrix of
directional cosines between the b1 and b2. They also
showed that the orientation and shape of the boundaries
are altered as a result of a homogeneous shear. Such a
shear also leaves an array of dislocations that may have
long range stress fields, which could be relieved by
nucleation of crystal lattice dislocations in both of the
phases. The nature of the interface resultant dis-
locations was derived from some simple orientations as a
result of passage of a dislocation through the boundary.
Further, the concepts related to grain-boundary disloca-
tions were claimed to be applicable to the deformation of
internal boundaries such as grain boundaries, twin

boundaries, two-phase interfaces, etc.

2.3.1 Deformation of Bicrystals of Two-Phase Materials
The deformation behavior of duplex and bicrystals

of alpha-beta brass was studied3'4'5

at room temperature
at different strain-rates. There were four types of

boundaries considered, namely, oriented duplex, flat

EsmiarY' corru
:‘ze progress ion

equiaxed dd

c'_
:1
m

and the oriente
ii of the biCI'
:ive. Low stra
flat interfaces
:lze boundary.

faces due to de
iid give an ind
Beta became ope
firmed at the 1:
iii: the slip t
;aralle1 to the
Slip was Obsery

ts Y
0m- Slip

Of
.’ Be
Labs"
th as a r
e._ es

23

boundary, corrugated boundary, and equiaxed duplex. In
the progression of deformation from one phase to the other,
the equiaxed duplex was the most effective type of barrier,
and the oriented duplex was found to be the least effective.
All of the bicrystals were found to be strain-rate sensi-
tive. Low strain-rate tests, especially on specimens with
flat interfaces, exhibited extensive cross-slipping near
the boundary. There was no void formation at the inter-
faces due to deformation. The flat boundary bicrystals
did give an indication that the dislocation sources in
Beta became operative, because of dislocation pile-ups
formed at the boundary in the Alpha region./’It was found
that the slip traces found in Beta phase need not be
parallel to the direction of primary slip lines in Alpha.
Slip was observed in Beta away from the phase boundary on
its own. Slip systems making shallower angles with the
phase boundary proved to be more effective in activating
dislocation sources in Beta phase than slip lines making
steep angles with the boundary. At room temperature, the
deformation of Alpha seemed to precede the deformation of
beta phase. Beta either deformed on its own, or it de-
formed as a result of stress concentration near the phase
boundary. Similar observations are found for specimens
with boundaries inclined to the tensile axis and are pre-
sented in Appendix A.

Elevated temperature deformation behavior of two-

phase bicrystals has not been studied so far. The present

:r'a is to fill in

fixation behavior

..3.2. Def rmatior

Honeycomb a
:aileo' netallograp‘.
itass containing 1+
:alp‘aa phase. I
:5 seat“; deformati
feta grains. Defo

.Q‘ 0 ‘l
{wills

F.8d and wer

:Eéppeared in Alp“

:rsssed the alpha—

d had Paral

..~P Propagat 1011 1
711.3)

..
7!-
l‘

.:3

e Orientation

53% c
de.ormation
511.1 .‘ ,_

.1; ~Q grains

 

 

24

work is to fill in the understanding of the overall de-

formation behavior of two-phase materials.

2.3.2. Deformation of Polycrystals of Two-Phase Materials

 

32 were the first to make de-

Honeycomb and Boas
tailed metallographic studies of deformed alpha-beta
brass containing 40% Zn. Initial deformation occurred
in alpha phase. It was only after an appreciable amount
of heavy deformation in alpha that slip was observed in
beta grains. Deformed specimens of alpha-beta brass were
repolished and were strained further. Slip lines again
reappeared in Alpha grains. Slip traces occasionally
crossed the alpha-beta phase boundaries. The grains that
deformed had parallel slip traces. The orientation re-
lationship required between the alpha and beta brass for
slip propagation through the boundary to occur was
(110)

(lll)a and <lll> <llO>a. Grains satisfying

Bil 8 ll
these orientation conditions are called contiguous grains.
More deformation was observed to occur in the vicinity of
alpha-beta phase boundary, than in the interior of the
beta grains.

Honeycomb and Boas32 made an attempt to study the
extent of deformation of individual alpha and beta phases
by studying the recrystallization temperature of each
phase through a series of annealing experiments. These

studies were complicated by precipitation in the alloy,

and by the order-disorder transformation in the beta phase.

clarebrO
:agnesium, soft
iard beta phase
alqm were defC
:ffie recrysta1
Ezaphase ir1 a]
taunts indicate
the alpha phase
:he volume frac1
the extent of de
Ilarebrough and
i110E’SOf c0ppet

Suery a:
ion and micros
53158 at 600°C
:92" Showed fib
'N‘Q’phase alpha
xvi?

The al

3251'
to

25

Clarebrough33

carried out a study on silver-
magnesium, soft silver grains have F.C.C. structure and
hard beta phase with cesium chloride structure. These
alloys were deformed at room temperature. Measurements
of the recrystallization temperature of the alpha and
beta phase in alloy specimens that were deformed in equal
amounts indicated that, below 30 volume percent of Beta,
the alpha phase deformed more than the beta phase. When
the volume fraction of Beta exceeded 30 volume percent,
the extent of deformation in both the phases was the same.

34

Clarebrough and Perger observed similar behavior in

alloys of copper and zinc.

Suery and Baudelet35

studied the plastic deforma-
tion and microstructure in superplastic 60% Cu-AOZ Zn
brass at 600°C (1112°F). Specimens were extruded, and
they showed fibrous structure with elongated grains. The
two-phase alpha-beta brass exhibited strain-rate sensi-
tivity. The alpha phase with fibrous shape lengthened

at first parallel to the tensile axis and then developed
to an approximately equiaxed structure. The shape change
was attributed to what was called cell structure formation
at the beginning of the deformation. The variation of

the phase size and, in particular, the microstructural
coarsening was aided by the deformation. The coarsening
was accounted for by the possibility of combining of
phases of the same nature, caused by their rotation during
the deformation and by mass-diffusion along the phase inter-

faces.

Baro36 SC

5:353 at temperat
fsrzation behavic
:ving dislocatic
:ion, along with
iepend on one am
ieforzation proce
:acur in the mate
:casiders grain 1
3f dislocations

itbsequent defon
ashear stress 1:
closed is deform.

temp.

be:
a Phase , Con

2‘ ‘
salt,

S along the

zr-s.
.mns Were also

 

26

Baro36

studied the superplasticity of alpha-beta
brass at temperatures above Tc for Beta. From the de-
formation behavior of 60-40 brass, it was determined that
moving dislocations also contributed to the total deforma-
tion, along with grain boundary sliding; both processes
depend on one another. The essential thing is that the
deformation proceeds so that no stress concentrations
occur in the material. A model for superplasticity which
considers grain boundary sliding, and gliding and climbing
of dislocations is suggested. The model illustrates the
subsequent deformation by grain boundary deformation,

a shear stress is produced on a grain and the grain en-
closed is deformed. The reorientation of hard phase Alpha
at elevated temperature is like flotation of Alpha in soft
beta phase. Continuous deformation and alignment of alpha

grains along the loading axis took place. Coarsening of

grains were also observed during the deformation.

2.3.3. Objectives of the Work

 

The deformation behavior of two-phase materials is
affected by the temperature and deformation rate. So,
under nearly identical deformation conditions and tempera-
ture, each phase exhibits properties of its own along with
additional changes that occur during the overall deforma-
tion because of the presence of the other phase.

The primary aim of this research is to study the

effect of temperature on the deformation behavior of

:s-phase bicrysta'
experiences order-
:ezperatures. The
behavior of such m
secondary ob jectiv
rate on the mechan
beta brass at elev
oniitions for obt
:18 effect of she;
and be studied c
itiented at diffel
axis (Observatn
If this t3198113,)
It is hop:
{fixation behaVio'

.:.peratures may -

“CH
5 fOI' hOt r01

 

 

 

27

two-phase bicrystals of alpha-beta brass. Beta brass
experiences order-disorder transformation at elevated
temperatures. The effects of disorder on the deformation
behavior of such materials is also investigated. The
secondary objective is to study the effect of the strain-
rate on the mechanical behavior of bicrystals of alpha-
beta brass at elevated temperatures and to find suitable
conditions for obtaining a uniform deformation. Meanwhile,
the effect of shear stresses imposed on a phase boundary
could be studied on specimens having their phase boundaries
oriented at different angles with respect to the tensile
axis. (Observations will be presented in Appendix A
of this thesis.)

It is hoped that a better understanding of the de-
formation behavior of two-phase materials at elevated
temperatures may be helpful in developing suitable condi-

tions for hot rolling and extruding two-phase materials.

3.1. Preparation
Alpha bras
single crystals we
imposition of 70:,
3.6 on in diamete:
Stick. Beta bras
;r 51+ ,
m purity to

minal compo s i t i

315148.57. Zn. TH

l‘antities Of twin:-

 

CHAPTER III
EXPERIMENTAL PROCEDURE

3.1. Preparation of Alpha and Beta Stock

Alpha brass stock that was used for preparation of
single crystals was of commercial purity and had a nominal
composition of 70% Cu and 30% Zn. Pieces, 6 cm long and
0.6 cm in diameter were cut off and machined from this
stock. Beta brass stock was produced by adding zinc of
99.99+ purity to Muntz metal (60% Cu and 40% Zn). The
nominal composition of beta brass produced was 51.5% Cu
and 48.5% Zn. This alloy was produced by melting measured
quantities of Muntz metal and zinc in a sealed quartz tube
at 950°C. The quartz tubes were flushed with Argon before
sealing to prevent any oxidation of the metal. After
solidifying the melt in the quartz tubes, the stock for
growing single crystals, 6 cm long and 0.6 cm in diameter,

were produced by machining.

3.2. Growth of Single Crystals of Alpha and Beta Brass
Single crystals of alpha and beta brass were pro-
duced by using the Bridgeman technique. For growing
single crystals, the stock material was kept in sharp-
tipped graphite crucibles. These crucibles containing the

stock material were kept in sealed quartz tubes to prevent
28

zinc loss. The t
:abes. The VOhl1
tube was filled
radial temperatt
:rated schemati<
This as.
to produce sing
terperature pro
'Ie constant te
fer growing al;
brass crystals
“351 CHI/hr. Tj

29

zinc loss. The quartz tubes were kept inside mullite
tubes. The volume between the quartz tube and the mullite
tube was filled with refractory cement to minimize the
radial temperature gradient. Such an assembly is illus-
trated schematically in Figure 3.

This assembly was lowered through a tube furnace
to produce single crystals. The set-up used and the
temperature profile of the furnace are given in Figure 4.
The constant temperature zone was maintained at 1860°F
for growing alpha brass crystals and 1820°F for beta
brass crystals. The crystals were grown at a growth rate
of l cm/hr. These single crystals were annealed at 1480°F
for sixteen hours to remove micro-segregation, as

suggested by Maddin.6

3.3. Growth of Two-Phase Bicrystals of Alpha-Beta Brass
To obtain the two-phase bicrystals used in this
work, beta brass was melted on a substrate of a single
crystal of alpha brass in a quartz tube. To minimize the
transition zone that developed in this joining operation,
a 60% Copper-40% Zinc brass foil, 0.2 mm thick, was placed
between the alpha single crystal and the beta stock be-
fore melting. The alpha brass single crystal and the beta
stock were chemically polished with 70 volume percent
nitric acid - 30 volume percent water to minimize any
contamination. The melting of the beta brass was achieved

by heating the assembly with a Nichrome heating element.

30

Figure 3. Schematic Diagram of the Crucible Assembly for

Growing Single Crystals of Alpha and Beta Brass. (:)

1 Chromel wire

Mullite tube

Fireclay (A1203)

Sealed quartz tube

Alpha brass stock <)_‘§“

2
3
4
5

 

 

 

 

 

 

 

 

 

 

. a... o. . o ...o oooooo ...o... o. A . ‘
. o... . 0.... o o n .. o o u . u ...uu... om. . A ...o..... o
J I
3
m
0..... .. ...uH0...0I.I..~....¢|...... . ...uo. .~... ...... 0 . 0....L..~...d .1
0..-0..\.0 . ..o‘ b. ....o ... I. 0.."?..§... 0.0.. mo. .0 .z‘rao’wko F

 

 

.:::: .12:

AAEAAmA

 

 

 

 

31

Figure 4. Schematic Diagram of the Furance for Growing

Single Crystals of Alpha and Beta Brass.

 

- monofilament line
- hooks

- furnace insulator
- mullite crucible
quartz tube

- heating element

1‘

(-_

-1

- one R.P.H. motor and pulley

- stabilizing weight

 

xo a: ~q cs Ln -D on tv hi
I

- wire suspension rod

We 3Y1
,. ’1
l

\’

H
O
I

 
 

fire brick top

,_.
._.
I

H e—J

W N

I I
mkfio

furnace tube

 

 

crucible assembly

glass wool

 

 

 

 

 

 

 

I 1700' 1300

 

.5oo‘

 

 

7V77wr Vo/VJ

 

 

(F)

Temperature

 

 

 

 

 

 

 

 

 

 

Figure 4

argon was passec‘
:xidation. The
Tris procedure
earlier works.3
The tra
reEion can be e
ZEJOugh a tempe
mealing . 3 . 4 ,5
transition 20m
:5 alone Prov:
13.9.3 1 mm. Th
Carefully cont
Eating and by
“Ed in this
Figure 6 illus
Tie maxirnum te
Lour' During
.ransition 201'

5

hurlirnize h -
C

32

Argon was passed through the assembly to prevent any
oxidation. The set-up used is illustrated in Figure 5.
This procedure is exactly the same as those used in
earlier works.3’4'5
The transition zone formed between alpha and beta
region can be eliminated by a combination of lowering
through a temperature gradient and by cyclic local

annealing.3’4’5

However, it seems possible to reduce this
transition zone to a flat boundary by cyclic local anneal-
ing alone provided that the transition zone is smaller~
than 1 mm. This successful joining can be achieved by
carefully controlling the temperature to reduce super—
heating and by some experimentation. All the specimens
used in this work were obtained by cyclic local annealing.
Figure 6 illustrates the local annealing set-up used.

The maximum temperature was maintained at 1450°F for one
hour. During the cooling cycle the temperature of the
transition zone must be brought back to room temperature.

To minimize handling and to maximize the production rate,

an automated cyclic annealing set up consisting of ten units
was used. The temperature of each furnace was maintained
by using carefully measured lengths of the heating elements.
The positioning of the transition zone in the hot zone was
also carefully arranged by vertical moving screws. Further,
the cooling of the specimens after each cycle of heating

was achieved by shutting off the power for the heating

elements and blowing cool air through the quartz tubes

33

 

Figure 5. Schematic Diagram of Apparatus for Joining
Beta Brass to the Single Crystal of Alpha
Brass.

- power supply

- single crystal alpha

- refractory brick

- aluminum block used for heat sink

argon gas inlet

- beta brass stock

- heating element

- alpha - beta foil

\omxloxw-waH
l

- quartz tube

..A:
O
I

refractory cement

®\
@\
A

Figure 6.

34

Schematic Diagram of the Apparatus for Local

Annealing.

l - air inlet

2 - bicrystal alpha—beta brass
3 - transition zone

4 - refractory cement (A1203)
5 - heating element extension
6 - asbestos platform

7 - aluminum holding fixture
8 - quartz tube

9 - heating element
10 - fire brick

ll - porous fire brick
l2 - adjusting screws

13 - aluminum holding rod

 

 

 

 

 

 

 

 

 

 

 

II III II —~®

 

 

 

containing the ct:
Tris operation wa
vice. After such
penitted to proc
cycles were about
fused to as shor
stages of the pr
The schematic of
The two-
EbiWe were machi
aeiiate speed.
1969. the final
keep the mechanfi

.‘JCSSlble,

 

 

35

containing the crystals for a period of five minutes.

This operation was achieved by an automatic timing de-

vice. After such cooling, further cyclic annealing was
permitted to proceed. Although the earlier heating

cycles were about one hour long each time, they were re-
duced to as short as fifteen minutes towards the final
stages of the preparation of flat boundary bicrystals.

The schematic of the set-up used is illustrated in Figure 7.

The two-phase bicrystal specimens produced by the
above were machined with a flying cutter at an inter-
mediate speed. Although the earlier cuts were 0.003 in.
deep, the final cuts were less than 0.001 in. deep to
keep the mechanical damage to the bicrystals as small as
possible.

After the machining operation, the specimens were
polished on all sides with 240, 320, 400 and 600 grit wet
carbimet papers and 600 grit wheel. The finishing was
done on a velvet wheel using 1 micron diamond compound
and Metadi fluid. The specimens were joined to steel
nuts by silver soldering. The silver soldering was done
while the rest of the specimen was kept cool with a wet

37 After silver

cloth as suggested by Brindley, et al.
soldering, the Specimens were chemically polished with a
solution containing 66% acetic acid, 17% Ortho-phosphoric
acid and 17% nitric acid. Back reflection Laue pattern

of the beta grain in contact with alpha single crystal was

obtained on two perpendicular faces. The Miller indices

Figure 7.

36

Schematic Diagram of Ten Units for Automatic

Local Cyclic Annealing Operation.

air pressure gauge

- automatic A.C. powered air valve
- air hose divider

air hose

- asbestos coated wire

0‘ U -I-\ b.) N H
I

- local annealing unit, detail is in

Figure (4)

\I
I

silver soldering joints

8 - insulating connectors

9 - fuse box, 15-17 amperes capacity
10 - ammeter

ll - power supply

12 - variac

13 - connecting electric wire

14 - electric motor (1 R.P.H.) and timing
pulley

15 - spring loaded micro-switch

l6 A.C. electrical input ![\RE

aka
(3)_-

-_A_

 

 

 

 

 

 

 

 

 

 

:‘fthe 912
the cryst

axis .

37

of the planes forming these poles were used to determine
the crystallographic direction parallel to the tensile

axis.

3.4. Mechanical Testing of Specimens at Elevated
Temperatures

Tensile tests were performed at 700°, 800°, 900°
and 1000°F. The first two of these temperatures are below
and the rest are above the ordering temperature of beta
brass. These temperatures were obtained by using a
split tube furnace having a constant temperature zone of
about four inches. The specimens were heated in an Argon
atmosphere to prevent oxidation and discoloration. A
glass tube with insulating seals at both ends was used to
keep the Argon atmosphere around the specimen. Further,
to keep the temperature of the Specimen uniform, a copper
sheet covered the interior surface of the furnace. The
furnace temperature was controlled by a thermocouple
which was kept very close to the heating element so that
it could sense the temperature fluctuations very easily.
The temperature of the specimen was monitored by four
thermocouples which were in contact with the specimens.
The setting of the controller for achieving a required
temperature of the specimen was usually achieved with
dummy specimens with several thermocouples silver soldered
to them. Further, to reduce the heating of the rest of

the system, and especially the load cell, water cooling

was employ
Figure 8.
Tn

. ' r 1-
3:33.06 WA.

:ergeratur
was left c
tion be'nav
oblique 11'
care was t
sPetinen c
the end of
sPecinen \

Contrc‘icth

38

was employed. This entire heating assembly is shown in
Figure 8.

The tests were performed using an Instron testing
machine with cross-head speeds of 0.02, 0.1, and 0.5
cm/min. The specimens usually reached the required test
temperatures in about 45 minutes. A very small crack
was left open in the split furnace so that the deforma-
tion behavior of the specimen could be studied using
oblique lighting. During the heating of the specimen,
care was taken to adjust cross-head position so that the
specimen did not experience any stress. Similarly, at
the end of the test, the load was released so that the
specimen would not experience any further stress due to
contraction during cooling.

The deformed samples were handled very carefully
and were viewed with an optical microscope to study the
deformation of Alpha, Beta, and regions near the phase
boundary. These specimens were always stored in vacuum
desiccators. Further, during the course of this investiga-
tion, retesting of any samples tested earlier was avoided
since part of the damage in such specimens would anneal
out on heating them again. So once a sample was strained
and the test stepped at the same stage, it was never
tested again regardless of the amount of deformation intro-
duced in the sample.

The strain, strain-rate and stresses experienced

by individual phases were also calculated for each specimen

Figure 8.

39

Schematic Diagram of the Apparatus Used for

Elevated Temperature Tests.

connecting rod to load cell
- water hose clamps

- direction of water flow
water cooling coil

— thermocouple wires

- glass envelope

- thermocouple insulator ceramic tubes

CD \I 0‘ U -I> 00 N I—'
I

- thermocouple beads controlling sample
temperature
9 - thermocouple beads controlling furnace

temperature

10 - specimen

ll - heating elements

12 - gas inlet tube

13 - direction of argon gas flow

14 - water cooling copper coil

15 - connecting rod to cross-head

l6 - upper and lower seal to the atmosphere

l7 - copper sheet lining

18 - insulated electric furnace

 

Figure 8

azvarious stag
sending of the

iicrystals of .

40

at various stages of the testing so that a better under-
standing of the overall deformation behavior of two-phase

bicrystals of alpha-beta brass could be achieved.

 

1;“ re;
"a” and

CHAPTER IV
RESULTS AND DISCUSSION

4.1. Deformation Behavior of Bicrystals of Alpha-Beta
Brass in the Temperature Range at which Beta Exists
in the Ordered State (less than 850°F).

4.1.1 Deformation Studies at 700°F

 

Specimens deformed at 700°F with a cross-head
speed of 0.02 cm/min had relatively high yield stresses.
In all specimens, the initial deformation took place by
single slip in Alpha at regions away from the boundary.
As deformation progressed, these slip lines in Alpha be-
came deeper and approached the alpha-beta phase boundary.
This left a triangular shaped undeformed region in Alpha
in the region near the phase boundary as shown in Figure
9(a). Upon further straining, slip in Alpha interacted
with the phase boundary and resulted in deformation in
beta phase. This is illustrated in Figure 9(b). Note,
T.A. represents the direction of the tensile axis and
"a" and "b" are used in all figures to point out alpha and
beta phases.

Grain boundary sliding, and slight deformation
within the grains were observed in beta regions. These
features can be seen in Figure 10. Grain boundary

sliding was observed in boundaries that had an orientation
41

Figure 9a.

42

Interaction of Slip in Alpha with the
Alpha-Beta Phase Boundary in a Specimen
Tested at 700°F with a Cross-Head Speed of
0.02 cm/min.

Yield Stress of Alpha 3.5 Kg/mmz.
Critical resolve shear stress of Alpha
1.65 Kg/mmz.

Total strain 3.4%.

 

‘ "5mm. flat 1*, l I tQIHJAW .11

.
al.-5:1

    

 

Figure 9(a)

 

 

Figure 9b.

43

Cross-slip in Alpha Due to Interaction of
Slip with the Boundary. Note: Region

marked by X has extensive cross-slip.

Yield stress of Alpha 3.5 Kg/mmz.

Critical resolved shear stress of Alpha

1.65 Kg/mmz.

Total strain 14%.

 

_ _- .. .... I’m ”4'1: 8' f .1“."‘"‘;‘~‘."’""'-.-:-Ii.--:.j

L\\\.&Wn\ ,
”Ks A:
«s a

"
Q\\

MO‘ $\\\\a\\ h

\\.\ \\\\.
‘0‘

$\~\i‘;l

QS.

...\.\.\\..~ .
\

 

Figure 9(b)

 

Figure 10.

44

Grain Boundary Sliding in a Beta Region
away from the Boundary in a Specimen Tested
at 700°F with a Cross-head Speed of 0.02

cm/min.

Yield stress of Alpha 3.5 Kg/mmz.
Critical resolved shear stress of Alpha
1.6 Kg/mmz.

Total strain 4%.

 

 

Figure 10

close to 45° cc
a: the grain bl
fmation of g
as shown in Ff
‘3 grain boun

The i
7W? Vith 8
51.9173 by 5111'
AIM intera
Boundary res
Phase to be:
regions {193
After GXten
semen are

V3389 b0

r.
a:

§

 

——+K

45

close to 45° to the tensile axis. Small cracks developed
at the grain boundaries in Beta due to non-uniform de-
formation of grains (caused by different orientations)

as shown in Figures ll. These specimens usually failed
by grain boundary fracture in Beta.

The initial deformation of specimens strained at
700°F with a cross-head speed of 0.1 cm/min occurred in
Alpha by single slip. On further straining, slip from
Alpha interacted with the phase boundary. The phase
boundary resisted progression of slip from the alpha
phase to beta regions. Multiple slip in alpha phase in
regions near the boundary can be seen in Figure 12.

After extensive deformation, severe reduction in cross
section area of Alpha occurred near the phase boundary.
This is illustrated in Figures 13 (a) and (b).

Beta deformed by grain boundary sliding and some
of the beta grains near the phase boundary also deformed
by slip. Stress-strain curves exhibited serrations that
could be associated with grain boundary sliding in Beta.
The early stages of these curves are similar to the stage
I of resolved shear stress versus resolved shear strain
curve for alpha brass single crystals.

The deformation behavior of Alpha in a bicrystal
of alpha-beta brass, and the interaction of slip with the
phase boundary at 700°F were similar to those observed in
specimens deformed at room temperature. In all these

cases alpha brass deformed first. Deformation of Beta,

k “Lxfi
._

Figure 11.

46

Small Cracks Developed in Beta at the Grain
Boundaries in a Specimen Tested at 700°F
with a Cross-head Speed of 0.10 cm/min.

Note: Region Marked with X has the Cracks.

Yield stress of alpha 3.26 Kg/mmz.
Critical resolved shear stress of Alpha
1.5 Kg/mmz.

Total strain 10.2%.

“9.

 

Figure 12.

47

Multiple Slip in Alpha near the Phase
Boundary in a Specimen Tested at 700°F

with a Cross-head Speed of 0.10 cm/min.

Yield stress of Alpha 3.39 Kg/mmz.
Critical resolve shear stress of Alpha
1.68 Kg/mmz.

Total strain 5.6%.

 

 

I.

y i”)?

y ' AI . »I ~
\ 1.). ... JV. .

t.
.\

I;)/.|o..\\r Vin ..fl .
A v |

 

  

Figure 12

 

Figure 13a.

48

Interaction of Slip in Alpha with the Phase
Boundary in Specimen Tested at 700°F with

a Cross-Head Speed of 0.10 cm/min.

Yield stress of Alpha 3.26 Kg/mmz.
Critical resolved shear stress of Alpha
1.50 Kg/mmz.

Total strain 10.2%.

 

(a)
‘JI‘E‘ 3

’1’]
H0

Figure 13b.

49

Macrograph of a Fractured Specimen. Notice
the Severe Deformation in Alpha Near the

Boundary (marked by X in this specimen).

Yield stress of Alpha 3.26 Kg/mmz.
Critical resolved shear stress of Alpha
1.50 Kg/mmz.

Total strain 10.2%.

 

Figure 13 (b)

however, w
Hell as by
sliding it
me test:

:he grain

4.1.2 De

8
cuss-he;
phase by
firing 1.
iavorahl
3iE‘dres
orientec
Grimm
°’ 5'1 c:
T:‘3ll.'ldar
“Com:
C5563 1
In the

50

however, was accommodated by grain boundary sliding as
well as by slip in individual grains. Grain boundary
sliding in Beta has never been observed in room tempera-

3,4,5

ture tests. Fracture took place in beta regions at

the grain boundaries due to non-uniform deformation.

4.1.2 Deformation Studies at 800°F

 

Specimens tested at 800°F and strained with a
cross-head speed of 0.02 cm/min initially deformed in beta
phase by grain boundary sliding as is shown in Figure 14.
During later stages of deformation, beta grains with a
favorable orientation deformed by slip as can be seen in
Figures 15 (a) and (b). If the deformation of a favorably-
oriented boundary is not stopped by the change in its
orientations relative to the tensile axis in some regions,
or by the interaction with other unfavorably-oriented
boundaries, the entire deformation could have been
accommodated by grain boundary sliding alone. In such
cases the deformation of beta grains by slip is unnecessary.
In the specimens tested during the course of this investi-
gation however, the grain boundaries in Beta often
intersected each other. Consequently, there was re-
sistance for the progression of grain boundary sliding.
So, beta grains deformed by slip due to shear stresses
imposed by uneven deformation between beta grains. This
behavior is illustrated in Figures 16 and 17. In partic-

ular, grains having smaller width and sharper edges in

 

Figure 14.

51

Grain Boundary Sliding in Beta Regions away
from the Phase Boundary in a Specimen Tested
at 800°F with a Cross-Head Speed of 0.02

cm/mmz.

Yield stress of Alpha 3.50 Kg/mmz.
Critical resolved shear stress of Alpha,
1.65 Kg/mmz.

Total strain 3.4%.

 

 

Figure 14

52

Figure 15. Deformation of Beta by Slip in Favorably-
Oriented Grains in Regions away from the
Phase Boundary in a Specimen Tested at 800°F
with a Cross-Head Speed of 0.02 cm/min.

(a) Fine Slip in Beta.

Yield stress of Beta 2.25 Kg/mmz.
Critical resolved shear stress of Beta
1.10 Kg/mmz.

Total strain 4.9%.

 

 

Figure 15 (a)

 

Figure 15b.

53

Rumple Appearance in Beta.

Yield stress of Beta 2.25 Kg/mmz.

Critical resolved shear stress of Beta
1.10 Kg/mmz.

Total strain 4.9%.

 

 

Figure 15 (b)

Figure 16.

54

Slip Initiated by Grain Boundary Sliding in
Beta Phase in a Specimen Tested at 800°F with
a Cross-Head Speed of 0.02 cm/min. Here Slip
is Caused by the Change in the Orientation

of the Boundary.

Yield stress of Beta 2.25 Kg/mmz.
Critical resolved shear stress of Beta
1.10 Kg/mmz.

Total strain 4.9%.

 

 

Figure 17.

55

Deformation of Beta in a Most Favorably-
Oriented Grain by Coarse Slip, when Grain
Boundary Sliding is Unable to Accommodate
the Entire Deformation, in a Specimen
Tested at 800°F with a Cross-Head Speed

of 0.50 cm/min.

Yield stress of Alpha 3.4 Kg/mmz.
Critical resolved shear stress of Alpha
1.35 Kg/mmz.

Total strain 12.9%.

 

Figure 17

G

 

_‘—

 

56

the vicinity of larger grains deformed more than others.
Figure 18 is an illustration of the severe deformation
near the tip of smaller grains. Similar observations
have been made with respect to non-uniformity in the de-
formation by Baro,36 and the observations presented here
are in complete agreement with his work. In Figure 19,
regions in the two grains "A" and "B" adjacent to their
common boundary deformed, since one of the grains had a
more favorable orientation with respect to the tensile
axis compared with the other. The vicinity of the grain
boundary appears to be more deformed because of the de-
formation in beta grain "A" compared with beta grain
"B". In Figure 20, three grain boundaries are meeting at
a point, and grain boundary sliding caused cracks in the
intersecting region.

In all specimens, Alpha did not deform plastically
at all. The interaction of slip from beta region with
the phase boundary did not result in any deformation in
a1Pha phase as illustrated in Figure 21.

Specimens tested at 800°F and strained at 0.10
cm/IIlin initially deformed in Alpha by single slip. Slip
in Alpha intersected with the phase boundary as can be
seen Iln Figure 22. A rumpled appearance of Beta in the

regiOTl near the phase boundary can also be seen in this
figurTE. Figure 23 illustrates the interaction of slip

from both alpha and beta regions with the phase boundary.

57

Figure 18. Severe Deformation in Beta Near the Tips of
Smaller Grains in a Specimen Tested at 800°F
(x and y indicate the small and large grains

respectively).

Yield stress of Alpha 2.25 Kg/mmz.
Critical resolved shear stress of Alpha
1.10 Kg/mmz.

Total strain 4.9%.

 

Figure 13

Figure 19.

58

Deformation of Regions in Beta near the Grain
Boundary in a Specimen Tested at 800°F with

a Cross-Head Speed of 0.02 cm/min. Note:
Uneven deformation in adjacent beta grains
due to different crystallographic orienta-
tions to the tensile axis "A" having more
favorable orientation compared to "B" and

"CH .

Yield stress of Alpha 2.25 Kg/mmz.
Critical resolved shear stress of Alpha
1.10 Kg/mmz.

Total strain 4.9%.

 

Figure 19

 

Figure 20.

59

Cracking near the Junction of Three Grain
Boundaries in Specimen Tested at 800°F with

a Cross-Head Speed of 0.02 cm/min.

Yield stress of Alpha 2.25 Kg/mmz.
Critical resolved shear stress of Alpha
1.10 Kg/mmz.

Total strain 4.9%.

 

Figure 20

Figure 21.

6O

Absence of Plastic Deformation in Alpha in
a Specimen Tested at 800°F with a Cross-

Head Speed of 0.02 cm/min.

Yield stress of Alpha 2.25 Kg/mmz.
Critical resolved shear stress of Alpha
1 . 10 Kg/mmz.

Total strain 4.9%.

 

Figure 22.

61

Interaction of Slip in Alpha with the Phase
Boundary in a Specimen Tested at 800‘F with

a Cross-Head Speed of 0.10 cm/min.

Yield stress of Alpha 3.72 Kg/mmz.

Critical resolved shear stress of Alpha

1.65 Kg/mmz.

Total strain 3%.

 

 

 

 

Figure 22

Figure 23.

62

Independent Slipping of Alpha and Beta in
the Region near the Phase Boundary in a
Specimen Tested at 800°F with a Cross-Head

Speed of 0.10 cm/min.

Yield stress of Alpha 2.25 Kg/mmz.
Critical resolved shear stress of Alpha
1.10 Kg/mmz.

Total strain 3%.

 

 

63

In this specimen Beta also deformed by grain boundary
sliding. The deformation in the entire gauge length of
beta phase seemed uniform. The grain boundary sliding
and slip in Beta can be observed in Figure 24. Stress-
strain curves of these specimens did not exhibit any
evidence of work-hardening. The process of grain boundary
sliding in Beta caused periodical and high amplitude

load drOps in load-deflection hyStEIESiS at the early
stages of the deformation. As the deformation pro-
gressed, the amplitude of the load drops decreased and
the fluctuations finally stOpped. From this point on,
the rest of the deformation occurred by slip in alpha and
beta grains.

At a cross-head speed of 0.5 cm/min and test
temperature of 800°F, initial deformation took place in
alpha phase by single slip. Some multiple slip lines
were observed in Alpha. The multiple slipping was
resulted from the interaction of slip in Alpha with the
phase boundary. Beta grains near the phase boundary were
deformed either due to the slip interaction in Alpha with
the phase boundary or on their own. The latter seems to
be more probable since no slip traces were found near the
phase boundary. These specimens fractured in beta phase
near the grain boundaries in Beta. The fracture progressed
along those grain boundaries that were nearly perpendicular

to the tensile axis.

Figure 24.

64

Grain Boundary Sliding Leading to Severe
Deformation of Beta Grains away from the
Phase Boundary in a Specimen Tested at

800°F with a Cross-Head Speed of 0.10 cm/min.

Yield stress of Alpha 3.72 Kg/mmz.
Critical resolved shear stress of Alpha
1.65 Kg/mmz.

Total strain 3%.

 

 

 

Figure 24

65

Observations made on specimens deformed at 800°F
and at various strain-rates show that at low strain-rates
following grain boundary sliding in beta phase, alpha
phase deforms in single slip. Grain boundary sliding has
not been very significant at high strain-rates, since
grain boundaries resist deformation at high strain-rates.
Most of the specimens failed in beta phase beyond 15% total
strain, as a result of build-up of stress concentration

at grain boundaries in Beta.

4.1.3 Remarks on Specimens Deformed at Temperatures
Below the OrderingTempgrature of Beta Brass

(less than 850°F)

 

Deformation by grain boundary sliding in Beta
occurs in all of the specimens. However, grain boundary
is important only at high temperatures and low strain-
rates. At low temperatures and high strain-rates,
specimens failed in beta phase at grain boundaries in
Beta. As the temperature was increased, more deformation
was accommodated by either of the phases. Alpha phase
deformed by single slip and beta phase deformed by grain
boundary sliding. These specimens exhibited a high strain-
rate sensitivity and resulted in inter-crystalline frac-
tures. At 700°F a cross-head speed of 0.02 cm/min, and
at 800°F a cross-head speed of 0.1 cm/min were found to
be suitable for imposing uniform deformation in both the

phases. The quantitative data for some of these tests

66

are given in Tables I and 11. Although in the results and
discussion, cross-head speeds are used in Tables I and II,
tabulations are made on the basis of actual strain-rates
experienced by the individual phases in bicrystals of
alpha-beta brass. These calculations are carried out
because the lengths of each phase present in the bi-
crystal specimens are not the same.

ea is the strain-rate in alpha phase and is calculated
by dividing the cross-head speeds by length of Alpha.

ea is the strain measured in alpha phase after the test
is completed.

In this table, the phase that deformed first is also in-
cluded, since the yield stresses given in this table may
belong either to alpha or beta phase. Similarly, strain-
rates éB and strains (88) were also calculated for
beta phase. The average strain was calculated by using
the total length of the bicrystals as the specimen

gauge length. The average strain was also determined by
using the gauge length of the specimens. For example,
specimen P tested at 700°F and deformed at a cross-head
speed of 0.02 cm/min was actually strained at a rate of
0.0066 cm/cm/min in alpha and 0.026 cm/cm/min in beta
phase. The table also includes the ratio of the strain
accommodated in alpha and beta phases. These calcula-
tions, in terms of strain-rate and strains in each phase,
become essential because the gauge lengths of alpha and

beta regions in these bicrystals were not the same. The

67

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test results of specimens tested at 700° and 800°F with
various cross-head speeds are presented on the same basis
in Tables I and II. The notations used in these tables
are explained in Table 1. Notations used in this table
are also valid for the tables presented in the following
sections. The stress-strain curves of some of the
specimens tested at these temperatures are presented in
Figures 25 and 26. The strain is calculated by using

the entire gauge length of the bicrystal specimen for
plotting these curves. Quantitative observations made

on specimens deformed at 800°F are presented in Table III.
4.2 Deformation Behavior of Bicrystals of Alpha-Beta

Brass in the Temperature Range at which Beta Exists
in the Disordered State (greater than 850°F)

4.2.1. Deformation Studies at 900°F

 

Specimens deformed at 900°F and strained at a cross-
head speed of 0.02 cm/min deformed initially by single
slip in beta grains. As a result the beta regions of de-
formed samples had a rumpled appearance. Grain boundary
sliding in beta phase was not a dominant factor. There
was no indication of work-hardening in the stress-strain
curves. Cracks were opened up at some of the grain
boundaries in Beta. Alpha did not deform plastically at
all, as can be seen in Figure 27(a), even though Beta de-

JEormed in regions away from the phase boundary as shown in

Figures 27(b) and 27(c).

Figure 25.

72

Stress-strain Curves for Bicrystals Tested
at 700°F and Strained at Various Cross-Head
Speeds.

Specimen H cross-head speed 0.02 cmfmin
Specimen P cross-head speed 0.02 cm/min

Specimen T cross-head speed 0.10 cm/min

Stress ( Kg/mm2 )

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73

Figure 26. Stress-strain Curves for Bicrystals Tested
at 800°F and Strained at Various Cross-Head
Speeds.
Specimen K cross-head speed 0.02 cm/min
Specimen R cross-head speed 0.1 cm/min
Specimen R' cross-head speed 0.1 cm/min

Specimen 0 cross-head speed 0.5 cm/min

Stress ( Kg/mmz)

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Figure 27. Deformation Behavior Near and away from the
Phase Boundary in a Specimen Tested at 900°F

with a Cross-Head Speed of 0.02 cm/min.

Yield stress of Beta 0.966 Kg/mmz.

Critical resolved shear stress of Beta
0.48 Kg/mmz.

(a) No observable plastic deformation in Alpha
near the phase boundary.

(b) Severe deformation in beta phase away from

the phase boundary

T.A.

 

Figure 27 (c)

76

Macrograph Showing Necking in Beta.

Yield stress of Beta 0.966 Kg/mmz.

Critical resolved shear stress of Beta
0.48 Kg/mmz.

Total strain 5.9%.

 

77

Observations made on deformed specimens at 900°F
and strained with cross-head speed of 0.1 cm/min indicated
that the entire deformation took place in Beta. Slip
lines formed in Beta during deformation were clearly
visible to the naked eye; these slip lines interacted with
the phase boundary during further straining. Severe
deformation resulted in reduction of cross sectional area
in beta phase. This behavior is illustrated in Figure 28.

The observations are similar to ones made at room

3’4’5 (cross-

temperature and deformed at high strain—rates
head speeds of greater than 0.50 cm/min). In room tempera-
ture tests Alpha behaves in a more ductile manner and
accommodates almost all of the deformation. Interaction
of slip in Alpha with the phase boundary initiates slip

in Betaat:low strain-rates. At high strain-rates, deforma-
tion does not progress through the boundary in room
temperature tests. However, in specimens tested at 900°F,
the initial deformation occurs by slip in beta regions.

The entire deformation at 900°F with a cross-head speed

of 0.10 cm/min is accommodated in the beta region. Al-
though slip in Beta interacted with the phase boundary,

it does not activate deformation in the alpha region.
Further, the absence of any work-hardening in Beta pre-
vents the deformation of Alpha from increased applied
stress.

Specimens tested at 900°F and pulled at a cross-

head speed of 0.50 cm/min initially deformed in Alpha by

78

Figure 28. Severe Deformation in Beta Region near the
Phase Boundary in a Specimen Tested at 900°F

with a Cross-Head speed of 0.10 cm/min.

Yield stress of Beta 1.72 Kg/mmz.

Critical resolved shear stress of Beta
0.85 Kg/mmz.

Total strain 12.65%.

 

Figure 28

79

single slip as illustrated in Figure 29 (a). Slip lines

in Alpha became:deeper and wider on straining as can be
seen in Figure 29 (b). The imposing strain-rate was still
low enough even at this cross-head speed of 0.50 cm/min to
promote climbing of dislocations by thermally activated
processes. As a result of dynamic recovery process, the
stress level remained low and new slip systems were not
activited in alpha phase. However, Beta deformed uniformly
by coarse slip. This observation can be seen in Figure

29 (c). It was found that a cross-head speed of 0.50
cm/min resulted in uniform deformation in both the phases.
The slip traces present in both the phases in regions

near the phase boundary can be observed in Figure 30.

This deformation behavior would imply that at 900°F, a
cross-head speed of 0.50 cm/min was suitable for imposing

a uniform deformation in both the phases and that the

phase boundary had very little or no effect on the de-
formation behavior of these bicrystals; whereas, the phase
boundary played a more significant role at room temperature

tests.3’4’5

4.2.2. Deformation Studies at 1000°F

Specimens deformed at 1000°F and strained at a
cross-head speed of 0.1 cm/min resulted in total plastic
deformation in beta phase by coarse slip. Grain boundary
sliding was not too important in the processes and most of

the deformation was accommodated by beta grains. Alpha

80

Figure 29. Deformation of Alpha in Single Slip away
from the Phase Boundary in a Specimen Tested
at 900°F and Strained at a Cross-Head Speed

of 0.50 cm/min.

Yield stress of Alpha 4.07 Kg/mmz.
Critical resolved shear stress of Alpha
1.98 Kg/mmz.

(a) Macrograph of Slip in Alpha.

(b) Micrograph of Slip in Alpha.

 

 

 

 

Figure 29 (C).

81

Deformation of Both the Phases Near
the Phase Boundary in a Specimen Tested
at 900°F with a Cross-Head Speed of 0.50

cm/min.

Yield stress of Alpha 3.73 Kg/mmz.
Critical resolved shear stress of Alpha
1.52 Kg/mmz.

Total strain 3%.

 

 

Figure 29 (0)

Figure 30.

82

Interaction of Single Slip in Alpha with the
Boundary. Deformation in Alpha has Progressed

Through the Boundary into Beta Regions.

 

 

Figure 30

83

did not deform plastically at all. Necking took place
in beta region and the process was similar to a needle
point shape deformation, as can be seen in Figure 31.
Specimens tested at 1000°F and strained at a cross-
head speed of 0.2 cm/min resulted in deformation of Beta.
The deformed beta region appeared rumpled. Grain boundary
deformation was not too significant. The beta region
present near the phase boundary deformed heavily. Necking
took place in beta grains and led to a needle point
fracture. Although some cracks were observed at several
points in Beta, the deformation at a later stage was
entirely accommodated within beta grains. A delay in

38 and was also de-

yielding of Beta had been observed
tected here. Since there are no strain-hardening, be-

cause of thermally activated dynamic recovery in Beta, the
deformation in Beta continued until fracture. Alpha
regions did not deform during this process.

Deformation studies of specimens tested at 1000°F
and a cross-head speed of 0.5 cm/min indicated that Beta
phase was very soft compared with alpha phase and the entire
plastic deformation took place in Beta. There was very
little grain boundary sliding. At a test temperature
of 1000°F, beta grains deformed with less strain-rate
sensitivity compared with their grain boundaries. This

non-uniformity resulted in cracks in beta phase. There

was no plastic deformation in alpha phase.

Figure 31.

84

Needle Fracture in Beta Phase, no Visible
Plastic Deformation in Alpha in a Specimen
Tested at 1000°F with a Cross-Head Speed

of 0.10 cm/min.

Yield stress of Beta 1.10 Kg/mmz.
Critical resolved shear stress of Beta
0.52 Kg/mmz.

Total strain 150%.

 

 

Figure 31

85

4.2.3. Remarks on Specimens Deformed at Temperatures
Above the 0rdering_Temperature of Beta Brass
(greater than 850°F)

Two-phase bicrystal specimens consist of four
entities that can undergo deformation. These are single
crystal Alpha, grains in Beta, grain boundaries in Beta,
and phase boundary between Alpha and Beta. Of these
four, at temperatures above ordering, the beta grains
accommodate most of the deformation. There is very
little grain boundary deformation in Beta at these tempera-
tures. The deformation of these entities are highly
strain-rate sensitive. There is no work-hardening of
Beta at these temperatures and, as a result, Alpha will
not deform unless the applied stress level is high enough
to initiate deformation in it. Such a condition exists
at a cross-head speed of 0.50 cm/min in specimens tested
at 900°F. This observation suggests that at higher
temperatures, deformation at higher cross-head speeds,
should promote deformation in both the phases. However,
this behavior was not fully true in the tests carried
Ont at 1000°F. Deformation at a cross-head speed of 0.50
arui 1.00 cm/min promoted grain boundary cracking in Beta;
ruxither alpha nor beta phase deformed by slip. Results
infiiicated that 1000°F was too high a temperature for
Creeiting uniform deformation in both the phases.

The deformation of Beta is usually made by

creeping at these temperatures. A quantitative data for

86

tests carried out are presented in Tables IV and VI. The
qualitative data for the same tests are presented in
Tables V and VII. The tabulations are made in a manner
similar to the ones presented for specimens tested at
temperatures below the ordering temperature for Beta.
The stress-strain curves for some of these specimens
tested at 900°F and 1000°F are given in Figures 32 and 33.
4.3 Supporting Studies on Single Crystals of Alpha and
on Single and Polycrystals of Beta Brasses

In order to understand the behavior of the in-
dividual phases present in the two-phase bicrystals, a
batch of single crystals of alpha and beta brass plus a
large number of polycrystals of beta with grain sizes
ranging from coarse to fine were tested at elevated
temperatures of 700°, 800°, 900° and 1000°F and at various
strain-rates by imposing cross-head speeds of 0.02, 0.1,
0.2 and 0.5 cm/min. Throughout the studies made on bi-
crystals at elevated temperatures, the deformation be-
haviors of the individual phases were considered in the
interest of arriving at favorable conditions before the
tests were stopped. The results obtained from the in-
vestigations made on single crystals were also helpful in
unrierstanding the features observed during the testing of

bi<2rystals, since the bicrystal tests were never inter-

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Figure 32.

93

Stress-Strain Curves for Bicrystals Tested
at Elevated Temperature of 900°F and
Strained at Various Cross-Head Speeds.
(Data points were transferred from an
instron chart.)

Specimen L cross-head speed 0.02 cm/min
Specimen J cross-head speed 0.1 cm/min

Specimen Q cross-head speed 0.5 cm/min

 

Stress ( Kg/mm2 )

 

 

 

 

 

 

mend!- § mHodmmdwo: v
wwmcwm mm

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Figure 33.

94

Stress-Strain Curves for Bicrystals Tested
at Elevated Temperature of 1000°F and
Strained at Various Cross-Head Speeds.

(Data points were transferred for an instron
chart.)

Specimen N cross-head speed 0.1 cm/min
Specimen A' cross-head speed 0.2 cm/min
Specimen D' cross-head speed 0.5 cm/min

Specimen S cross-head speed 0.5 cm/min

Stress ( Kg/mm2 )

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95

4.3.1 Deformation Behavior of Alpha Brass Single Crystals

at Elevated Temperatures

 

A batch of alpha brass single crystals were tested
at 700°, 800°, 900° and 1000°F. Cross-head speeds of
0.02, 0.1 and 0.5 cm/min were employed in these tests.
The data on the yield stresses (critical resolved shear
stresses) for alpha brass single crystal specimens de-
formed at 800°F with different cross-head speeds were
used to draw a graph in terms of yield stresses (critical
resolved shear stresses) as a function of strain-rates.

A similar plot was also made from the data for specimens
deformed at 900°F. From these graphs, yield stresses
(critical resolved shear stresses) for strain-rates of
0.01, 0.02, 0.05, 0.10, 0.15 and 0.20 cm/cm/min at 800°
and 900°F were obtained and this data is presented in
Table VIII.

Based on this table a graph combining the effect of
temperature and strain-rate on yield stress and critical
resolved shear stress of alpha brass single crystals is
sketched in Figure 34. These graphs illustrate how both
temperature and strain-rate influence the yield stresses
of alpha brass single crystals. The increase in the
temperature and the decrease in the strain-rate, allow
the mobile dislocations to move out of a crystal with
less resistance. The thermal energy provided by the

test temperature, helps to untangle the dislocations

96
Table VIII
Yield Stress (critical resolved shear stress) of Single

Crystals of Alpha-Beta Brass at Various Strain-Rates
and Temperatures

Strain rate Temperature Yield Stress Critical Resolved

 

 

 

 

(cm/cm/min) (°F) (Kg/mmz) Shear Strgss
(Kg/mm)
0.01 800 2.85 1.10
0.01 900 2.70 1.05
0.02 800 2.90 1.15
0.02 900 2.75 1.10
0.05 800 3.10 1.30
0.05 900 2.80 1.20
0.10 800 3.45 1.55
0.10 900 3.10 1.40
0.15 800 3.80 1.80
0.15 900 3.30 1.60
0.20 800 4.15 1.95
0.20 900 3.50 1.75

Figure 34.

 

97

Yield Stress (Solid Lines) and Critical
Resolved Shear Stress (Dotted Lines) for
Alpha Brass Single Crystals Tested at

Temperatures Ranging from 700° to 1000°F.

(Data points are presented in Table VIII.)

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98

locked in their positions, resulting in further deforma-
tion. At medium.and low strain-rates, where interaction
of dislocations with each other is limited, specimens

deformed easily.

4.3.2 Deformation Behavior of Beta Brass Single Crystals

at Elevated Temperatures

 

Beta brass single crystals were tensile tested by
imposing cross-head speeds of 0.02, 0.10 and 0.50 cm/min.
The test temperatures used were 700°, 800°, 900°, and
1000°F. Two of the temperatures are above and two tem-
peratures are below the ordering temperature of Beta. A
procedure similar to the one used for alpha brass single
crystals was used to obtain the yield stress at strain-
rates of 0.01, 0.02, 0.05, 0.10, 0.15 and 0.20 cm/cm/min
at these temperatures. The results of such an analysis
are presented in Table IX. Based on this table a graph
combining the effect of temperature and strain-rate on
yield stress of beta brass single crystals is sketched
in Figure 35. These graphs illustrate how both tempera-
ture and strain-rate influence the yield stresses of beta
brass single crystals.

Due to the fact that beta brass experiences
structure change above 850°F (454°C) from Cesium-Chloride
(CsCl) to B.C.C., a drop in yield stress occurs. Figure
35 illustrates the results obtained from tensile tests

performed on single crystals of beta brass at various

99

Table IX
Yield Stress (critical resolved shear stress) of Single

Crystals of Beta Brass at Various Strain-Rates and Tem-
peratures

Strain-rate Temperature Yield Stress Critical Resolved

 

 

 

 

(cm/cm/min) (°F) (Kg/mmz) Shear Strgss
iKa/rrm )
0.01 700 3.35 1.65
0.01 800 2.75 1.30
0.01 900 1.95 0.92
0.01 1000 0.40 0.20
0.02 700 3.55 1.70
0.02 800 2.90 1.40
0.02 900 2.00 0.95
0.02 1000 0.42 0.21
0.05 700 4.32 2.15
0.05 800 3.40 1.65
0.05 900 2.15 1.05
0.05 1000 0.45 0.22
0.10 700 5.50 2.20
0.10 800 4.15 2.04
0.10 900 2.35 1.13
0.10 1000 0.50 0.24
0.15 700 6.70 3.32
0.15 800 4.95 2.40
0.15 900 2.55 2.25
0.15 1000 0.55 0.25
0.20 700 7.78 3.90
0.20 800 5.57 2.80
0.20 900 2.75 1.35
0.20 1000 0.60 0.29

100

Figure 35. Yield Stress for Beta Brass Single Crystals
Tested at Elevated Temperature and Strained
at Various Strain-Rates. (Data is presented
in Table IX.)

(a) Strain-rate .01 cm/cm/min

(b) Strain-rate .02 cm/cm/min

(c) Strain-rate .05 cm/cm/min

(d) Strain-rate .10 cm/cm/min

(e) Strain-rate .15 cm/cm/min

000000

(f) Strain-rate .20 cm/cm/min

 

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, 900

850
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800

Figure 35

101

temperatures and strain-rates. A drop in yield stress
for all strain-rates in the vicinity of order-disorder
transformation can also be seen in Figure 35. It was
observed that at low strain—rates, the deformation pro-
ceeded by creeping at temperatures above Tc' Coarse
slip lines were seen on deformed samples of beta brass
single crystals strained at low strain-rates and fine
slip lines on specimens strained at high strain-rates.

Often heavily deformed beta brass single crystals had a

rumpled appearance.

4.3.3 Deformation Behavior of Beta Brass Polycrystals
at Elevated Temperatures

Coarse-grained polycrystals of beta brass similar
to the ones in the two-phase bicrystals of alpha-beta
'brass, and some bicrystals of beta brass were tested at
700°, 800°, 900°, and 1000°F by imposing cross-head speeds
(Jf 0.02, 0.1 and 0.5 cm/min. Bicrystals either deformed
11y grain boundary sliding or fractured after 15% defonma-
'tions Grain boundary orientation with respect to the
‘tensile axis played an important role. Those grain
Imaundaries parallel or perpendicular to the tensile axis
Lauderwent very little deformation and specimens failed at
a grain boundary perpendicular to the tensile axis. This
i1; in agreement with the observations made by Mera.39
Some of the beta grains appeared intact at their centers.

Beta grains were reoriented along the tensile axis when-

ever the deformation proceeded beyond 30% straining. In

102

bicrystals, normally the grain with most favorable-
orientation with the tensile axis deformed and the de-
formed grain accommodated the rest of the deformation.
The stress-strain curves did not exhibit any work-harden-
ing. Beta grains as well as grain boundaries, resisted
deformation at high strain-rates. Cracks developed at
grain boundaries at high strain-rates in bicrystals of
beta brass. This phenomenon was observed quite fre-
quently in specimens that underwent incompatible deforma-
tion between grains and the grain boundaries.
Medium-grained beta brass Specimens exhibited
more fractures, since the probability of formation of
cracks were increased by the presence of more grain
boundaries oriented unfavorable to the tensile axis. Once
a local yielding was initiated, the specimen deforms very
little and fractures abruptly. Fine-grained specimens of
beta brass deformed easier than coarse-grained specimens
or single crystals at elevated temperatures. Grain
‘boundaries at room temperature tend to contribute to the
strength of beta brass polycrystal; but at elevated tem-
‘peratures the presence of more grain boundaries weakened
the material and polycrystalline beta brass specimens de-
formed very easily. A procedure similar to the one used
:hn the case of alpha brass single crystal was utilized to
<fl1tain.yield stress at strain-rates of 0.01, 0.02, 0.05,
0.]l), 0.15 and 0.20 cm/cm/min, at various temperatures.

ITua data are presented in Table X, and the graph that

103

Table X

Yield Stresses of Polycrystals of Beta Brass at Various
Strain-Rates and Temperatures

 

 

 

Strain-rate Temperature Yield Stress
(cm/ ml min) (°F) (Kg/mmzl
0.01 700 3.55
0.01 800 3.35
0.01 900 2.35
0.01 1000 0.40
0.02 700 3.75
0.02 800 3.55
0.02 900 2.45
0.02 1000 0.42
0.05 700 4.50
0.05 800 4.10
0.05 900 2.65
0.05 1000 0.45
0.10 700 5.70
0.10 800 5.05
0.10 900 3.05
0.10 1000 0.50
0.15 700 6.85
0.15 800 6.00
0.15 900 3.40
0.15 1000 0.55
0.20 700 8.05
0.20 800 6.95
0.20 900 3.80
0.20 1000 0.60

104

illustrates the data in this table is given in Figure 36.
Polycrystals of beta brass also undergo a structure change
in the vicinity of 850°F (454°C). The structure changes
occur both in the grain boundaries and beta grains
simultaneously, since grain boundaries are found to under-
go continuous structure change with changing of test
temperatures. However, the overall effect of temperature
on the yield stress is similar to that of beta single

crystals in the vicinity of 850°F.

4.3.4 Deformation Behavior of Two-Phase Muntz Metal at
Elevated Temperatures
A number of specimens made out of Muntz metal
‘were tested at 700°, 800°, 900° and 1000°F and were sub-
jected to various strain-rates by imposing cross-head
speeds of 0.02, 0.1 and 0.5 cm/min. It was learned that
the yield stress is directly related to the strain-rate
and.inversely to the test temperature. This agrees with
the results obtained for most of polycrystalline two-phase
materials.36 Table XI contains the yield stresses for

specimens tested at various temperatures and cross-head

speeds.

4.li Factors that Influence Uniform Deformation of Both
the Phases Present in a Two-Phase Material

One of the main objectives of this work is to
fixud conditions for obtaining uniform deformation in

‘botfii the phases present in a two-phase material. The

105

Figure 36. Yield Stress for Beta Brass Polycrystals
Tested at Elevated Temperatures and Strained
at Various Strain-Rates. (Data points are
presented in Table X.)

(a) Strain-rate 0.01 cm/cm/min
(b) Strain-rate 0.02 cm/cm/min
(c) Strain-rate

.05 cm/cm/min

(e) Strain-rate

0

(d) Strain-rate 0.10 cm/cm/min

0.15 cm/cm/min
0

(f) Strain-rate .20 cm/cm/min

Yield Stress ( Kg/mm2 )

1:.

.5

\)u

1)

I?

 

 

800 550 900 1-

Temperature

(‘F)
Figure 36

 

Yield Stresses of 60-40 (Cu-Zn) Commercial Brass (Muntz
metal) at Various Cross-Head Speeds and Temperatures

Temperature

(°Fi
700
800
800
800
900
900
1000

Cross-Head Speed Strain-rate

106

Table XI

 

 

(cm/min) (cm/cm/min)
0.10 0.0394
0.50 0.197
0.10 0.036
0.02 0.008
0.50 0.212
0.10 0.039
0.10 0.042

Yield

(Kg/mm

St

9.35
8.64
6.4
4.
6
4
3

35

.01
.55
.96

688

J

107

total number of available slip systems in each of the
phases present in two-phase materials are different. As
a result, temperature sensitivity, strain-rate sensitivity
and phase transformations have been utilized to promote
uniform deformation in both the phases. Phase trans-
formation can give rise to different deformation char-
aracteristic of a material. Obtaining a uniform deforma-
tion in two-phase bicrystals of alpha-beta brass at
various temperatures is a complicated process. There
are many factors that control the deformation behavior of
a two-phase material. For instance there is always a
possibility that one phase may still be deforming in an
elastic manner while the other is deforming plastically.
Generally, at different test temperatures, one phase re-
‘mains harder than the other. By imposing a proper cross-
head speed (strain-rate) on a bicrystal, a uniform deforma-
tion could be achieved provided the strain-rate sensitivity
of both the phases are different. The role of the phase
‘boundary in the overall deformation behavior of such two-
phase bicrystals can also be a controlling factor.

One can formulate the following relationships
*with.respect to two-phase samples (having alpha and beta
phases) having both the phases in series and deformed

under uniaxial loading:

A2 A2.“ + A28 (1)

EL = eaLa + eBLB (2)

108

where: AI is the total elongation of the specimen,
Aka is the elongation in alpha phase,

A2 is the elongation in beta phase,

mlm

is the average strain in specimen,
L is the total length of specimen,
5 is the strain in alpha phase,

L is the length of alpha phase,

a
68 is the strain in beta phase and
LB is the length of beta phase.

Moreover, at the start of the test when the cross-
section area remains constant throughout the sample, one

can assume that:

5=o=08 , (3)

a
‘where 5 is the stress applied to the total specimen

0 is the stress applied to the alpha phase, and
is the stress applied to the beta phase.
By combining both equations (2) and (3) one can

arrive at:

oeL = anaLa + OBEBLB . (4)

quuation (4) holds at the start of the tensile test, since
all.the components of the bicrystal specimens have a
1n1iform.cross-section area. If both the phases have
:identical mechanical properties and suitable conditions
i11 terms of temperature, strain-rate and other influenc-

ing factors, then both the phases would undergo a uniform

109

deformation. Otherwise, one has to consider the following
factors:

(1) At test temperature below Tc alpha phase
is softer than Beta, even though Beta deforms slightly
by grain boundary sliding mechanism. However, at low
test temperatures and strain-rates, some regions in Alpha
deform first, then Alpha experiences strain-hardening.
Consequently, the stress level rises in the specimen and
ultimately Beta deforms either by the interaction of slip
from alpha phase with the phase boundary or deforms on its
own.

(2) Above TC beta phase is the softer phase.
Once Beta deforms, either Beta fractures after 15%
straining (low temperature, high strain-rates, and pre-
sence of grain boundaries perpendicular to tensile axis)
or deforms by creeping (high temperature and low strain-
rates) until the end of the test. At temperatures above
Tc Beta exists in B.C.C. structure and it has been found
out.Beta deforms easier than alpha phase. Since there is
In: way of producing the stress level in the alpha phase
(hard phase) required to deform it. It is only by applying
a high strain-rate to beta phase at the start of the
test that the deformation of alpha phase becomes possible.
'Fhe stress 5 (average stress), 00 (stress in Alpha) and
0 (stress in Beta) are related to each other in a

B
complicated way and can be written as follows: 0

110
o(T,F,E,A(t),A) is related to 0a(T,F,éa,Aa(t),Aa)

and 08(T,F,é ,A8(t),AB)

B

where: T is the test temperature,

5 is the total applied stress,

F applied tensile force or load,

E average applied strain-rate and

A(t) instantaneous cross-section area,

A represents parameters such as grain boundary orienta-
tion, crystallographic orientation of individual phases

with respect to the tensile axis, structural changes during
the testing and other minor factors involved in machining
and handling of specimens. This is a complicated funda-
mental relationship and only by experimental observations
can one arrive at suitable conditions for obtaining uni-
form deformation. However, such a process will be extremely
complicated and one may not be able to find a correct solu-
tion at all.

In this work, a large number of single and poly-
crystals of Alpha (single crystals) and Beta (single and
poly) brass crystals were tensile tested at 700° and 800°F
below Tc, and at 900° and 1000°F above the TO by
imposing cross-head speeds of 0.02, 0.1, 0.2, and 0.5 cm/
1min. Graphs were made from tabulated results by using
yield stresses obtained for specimens deformed at various
temperatures and strain-rates. These graphs were in-

strumental in predicting some of the deformation behavior

111

of a bicrystals tested at certain temperatures.

Once the dimensions of the specimens are measured
(length of each phase and cross-section area), a cross-head
speed can be selected. Thus, by imposing a desirable
strain-rate, both the phases would experience a uniform
plastic deformation.

Cross-head speeds of 0.02 cm/min. at 700°F,
0.1 cm/min. at 800°F, and 0.5 cm/min. at 900°F, resulted
in producing a uniform deformation in both the phases for
specimens with total length of about 2 inches and each
phase having nearly the same length.

Grain boundary deformation was observed in most
cases where the test temperature was high and the strain-

40 made his studies on beta brass

rate was low. Margolin
bicrystals and as a result, formulated a set of equations
relating the total applied stress to the stress away from
the grain boundary and stress in the grain boundary de-
formation zone. From the slip behavior, it was found out
that progression of slip from one grain to the other de-
pends upon the compatibility of strain within the grain
and the grain boundaries. The yield stress of specimens
tested at various temperatures and strain-rates were
affected by the nature and the deformation behavior of
grains and their grain boundaries.

Formation of cracks at grain boundaries in beta

35

brass was observed quite frequently. Below the ordering

112

temperature, stress concentration due to incompatibility
of strain between grains and their boundaries resulted,
since the grain boundary sliding is limited to the first
15% of straining. This limit of 15% strain for grain
boundary sliding was obtained from observations based on
load fluctuation during the course of the tests. When
load amplitude fluction faded out, grain boundary
sliding process was assumed to have stOpped. Moreover,
the grain boundary sliding mechanism accommodates almost
all of the strain in specimens with few large grains.
Whenever smaller grains and, especially, interpenetrating
grains with intersecting grain boundaries were present,
grains were sheared from Opposite directions. Upon further
straining, grains deformed to some extent and ultimately
due to excessive stress concentration build-up, grains
were lifted from their positions and cracks developed.
Figure 18 illustrates the interference of grain boundary
sliding with grains. In Figure 37, it is shown that slip
initiated at point "A" and slip progressed to point "B".
.A reorientation of grains with respect to the tensile
axis also results. Fracture usually occurs where the
local stress concentration becomes excessive. Reorienta-
tion of grains and rounding off of the edges of grains in
two-phase materials were also cited by Baro.36
By imposing different cross-head speeds on
‘various bicrystal specimens tested at different tempera-

‘tures a uniform deformation and/or deformation in both

113

Figure 37. A Simulated Model Illustrating the Inter-
action of Grain Boundary Sliding with Beta

Grain.

 

Figure 37

 

114

the phases were set up in order that the role of the phase
boundary could be studied. The deformed samples revealed
in most cases that each phase had deformed on its own
without the influence of the other phase. In rare
occasions slip progressed through the phase boundary and
it produced deformation zones in the other phase. De-
formation in either phase proceeded by single slip and
phase boundary did not play an important role in the
deformation behavior of two-phase bicrystal of alpha-beta
brass at elevated temperatures.

The structure change in beta phase in the vicinity
of Tc’ from order (superlattice structure) below TC to
disordered B.C.C. above Tc’ a thermally aided process,
plays an important role in the deformation behavior of
bicrystals. By increasing the test temperatures, the
short range order is decreased and no more superlattice
structure would be present. Dislocations can move more
easily and contribute to the ease of deformation.

A series of tests were performed on polycrystals
of two-phase alpha-beta brass at test temperatures of
700°, 800°, 900° and 1000°F and strained by using cross-
head speeds of 0.02, 0.1, and 0.5 cm/min. Below Tc
Alpha is soft and beta phase is hard. Above TC Beta
becomes softer than Alpha. In either case, the softer
phase plays the role of a matrix. It was also cited by

36

Baro that alpha platelettes, originally present with

115

sharp corners in a beta matrix of a two-phase brass
specimen, were rounded off. Some of the photomicro-
graphs showed that the alpha phase became equiaxed and
parallel to the tensile axis. The coarsening of micro-
structure of alpha phase took place due to assembly of
phases of the same nature, caused by their rotation during
the deformation and also by mass-diffusion along the phase
interfaces. At temperatures above TC where Alpha is
harder than Beta, the softer phase (Beta) accommodates
almost all of the deformation and reorientation of alpha
grains becomes possible.

In order to comprehend the deformation behavior of
two-phase alpha-beta brass at elevated temperatures, a
description and discussion of a series of simulated
models based on actual specimens are helpful. Since shape,
orientation, and location of grains with respect to each
other and their neighboring grains play important roles
during the deformation, step by step additions to some of
the simpler models are made in the following sections.

The most important factors involved are pointed out and
are reviewed below.

Coarse grain alpha brass tested at room temperature
and also at elevated temperatures deforms easily. At
low strain-rates, specimens did not fracture up to 100%
elongation. Grain boundary sliding at elevated tempera-

tures accommodates the straining. At room temperature,

116

grain boundaries resist progression of slip from within
one grain to the neighboring grains. Dislocation pile-
ups against the grain boundaries were observed.36

Coarse grain beta brass tested at room temperature
exhibited very little deformation, and specimens fractured
before 5% deformation. Grain boundary sliding was ob-
served in beta brass at temperatures above 112°F (50°C).
Strain incompatibility between beta grains and their
boundaries often led to fracture at grain boundaries.

The deformation of alpha and beta brass bicrystals
with three possible grain boundary orientations are dis-
cussed next.

Grain boundaries could have three extreme possible
orientations with respect to the tensile axis. Figure
33 (a), (b) and (c) are the three possible models.
Specimens with grain boundary orientations given in
Figures 38 (a) and (b) deform very little, when tested
at elevated temperatures and deformation ends in fracture
after 15% deformation. Grain boundary sliding is minimal
and strain incompatibility causes fracture. Specimens
with Figure 38 (c) configuration, when tested at elevated
temperatures, undergo grain boundary sliding at low strain-
rates. A dislocation model for grain boundary sliding36
is presented in Figure 39. In this figure a region near
the grain boundaries that experiences shear stress de-
forms by slipping due to grain boundary sliding. At the

same instance those regions near the boundary that are

Figure 38.

117

Simulated Models Representing Three Possible

Grain Boundary Orientations in Bicrystals

of Beta Brass.

(a) Grain boundary is perpendicular to the
tensile axis.

(b) Grain boundary is nearly parallel to the
tensile axis.

(c) Grain boundary makes 45° with the tensile

axis.

TIA.

T.A.

 

 

)

r'c

(

 

 

 

llllrIVl

 

(b)

 

 

 

 

 

(a)

 

 

Figure 38

118

Figure 39. A Dislocation Model for Grain Boundary
Sliding in Single Phase Alpha and Beta

Brasses.

 

4 l-J- l .1

 

 

 

 

 

 

Grain boundary sliding

Figure 39

119

not able to deform by grain boundary sliding cause
stress concentration and as a result slip is induced
into the beta grains. The experimental observations
illustrating this feature may be seen in Figure 24. At
high strain-rates and below Tc’ one of the grains de-
forms and deformation continues until needle point
fracture occurs. The other grain remains intact. But,
at temperatures above Tc’ both grains experience some
plastic deformation and one of the grains deforms more
than the other. In the three mentioned cases, deforma-
tion behavior is highly strain-rate sensitive. Grain
boundary sliding is the dominant factor with specimens
having grain boundary orientation near 45° to the tensile
axis.

A step closer to two-phase alpha-beta brass is a
model system containing both the phases. Such a model

3’4 5 and the deforma-

‘was introduced by Hingwe and Nilsen,
tion behavior of such specimens was the subject of their
investigations at room temperature. In this work, tests
were performed at elevated temperatures. Some of the
major differences found in the deformation behavior of
bicrystals of alpha-beta brass at room temperature and at
elevated temperatures are reviewed in Table XII. One
can conclude that the deformation behavior of bicrystals

0f alpha-beta brass is temperature sensitive at a given

Strain-rate.

120

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121

An ideal simulated model duplicating two-phase
alpha-beta brass is shown in Figure 40. Let lines AB, BC,
CD, DE, FF', IJ, KK' and LA represent the grain boundaries
between Alpha-Alpha and Beta-Beta grains. And lines EF,
FG, GH, HI, II', JJ', JK, KL and LL' represent the phase
boundary between Alpha and Beta grains. Applied normal
stress (a), in the direction specified, causes grain
boundary sliding. Grain boundaries such as FF', KK' and
IJ undergo grain boundary sliding. This process results
in formation of shear stresses across some alpha grain
edges. Alpha deforms to some extent and shear stresses
are reduced. Further straining results in activation of
numerous local stress concentration zones at the inter-
penetrating phase and grain boundary corners such as
corner "B" and neighboring grains undergo plastic de-
formation. It was observed that phase boundaries do not
play an important role in alpha-beta brass bicrystals de-
formation at elevated temperatures. In the case when
shear stresses are present, at the boundaries, it is
possible for phase boundaries to accommodate some of the
deformation. However, it is not a necessary condition
that all grain and phase boundaries undergo some kind of
deformation, because deformation proceeds wherever a
favorable condition exists. Usually, with the build-up
of local stress concentration regions, even the most

inaccessible places in a material are deformed.

122

Figure 40. A Simulated Model of Two-Phase Alpha-Beta

Brass Deformed Under Normal Stress.

T.A.

 

 

 

 

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123

A model closer to reality for two-phase alpha-
beta brass Muntz metal is shown in Figure 41. The de-
formation behavior of alpha-beta brass is greatly in-
fluenced by the test temperature and strain-rate. At
room temperature, the deformation ends in brittle fracture
before 30% deformation. At elevated temperatures below
TC, the deformation proceeds in a rather uniform manner.
Above TC where beta phase exists in disordered B.C.C.
structure, the hard phase alpha, existing in platelettes
shapes, reorients itself with respect to the tensile
axis. This behavior is illustrated in Figure 42.

Baro,36

made observations on samples of 60-40
alpha-beta brass deformed at elevated temperatures and
reported that alpha platelettes (harder phase above Tc)
were reoriented along their longer dimensions with the
tensile axis. Beta phase played the role of a soft
matrix, making the alignment of alpha platelettes possible.
The sharp edges of the alpha platelettes were rounded

off, and a coarsening of alpha platelettes resulted during
the deformation.

During the course of this investigation attempts
were made to understand the deformation behavior of two-
phase materials. A part of this work was devoted to the
development of a method by which the deformation behavior

studies made on bicrystals of alpha-beta brass could be

applied in hot-rolling, extrusion and shaping of materials.

Figure 41.

124

Free Hand Sketch of Alpha-Beta Brass. Note,
Alpha Platelettes are Randomly Oriented in

the Beta Matrix.

 

-__ .—._-.._ .._._—__.._..- a.

 

 

 

125

Figure 42. A Simulated Model of Two-Phase Alpha-Beta
Muntz Metal (60-40) Brass.

126

A summary of the observations made on the deformation
behavior of two-phase alpha-beta brass bicrystals tested

at elevated temperatures is presented in Table XIV.

 

127

 

 

 

 

 

 

 

 

 

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CHAPTER V
SUMMARY AND CONCLUSIONS

Deformation studies on two-phase bicrystals of alpha-
beta brass at temperatures below TC for beta phase
show that, at low strain-rates, Beta deforms by
grain boundary sliding and the initial deformation
occurs usually in Alpha. At high strain-rates, grain
boundary sliding in Beta is minimal and most of the
deformation is accommodated in alpha phase.
Deformation studies on two-phase bicrystals of alpha-
beta brass at temperatures above TC show that, at
low strain-rates, Beta deforms by slipping in beta
grains and alpha phase does not deform at all. At
high strain-rates, both Beta and Alpha deform by
single slip.
At temperatures above Tc’ the individual grains in
Beta with B.C.C. structure deform more easily than
the grain boundaries in Beta.
Uniform deformation of two-phase bicrystals of alpha-
beta brass with total lengths of 2.0 inches (Alpha 2
Beta 2 1 in.) can be achieved by using low strain-rate
(cross-head speed of 0.02 cm/min) at 700°F, moderate
strain-rate (cross-head speed of 0.10 cm/min) at 800°F
129

130

and high strain-rate (cross-head speed of 0.50
cm/min) at 900°F.

The phase boundary that exists between alpha and beta
phases does not play any role in the deformation of
such two-phase bicrystals at elevated temperatures.
However, the grain boundaries present in Beta regions
deform by grain boundary sliding at temperatures be-
low Tc’ provided they are favorably oriented and the
strain-rate is small or moderate.

The deformation behavior of beta phase is highly
sensitive to strain-rate. The sensitivity is not
affected by variation in temperature, although the
yield stress depends strongly on the rate of deforma-
tion. On the other hand, the deformation of alpha
phase is relatively insensitive to strain-rate.
Deformation at temperatures above TC is dominated
by creeping in Beta with an absence of work-hardening.
So, alpha phase does not deform unless the initial
yield stress is high enough to initiate slip in alpha
phase. The plastic deformation of both the phases
normally occurs in single slip mode.

In room temperature tests, the deformation of two-
phase bicrystals was dominated by the interaction of
slip in alpha phase with the phase boundary. At

high temperatures, each phase deforms on its own and

slip interaction with the phase boundary is not of

131

any significance. This phenomenon is attributed to
the thermally activated dynamic recovery of the
material, which will dissipate any stress concentra-
tion due to the pile-ups. Cross-slip in Alpha was
not observed frequently during the course of this
work, although it was a very common feature in room

temperature deformation.

’I‘tl.

 

[.1135

 

CHAPTER VI
SUGGESTED TOPICS FOR FURTHER INVESTIGATION

Deformation of specimens with phase boundaries in-
clined at various angles to the tensile axis can be
carried out to understand the role of the resolved
shear stress on the phase boundary. In this research
and previous ones, the phase boundaries were per-
pendicular to the tensile axis. The effect of tem-
perature on the deformation behavior of inclined
boundary specimens at elevated temperatures are still
desirable to be pursued.

The interaction of slip with the phase boundary is
not fully understood at the microstructural levels.
Transmission electron microscope studies of thin
foils containing the phase boundary should be carried
out in order to further explore the behavior of the
interaction of slip dislocations with one another at
the phase boundary.

Studies on the deformation behavior of bicrystals
could be extended to multi-crystals containing coarse
grains of Alpha and Beta. This will result in a
better understanding of the deformation behavior of
two-phase materials.

132

133

As an extension to this investigation, one may
utilize some of the procedures used in the text re-
lated to obtaining uniform deformation in two-phase
materials. A systematic method (incorporating all
of the factors involved in the deformation behavior
of two-phase materials at elevated temperatures)
could be devised for practical applications during
hot rolling, hot extruding and shaping of two-phase

materials.

REFERENCES

\OGDNO

10.

ll.

12.

13.
14.

LIST OF REFERENCES

H. Margolin, P.A. Farrar, M.A. Greenfield, "The
Science Technology, and Application of Titanium",
Ed. R.I. Jaffe, N.E. Promisel, Pergamon Press, N.Y.
(1970).

C.S. Smith, Met. Rev. 2, p. 12 (1954).

A. Hingwe and K.N. Subramanian, Journal of Crystal
Growth, 21, p. 287 (1974).

A. Hingwe, "Duplex Crystals and Two-Phase Bicrystals
of Alpha-Beta Brass, Growth and Mechanical Pros
prieties", Ph.D. Thesis, Michigan State University
(1973).

C. Nilsen, "Mechanical Properties of Alpha-Beta
Brass-Studies on Model Systems", Ph.D. Thesis,
Michigan State University (1973).

R. Maddin, Trans. A.I.M.E., 175, p. 86 (1948).

E. Schmidt, L. E1ectrochem., 31, p. 447 (1931).

E. Orwan, Proc. Phys. Soc., 52, p. 8 (1940).

W.G. Johnston, J.J. Gilman, "Dislocations and
Mechanical Properties of Crystals", Ed. Fisher,
John Wiley and Sons, Inc., N.Y., p. 116 (1957).

D. McLean, "Creep Processes in Coarse-Grained
Aluminum", Journal of Metals, 82, p. 507 (1951-52).

D. McLean, "Grain Boundary in Metals", Claredon
Press, Oxford, p. 157.

R.D. Heidenreich, W. Shockly, Phy. Soc. London,
p. 57 (1948).

N. Brown, Phil. Mag., 4, p. 693 (1959).

J.P. Hirth and J. Lothe, "Theory of Dislocation”,
McGraw-Hill, N.Y., p. 764, (1968).

134

15.

16.

17.
18.

19.

20.

21.

22.
23.

24.

25.

26.

27.
28.
29.

30.

31.

135

.ALH.Cottre11, "Dislocation and Plastic Flow in
Crystals", Clarendon Press, Oxford (1953).

J.H. Westbrook, "Mechanical Properties of Inter-
metalic Compounds -- A Review of the Literature",

in Mechanical Properties of Intermetallic Compounds,
John Wiley and Sons, Inc., N.Y., p. 180 (1960).

 

A.B. Greninger, Trans. A.I.M.E., 128, p. 369 (1938).

Y.D. Chung and H. Margolin, Metall. Trans., 4,
p. 1905 (1973).

M.C. Chuang, ”Mechanical Properties of Intermetallic
Compounds", John Wiley and Sons, Inc., New York,
London, p. 177.

S. Karashima, Proc. 2nd Japan Congr. Test. Mat.,
p. 59 (1958).

J.D. Meakin, H.G.F. Wilsdrof, Trans. A.I.M.E., 218,
p. 737 (1960).

R.N. Stevens, The Phil. Mag., g;, p. 265 (1971).
P.R. Swann, "Dislocation Arrangements in Face—
Centered Cubic Metals and Alloys", Electron Micro-
scopy and Strength of Crystals, Interscience, New
York (1963).

A.B. Greninger and V.J. Moordin, Trans. A.I.M.E.,
128, p. 33 (1938).

M. Asamo, O. Izumi and E. Tanaka, Trans. A.I.M.E.,
p. 349 (1968).

M. Ohmori, K. Wakasa, Jap. Jour. Sci., _1, p. 1188
(May 1953).

M. Chunke, Jap. Jour. Sci., 25, p. 380 (October 1950).
C.T. Wang, Jap. Jour. Mat. Sci., p. 702 (1962).

K. Sadananda, M.J. Marcinskowski, Jour. Appl. Phys.,
45, No. 4, p. 1259 (April 1974).

K. Sadananda, M.J. Marcinskowski, Jour. Appl. Phys.,
45, No. 4, p. 1521 (April 1974).

K. Sadananda, M.J. Marcinskowski, Jour. Appl. Phys.,
45, No. 4, p. 1523 (April 1974).

32.

33.
34.

35.

36.
37.

38.

39.
40.

41.

136
K.W.K. Honeycomb, W. Boas, Aust. J. Sci. Res.,
p. 70 (1948).
L.M. Clarebrough, ibid, 5, p. 72 (1950).

L.M. Clarebrough, G.R. Perger, ibid, 5, p. 114
(1952). ""“*

M. Surey and B. Baudelet, J. Mat. Sci., 5, p. 363
(March 1973).

G. Baro, Z. Metall. Kunde, Z, p. 384 (July 1972).

B.J. Brindley, D.J.H. Corderoy, R.W.K. Honeycomb,
Acta. Met., 59. p. 1043 (1962).

J. Broich and H. Feldmann, Metall., 51, p. 1069
(1973).

S. Mera, Z. Metall. Kunde. 59, p. 289 (November 1970).

Y.D. Chung and H. Margolin, Metall. Trans , 4, p. 72
(August 1950).

M.H. Yoo, "Growth of Mechanical Twins in Zinc
Crystals", Ph.D. Thesis, Michigan State University
(1965).

APPENDIX

APPENDIX
DEFORMATION BEHAVIOR OF TWO-PHASE BICRYSTALS OF ALPHA-

BETA BRASS HAVING THEIR PHASE BOUNDARIES INCLINED TO
THE TENSILE AXIS

The fundamental unit for a two—phase material is
a two-phase bicrystal. In the investigation carried out

3’4 and Nilsen,5 the orientation of

previously by Hingwe,
the phase boundaries of the specimens tested were per-
pendicular to the tensile axis and the phase boundaries
experienced atensile stress. Other orientation configura-
tions such as parallel and inclined orientations of phase
boundaries with respect to the tensile axis are of great
interest. The inclined boundaries will experience shear
stresses during tensile deformation. The parallel boundary
will require both the phases to have the same strain.

So far, there is not a technique available for
preparation of two-phase bicrystal specimens with phase
boundaries parallel to the tensile axis. Such studies
with grain boundaries parallel to the tensile axis, were
carried out elsewhere in single phase materials.41

An alternative method, different from that used

for producing bicrystals with perpendicular boundaries,

is utilized in the preparation of bicrystals of alpha-

137

138

beta brass with inclined boundaries. A straightforward
joining operation is carried out with a prepared alpha
brass single crystal having an inclined and carefully
polished joining surface, and beta brass stock having
equal dimensions and matching inclined surface. Such a
joining operation, with associated heat-treatments, does
not provide a flat bicrystal phase boundary. The boundary
tends to rotate during heat treatment, and one ends up
with a phase boundary perpendicular to the length of the
specimen.

In order to prepare the inclined phase boundary
bicrystals, the entire heat-treatment procedure had to be
eliminated. A technique was devised wherein beta brass
was melted onto alpha brass single crystal substrates with
inclined faces, in quartz tubes. Extremely slow cooling
of molten Beta then created the large grains of Beta for
the bicrystal specimens. Since, the process took a long
time, Argon gas was passed through the quartz tube to avoid
any oxidation problems. The probability of obtaining a
flat alpha-beta interface was only about one in ten. The
results presented in this appendix on the deformation be-
havior of inclined boundary alpha-beta brass bicrystals
are from the specimens having good inclined flat boundaries.
Specimens used in this work had phase boundaries inclined
to the tensile axis by 60°, 45° and 30°. These specimens
‘Were deformed at cross-head speeds of 0.01, 0.1 and 1.0

cul/min. The gauge length of the entire specimen was 135"

139

long with %” of which was Alpha and the other %”

was beta
brass. Since the gauge lengths in all of the specimens
were about the same, the strain-rates are presented in
terms of cross-head speeds directly. All of the tensile
tests were carried out at room temperature. Some of the
tests were stopped for photographing the specimens.
Specimens were handled with extreme care.

Specimens having 60° inclined phase boundary with
respect to the tensile axis tested at a cross-head speed
of 0.01 cm/min initially deformed in Alpha. Single slip
in Alpha approached the phase boundary. Figure 43 illus-
trates deformation in Alpha and,Beta is left intact after
2.7% elongation. Upon further straining, at 13.2%
elongation, fine cross-slip was observed in Alpha near the
phase boundary. Observations are illustrated in Figures
44 and 45. At 21.8% elongation, cross-slip lines became
heavier due to the resistance of phase boundary in allow-
ing slip in Alpha to progress through the boundary.
Figures 46 and 47 illustrate the extent of the deformation
0f Alpha and the effectiveness of phase boundary as a
barrier in resisting the progression of slip in alpha
‘Phase through the phase boundary. At the same strain
1£nrel of 21.8%, beta regions away from the phase boundary
Were deformed. The deformation behavior is shown in
Figure 48. At 48.9% elongation, a beta grain in contact

Witfl another beta grain adjacent to the phase boundary

140

Figure 43. Single Slip in Alpha Approaching the Boundary.
Boundary makes 60° to the tensile axis.
Cross-head speed: 0.01 cm/min

Stress: 3.358 kg/mmz Elongation in Alpha: 2.77.

 

 

 

Figure 44.

141

Fine Cross-Slip in Alpha Near the Boundary.
Boundary makes 60° to the tensile axis.
Cross-head speed: 0.01 cm/min

Stress: 4.328 kg/mmz

Elongation in Alpha: 13.2%

ToA.

 

ure 44

Fig

Figure 45.

142

Cross-Slip in Alpha Near the Boundary Region.
Boundary makes 60’to the tensile axis.
Cross-head speed: 0.01 cm/min

Stress: 4.328 kg/mm2

Elongation in Alpha: 13 2%

 

Figure 45

Figure 46.

143

Cross-Slip in Alpha near the Boundary at
a Higher Stress.

Boundary makes 60° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 5.97 kg/mm2

Elongation in Alpha: 21.8%

FA.

 

igure 46

I:
.L

Figure 47.

144

Extensive Cross-Slip in Alpha near the Boundmw.
Boundary makes 60° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 5.97 kg/mm2

Elongation in Alpha: 21.8%

 

Figure 47

Figure 48.

145

Slip in Beta in a Region away from the
Boundary.

Boundary makes 60° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 7.1 kg/mm2

Elongation in Alpha: 21.8%

 

Figure 48

146

underwent deformation. Figure 49 is the macrograph of
the deformed sample after 48.9% deformation of Alpha.
Note that the beta grain adjacent to the phase boundary
did not deform plastically. The beta region near the
phase boundary is deformed the least. The macrograph
of deformed specimen after 90.2% deformation is presented
in Figure 50.

Specimens with grain boundaries inclined at 45°
to the tensile axis and strained at a cross-head speed
of 0.01 cm/min initially deformed in Alpha. Figures 51
and 52 illustrate the extensive deformation in Alpha and
no observable deformation in Beta near the phase boundary
at 37.9% elongation of alpha phase. Cross-slip near the
phase boundary is observed as an indication of phase
boundary playing an effective role in resisting the pro-
gression of slip in Alpha through the phase boundary.
However, the beta grain in contact with the phase boundary
deformed. This is illustrated in Figure 53. Heavy de-
formation in Alpha and slip in Beta in a region near and
away from the phase boundary are shown in Figures 54 and
55. On one of the faces of the specimen, slip in Alpha
interacted with the phase boundary and Beta deformed in
the boundary region. This case was considered to be rare
and was believed to be insignificant. In most cases,
beta grains in contact with the phase boundary and away

from the phase boundary deformed on their own. The

Figure 49.

147

Macrograph Showing Slip in Beta at a Higher
Stress.

Boundary makes 60’to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 12.98 kg/mm2

Elongation in Alpha: 48.9%

IA.

 

J

Figure 49

Figure 50.

148

Macrograph of the Tested Specimen.
Boundary makes 60° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 18.5 kg/mm2

Elongation in Alpha: 90.2%

his

 

r
x

. 1‘”UI‘9

Figure 51.

149

Extensive Deformation in Alpha with no
Observable Deformation in the Beta Region
Adjoining it.

Boundary makes 45° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 9.836 kg/mm2

Elongation in Alpha: 37.9%

 

Figure 51

Figure 52.

150

Cross-Slip in Alpha Occurring at the Inter-
face Regioni

Boundary makes 45° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 9.836 kg/mm2

Elongation in Alpha: 37.9%

 

 

 

Figure 53.

151

Slip in a Beta Grain that was in Contact
with the Boundary.

Boundary makes 45° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 9.836 kg/mm2

Elongation in Alpha: 37.9%

 

 

Figure 53

Figure 54.

152

Interaction of Slip in Alpha with the
Boundary. Beta has Deformed in the Boundary
Region.

Boundary makes 45° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 9.836 kg/mm2

Elongation in Alpha: 37.9%

 

 

 

 

 

 

 

 

   

 

  

Figure 54

 

 

WW“

 

Figure 55.

153

Heavy Deformation in Alpha and Slip in
Beta in a Region away from the Boundary
Boundary makes 45° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 9.836 kg/mm2

Elongation in Alpha: 37.9%

 

,m
3...

ndéfi

 

axis

ulgure 55

154

severity of deformation in beta grains in regions away
from the phase boundary, shown in Figure 56, was much
more pronounced compared with the deformed beta region
near the phase boundary as shown in Figure 54, the
latter is a result of the interaction of Slip in Alpha
with the phase boundary.

Specimens with phase boundary orientations of 30°
with respect to the tensile axis and strained at cross-
head speed of 0.01 cm/min, initially deformed in Alpha by
Single slip. One of the specimens was photographed after
24.8% elongation in Alpha. Figure 57 illustrates the
interaction of slip in Alpha with the phase boundary on
one of the faces. There is no observable deformation in
Beta near the phase boundary. Figures 58 (a) and (b) are
the micrographs of another face showing the interaction
of slip in Alpha with the phase boundary. Deformation
seems to have gone through the phase boundary. This
observation suggests that the orientation relationship
required between the Alpha and Beta for Slip propagation

through the boundary to occur was satisfied. That is:

(110)8||(111)a and <111>B|k110>a .

Beta regions away from the phase boundary and a grain in
contact with Alpha were also deformed more severely than
the region near the phase boundary on one of the faces.

IFigures 59 and 60 illustrate the deformation of beta regions

Figure 56.

 

155

Macrographs Showing Extensive Slip in Beta
Regions away from the Boundary.

Boundary makes 45° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 9.836 kg/mm2

Elongation in Alpha: 37.9%

 

A. HAHCHom mm.

Figure 57.

156

Interaction of Single Slip in Alpha with
the Boundary.

Boundary makes 30° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 8.52 kg/mm2

Elongation in Alpha: 24.8%

 

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ure 5?

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Figure 58.

157

Interaction of Single Slip in Alpha with
the Boundary. (Deformation seems to have
progressed through the boundary).
Boundary makes 30° to the tensile axis.
Cross-head speed: 0.01 cm/min

Stress: 8.52 kg/mm2

Elongation in Alpha: 24.8%

 

 

58

Figure

Figure 59.

158

Macrographs of Slip in Beta in a Region away
from the Boundary.

Boundary makes 30’to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 8.52 kg/mm2

Elongation in Alpha: 24.8%

 

 

 

 

T.A.

2mm

 

Figure 59

Figure 60.

159

Slip in the Beta Grain that was in Contact
with Alpha.

Boundary makes 30° to the tensile axis
Cross-head speed: 0.01 cm/min

Stress: 8.52 kg/mm2

Elongation in Alpha: 24.8%

 

 

 

Figure 60

160

away from the boundary and in the beta grain that was in
contact with Alpha. Table XIII contains the data on the
deformation behavior of alpha-beta brass bicrystals with

inclined boundaries.

Summary

In specimens having their phase boundaries per-
pendicular to the tensile axis, deformation of Beta is
initiated by the interaction of slip in Alpha with the
phase boundary. In Specimens with inclined boundaries,
the interaction of slip in Alpha with the phase boundaries
is not the motivating force for creating large scale
deformation in Beta. In such specimens slip in Beta
normally occurs on its own. This result may be from the
Shear stresses acting on the inclined boundaries.

Even in specimens with perpendicular boundaries,
there can be shear stresses at the phase boundary during
deformation because of the phase boundary of the phases
involved. However, the results obtained with inclined
boundary specimens, in which the boundary experiences
shear stresses during loading, are quite different from
those observed in perpendicular boundary specimens. This
observation suggests that the shear stresses caused by

anisotropy are not of significance.

161

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