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This is to certify that the

dissertation entitled

THE EFFECT OF OVERLOAD 0N THREE
DIFFERENT KINDS OF STEEL

presented by
MOHAMMAD GHO BAD I

has been accepted towards fulfillment
of the requirements for

Ph. 0. degreein Mito‘“w%3

 

 

Major professor

QMJMM ’
, / 7
Date Jfr/fi/XL’L

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

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2“-'*,-“**°;*-‘ r r 1:: m: T ‘y
in 9‘}? ' '

 

 

 

THE EFFECT OF OVERLOAD ON THREE
DIFFERENT KINDS OF STEEL

By

Hoke-med Ghobedi

A DISSERTATION

Submitted to
liehigen State University
in pertiel fulfillment for the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Ietellnrzy. lecheniee end Heteriele Science

1984

THE.EFFECT'OF(NHHHJNU)ON THREE
DIMT mm 0F Sim.

By

lbhemmmd Ghobedi

Ariel strein controlled tests were performed on plein cerhon
steels (1018. 1020. end 1030 steels) specimens of three different
geometries in order to determine the effect of initiel end periodic
overloediu; on fetigue properties end microstructures. The overloed
wes epplied in the renge thet wes expected to hsve e significent
effect. the merimum strein emplitude being one percent. To study the
effect of cycling on the microstructure, some of the specimens were
polished end etched. end plestic replices were teken et reguler inter-

vels during the fetigue test.

Initiel overstreiu resulted in e decreese of the fetigue life of
ell specimens. For 1020 end 1030 specimens periodic overstrein
resulted in even shorter life. while 1018 specimens were not effected

by periodic overstrein.

Processed replices showed thet fetigue microcrecks initiete end
prOpegete more repidly in the coerser greins of 1020 end 1030 speci-

mens competed with 1018 specimens.

TABLE OF CONTWTS

Pepe

LIST OF TABLES ....................................................iii
LIST OF FIGURES ....................................................iv
GAPTER 1 INTRODUCTION ..............................................1
CHAPTER 2 GWERAL REVIEW ............................................6
2.1 MINEERING CONSIDERATION OF FATIGUE .......................6

2.2 BAN STRESS ................................................7

2.3 INITIAL AND PERIODIC OVRLOAD ..............................9

2.4 EFFECT OF LOAD HISTORY 0N 'lHE FATIGUE PROPERTIES ..........12

2.5 ETALLURGICAL ASPECTS OF FATIGUE ..........................13
CHAPI'ER3 ..........................................................19
3.1 FATIGUE DAMAGE ANALYSIS TECHNIQUES ........................19

3.2 SHESS-SIRAIN HYSTERESIS LOOPS ............................22

3.3 CYCLIC HARDENING AND SOF'I'DIING ............................22

3.4 STRAIN LIFE ANALYSIS ......................................26
CHAPTER4 MATERIALS AND SECIIENS ..................................29
CHAPTER 5 EXPERIWTAL ECHNIQUE ...................................37
CHAPTER 6 RESULTS AND DISCUSSION ...................................53
6.1 FATIGUE TEST RESULTS ...........................................53
6.2 SURFACE DAIAGE ................................................102
6.2.1 NIGOS'IRUCTURE 0F NCNSTRAIN. SPECIES ................103
6.2.2 IIGOS'IRUCI‘URE OF NCN-OVHSTRAINED SPECIES ...........105

6.2.3 mnm wmsmmmc OOOOOOOOOOOOOOOOO0.0.0.00000000000122

6.2.4 mRIODIC ovmsmmmc 0.0.0000...0.0.00.0...0.0.0.0....137
CHAPTER 7 SUMMARY AND CONCLUSIONS .................................152

was 0.0.0..0.00....0..0.0...0..OOOOOOOOOOOOOOOOOOOOOO0.00.00155

ii

Thhle
4.1

4.2

6.1.1
6.1.2
6.1.3
6.1.4
6.1.5
6.1.6
6.1.7
6.1.8

6.1.9

6.1.10

6 .1 .11

6.1.12

LIST OF TABLES

Pege
Chemicel Composition of the Specimens ......................30
lechenicel Properties of Specimens Isteriels es received ...30
OONSTANT'STRAIN AIPLITUDE DATA FOR BAR STEEL SPECIMENS......54
INITIAL OVERSTRAJN DATA FOR BAR STEEL SFECIIENS ............55
PERIODIC OVERSTRAIN DATA.FOR BAR STEEL SPECIIENS ...........56
OONSTANT'STRAIN AIRLITUDE DATA FOR.THJN SHEET SPECIMENS ....57
INITIAL OVERS'IRAIN DATA FOR THIN SHEET SPECIIIENS ...........58
PERIODIC OVERSTRAIN DATA.FOR.THIN SHEET SPECIMENS ..........59
CONSTANT STRAIN AMPLITUDE DATA FOR THICK SHEET SPECIMENS ...60
INITIAL OVERS'mAlN DATA FOR THICK SHEET SPECIMENS .........61
PERIODIC OVERS'mAlN DATA FOR THICK SHEET SPECIES .........62
Cyclic stress-strein end fetigue properties of
Ber Steel Specimens ........................................94
Cyclic stress-strein end fetigue properties of
Thin Sheet Steel Specimens .................................94
Cyclic stress-strein sud fetigue properties of

nick St.°l specil.n‘ 00......0....00......0.0.0.0000000000095

iii

Figure

2.1

2.2

3.1

3.2

3.3

4.1

4.2

4.3

5.1

5.2

5.3

5.5

LIST OF FIGURES

Pege
Slip in ductile metels due to externel loeds.
(e) Stetic. steedy stress. (b) Cyclic stress...............17
Schemetic Extrusion in e slip bend..........................17
Schemetic of e Stress-Strein Hysteresis Loop................23
Stress-Strein Loops for Stress Control
(e) Cyclic Softening (h) Cyclic Herdening...................25
Stress-Strein Loops for Strein Control
(e) Cyclic Softening (b) Cyclic Herdening...................25
Strein-Life Curves showing Totel.
Elestic end Plestic Components..............................28
Specimen Configuretion of Flet Sheet Specimens .............31
Specimen Configuretion of Thin Sheet Specimens .............33
Specimen Configuretion of Cylindricel Specimens ............33
Pictoriel representetion of flet specimens..................34
An ideelized cycling test system which wes
used for ell tests .........................................38
Sheet Steel Specimen end Ertensometer.......................40
(e) Sheet Steel Specimen mounted in loed frem
(b) Sheet Steel Specimen.mounted in loed frem
with ertensometer etteched .................................4l
Schemetic of ene10g computer strein ciruit .................43

Specimen. Grips end Shims for thin sheet specimens..........45

iv

5.6

5.7

6.1.1

6.1.1

6.1.2

6.1.3

6.1.4

6.1.5

6.1.6

6.1.7

6.1.8

6.1.9

6.1.10

6.1.11

Test fecility:

Loed frem. I?! plotter. ITS control

“it .nd “.108 computotOOOOOOOOO0.00.00.00.00...0.0.0.0....46

Indicetion of crecked specimen by irregulerity

in compressive helf of hysteresis loop .....................49

(e) Stress-Strein response of Specimen F.S.36

( N s 1 end 2 )

OO..0...OOIOOOOOOOIOOOOOOOOOCOOO.00.0.0.000063

(b) Stress-Strein response of Specimen F.S.36

( N'- 1000 )

0.000000000000000...0.00.0.0...0.0.0.000000000063

Stress-Strein response of Specimen B.S.25

Darin“ . Can't.nt .tr‘in t0‘t eeeeeeeeeeeeeeeeeeeeeeeeeeeeee65

Stress-Strein response of SPecimen F.S.20

Durin Initi‘l-WOr.tr‘in To'tOOOOOOOOOOOOOOO0.0.0.000000000066

Stress-Strein response of Specimen F.S.14

Durin‘ P’tiOdic OVCtBtrIin T..t eeeeeeeeeeeeeeeeeeeeeeeeeeee67

Life History
Subjected to
Life History
Subjected to
Life History
Subjected to
Life History
Subjected to
Life History
Subjected to
Life History

Subjected to

Plot of Her Steel Specimen 6

Constent Strein Cycling .......................71
Plot of Her Steel Specimen.20

Initiel 0verstreining..........................72
Plot of Ber Steel Specimen 3

Periodic Overstreining ........................73
Plot of Thin Sheet Specimen 24

Constent Strein Cycling........................74
Plot of Thin Sheet Specimen 22

Initiel Overstreining .........................75
Plot of Thin Sheet Specimen 25

Periodic Overstreining ........................76

Stress Amplitude versus Reversels of Her Steel

V

6.1.12

6.1.13

6.1.14

6.1.15

6.1.16

6.1.17

6.1.18

6.1.19

6.1.20

6 .1 .21

6.1.22

6.1.23

6.1.24

6.1.25

Specimen for Constent Strein Test...........................77
Stress Amplitude versus Reversels of Thin Sheet

Specimen for Constent Strein Test ..........................78
Stress Amplitude versus Reversels of Thick Sheet

Steel Specimens for Constent Strein Test ...................79
Plestic strein history of specimen B.S.25 Cycled

et Constent Amplitude of 0.001% ............................81

Plestic strein history of specimen.B.S.12

which receiving Initiel Overstrein followed

by 0.001% Strein Amplitude Cycling .........................81
Plestic strein history of specimen B.S.21

which Periodicelly Overstreined ............................82
Right portion of Figure 6.1.16 .............................82
Plestic strein history of specimen T.S.24

Cycled et constent strein emplitude of 0.0008 ..............84
Plestic strein history of specimen T.S.22 which

receiving initiel overstrein followed by 0.00085 ...........84
Plestic strein history of specimen T.S.25

which periodicelly overstreined ............................85
Right portion of Figure 6.1.20 .............................85
Plestic strein history of specimen F.S.2 cycled

et constent strein emplitude of 0.001 ......................86
Plestic strein history of specimen F.S.20 which receiving
initiel overstrein followed by 0.00084 emplitude cycling ...86
Plestic strein history of specimen F.S.17

which periodicelly overstreined ............................87
Right portion of Figure 6.1.24 .............................87

vi

6.1.26

6.1.27

6.1.28

6.1.29

6.1.30

6.1.31

6.1.32

6.1.33

6.1.34

6.1.35

6.1.36

6.1.37

6.1.38

6.1.39

Stress-plestic strein emplitude dete from constent

strein test results of Ber Steel Specimens .................89
Stress-plestic strein emplitude dete from Ber Steel

Specimens subjected to initiel overstreins .................89
Stress-plestic strein emplitude dete from Ber steel

specimens subjected to periodic cyclic overstreins .........90
Stress-plestic strein emplitude dete from constent

strein test of Thin Sheet Steel Specimens ..................90
Stress-plestic strein emplitude dete from Sheet

Steel Specimens subjected to initiel overstreins ...........91
Stress-plestic strein emplitude dete from Sheet Steel
Specimens subjected to periodic cyclic overstreins .........91
Stress-plestic strein emplitude dete from constent

strein test of Thick Sheet Steel Specimens .................92
Stress-plestic strein emplitude dete from Thick Sheet

Steel Specimens subjected to initiel overstreins ...........92
Stress-plestic strein emplitude dete from Thick Sheet

Steel Specimens subjected to periodic cyclic overstrein ....97
Strein-reversels to feilure for Her Steel

Specimens (no overstreining) ...............................97
Strein-reversels to feilure for Her Steel

Specimens subjected to initiel overstreins .................98
Strein-reversels to feilure for Ber Steel

Specimens subjected to periodic cyclic overstreins .........98
Strein-reversels to feilure dete for Sheet Steel

Specimens (no overstrein) ..................................99
Strein-reversels to feilure dete for Sheet Steel

vii

6.1.40

6.1.41

6.1.42

6.1.43

6.2.1
6.2 .2
6.2.3
6.2 .4

6.2 .5

6.2.6
6.2.7
6.2.8
6.2.9
6.2.10
6.2.11
6.2.12
6.2.13
6.2.14
6.2.15
6.2.16

6.2.17

Specimens subjected
Strein-reversels to
Specimens subjected
Strein-reversels to
Sheet Specimens (no
Strein-reversels to
Specimens subjected

Strein-reversels to

feilure dete for Thick

to initiel overstreins .................99
feilure dete for Sheet Steel

to periodic cyclic overstreins ........100

ovcr'tr‘in) ...OOIOOCOOOOOOOOOOOO0.0.0.100
feilure dete for Thick Sheet
to initiel overstreins ................101

feilure dete for Thick Sheet

Specimens subjected t periodic cyclic overstreins .........101

TEN Replice Nicrogreph of 1018 Steel Before test ..........103

TEH'Replice Hicrogreph of 1020 Steel Before test ..........103

TEN Replice Hicrogreph of 1230 Steel es received ..........106

TEN Replice Hicrogreph of 1230 Steel After Anneeling ......106

A typicel Hicrogreph of Specimens After

”ch.ni°‘l Paliains OO...OOOOOOOOOOOOOOOOOOOOO00.00.00.000107

licrostructure
Hicrostructure
licrostructure
Hicrostructure
licrostructure
Hicrostructure
Iicrostructure
licrostructure
Iicrostructure
licrostructure
Hicrostructure

Hicrostructure

of

of

of

of

of

of

of

of

of

of

of

of

B.S.27
B.S.27
B.S.27
B.S.27
3.8.27
8.8.22
3.8.22
3.8.25
3.8.25
T.S.16
T.S.16

T. 8.16

After
After
After
After
After
After
After
After
After
After
After

After

viii

100.000 Cycles

500.000 Cycles

0.0.00.000000107

00.00.00.0000109

100000000 CYCIOS eeeeeeeeeeelog

2.000.000 Cycles ...........110

F‘ilu. 0.0.00.0000000000000110

100.000 Cycles
500.000 Cycles
100.000 Cycles
500.000 Cycles
100.000 Cycles

500.000 Cycles

.............111
.............111
.............112
.............112
.............114

0.00.00.00.00114

F‘il“. 0.0.0.00000000000000115

6.2.18
6.2.19
6.2.20
6.2.21
6.2.22
6.2.23
6.2.24
6.2.25
6.2.26
6.2.27
6.2.28
6.2.29
6.2.30
6.2.31
6.2.32
6.2.33
6.2.34
6.2.35
6.2.36
6.2.37
6.2.38
6.2.39
6.2.40
6.2.41
6.2.42
6.2.43

6.2.44

Hicrostructure
licrostructure
licrostructure
licrostructure
Iicrostructure
Hicrostructure
Ricrostructure
Hicrcstructure
Hicrostructure
Hicrostructure
Hicrostructure
Iicrostructure
Nicrostructure
licrostructure
Ricrostructure
licrostructure
Hicrostructure
Iicrostructure
Hicrostructure
Hicrcstructure
Hicrostructure
Ricrostructure
licrostructure
Hicrostructure
Hicrostructure
Hicrostructure

Nicrostructure

of T.S.18 After 5.000.000 Cycles ...........115

OfFOSO4 Aft.‘ 300.000 cyclo‘ .00000000000000118

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

of

F0804 “to: 400.000 cycl.‘ .0000000000000118

F0804 Aft.’ 500,00 cycl.. .00000000000000119

F0304 Aft.t F.ilu. 00.00.00.000000000000119

F's.‘ “tar F‘ilua .00000000000000000000120

F.S.11
F.S.11
F.S.10
F.S.16
8.8.16
8.8.17
3.8.20
3.8.20
3.8.12
3.8.12
T.S.19
T.S.19
T.S.19
T.S.10
T.S.10
F.S.20
F.S.20
F.S.20
F.S.16
F.S.16

F.S.13

ix

After
After
After
After
After
After
After
After
After
After
After
After
After
After
After
After
After
After
After
After

After

50.000 Cycles ..............120
Feilure ....................122
FAilure ....................122
Initiel Overstrein .........124
5.200.000 Cycles ...........l24
5.400.000 Cycles ...........126
100.000 Cycles .............l26
800.000 Cycles .............127
100.00 Cycles ..............127
500.000 Cycles .............128
Initiel Overstrein .........128
200.000 Cycles .............130
Feilure ....................130
200.000 Cycles .............131
Feilure ....................l31
Initiel Overstrein .........133
1.000.000 Cycles ...........133
12.206.494 Cycles ..........134
Cycles .....................l34

F‘llu. 00.00.00.00000000000135

1000000 CYOIOI eeeeeeeeeeee0135

6.2.45
6.2.46
6.2.47
6.2.48
6.2.49
6.2.50
6.2.51
6.2.52
6.2.53
6.2.54
6.2.55
6.2.56
6.2.57
6.2.58
6.2.59
6.2.60
6.2.61
6.2.62
6.2.63
6.2.64
6.2.65

6.2.66

licrostructure
licrostructure
licrcstructure
licrostructure
Iicrostructure
Hicrostructure
licrostructure
licrostructure
Hicrostructure
Hicrostructure
Hicrostructure
Hicrostructure
Hicrostructure
Hicrostructure
licrostructure
Hicrostructure
Hicrostructure
licrostructure
Hicrostructure

Hicrostructure

.f
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of

of

F.S.13 “to: F.11u. 0.0.0.00000000000000136

3.8.5 “to: Third 07.“tr.in 00.00.000.00136

8.8.5 After Seventh Overstrein ..........138

3.8.5 After Sixteenth Overstrein ........138

3.8.23
8.8.23
8.8.23
T.S.23
T.S.23
T.S.23
T.S.23
T. 8.23
F.8.17
F.S.17
F.S.17
F.S.18
F.S.18
F.S.18
F.S.12

F.S.12

After
After
After
After
After
After
After
After
After
After
After
After
After
After
After

After

Second Overstrein ..........l40
Fourth Overstrein ..........140
Sixth Overstrein ...........l41
Second Overstrein ..........141
Fourth Overstrein ..........142
Sixth Overstrein ...........142
Seventh Overstrein .........143
Feilure ....................143
Second Overstrein ..........144
Tenth Overstrein ...........144
Feilure ....................145
Second Overstrein ..........145
Fifth Overstrein ...........147
Feilure ....................147
Second Overstrein ..........l48

Third Overstrein ...........148

The seme es 6.2.64 but higher legnificetion ...............149

Iicrostructure of F.S.12 After Feilure ....................148

CHAPTER 1

INTRODUCTION

The term fatigue is used to describe the behavior of a material
that is subjected to a cyclically varying load of sufficiently large
magnitude such that the material fails. What constitutes failure
depends on the problem. but in general. failure means the fracture of
the component. At any rate. some detectable change in mechanical

behavior of the material must take place.

Generally speaking. fatigue consists of three stages: crack ini-
tiation. crack growth. and fracture. These stages sometimes overlap.
In the conventional fatigue test. a particular type of specimen is
subjected to a cyclic load with constant stress or strain emplitude
and its life. i.e.. the number of cycles to failure. is determined.
In practice. conditions are different. For example a mechanism. espe-
cially a high speed one. is usually subjected to a loading program
which varies continuously with time. In such circumstances. it is
very likely that a member will be subjected to a very high stresses in

some portion of the loading program while experiencing idling or rest

intervals et some other part of the program. The stress history built
up is thus a very complicated one. The harmful or beneficial effects
of such a complex loading program cute member cannot be related to any
level of stress. More sophisticated tests are thus required. and much
work has been done in this direction. Before describing these. a few

introductory remarks are in order.

Nearly all machine. engine and structural components are subject-
ed to loads which result in stresses higher than their rated stresses.
Such high loads are to a great extent occasional and are called over-

loading.

The effects of overloading depend on the magnitude of overload or
overstrein and. in the case of cyclic overload. on the number of
cycles. It has been observed in practice and confirmed by laboratory
investigation that overloading usually decreases the strength of
metalsll] and machine components which have been most highly overload-

ed are bound to fail during further service at normal loads.

The term overload as defined above is not precise enough. so the
following definition will be adopted in this work. A specimen is said
to have been overloaded (or overstreined) if the elastic strain is
negligible in comparison with plastic strain. The following defini-
tions are also used. If the specimen is subjected to an overload at
the beginning of the experiment. it is said to have been initially

overstreined. Periodic overstrein means that the specimen is over-

strained repeatedly during the experiment such that two successive
overstreins are separated by a block of cyclic straining with a lower
amplitude. The term no—overstrein is. of course. self explanatory.
Overstreining. or overloading. end its effects on the fatigue life are
not well understood. Consequently. no quantitative and generally
accepted rules are aveilable[2]. But as design stresses are raised
and the service life of many components is increased. the influence of

occasional cycles of overload has become increasingly importantl2.3].

The results published to date indicate that. for several materi-
als. application of short initial blocks of high strein cycles result
in a reduction of the fatigue life at subsequent low strain levels.
On the other hand. periodic overstreining. especially during fatigue
crack propagation. has a beneficial effect since it usually slows down
the propagation process[4.5]. But this is not always the case. There
is evidence that the crack propagation rate under periodic overstrein-
ing is 100 times higher then the rate under steedy strein
conditionll]. Such an overload or overstrein can cause considerable

reduction in fatigue lifel6].

The results referred to above are clearly phenomenological. No
serious attempt has been made to examine the microstructural changes.
In the work reported here. microstructural examination has been under-
taken and correlation between the microstructural changes and observed

phenomena attempted.

In this investigation three different kinds of specimens. smooth
round hour-glass. thickrsheet hour-glass. and thin-sheet hour-glass
profile. were prepared for fatigue testing to failure at room tempera-
ture. The specimens were made from the following grades of low carbon
alloy structural steels: 1018. 1032. and 1020. respectively. These
were chosen because of their wide use in structures and machinery.
Furthermore. their microstructures are relativly simple. thus making
the metalcgrephical examinations easier. The experimental program
consisted of three series of tests for each kind of specimens. namely:

no overstrein. initiel overstrein and periodic overstrein.

Since the surface grains are weaker compared with those inside
the specimen. the changes start on the surface of the specimen.
Because the initial changes in surface appearance. which result from
fatigue action. are apparently extremely minute. methods which could
reveal very small changes in surface appearance were employed. It was
possible to display changes at an early stage. and to follow the
course of these changes to the final. complete failure of the speci-
men. This was accomplished by using polished fatigue specimens. a
simple plastic replica technique. and cpticel and electron microscope

examinations.

The parameters under study were initiel overloads and periodic
overloads. Their effects on the fatigue life of three steels were
demonstrated. The investigation consisted of both phenomological stu-

dies and direct microscopic observations of the fatigue process.

An attempt was made to compare the effects of periodic
overstreining and initial overstreining with the case of

non-overstreining on the life of each specimens.

CHAPTER 2

GENERAL REVIEW

In this chapter a brief review of litreature is presented and
some of the results obtained in previous investigations is briefly

discussed.

Fatigue is the main cause of most mechanical failures encountered
in engineering practice. In the study of this phenomenon. it is con-

venient to treat the engineering and metallurgical aspects separately.

24; ENGINEERING CONSIDERATION OF: FATIGUE

Systematic investigations of fatigue began with the work of
A. W3hler in 1852(7] and has been pursued intensively ever since.
Much of the early work on fatigue is concerned with the determination
of the fatigue (or endurance) limit. This is the maximum value of
uniaxial cyclic stress below which no failure will occur. As men-
tioned in the introduction. the concept of endurance limit. while of
importance. is not adequate. This is because the loading of most

structural and machine elements are far more complex than the simple

loading conditions under which the usual fatigue tests are performed.
Furthermore. as will be discussed. the endurance limit itself depends
on the loading history. It is thus clear that for a better under-
standing of the fatigue phenomenon. the effects of factors influencing
it must be studied. The list of such factors is rather extensive and
thus all of them cannot be discussed here. In the following. the most
important of these factors will be considered and the results.that are

reported in the literature briefly discussed.

The factors to be discussed are mean stress. initial overstrein.
and periodic overstrein. The effect of loading history on the endu-
rance limit and the question of fluctuating load amplitudes will be

briefly discussed.

gins mass

 

In any real life fatigue problem. some mean stress or mean strain
is present. In many cases. both mean stress and mean strain are
present. It is well-known that the mean stress influences the fatigue
life. For instance. tensile mean stresses shorten the fatigue life.
while compressive mean stresses lengthen it. The process by which
this comes about is not well understood. but alternate hypotheses
abound. It has been suggested that stable stress-strain behavior. the
rate of crack initiation. the size of the shear crack required to
start a normal mode crack. the rate of prepegation. and the crack sire

necessary to cause rupture are all influenced by the mean

stress[3.6.8]. But this hypothesis has not been accepted by everyone.
Some have argued that the amplitude of shear stress is the only factor
influencing crack initiation and that mean stress has no effectl8].
It is widely believed that. for crack propagation. a tensile stress
must be present. Therefore. during compressive cycling. a crack may

initiate but it cannot propagate.

Since (for constant amplitude) the critical crack sire is
inversely prOportional to the maximum tensile stress. one sees that
the number of cycles required to produce a crack of critical size is
smaller with a tensile mean stress than with zero or compressive mean

stress.

The damage caused by occasional mean stress blocks is similar to
that which results from initial overstreins provided that these blocks
cause appreciable deformationl8]. Therefore. a loading with a com-
pressive mean stress applied for a short block will cause the same
damage as a few high strain cycles. Watson and Topperl3] have shown
that. for short overload blocks. the sign of the mean stress has very

little effect.

Topper and Sendorl6] conducted two experiments. In the first one
the specimens were subjected to a stress pattern consisting of blocks
of fully reversed cycles (i.e. no mean stress) followed by one cycle
with some tensile mean stress. In the second experiment the specimens

were cycled under a constant tensile mean stress. The total number of

cycles in both experiments were the same. Chmparison of the results
were showed that the damage suffered by the specimen in the first
experiment was half the damage suffered by the ones in the second
experiment. This shows that most of the plastic straining caused by
mean stress occurs during the first cycle. In other words. the
remaining cycles do not have a very significant effect and hence their

removal will not reduce the amount of damage appreciably.

In the presence of mean stresses. the experimental data show sig-
nificant deviations from damage summation calculations (based on
completely reversed strain-life data with constant amplitude)[9]. The
present state of knowledge is not sufficient to make any quantitative
predictions regarding the effects of mean stress on fatigue damage.
The work of Topper et al[3] indicates that. at strain levels high
enough to cause appreciable repeated plastic straining. the effect of
mean stresses is somewhat diminished and damage summations are nearly
one. However. when large plastic strains are followed by strains in
the elastic range. the effect of mean stresses is appreciable and

values show considerable deviations from one.

_2_,_3_ INITIAL sup PERIODIC ovmow

A.machine or structural element is occasionally subjected to
loads which result in appreciable amounts of plastic strain. This. as
pointed out in the Introduction. is called overloading. The plastic

strain thus developed has a considerable effect on the fatigue proper-

10

ties and has thus attracted the attention of many investigators. A
comprehensive study of initial overloading has been done by
KonmerllO-lZ]. His conclusions may be summarized as follows. For a
given cycle ratio. a high initial overstress followed by a lower
stress (in some cases) show equal damage to endurance life at the high

and low stresses.

On the other hand. if the initial overstress and cycle ratio is
low. an actual increase of the normal endurance life at subsequent
higher stresses can be observed. Furthermore. it has been shown that.
in the case of steel. specimens of higher tensile strength and lower
ductility are more sensitive to damage than those of lower strength
and higher ductilityllZ]. Finally. it has been demonstrated that a
low initial overstress will cause equal damage to endurance life at a
subsequent higher stress. while a high initial overstress can cause
much more than equal damage to endurance life at a subsequent lower
stress. The work of Watson et alll3] concerning the effects of over-
streining on the fatigue life of five different kinds of steels:
SAE-1015 steel. CSA 64012. 9501. VAN-80 and ADS-1122: has shown that
as a result of overstreining the fatigue life is drastically reduced
near the fatigue limit. For three of these steels. the damaging
effect is reduced with the increase in succeeding strain levels.
SAE-lOlS suffers the most damage as a result of overstreining. while
VAN-80 appears to be unaffected by it. However. there is a consider-
able body of literature which shows that the fatigue life is improved

when high amplitude pro-load or pro-strain is applied. Results.

11

reported in a paper by Belyaevl2] on the effect of overloading on the
fatigue life. indicate that prolonged overloading causes the failure
of the component while a short overloading may result in its harden-

ing.

Thrning next to the effects of periodic overstrein. there is some
evidence that periodic overloading can result in higher fatigue resis-

tance under variable amplitude conditions.

The results obtained by Schijve[5] from work on Aluminum 2024-T3
Alclod and 7075-T6 Clad sheet show that an increase in the maximum
stress increases the subsequent life-to-failure. Ditschum[4] has
observed that periodic overstreining of ferrovac E leads to a higher
fatigue life compared with the material that has been subjected only
to an initial overstrein. 0n the other hand. the fatigue life of this
material is only slightly increased if it undergoes constant amplitude

cycling.

The work of Watson et alll4] on periodic overloads on mild steels
has shown that. in the absence of residual stresses. periodic high
overstreins cause appreciable fatigue damage and reduction of life.
This can be explained by the fact that overstrein accelerates Stage I.

and to a lesser extent. Stage II of crack growth.

12

As mentioned previously. fatigue properties are extremely
history-dependent. Bennet[15] investigated this history dependence by
subjecting a series of specimens to initial overload and then retest-
ing them at a second stress level and observing the relative number of
cycles to failure. 0n the basis of his experiments. Bonnet reached
the conclusion that. when a specimen is loaded at different stress
levels. the apparent rate of damage depends on the value of both
stresses. He observed that. if the damage caused by one stress level
is measured by the demage occuring at a subsequent stress level. the
overall damage is dependent on both stress levels. Specifically. if
the initial stress is higher than the stress applied subsequently. the
damage suffered is higher and it decreases later. The opposite is the
case when the specimen is first subjected to a low stress and then to
a higher one. These and other results obtained by Bonnet and Konmers
lead to the conclusion that the fatigue limit is a function of stress
history of the component. More generally. load history must be taken
into account when determining the fatigue preperties of a material.
Dolan et al[16] performed a number of tests to failure on SAE-2340.
SAE-1045 and 758-T aluminum alloy on both notched and unnotched pol-
ished specimens. They reached the following conclusions. For ferrous
metals. the fatigue limit is highly dependent on stress history. and
it is therefore not well-defined. Generally. repetitions of an under-
stress alternated with repetitions of a stress 10 to 20 percent above

the original fatigue limit. result in an appreciable increase in fati-

13

gue life. This can be interpreted as an increase in fatigue limit.

Recent investigations have shed some light on the problems
encountered in complex history analysis. It is now recognized that
difficulties encountered are mostly due to the fact the sequence
effects were not prOperly taken into account in the early work in this
area since much of this work was concerned with determining the effect
of overloading.on the fatigue limit[8.l7]. The results obtained from
these investigations have indicated both beneficial and detrimental

effects. and this has led to confusion.

As was pointed out in the Introduction. the crack initiation and
propagation which leads to the fracture of a component is of great
importance in the study of fatigue. These phenomena are explained in
terms of metallurgical concepts. The remainder of this chapter is
devoted to a brief examination of these concepts and their signifi-

cance e

245 IETALLURGICAL ASPECTS QB FATIGUE

The process of crack nucleation starts with slip. In some grains
the slip bands form very fine cracks which can be seen only at very
high magnification. As the body undergoes cyclical loading. the
cracks grow and combine into a few major cracks which can be seen with
the unaided eye. The growth of a crack (or cracks) continues until a

critical size is reached and fracture occurs suddenly. The speed at

14
which these processes take place depends on the magnitude of the
stress. If stress is increased. the speed would likewise be

increased.

Crack initiations follow the occurrence of slip in grains[18].
It is evident that the microstructure of a metal has great influence
on its behavior under cyclic loading. It should also be realised that
the microstructure of a metal can be altered by cyclic deformations.
These alterations may have great influence on the fatigue performance

of a material.

Most structural metals are made up of a large number of ordered
crytels or grains. Such materials are called polycrystalline. Two
different grains are separated by the grain boundaries. which have a
great influence on the behavior of metals under different operating
conditions. It is interesting that. while grain boundaries are
regions where the lattice is imperfect. they are not necessarily

regions of weakness.

It is well-known that the grains are anisotropic and their
mechanical prOperties are. in general. different. Since neighboring
grains have different orientations. the slip planes are not parallel.
As a result. slip is hindered when the metal is strained into the
plastic range. The grains at a free surface are less-constrained than
the grains in the interior of the metals. Accordingly. plastic defor-

mation in surface grains takes place at a lower stress than in

15

internal grains[l9]. Thus. surface grains behave in a more ductile
manner. Since. in most cases. the stress is maximum at the
surface[l9]. it follows that surface grains deform more than the
grains in the interior. It is well-known that fatigue cracks origi-
nate at the free surface. Furthermore the surface is both a favored
place for dislocation movement and a place for the formation of
slip-band grooves. The orientation of some grains is such that the
places of slip and planes of maximum applied shear stress coincide.
In fatigue experiments. slip appears first in those crystals in which
the resolved shear stress on slip planes has the highest value[20].
In ductile metals. dislocations in each grain move along crystallo-
graphic planes and thereby cause slip. Thus. within each grain. there
are one or more planes sliding relative to each other. Slip occurs
both in monotonic and cyclic loadingl21]. Although the slip lines
produced by these two types of loading are in many ways similar. there

are some subtle differences.

The most remarkable difference is that slip bands appear in gro-
ups or striations which are more-or-less evenly spaced in each grain.
These striations first appear after a few thousand cycles. As the
cyclic loading continues. they become broader and more pronounced.
This broadening goes on until either the bands cover the surface of a
particular grain or failure by cracking occurs. If examined under an
electron microscope. the slip bands in a specimen subjected to a
steady stress. are seen to be straight and parallel whereas those in a

specimen subject to fatigue. appear to be curved and generally short-

16

er. This can be clearly seen in Figure 2-1. In general. most of the
directions of the slip lines are the trace of crystallographic plane.
It is interesting that the slip bands produced by fatigue hardly ever
cross the grains. although striations (or grouped bands) sometimes

extend from one grain boundary to another.

Using electron microscopy. it has been shown[19] that both slip
band intrusions and extrusions occur on the surface of a metal subject
to fatigue loading. Figure 2-2 shows a typical extrusion schematical-
ly[22]. Slip band intrusions act as stress raisers causing high
stress concentrations and a natural location for crack initiation.
Shear stresses are the main controlling factor in this type of slip.
If the gross stress (or strain) is raised or the material is subjected
to a larger number of cycles. the number of slip bands and their
lengths increase. It was noted previously that the slip lines are.
for the most part. contained within each grain. As the number of
cycles is increased. more and more slip lines appear and the slip
bands themselves thicken. These "thick" bands are the source of fati-
gue cracks. It is worth noting that slip band intrusion is a local
phenomenon occurring at regions of high stress and strain while most
of the grains of the component may be free of any slip. even at frac-
ture. The removal of several microns from the surface of the
component by electrOpolishing eliminates most of the slip bands. Some
of these slip band do remain and become more distinct. These have
been called persistent slip bands. The number of these persistent

slip bands increases as the cycling goes on. For most metals and

17

Metal

Surface ‘——————---

(a) Steady stress

 

(b) Cyclic stress

Figure 2-1 Slip in ductile metals due to external loads.

(a) Static, steady stress. (b) Cyclic stress.

 

Figure 2-2 Schematic Extrusion in a slip band.

18

alloys there is an apparent fatigue limit associated with the forma-
tion of persistent slip bands. If the stress is not high enough for
their formation. no fracture takes placel23]. It has been observed
that. in a large number of materials. the fatigue cracks initiate in
these persistent slip bands. Very little is known about the mechanism
of slip band production and crack initiation apart from the fact that
cracks always start on the slip planes. which have the highest

resolved shear stress.

The fatigue life of a component can be significantly increased by
removal of persistent slip bands. In some cases. the life of e compo-
nent has been extended indefinitely by intermittent cycling and
electropolishing. These observations strengthen the widely-held view
that fatigue is very much a surface phenomenon and its early stages

are controlled by surface conditions.

CHAPTER 3

I

_3_L1_ FATIGUE DAMAGE ANALYSIS TECHNIQUES

The accurate prediction of fatigue life of metalic components has
long preoccupied fatigue researchers. Various properties of metals.
such as ultimate strength. hardness. true monotonic fracture ductility
and strength. and cyclic stress-strain properties have been used as

indices of fatigue life.

Use of these properties. in conjunction with empirical formulas.
permits an estimation of the approximate account of the phenomenologi-
cal fatigue damage that occurs on smooth specimens subjected to

completely-cyclic loading.

For a given material. one can plot a S-N curve which is a diagram
showing the variation of stress versus the number of cycles to
failure. Using this diagram. the endurance limit and the fatigue life

of the specimen can be determined.

While an S-N curve provides useful information. it is inadequate
for practical problems since. in most cases. a component is subjected

to more than one stress level. The question. then. is how to account

19

20

for varying stress levels in determining the fatigue life of the com-

ponent.

To answer this question. a number of "cumulative damage" theories
have been proposed. In one such theory. it is assumed that no matter
how stress varies from one cycle to the next. the damage will accumu-
late. Demage at each stress level is defined as the number of cycles
divided by the number of cycles that result in failure at that stress
level. Under a complex loading. failure will occur when the sum of
the damage increments reaches one. It is clear that one needs a com-
plete S-N curve for each individual cycle in order to predict the

fatigue life under a complex loading.

It is reasonable to assume that. at any particular stress value.
each cycle contributes an equal amount of damage and. furthermore.
that the cumulative damage under cyclic loading and the net work
absorbed are proportional. These are the assumptions on which one of
the most widely used damage accumulation rules. the so called Miner's
rulel24]. is based. Tb derive this. let W and Nf zgpggggnt the ngt
work absorbed and the number of cycles at failure for some stress
level. Denoting the net work absorbed by the specimen as 'i and the

number of cycles as n1 for the same stress level. one has

vi/v - aimf (3-1)

with

21
E 'i = W or
EwilW = 1. (3-2)
Substituting into this from (3-1). we have:
2 nilei = 1 (3-3)

where Nfi' i = 1..... k. are fatigue lives at given load levels. and

n1. i=1.....k. are the number of cycles acting at each load level.

In addition to assumptions already mentioned. Hiner's rule
assumes that the load is completely reversible with no mean stress.
Furthermore. the damage which occurs is independent of the loading

history. loreover. there is no sequential effect.

Unfortunately. none of these assumptions are quite true. For
instance. experiments contradict the last assumption regarding the
order of amplitude change. Given identical block sizes and ampli-
tudes. the high-to-low causes more damage than the low-to-high one.
That it should be so is reasonable and can be explained. The high
loads initiate cracks which then propagate at lower loads. but smaller

loads cannot initiate cracks as rapidly as the high loads.

Despite its shortcomings. the linear damage accumulation theory

yields fairly accurate results when its basic underlying assumptions

22

are nearly satisfied.

3‘; STRESS-STRAIN HYSTERESIS LOOPS

The stress-strain hysteresis loop. shown schematically in Figure
3-1. is the best means of describing the cyclic behavior of metals.
In a hysteresis loop. the total strain range (As) is twice the strain
amplitude (As/2). and the total stress range (do) is twice the stress
amplitude (Ac/2). The total strain amplitude can be represented as

the sum of its elastic and plastic components:

As/2 = Ace/2 + Asp/2. (3-4)
Using Hook's law one can write

Ac. = Ac/E (3-5)
where E is Young's modulus and hence

Ac/2 = Ao/ZE + Asp/2. (3-6)
24;,gzgplg HARDENING AND SOFTENING

Application of a completely reversed cyclic load to a metal

results in either hardening or softening depending on its initial con-

dition and the load amplitude. These phenomena are called cyclic

23

 

 

   

 

 

6e 2 A69 A612

 

 

Figure 3-1 Schematic of a Stress-Strain Hysteresis Loop.

24

hardening or softening. After a period of cyclic hardening and sof-
tening. an intermediate strength level is attained. This represents a
cyclicelly stable condition. Fatigue hardening is more complicated
than the work-hardening encountered in the familiar static tests.
This complication is mainly due to the reversal and repetition of
loads. Fatigue tests can be carried out under stress or strain con-
trol. The behavior of the material. however. would be different as
can be seen from the Figures 3-2 and 3-3[25.26]. These Figures show
cyclic stress-strain behavior of an initially annealed metal.
Annealed metals have the characteristic of getting harder when they
are subjected to high strain (or stress) cycling and becoming softer
when subjected to low strain (or stress) cycling. In Figure 3-2 the
cyclic behavior under stress control is depicted. It can be seen
that. as the material softens. the strain amplitude increases. Figure
3-2(b) shows the hardening procedure. Figure 3-3 on the other hand
shows the behavior of the material under strain control. One can get
a fatigue curve by drawing the maximum stress against the number of
cycles in a strain-controlled test. If the specimen is initially

work-hardened. it would soften and cyclic softening would result.

Fatigue softening-hardening characteristics can be shown on
curves that indicate the variations of stress versus cycles of load-
ing. This curve. which depends on the initial condition of the
material. also shows its equilibrium fatigue behavior. Stable stress

and strain amplitudes can be related by a power law of the forml27l

25

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A I)
1 3 5 5 3
4 2 2 4
(a) (b)
Figure 3-2 Stress-Strain Loops for Stress Control
(a) Cyclic Sofening (b) Cyclic Hardening.
A 1
3
S
4
2
2
z.
(a) (b)

Figure 3-3 Stress-Strain Loops for Strain Control

(a) Cyclic Softening . (b) Cyclic Hardening.

 

26

Ao/2 . x' (Asp/2)“. (3-7)

in which K' is the cyclic strength coefficient and n' the cyclic

strain hardening exponent.

gjg_sasarn LIFE ANALYSIS

 

In experiments carried out at different strain ranges. it has
been observed that if a log-log plot of the stable plastic amplitude.
Asp/2. versus the number of reversals to failure. 2Nf. is drawn. one
will generally get a band of points narrowly scattered about a
straight line. The plastic strain-life data can be related in the

following form:
Asp/2 = ef' (2Nf)° (3-8)

where sf' is the fatigue ductility coefficient and 2Nf is the number
of reversals to failure. In a similar fashion a log-log plot of
stable stress amplitude. Ach. versus the number of reversals to

failure. 2Nf. could be drawn. This again yields a straight line.

From this plot the stress amplitude and life can be related by

the formula:

Ao/Z = of' (zuf)b. (3-9)

27

Dividing (3-4) by the Young's modulus. B. one gets:
Ase/2 = (af'Is) ml.)b (3-10)

which gives the elastic-strain amplitude in terms of fatigue-strength

coeficient. cf'. and the fatigue strength exponent. b.
Substitution of (3-9) and (3-10) into (3-4) yields:
Ae/Z = (af'ls) (2a.)b + ef' (2Nf)°. (3-11)

The above equation. called the strain-life relation. is the foundation

of the cyclic strain-based approach to fatigue.

In Figure 3-4 the heavy curve represents equation (3-11). while
the two straight lines show the elastic strain versus 2Nf and plastic
strain versus 2Nf. The data to be used for drawing these graphs are
obtained from testing smooth specimens to failure under fully reversed

constant amplitude strain control.

The application of the formulas discussed here will be found in

Chapter 6 in connection with the experimental data.

28

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CHAPTER 4

MATERIAL AND SPECIMENS

For the investigations reported here. three widely-used low car—
bon steels were chosen. These were 1018. 1020. and 1030. Detailed
information regarding the chemical compositions and mechanical proper-

ties of these materials is given in Tables 4-1 and 4-2. respectively.

The specimens used were of three different types:

1) Thick-sheet hour-glass specimens. These were made from 1030
sheet steel of 7.62 mm (0.03 inch) thickness. In order to make the
metallogrephical structure of these specimens as similar to the 1018
and 1020 specimen as possible they were heat-treated. Tb accomplish
this. they were annealed at 850° C for 20 minutes in an electric fur-
nace and left to furnace cool. Figure 4-1 shows the dimensions and

geometry of these specimens.
2) Thin hour-glass sheet specimens. These specimens were made

from 1020 sheet steel of 1.78 mm (0.070 inch) nominal thickness. This

material was cold-rolled and annealed. The gage sections of all the

29

30

Table 4-1 Chemical Composition of the Specimens.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

carbon Manganese Phoshorus Sulfur
1018 0.18 0.70 0.20 0.025
1020 0.20 0.41 0.10 0.011
1030 0.30 0.70 0.20 0.025
Weighti
Table 4-2 Mechanical PrOperties of Specimens lateriel as received.
Tensile Yield Elongation Reduction Briuell
Material Strenght Strength in 2 in.. S in area i hardness
psi psi
1018 62 43 20 45 i 120
1020 58 40 20 45 116
1030 73 51 16 39 142

 

 

 

 

 

 

 

 

31

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32

thickrsheet and thin-sheet specimens were parallel to the rolling
direction. Figure 4-2 shows the dimensions and geometry of these thin

sheet specimens.

3) Bar specimens. These specimens were machined from an extruded
bar of 1018 steel of 15.88 mm (0.625 inch) diameter. Figure 4-3 shows
the geometry and dimensions of the bar steel specimens. Although
machining might have caused some surface hardening. no heat-treatment

was done on specimens made of the 1018 and 1020 steels.

The flat side (surface A and B of Figure 4-4) of all 1020 and
1030 specimens. that were chosen for metallogrephical examination.
were polished. The polishing was done in three stages. First. the
specimens were manually polished on 180. 240. 320. 400. and 600 grit
papers. Then. in the second stage. lapping wheels were used. These
wheels were covered with a short-mapped felt cloth and impregnated
with alumina slurry. Alumina particles of 1.0. 0.3. and 0.05 micron
sizes were used for fine polishing. In the second stage of polishing.
the A and B surfaces of all specimens were examined with an optical
microscope to make sure that no circumferential markings were present.
In cases were such markings were found. the polishing was repeated
until they were removed. In view of the fact that cracks generally
initiate at surface damages and irregularities. and the results
obtained from tests on such specimens are questionable. these precau-
tions were very necessary. In order to reduce the likelihood of crack

initiation at the corners. all specimen corners were slightly pol-

33

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Figure 4-2 Specimen Configuration of Thin Sheet Specimens
(1020 Steel).

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Figure 4-3 Specimen Configuration of Cylindrical Specimens (1018 Steel).

(All dimensions are in millimeter).

34

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35

ished. Despite this precaution. the cracks initiated at the corners
in nearly all specimens tested. Finally. all specimens were
electro-polished using a solution of 20 percent perchloric acid and 80
percent glacial acetic acid. The electro-polishing was done at room
temperature with a voltage of 10-20 volts. Once the specimens were
polished. surface replicas were taken of the whole gage length and

were then examined under the microscope and photographed.

In preparing the bar steel specimens. the gage lengths were pol-
ished with 600 grit paper followed by 0.3 and 0.05 micron alumina
powder. To get a mirror-like surface finish. an electro-chemical
reagent of 20 percent perchloric acid and 80 percent glacial acetic
acid was employed. The polishing was done with a stainless steel

cathode and a voltage of 5 to 8 volts. This took about 2-3 minutes.

After electro-polishing. the following reagent was used: nital.
consisting of 5 milliliter nitric acid (HNOB) and 95 milliliter methyl
alcohol(CH3OH). Specimens were immersed in the nital solution for
about thirty seconds at room temperature. This etchant was found to
be very effective in delineating both the grain boundaries and slip

bands.

To obtain more micorostructural details. the specimens were first
etched and then polished and re-etched. In these cases. some surface
material had to be removed since the grain boundaries would otherwise

have appeared wide upon re-etching.

36

Treating the specimen in this way gave a very smooth and polished
surface in which the smallest change could be seen. It had the added
advantage of removing the worked surface layer which is always present
in surfaces that have been polished mechanically. This is important
since the worked surface may effect the fatigue behavior.
Furthermore. as a result of this chemical polishing treatment. many
features of the microstructure of the specimen were revealed. The
study of these features led to the establishment of the relationship
between the structure of the specimen and the starting point of the

fatigue cracks.

CHAPTER 5

EXPERIMENTAL TECHNIQUE

The machine used for testing all specimens was an axial loading
electro-hydraulic closed loop. servo-controlled mechanical test system

with a maximum load capacity of 11 kips (48.928 IN).

The cyclic fatigue data collected for this investigation were
generated under completely reversed strain control with zero mean
strain. A system of the type used is shown in Figure 5-1. The com-
mand signal used in the investigations was a sine function. In each
test. the frequency was the highest possible frequency compatible with
preservation of amplitude and prevention of the distortion of the hys-
teresis loop. When taking data. the frequency was lowered to between

0.1 to 0.2 Hz.

Tb measure strain in the 1018 bar steel specimens and 1032 thick
sheet specimens. a clip-on extensometer was directly attached to the
specimens. The gage length over which the strain was measured was 0.5

inch.

37

38

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Figure 5-1 An idealized cycling test system which was used for all tests

39

Tb prevent slippage of the knife edges and reduce contact
stresses at the points where these were attached to the specimen. a

soft plastic tape was wound around the specimens.

Occasionally the extensometer drifted because the knife edges had
not settled completely into the plastic tape. In such cases. enough
time (10 to 15 minutes) was allowed for the effects of creep to die

out.

Because of the relatively small thinness (which creates a problem
with buckling) and small gage length of the 1020 sheet steel speci-
mens. the attachment of an extensometer similar to that used for the
other two types of specimens was not possible. Instead. a transverse
extensometer was attached (Figure 5-2) to measure the transverse
strain. ‘tr' across the thickness of specimens. The details of con-
tact between the extensometer and the specimens are given in Figure
5-3. It can be seen that on one side of the specimen there is a point
contact while the other a flat surface is in contact with the speci-
men. The gage length was the thickness of the specimens. Axial
stress was taken to be equal to the applied load divided by the mini-
mum cross sectional area. The axial strain. which was used as the
controlling parameter for all tests. was calculated from the axial
stress and transverse strain. The relation between transverse strain

“tr axial stress. o. and the total axial strain is given by:

e = (o/E) - (llup) [etr + p. (c/E)] (5-1)

40

 

Figure 5-2 Sheet Steel Specimen and Extenscmeter.

41

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42

in which E is the elastic modulus. and u. and up are the elastic and
plastic Poisson ratios. respectively. The elastic strein component is

determined from o/E. while the plastic strain component is given by:

ep = (l/up) [ctr + u. (o/E)]. (5-2)

Assuming that no volume change occurred during plastic deforma-
tion. the plastic Poisson ratio was assumed to be 0.5 which. upon

substitution in Equation (5-1). resulted in:
s = (c/E) - 2 ”tr - 2 "e (c/E). (5-3)

The controlling parameter throughout the entire test was the
total strain given by the above equation whose analog circuit is shown
in Figure 5-4. As can be seen. the inputs to the circuit are the load
P and transverse strain. ‘tr‘ The circuit contains two variable
potentiometers. V1 and V2. which were used to set the circuit such
that the final output would be the total strain. Tb do this. first a
dummy load voltage was applied. Since the specimen cross-section area
and its Young's modulus were known. VI was adjusted such that its out-
put would be the elastic strain. Then. with the specimen undergoing
cyclic loading in the elastic range under a load-control. potentiome-
ter V2 was adjusted such that its output at amplifier 2 would be zero.
This output is the analog of plastic strain. Finally. amplifier 3
gives the sum of elastic and plastic strain. which is the desired con-

trolling parameter. i.e. total strain. A more detailed account can

43

s = (c/E) - 2 'tr - 2 a. (c/E)

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44

be found inl28].

A load cell mounted in series with the specimens was used to
measure loads. In experiments with 1032 flat specimens and 1020 sheet
steel specimens wedge type grips were used. The grips were chosen
with care so that they would produce sufficient friction to hold the
specimens in place throughout the loading program. Tb prevent buckr
ling of the 1020 sheet steel specimens. a set of shims. as shown in

Figure 5-5. were used to support the specimens.

In the presence of small plastic strains. a small misalignment or
distortion due to clamping can have a disproportional effect on the
results. Tb eliminate these difficulties. Iblten Wood's metal joint

grips were used.

Under isothermal conditions and frequencies in the 0.1 to 30 Hz
range. the life of a metal is virtually independent of frequencyl29].
However. when isothermal conditions cannot be maintained. the heat
developed as a result of plastic distortion may cause significant
changes in the properties of the metal. Such changes. however. are

rarely encountered at room temperature.

An x—r recorder was used for the permanent recording of the data
(see Figure 5-6 for entire test facility). For this purpose. analog
signals of load and strain were fed into an analog computer. Here.

they were scaled to produce stress and strain on the recorder which

45

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47

thus recorded the complete hysteresis loop. Tb record the
stress-strain response of the specimens to overstreining. all such
overstreins (initial or periodic) were done at low frequencies between
0.06 to 0.08 Hz. During all tests. the frequency was changed often to
allow the application of a large number of cycles within a reasonable
time. For monitoring loads and strains in all ranges of frequency. an
oscilloscOpe with variable persistence was used. This ensured that
any change in the system which depended on the frequency would be

detected.

Where possible. the hysteresis loops were recorded at fixed

intervals (namely after 1. 2. 3. 5. 10. 20. 30. 50. 100. ...cycles).

Three different load patterns were used for this study:

1) No overstrein. A constant amplitude completely reversed cycl-

ic strein.

2)Initial overstrein. An initial cyclic overstrein followed by

completely reversed cyclic strain.

3) Periodic overstrein. Periodic overstrein between every

100.000 cycles of completely reversed cyclic strain.

For both the initial and periodic overstreins (tests of type 2

and 3). the maximum strain used was $0.010 (one percent). Each over-

48

strain block consisted of 20 decreasing cycles and was followed by a
constant magnitude cycling. Before the start of the test. replicas of
the whole gage section area were taken and then the strain gage was

mounted.

In experiments with strain control. it often occurs that a speci-
men continues to cycle after it has been broken into two pieces and
the tensile load response has dropped to zero. This causes "hammer
damage" and results in inaccuracies in the number of cycles to
failure. Tb prevent this shut-off. a device known as an underpeak
detector. which signals the initiation of a crack. was used. Figure

5-7 shows the behavior of a specimen in such a situation.

Studying the changes in the surface of the specimens due to fati-
gue typically involves the removal and remcunting of each specimen
during the test. In order to improve the procedure. plastic replicas
were found to be ideal since they caused no damage to the surface and
were very efficient. The replica procedure consisted of the following

steps:

1) electro—polishing the specimen by conventional methods and
then making two sets of plastic replicas of the whole gage section of

each specimen in the virgin condition;

2) mounting the specimen. cycling it at the specified loading and

then repeatedly overstreining. with plastic replicas made before and

49

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mm

50

after each overstrein (the specimen remains mounted on the machine);

and

3) in non-overstrein and initial overstrein cases. replicas were

taken after each 100.000 cycles

In all the steps detailed above. the procedure was repeated until
failure occurred. In all cases. each replica was allowed to dry (2 to
5 minutes) and then was stripped off. mounted on a glass slide. and
labeled. Afterwards the replicas were shadowed with vaporized chromi-
um for observation with both light and electron microscopes. In
preparing the replicas. one difficulty was encountered. namely that it
was not possible to take a carbon replica directly from the specimen
in one stage. This difficulty was overcome by adopting a two-stage
procedure. In this procedure. acetone was first applied to the sur-
face of the specimen so that it was completely wet and then a piece of
plastic (acetate tape) was immediately laid across. The plastic
attached to the specimen took on the surface contours of the specimen.
After the plastic dried for about five minutes. it was peeled off with
tweezers. mounted on glass slides. and labeled. This constituted our
primary replica. but it was not suitable for work under the electron
microscope. Tb obtain a replica suitable for electron microscopy. the
primary replica. with the side which had been in contact with the spe-
cimen surface upwards. was placed directly under the carbon arc of a
vacuum evaporator and carbon was deposited on the replicas. For more

details see reference[30].

51

In the carbon replica thus made. the carbon thickness is more or
less constant. This uniformity of thickness results in rather poor
contrast under electron.microscopy. Tb remedy this. replicas were
shadowed with chromium. The procedure was as follows. As soon as
carbon was deposited on the plastic replicas. a coating of chromium
was deposited at an angle of almost 45 degrees to the specimen sur-
face. The purpose of this was to cast a shadow containing no chromium
behind high spots of the specimen. thus accentuating surface topogra-

phy and producing better contrast under microscopy.

After shadowing. the composite films (consisting of carbon and
plastic) were cut into pieces of appropriate dimensions. The pieces
were then placed on grids. The grids had been placed on a piece of
filter paper which had been wetted with acetone and inserted into a
Petri dish. After the plastic pieces were added to the grids. the
Petri dish was covered. Once the plastic had softened. more acetone
was added until the filter paper was quite moist. At this stage the
lid was replaced and the Petri dish left undisturbed for some time
(occasionally overnight) until the plastic had been completely washed
away. The secondary replica was then ready. The lid of the Petri
dish was removed and the grids and the replica mounted on them were

left to dry.

The testing techniques for 1018 and 1030 specimens are fairly
standard. The procedure followed for 1020 specimens is different and

more time consuming. However. since these specimens have very small

52

thickness and would easily buckle the precautions here are essential.
Replica techniques necessitate long preparation time also. but the
advantage of obtaining an exact copy of the surface microstructure at

any stage of testing justifies the effort.

CHAPTER 6

RESULTS AND DISCUSSION

1,; FATIGUE msr RESULTS

In this chapter. first. the results which were obtained are

presented and then their significance is briefly discussed.

For each kind of specimen and each type of test. used in this
investigation. a table indicating specimen label. modulus of elastici-
ty. value of constant strain amplitude of the stable loops. and
reversals to failure was made. Elastic and plastic strain amplitudes
in these tables are calculated by the aid of the formulas discussed in
Chapter 3. These tables are numbered from 6.1.1 to 6.1.9. In these
tables. and throughout the text label "8.8" stands for cylindrical bar
specimens made of 1018 steel. "T.S" for thin sheet specimens made of

1020 steel and "F.S" for thick sheet specimens made of 1030 steel.

As mentioned previously. during each test a series of
stress-strain loops was recorded after a certain number of cycles.
Examples of these are given in Figures 6.1.1 to 6.1.4. Figures 6.1.1

(a) and (b) display the stress-strain response of thick sheet specimen

53

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Figure 6.1.1 (I) Stress-Strein response of Specimen F.S.36

(N = 1 Ind 2).

    

!
u

Figure 6.1.1 (b) Strees¢Strein response of Specimen F.S.36
(N = 1000).

64

number 36 (F.S.36) which was subjected to a cyclic load with $0,005
strain amplitude. The upper yield point of 295 lPa is clearly seen in
the first cycle. A hysteresis loop recorded very near to the
half-life of this specimen (1000 cycles) appears in Figure 6.1.1 (b).
As can be seen in Figure 6.1.1 (a and b) the height of the loops
increases with the number of cycles. which indicates that this materi-
al undergoes cyclic hardening at this strain amplitude. The
stress-strain response of bar steel specimen number 25 (8.8.25) is
shown in Figure 6.1.2. It can be seen that the material undergoes
cyclic softening at this smaller strain amplitude. It is also seen
that the cyclic softening or hardening is prominent in the first 50
percent of the life of the specimen after which a steady state condi-
tion is reached for the rest of the specimen's life. Figure 6.1.3
shows a typical stress-strain response of an initially overstrained
specimen (specimen F.S.20) and corresponding loops which were recorded

during its fatigue life.

Figure 6.1.4 illustrates the hysteresis loops observed during the
fatigue test of specimen F.S.l4. In this figure. hysteresis loops
observed before and after subjecting this specimen to overstrein are
shown. The hardening experienced by this material during each over—

straining is clearly illustrated in this figure.

As can be seen from Figures 6.1.1 to 6.1.4. if the material
undergoes cyclic hardening or softening. then the stress amplitude

(height of loops) and elastic and plastic strain amplitudes change

65

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70

during cycling nndor tho conditions of oonstont totsl strsin. Tho
hoight (stross) snd tho width (totsl strsin) of thoso loops woro loss-
nrod. Fro- tho posh wslnos. tho stross snplitndo. AoIZ. snd strsin
mnplitndo. Aslz. woro cslcnlstod. In.nost cssos tho olsstic nodnlns.
E. wss oslcnlstod fro- tho first hystorosis loop snd nsod in s11 snh-
soqnont cslcnlstions. 1b obtsin tho olsstic strsin. tho stross
onplitndo wss dividod by tho olsstic nodnlns. B. Subtrootion of this
wslno fro. tho totsl strsin thon.yioldod tho plostio strsin (soo oqns-
tions 3-5 snd 3-6). Bosod on tho inforlstion ohtoinod from thoso
loops. s lifo tshlo for owory spocinon. showing tho olsstic nodnlns.
E. °Yolos to foilnro. ZNf. tho totsl stross snd totsl strsin ss woll
so tho cslcnlstod olsstic snd plsstic strains for osch rogistorod loop
woro proporod. Fro- thoso dots. fignros showing tho wsriotions of
thoso qnsntitios with tho nnnbor of cyclos woro thon drown.
Ioprosontstiwo Fignros sro shown in tho .rsphs inclndod. Fignros
6.1.5 to 6.1.10 sro plots of conploto history of spocinons 8.8.6.
3.8.20. 3.8.3. T.S.24. T.S.22. snd T.S.ZS. rospoctiwoly. Bxporinonts
show thst tho notoriols nndor inwostigstion nndorgo cyclic hordonin;
or softonin; dopondin; on tho strsin rsngos. Tho cyclic ohongo of
stross snplitndo vorsns rovorssls (holf cyclos 2N) of conplotoly
roworsod strsin st difforont strsin snplitndos for throo difforont

notsls hos hoon shown in Fignros 6.1.11 - 6.1.13.

Fnrthornoro. tho cyclic hordoning (or softoning) of tho notorisl
con ho ossily dotorninod frol thoso dots if ono draws tho wsristions

of tho plostic snplitndo worsns tho rovorsols. Fignro 6.1.14 shows

71

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80

such a curve for bar steel specimen number 25 (3.8.25) which was
cycled at a constant strain (0.001 percent). It is evident that this
material experienced cyclic softening at this strain amplitude. This
occured because the plastic strain was increasing with the number of

cycles.

The same trend was observed in the initial overstrain test on the
specimen 8.8.12. But the increase in the magnitude of the plastic
strain was much more rapid which. as expected. resulted in a shorter
life to failure (see Figure 6.1.15). In the case of periodically
overstrained specimens. the amount of plastic deformation was small
compared with the case of initially overstrained specimens. For the
same strain amplitude. the life to failure of these specimens was
close to specimens that had received no overstraining. Figure 6.1.16
shows the variation of plastic strain amplitude of specimen 8.8.21
which was subjected to 10.0011 percent strain and periodically over-
strained. Figure 6.1.17 is an enlargement of the right portion of
Figure 6.1.16. As can be seen in this figure. the specimen hardens
slightly after each cyclic overstrsin and as a result. the amount of
plastic strain decreases. However. continued cycling with constant
amplitude softens the specimen and it recovers its stable condition.
This phenomenon may be due to strain hardening of this material. This
explanation is supported by the fact that successive overstrains. and
especially cyclic hardening during overstrains. increase the fatigue

life of the bar steel specimens subjected to periodic overstraining.

Plastic Strain Amruitude.

Plastic Strain Anguitude.

S
b.)
1
r

 

x1a'3
n.4-r

‘

@01-

 

81

l

l J I l l l
VVVI'V‘I' Vfi I VV'VTI V V V '17—'71 V V V'VVIV' V T ‘VVYVV V 71—77." V V YVVVV
1m 112 103 10 1&5 1&5 107
luwcunds.28

Figure 6.1.14 Plastic Strain history of Specimen 8.8.25

Cycled at Constant Strain Amplitude of 0.001

10 1 1w 1 1m 1m 1 7
Bananas.2N

Figure 6.1.15 Plastic Strain history of Specimen 3.8.12
which receiving Initial Overstrain followed by 0.001%
Strain Amplitude Cycling.

Plastic Strain Mplitude

Plastic Strain Allplitude.

x1m‘3
M»

092

 

x1m’3

—-c

M

. . u, . . -1 .....I . .1 , ..1
1a 102 1113 11114 1115 1955 1m7
Reversals,2N

Figure 6.1.16 Plastic Strain history of Specimen 3.8.21
which Periodically Overstraincd.

 

 

1 . . .J
165 135 1017
Reversals, 2N

Figure 6.1.17 Right portion of Figure 6.1.16.

83

The trend was almost the same for 1020 and 1030 specimens. In
spite of the fact that these specimens had hardened because of over-
straining. the rate of increase in the magnitude of plastic strain for
periodic overstrain (recovery of stable condition) was much more rapid
compared with the initial overstrain cases. The amount of plastic
deformation in the periodically overstrained specimens was relatively
high in comparison with those specimens that had either received no
overstrain at all or had been initially overstrained. Typical exam-
ples of these observations are shown in Figures 6.1.18 to 6.1.25.
These observations. coupled with the results of other
workers[3.6.8.18]. lead to the conclusion that the plastic strain can
cause damage resulting in shorter lives. As can be seen from Figure
6.1.14 - 6.1.25 the hysteresis loops for 1018 specimens recover their

stable conditions more rapidly than those of 1020 and 1030 specimens.

At approximately half the fatigue life of each specimen a loop
was chosen as the representative loop (reference cycle). The reason
for this choice was that the stress-strain response could be assumed
to have stabilized at this stage. In the case of periodically over-
strained specimens. the representative loop at approximately half the
fatigue life and just before overstraining was chosen. The cor-
responding data obtained from these loops were used in plotting the
graphs and finding fatigue properties of each material. A summary of
the results found from these loops for different types of specimens is
presented in Tables 6.1.1 - 6.1.9. Throughout this study. with very

few exceptions. a specimen was considered to have failed only when it

Plastic Strain Anplitude.

Plast ic Strain Anplitude

84

 

 

.

1

. e 0
@JW'

0
I
. ' ' ' ' ' ' es s a e
0.0 14..-“; -.H "i l l 1 1 1
TV ViYTYYWI v V‘lvvvww v w wwwvul v wwwwwwv w w srvvvu'
1 1a 102 103 114 105 105 107
Rmnmsahh 2N

1110'3

@021-

0.0

 

Figure 6.1.l8 Plastic strain history of specimen T.S.24
cycled at constant strain amplitude of 0.0008

......1 ---.....: .......: ......1 -......: . ...4
1m 1m? 103 11‘ 105 105 107

Remusahh 2N

Figure 6.1.19 Plastic strain history of specimen T.S.22
which receiving initial overstrain followed by 0.00085

Plastic Strain Mplitude

Plastic Strain Mplitude.

85

 

 

 

 

X10
9.2“”
‘ I
. I
a"! .
‘ m e e e
. t I
a 1 . I . I I I
. «P- . . .
I . . .
I
‘ . e m
000 V Y vwwwwv§ v w Irv-1vJ T ' VIVIIIl v v wvvvuvl v w vvwwww: v v Ivvwww 5
1 1a 1b? 1113 111‘ 1115 1d
nmnmsnhh.2N
Figure 6.1.20 Plastic strain history of specimenT.S.25
which periodically overstrained.
-1
X10 "
0.2T
4
1
I
I I
4 . . I . . I
0 ..s ‘e
I O I
001“” 0 .
a e
I I
Q 3 f T 1 __1
e 4 v r 1' w r v v r v 1 w W 'fiv '
10 lbs lea

Rmnusnhm.2N

Figure 6.1.21 Right portion of Figure 6.1.20.

86

 

 

 

 

X10
“02'1”
- 1
8
3 I
2:
g I I I
I
E 001‘” .
3
U.)
U
0:3 I
m
53
De 4
I
‘ . I . I
0.0 ......L ......4 . ......1 ..--.-..§ . ......1 .--. .
*1 1m 1m? 103 104 105 105
Reversals,2N
Figure 6.1.22 Plastic strain history of specimen F.S.2
cycled at constant strain amplitude of 0.001
x1121‘3
602‘"—
4
g 1
E3
2 1 . . -
c I
"1 s e e
g 0.1.“- ‘a' e m sue. a s.. ....
U I I . . I
.3 1 I
In
2
0.
new fl Tl * l V 1 fl I
1 1m? 11‘ 105 118
Rmnusmuh 2N

Figure 6.1.23 Plastic strain history of specimen F.S.20
which receiving initial overstrain followed by 0.00084
amplitude cycling.

Plastic Strain Anplitude .

Plastic Strain Mplitude.

87

 

 

x1113

01.3—1—
.1
1

002‘"

Gal—“-

0.0 .-...-1 .--.....: ..... '3. .....-14. ""‘"'S‘ "'""16""""'7
1 111 1s2 1% 111 1b 111 1a

Reversals. 2N

Figure 6.1.24 Plastic strain history of specimen F.S.l7
which periodically overstrained.

 

 

0.3T
1.21-
1.11:.
”:5 . ~~~~135 . .....W

Reversals. ZN

Figure 6.1.25 Right portion of Figure 6.1.24.

had completely separated into two parts.

Figures 6.1.11 - 6.1.13 depicts a stress-strain response that is
of a complex nature since. for some specimens. both cyclic hardening
and softening is observed. As has already been.mentioned. the cyclic
stress-strain behavior. that can be obtained from a curve passing
through the tips of a set of stable hysteresis loops. would describe
the cyclic response. For most metals. the relation between stress
amplitude and the plastic strain amplitude (in stable condition) is of

the form

Act/2 = r' (Asp/2111' (6-1)

(i.e. a power law) where K' and n' represent the cyclic strength

coefficient and cyclic strain hardening exponent. respectively.

It is obvious that the graph of the above equation in log-log
coordinates. is a straight line. The slope of this line represents
the cyclic hardening exponent. n'. The data points that characterize
each test correspond to the loops which were taken at one-half the
fatigue life. Figures 6.1.26 to 6.1.34 show the plots of plastic
strain amplitude versus stress amplitude for the three different
materials used in this investigation. with three types of cyclic
straining. The least-squares method was used to fit a straight line

for each set of data. The lines thus obtained are quite distinct in

Stress Mplitude (MPa) .

Stress Mplitude (MPa) .

...-m
S
N

10

10

 

89

 

 

 

.1
1 I’ertn ‘1 I ITIIH I 1 Ivrrn I 1 1111” 1 1 1111“
11'5 111" 10'3 11'? 11 1 1
Eumtn:Stnun1Nqniuxb.
Figure 6.1.26 Stress-plastic strain amplitude from
constant strain test results of Bar Steel Specimens.
i—
.1
"1
.1
I
I
I
I
I 1 [1'1”
I 1111111 I ljlllll I I‘ll!” IYIIIHI-
1:1‘5 111" 10'3 111 3 1m 1

ldasthcinxainiumdiuxku

Figure 6.1.27 Stress-plastic strain amplitude data from
Bar Steel Specimens subjected to initial overstrains.

Stress Mplitude (HPa) .

Stress Mplitude (MPa) .

10

L.)

...
S

p—n
S
N

10

 

90

 

 

 

 

 

I IIIITTT T I IIIIII I I IIIIII 2 I I IIIIII 1| IIIIIII
111'5 1a" 10'3 111 111 1
lflastk:$tnfln.flnfliflxhu

Figure 6.1.28 Stress-plastic strain amplitude data from
Bar steel specimens subjected to periodic cyclic
overstrains.
1
l T IIIIIII I IIIIIII I IIIIIII I I IIIIII‘»1 I I IIIIII
111' 111'4 10'3 111 2 111 1

Phnfliclfixmki1hnflitufih

Figure 6.1.29 Stress-plastic strain amplitude
constant strain test of Thin Sheet Steel Specimens.

from

Stress Mplitude (HPa) .

(MP3) .

Stress Mplitude

10

IB

 

91

 

 

18'5

 

I IIIIIII I IIIIIII

1a“ 10'3

I IIIIII I I IIIIII I I IIIIII

111'2 10'1 1

Plastic Strein Anplitude.

Figure 6.1.30 Stress-plastic

strain amplitude data from

Sheet Steel Specimens subjected to initial overstrains.

 

 

111'5

I IIIIIII I IIIIIII

1m“ 10'3

I IIIIII

IIIII" I IIIIII

1111‘2 111’1 1

Idasth:£kxain1Nqflitude.

Figure 6.1.31 Stress-plastic

strain amplitude data from

Sheet Steel Specimens subjected to periodic cyclic

overstrains.

Stress Amplitude (HPa).

Stress Amplitude (MPa).

92

 

 

 

1% I IIIWII I I IIIIII

11'5 111" 10'3 10'? 111'1

lflestk:$tndn1Nuniuxhu

Figure 6.1.32 Stress-plastic strain amplitude from
constant strain test of Thick Sheet Steel Specimens.

l 14L]

J

 

 

I IITIII I I IIIIII I T IIIIII

 

10 5 I I 111111 4 r I IIIIII 3 I I IIIIII 2 I'I IIIIH 1 1 I IIIIU
10' 10' 10 10 10
Plundc lkzeflm awning».
Figure 6.1.33 Stress-plastic strain amplitude data from

Thich Sheet Steel Specimens subjected to initial
overstrains.

1

93

the sense that they have markedly different slopes and intercepts.
The obtained data fit the linear log-log relationships relatively well
for 1018 and 1020 specimens. For 1030 specimens. the smell deviations
from the straight line may be attributed to the heat-treatment that
was performed on these specimens. A summary of the results obtained
from these graphs are shown in Tables 6.1.10 - 6.1.12. The strain
hardening exponent obtained was high for cases of non-overstrained
specimens (of all three types of material) whereas initial and period-
ic overstrain decrease the strain hardening exponent. In the case of
bar steel. however. periodic overstrain yielded a strain hardening

exponent nearly the same as that of the nonroverstrained specimens.

From the data of Tables 6.1.1 - 6.1.3. the elastic and plastic
strain amplitudes at half life has been plotted versus the reversals
(ZNf) to failure for bar steel specimens. The least-squares method
was used to find the best line showing the variation of elastic strain
with life and plastic strain with life. The total strain curve was

then found by adding the elastic and plastic strains.

From the plastic line. the fatigue ductility coefficient. 3",
(the intercept of the plastic line at one reversal) and the fatigue
ductility exponent. c. (the slope of the line) were calculated. The
fatigue strength coefficient. of'. and fatigue strength exponent. b.
(the slope) were determined from the elastic line. Figure 6.1.35
shows strain amplitude versus reversals to failure for 1018 specimens

which received no overstrain.

94

TABLE 6 .1 .10

Cyclic stress-strain and fatigue properties
of Bar Steel Specimens.

No Initial Periodic
Overstrain Overstrein Overstrein
Cyclic strength
coefficient. (lPa) 1345 1259 1299
Cyclic strain hardening
exponent 0.274 0.259 0.268
Fatigue Strength
coefficient. (lPa) 878 805 887
Fatigue strength
exponent -0.120 -0.114 -0.l23
Fatigue ductility
coefficient 0.164 0.209 0.189
Fatigue ductility
exponent -0.417 -0.454 -0.438
TIBLB 6.1.11
Cyclic stress-strain and fatigue properties
of Thin Sheet Steel Specimens.
No Initial Periodic
Overstrein Overstrein Overstrein
Cyclic strength
coefficient. (lPa) 1281 906 775
Cyclic strain hardening
exponent 0.285 0.229 0.208
Fatigue Strength
coefficient, (lPa) 667 744 954
Fatigue strength
exponent -0.108 -0.119 -0.l40
Fatigue ductility
coefficient 0.106 0.362 0.864
Fatigue ductility
exponent -0.382 -0.503 -O.S85

95

TABlB 6.1 .12

Cyclic stress-strain and fatigue properties
of Thick Steel Specimens.

No Initial Periodic
Overstrain Overstrain Overstrain
Cyclic strength
coefficient. (IPa) 871 801 605
Cyclic strain hardening
exponent 0.210 0.188 0.152
Fatigue Strength
coefficient. (lPa) 743 588 650
Fatigue strength
exponent -0.115 -0.089 -0.103
Fatigue ductility
coefficient 0.385 0.191 0.798
Fatigue ductility
exponent -0.533 -0.472 -0.612

96

The results from the tests. with strain amplitudes more than
0.0012 of no overstrain. have been used in conjunction with the data
obtained from the overstrained specimens cycled at amplitudes less
than 0.0012. to obtain plots of strain amplitude versus reversals to
failure for initial and periodic overstrain cases. This procedure was
adopted because the effect of overstrain at short lives is hardly ever
noticeable[2.6.32]. Figures 6.1.36 and 6.1.37 show such plots for

initial and periodic overstrain cases of 1018 specimens.

From these figures. it is evident that bar steel specimens which
when periodically overstrained. exhibit a behavior very similar to
specimens with no overstrain. It is also worth noting that the beha-
vior of both types of specimens (no overstrain and periodic
overstrain) is distinctly different from that of initially over-

strained specimens.

Figures 6.l.38 to 6.1.43 show the graph of stable values of
plastic. elastic and total strain taken from Thble 6.1.4 - 6.1.9 and
plotted versus the reversals to failure for 1020 and 1030 specimens.
Comparison of these plots reveal that no appreciable change was
observed in the life of specimens which were subjected to initial
cyclic overstraining. Periodic cyclic overstraining. on the other
hand. caused a sharp decrease in the life of 1030 specimens and a
noticeable decline in the life of 1020 specimens. A summary of fati-
gue properties of the three materials under investigation. based on

Figures 6.1.26 - 6.1.43. are shown in tables 6.1.10 - 6.1.12.

Stress Mplitude (MPa) .

Strain Mplitude.

97

l lllJJ

 

 

 

 

 

1112
1
1% I I IIIIII I I IIIIII I I IIIIII I 1 IIIIII I IIIIIII
111'5 1a" 10'3 111'2 111‘1 1
PhunicinxenilUpLumde.
Figure 6.1.34 Stress-plastic strain amplitude data from
Thich Sheet steel Specimens subjected to periodic cyclic
overstrains.
l =—
111'1
11'?
10‘3
113"
18-5 . L l l l J
I I I I I 10
1 102 10‘ 106 139 1a

Reversals to Failure. ZNf

Figure 5.1.35 Strain-reversals to failure for Bar Steel
Specimens (no overstreining).

Strain Mplitude .

Strain Ancnitude.

l 1 llllllI l llllllfifi l l llllllI J l lJllllI l IL|||||

 

98

Solid Symbols - Initial Overstrain

 

Non - Overstrain Data

 

 

 

 

 

 

l J l l l
‘ 2 ‘ 4 ' s ‘ a ' 1m
1 10 10 10 10 10
Rmnxamhstclhulunm,2Nf
Figure 6.1.36 Strain-reversals to failure for Bar Steel
Specimen subjected to initial overstrains.
i
: Solid Symbols - Periodic Overstrain
'5— Non - Overstrain Data
5
—(
;
_J
1
I l I l I I I I I J
1 1m2 1:4 105 1119 101“

Revenuus holhulunm.2Nf

Figure 6.1.37 Strain-reversals to failure for Bar Steel
Specimens subjected to periodic cyclic overstrains.

Strain Amplitude.

Strain Mplitude.

10“

10'?

11’3

10"

L1 L111“[ 1 lllllllI l liililll i l 11““' 1 1111111]

 

10'5

 

1 gF‘
13" 2“
111'2 =-

1
10'3 =—-
10'4 :_—
19'5

99

 

Elvenuu.tclhu1unm,2flf

Figure 6.1.38 Strain-reversals to failure data for Sheet
Steel Specimens (no overstrain).

Solid Symbols - Initial Overstrain

--- Nom'- Overstrain Beta

 

l I l J J

 

112 104 105 108 101“

Reversals to Failure. ZNf

Figure 6.1.39 Strain-reversals to failure data for Sheet
Steel Specimens subjected to initial overstrains.

Strain mplitucb.

Strain Mplitde.

 

1(H)

 

 

 

I Solid Symbols - Periodic Overstrain

__ Non.- Overstrain Data
'5‘
I
i

J J J J J
I 2 I 4 I 6 I 8 1 1a

1 19 10 10 10 10

 

lumenuus unrhihue.:hfl

Figure 6.1.40 Strain-reversals to failure data for Sheet
Steel Specimens subjected to periodic cyclic overstrains.

 

 

q I J I J ‘ J 1 I ‘ J
1 1a? 10‘ 105 109 101“

lumenuns unthihuu.iufi

Figure 6.1.41 Strain-reversals to failure data for Thick
Sheet Steel Specimens (no overstrain).

Strain Mplitude .

Strain Anpnitude.

 

101

—.

 

 

 

.T Solid Symbols - mm: Overstrain
.1 ;
18 3" Non - Overstrain Date
"1
1m‘2 .1—
3
111‘3 %
m“ g-
( Q '5 1 l 1 l r J
l ‘ 7 f I I 8 - [a
1 1112 1m4 105 111 10
Rmnxsausuolmuhun.:nfl
Figure 6.1.42 Strain-reversals to failure data for Thick
Sheet Steel Specimens subjected to initial overstrains.
1 i—
. Solid Symbols - Periodic Overstrain
«3'1 L.

 

Non - Overstrain Data

J
10111

invenuns hafaihuuh Zflf

Figure 6.1.43 Strain-reversals to failure data for Thick

Sheet Steel Specimens subjected to periodic cyclic
overstrains.

102

The influence of initial and periodic overstraining on the fati-
gue prOperties of the materials which were used (as shown in tables
6.1.10 through 6.1.12) and the results of other works[1.2.4.5.13].
suggest that the effect of initial and periodic overstreining on a
material depends on the condition of the material. In general both
initial or periodic overstreining have a detrimental effect on a

material but the extent of the effect depends on the material itself.

Ll. SURFACE muss

Various studies have suggested that the changes associated with
damage occurring in a fatigue specimen are continuous. The question
of when. in the fatigue life of a specimen. microscopical changes
(slip bands. dislocations etc.) occur and how long they last depends
on many factors. Chief among these are the stress level and the pro-
perties of the material under examination. It is therefore to be
expected that all changes may not be observed in a given test or for a
given material. Furthermore the type of instrument used. particularly
its sensitivity. and the frequency of examination strongly influence

the observation of changes which occur.

Tb assess the effects of various load histories that were imposed
in these investigations. the surface damage caused by the cyclic
strain.was examined. Plastic replicas as described in the procedure
section.were employed to record the changes which had taken place as a

result of fatigue loading. A series of these replicas were taken at

103

different stages (after each 100.000 cycles) of the test and examined
by an optical and an electron microscope. Since the replicas recorded
the microstructure very accurately. examining them provided the same
information that would have come from an examination of the specimens
themselves. In this way a permanent record of the microstructure of
the specimen during periodic phases of its fatigue life was assembled.
Replicas were first made before each test to show the unstrained
microstructure of specimens which were chosen for metallogrephic
study. Examples of these microstructures are shown in Figures 6.2.1
to 6.2.5. A description of the various specimens' microstructures as

affected by different loadings is provided in the next sub-section.

6,2 ,1 IIICROSTRUCTURE QE NW§TRAEED SPECIES

Bar steel specimens. that were made from 1018 annealed steel.
show coarse lamellar pearlite. ferrite and bainite containing carbide

particles. Figure 6.2.1.

Thin sheet stool specimens and thick sheet stool specimens were
made from 1020 and 1030 steel. respectively. The microstructure of
thin sheet specimens consists mainly of ferrite. with carbide parti-

cles located at grain boundaries. Figure 6.2.2.

The microstructure of the 1030 steel in the as received state is
shown in Figure 6.2.3. Evidently the structure is different from the

material of the other two specimens. The material was heat-treated

104

 

Figure 6.2.2 TEN Replica Micrograph of 1020 Steel Before test (3000K)

105

(annealed) in order to make it as similar to the other ones as possi-
ble. The microstructure of the heat-treated specimen is shown in
Figure 6.2.4. The structure of this material after annealing consist-

ed of ferrite and lamellar pearlite.

It should be mentioned that all micrographs were taken from the
gage length sections (the rolled side) and after electro-polishing and
etching. Figure 6.2.5 shows a typical microstructure of a specimen
after mechanical polishing but before electro-polishing. As can be
seen in this photo. there are always some scratches after mechanical

polishing.

The following three sub-sections describe the metallographical
results due to three types of loading. Frequently. while replicas
were examined under the electron microscope. the magnification was
changed. permitting a particular spot within a grain or changes in

neighboring grains to be viewed.

6.2 :2 NICROSTRUCI'URE 9_E NW-OVERSTRAINED SPECIES

Specimen B.S.27 was subjected to 0.085 percent constant strain.
Replicas were taken of the gage surface after each 100.000 cycles
until failure. Figure 6.2.6 shows the microstructure of a ferrite
grain of this specimen at 10000X after 100.000 cycles. Figure 6.2.7
is a smaller magnification (45001) of the microstructure of the same

specimen after 500.000 cycles which shows several neighboring grains.

106

 

Figure 6.2.3 TEM Replica Micrograph of 1230 Steel as received (30001)

 

15 \ m'

Figure 6.2.4 TEM Replica Micrograph of 1230 Steel After Annealing

(3000K)

107

 

Figure 6.2.5 A typical Micrograph of Specimens After Mechanical

Polishing (100001)

 

Figure 6.2.6 Microstructure of B.S.27 After 100,000 Cycles (10000X)

108

No change can be detected from these pictures. As the cycling was
continued. however. slip bands were observed in some grains. A typi-
cal microstructure of this specimen after 1.000.000 cycles appears in
Figure 6.2.8. As can be seen in this picture there are some slip
bands in a few grains. Subjecting the specimen to more cyclic loading
results in a larger number of deformed grains (i.e. grains in which
slip bands have appeared). as well as an increase in the number of

slip bands in each grain.

As cycling continued. more and more slip bands are produced.
which eventually resulted in the appearance of fine cracks. Figure
6.2.9 displays a typical portion of the microstructure of this speci-
men after 2.000.000 cycles. There were evidences of some slip bands
in the ferrite grains and some fatigue microcracks along some of the

slip bands.

With more cycling the number of cracks increases until the speci-
men finally fails. The microstructure of this specimen after failure
(6.266.000 reversals) is shown in Figure 6.2.10 which consists of two
ferrite and one pearlite grain. Fell-deveIOped fatigue microcracks

can be seen in the left ferrite grain.

Specimens 8.8.22 and 8.8.25 were subjected to 0.095 and 0.1 per-
cent of cyclic strain. respectively. Typical microstructures of these
specimens are shown in Figures 6.2.11 to 6.2.14. Examination of the

gage sections of these two specimens showed extensive slip band activ-

109

 

 

dc

Figure 6.2.8 Microstructure of B.S.27 After 1.000.000 Cycles (2000K)

110

 

...... . .' ‘ , , ‘).f:-\ 1"" ' . Q!"

Figure 6.2.10 Microstructure of B.S.27 After Failure (4500K)

111

 

.3 ,V. " .. «_ ,. .p-‘fi '. v 1 ' ‘.

Figure 6.2.12 Microstructure of B.S.22 After 500.000 Cycles (7000K)

112

 

Figure 6.2.14 Microstructure of B.S.25 After 500.000 Cycles (2000K)

113

ity. The slip band structures of these specimens were extremely dense
and they appeared earlier in the test compared with specimen B.S.27.
as can be seen in Figure 6.2.12 and 6.2.14. Comparison of these two
specimens (even though they were subjected to strain amplitudes close
to each other) reveals that slip bands of specimen B.S.25 which was
subjected to a relatively higher strain is coarser than those of spa-
cimen B.S.22. Figure 6.2.13 shows microcracks in developed slip hands

after 100.000 cycles.

(bmparison of the results of these three specimens revealed that:
specimens subjected to a higher strain range have a significantly
higher slip band density than those subjected to a lower strain range.
Coarse grains in these specimens undergo more deformation than fine
grains. Transmission electron microscope examination of the replicas
of these specimens shows more extensive slip band activity in coarse
grains than in the finer ones. This may be due to the existence of
more favorable orientations for slip or areas of high stress concen-

tration in these grains.

The structure of a 1020 sheet steel specimen that was subjected
to 0.1 percent strain of constant amplitude only (specimen T.S.16) is
presented in Figures 6.2.15 to 6.2.18. In Figures 6.2.15 and 6.2.16
the successive growth of slip bands from 100.000 to 500.000 cycles is
displayed. These micrographs are taken from.large grains to demon-
strate this phenomenon more clearly. The same phenomenon is observed

in small grains. In Figure 6.2.15 which was taken at 30001. slip

114

 

Figure 6.2.16 Microstructure of T.S.16 After 500.000 Cycles (4500K)

115

 

Figure 6.2.18 Microstructure of T.S.18 After 5.000.000 Cycles (3000K)

116

bands have formed in three adjacent grains while the rest of the
grains in this micrograph has no slip bands. This micrograph was
taken at this relatively low magnification in order to show more

grains.

As the number of cycles increases. slip bands develOp very slow-
ly. Ihile the favored direction for the development of the slip lines
is usually the longitudinal one. the band sources are activated almost
parallel to the primary bands. This formation of new bands. parallel
to the primary ones. reduces the band separation and ultimately
results in blurring of the bands. Figure 6.2.17 shows the microstruc-
ture of this specimen after failure (3.220.000 reversals). which
exhibits microcracks in highly deve10ped slip bands and their blockage
by grain boundaries. These features (with the exception of the densi-
ty of slip lines) were also easily observable under optical

microscOpy.

As can be seen in the photos in most cases. the only sources of
blockage that could be detected within each grain were the grain boun-
daries. This is not unexpected. since these boundaries are saturated
with foreign atoms and foreign phase precipitates. i.e. carbide par-
ticles in case of 1020 specimens. and thus provide very strong
barriers to the hands. This is shown very clearly in Figure 6.2.16

and 6.2.17.

For a thin sheet steel specimen tested at a strain of 0.085 per-

117

cent (specimen T.S.18) grain boundaries prove to be the ultimate
barrier. No slip could be detected in neighboring grains. even after
5.000.000 cycles. Figure 6.2.18 shows a picture taken after 5.000.000
cycles from this specimen. Very fine slip bands can be seen in almost
all grains of this specimen at this stage. This specimen failed after
12,695,000 reversals and very few microcracks were observed in a small
number of scattered grains. The data of T.S.15 and T.S.17 were disre-
garded. since they failed as a result of material defects rather than

fatigue damage.

Specimen F.S.4. which was made of 1030 steel. was subjected to
0.1 percent strain. Replicas were taken after every 100.000 cycles.
These are shown in Figures 6.2.19 to 6.2.24. Close examination shows
that there are no slip bands in the gage section up to 300.000 cycles.
As the cycling is continued. however. slip bands are found on some
grains. Figures 6.2.20 and 6.2.21 show the gage surface after 400.000
and 500.000 cycles. respectively. Again. in order to show more grains
in the micrograph. the magnification was reduced. Some fine slip
bands in a coarse ferrite grain can be seen in these pictures. As one
would expect. the density of slip bands has increased with increased

cycling number.

If the cyclic loading is continued. the slip bands give rise to
microcracks. which then propagate and finally cause the rupture of the
specimen. The appearance of microcracks on the edge of some slip

bands can be seen in Figures 6.2.22 and 6.2.23. These were taken from

118

 

Figure 6.2.19 Microstructure of F.S.4 After 300.000 Cycles (4500K)

 

Figure 6.2.20 MIcrostructure of F.S.4 After 400.000 Cycles (30001)

119

 

Figure 6.2.22 Microstructure of F.S.4 After Failure (4500K)

120

 

Figure 6.2.23 Hicrostructure of F.S.4 After Failure (45001)

 

Figure 6.2.24 Microstructure of F.S.ll After 50.000 Cycles (4500K)

121

different areas of the gage surface of the specimen after failure

(1.644.000 reversals).

Figures 6.2.24 to 6.2.26 show the microstructure of specimen
F.S.11. which has been subjected to a cyclic load with a slightly
higher amplitude (0.13 percent strain). In this case the slip band
networks in most areas were moderate to sparse. with some slip bands
near grain boundaries in isolated areas. Figure 6.2.25 which has
taken at a slightly lower magnification (3000!) shows that even though
there exist coarse and well developed slip bands in some grains. still

there are other grains without slip bands.

Typical microstructures of the specimens cycled at a constant
strain amplitude of 0.2 percent (F.S.10) after failure (127.000 rever-
sals) are displayed in Figure 6.2.26. Microcracks in highly develOped
slip bands and their blockage by grain boundaries are evident in this
picture. Slip bands were observed in most of the grains. The dis-
tances between slip bands in this case were greater than in the case

of F.S.ll.

The obvious conclusion of this part of experiment is that the
formation of the slip bands depends on the plastic deformation. In
all these samples. small damage in the form of slip bands was always

visible around the grain boundaries.

122

 

is,»

Figure 6.2.26 Microstructure of F.S.10 After Failure (4500K)

123

6.2 .3 INITIAL OVERSTRAINING

Specimens F.S.20. F.S.16 and F.S.12 (of the 1018 bar steel ) were
subjected to initial overstrains. After overstraining. these speci-
mens were cycled at a constant strain of 0.097. 0.085 and 0.1 percent.
rspectively. until they failed. A typical microstructure of these
specimens after initial overstraining is shown in Figure 6.2.27. In
all the replicas that were taken after initial overstraining on this
material. some coarse slip bands were observed at grain boundaries and

in the interior of some grains.

It should be mentioned here that all materials used for this
investigation. namely 1018. 1020 and 1030 steels. showed cyclic har-
dening when subjected to overstrain. This was expected. since all of

these materials were in annealed conditions.

The behavior of specimen F.S.16 was somewhat anomalous. After
this specimen was overloaded and subjected to 5.000.000 cycles. the
number of slip bands observed was very small and increased very slow-
ly. After 5.000.000 cycles this specimen was periodically
overstrained (this was a break in the standard test program) after
every 100,000 cycles 10 times. As a result. some rough slip bands did
appear. but the rate of increase was very slow. This specimen did not
break and the test was stopped after 6.000.000 cycles. The microtruc-
ture of this specimen after initial overstraining is shown in Figure

6.2.27. This micrograph shows a few coarse slip bands in a grain in

124

 

a». V . ‘5‘

Figure 6.2.27 Microstructure of F.S.16 After Initial Overstrein

(3000K)

Figure 6.2.28 Microstructure of B.S.16 After 5.200.000 Cycles (3000X)

125

the center of the picture. Examination of the replicas taken from the
gage sections of this specimen showed the existence of some slip bands
right after overstraining. lost of these slip bands were found on
coarse grains. but as cycling continued -after overstraining- some

lines were observed on the finer grains too.

As in the case of no overstrain. the number of slip bands per
grain increased with the number of cycles. However. the density of
slip bands was higher in the present case. Figure 6.2.28 shows the
microstructure and appearance of this specimen after 5.200.000 cycles
at 30001. This micrograph shows some despersc slip bands in some
grains. Figure 6.2.29 which was taken after 5.400.000 cycles at 70001
clearly shows well developed slip bands in neighboring grains that

were blocked by grain boundaries.

The deformation resulting from the larger strain amplitude after
initial overstraining (specimen 8.3.20) is shown in Figures 6.2.30 and
6.2.31. It can be seen that the deformation is completely homogene-
ous. with slip bands present throughout the entire grain (Figure
6.2.30). Close examination of Figures 6.2.30 and 6.2.31 reveals that
the slip bands are not uniform. being coarser in the interior of the
grain. Iicrostructures of specimen.B.S.12 after 100.000 and 500.000
cycles are shown in Figures 6.2.32 to 6.2.33. As can be seen in Fig-
ures 6.2.31 and 6.2.33. there is not much difference between this

specimen and specimen F.S.20.

126

 

Figure 6.2.30 Microstructure of F.S.20 After 100.000 Cycles (70001)

127

 

Figure 6.2.32 Microstructure of B.S.12 After 100.000 Cycles (20001)

128

 

Figure 6.2.34 Microstructure of T.S.19 After Initial Overstrain

(30001)

129

From the 1020 sheet steel specimens. specimens T.S.19 and T.S.10
were chosen for microstructural examinations during the fatigue test.
These specimens were first overstrained. The replicas. which were
taken just after overstraining. showed that slip bands had developed
in some coarse grains. Figure 6.2.34 shows several grains of the spe-
cimen number T.S.19 after overstraining. Slip bands are observed only

in a grain located on the left side of this micrograph.

After overstraining. specimen T.S.19 was subjected to 0.1 percent
and specimen T.S.10 to 0.085 percent strain. Examination of the elec-
tron micrographs of the replicas taken from the gage sections shows
that the number of grains in which slip bands have deveIOped increased
with the number of cycles. and the rate of increase was higher than in
the case of no overstraining. Some micrographs of gage surfaces of
specimen T.S.19 after 200.000 cycles and after failure are shown in
Figures 6.2.35 and 6.2.36. respectively. Figure 6.2.37 and 6.2.38
show the develOpment of slip bands in specimen T.S.10 after 200.000
cycles and after failure. respectively. As can be seen in these pic-
tures. slip bands and some fatigue microcracks almost always cover the
entire deformed grains. while in the non-overstrain case slip bands
mostly cover the centeral portion of deformed grains (see Figure

6.2.17) 0

From 1030 flat specimens which had been overstrained. specimens
F.S.20. F.S.16 and F.S.21. which were strained at 0.09. 0.1 and 0.11

percent. respectively. were selected for microstructural examination.

130

 

Figure 6.2.36 Microstructure of T.S.19 After Failure (30001)

131

 

Figure 6.2.38 Microstructure of T.S.10 After Failure (45001)

132

The examination showed that the behavior of slip bands in this materi-
al was slightly different in comparison with the other two materials
studied. Figures 6.2.39 to 6.2.45 show different parts of gage sec-
tion of these specimens. This material showed more sensitivity to
overstrain than the other two. As a result of overstraining. large
numbers of coarse slip bands were formed on some grains (Figure
6.2.39). Cycling this specimen after initial overstraining at the
abovementioned strain level caused the slip bands. which were produced
by overstrain. to enlarge and resulted in some fine microcracks to
appear along them. Figure 6.2.40 shows the fine microcracks along the
slip bands in a ferrite grain. while Figure 6.2.41 shows well
developed microcracks along slip bands and some fine microcracks
around the boundary of two ferrite grains. Figures 6.2.42-6.2.45 are
other examples of formations of slip bands and microcracks on some

grains of this material after cycling at different strain amplitudes.

In the initial overstraining case it is observed that slip bands
appear at a relatively low rate if the overstrainig is followed by low
strain amplitude cycling. 0n the other hand. if the overstraining is
followed by a high strain amplitude cycling. the rate of appearance of
the slip bands is also higher. Comparing the results of initial over—
straining. with that of no overstraining. one finds that initial
overstraining accelerates the appearance of the slip bands. lore
specifically. if in a specimen subjected to cyclic loading of a given
amplitude. the slip bands appear after a certain number of cycles. the

same phenomenon in an overstrained specimen subjected to the ammo

133

 

Figure 6.2.39 Microstructure of F.S.20 After Initial Overstrain

(45001)

 

Figure 6.2.40 Microstructure of F.S.20 After 1.000.000 Cycles (70001)

134

 

Figure 6.2.41 Microstructure of F.S.20 After 12,206,494 Cycles

(30001)

 

Figure 6.2.42 Microstructure of F.S.16 After 300.000 Cycles (30001)

135

 

Figure 6.2.44 Microstructure of F.S.13 After 100.000 (30001)

136

 

Figure 6.2.45 Microstructure of F.S.13 After Failure (45001)

 

5 After Third Overstrain (30001)

Figure 6.2.46 Microstructure of 3.8.

137

cyclic loading occurs much earlier.

In some cases the life of initially overstrained specimens was
longer than these specimens which had not been overstrained at all.
The reason for this increasing fatigue life could be both the disper-

sion hardening effect of the carbids and the smaller grain size.

6 l2 I4 PERIODIC QESTRAINING

The following specimens were chosen for metalIOgraphic
examination in the periodically overstrained test series: Specimens
B.S.3 .B.S.5. 8.8.19 and 8.8.23 from the bar steel specimens; speci-
mens T.S.21 and T.S.23 from the sheet stool specimens; and specimens
F.S.17. F.S.18 and F.S.12 from the thick sheet stool specimens. These
specimens were overstrained after each 100.000 cycles. The constant
strain that each specimen was subjected to during the fatigue test is
shown in Tables 6.2.8 - 6.2.16. Figures 6.2.46 to 6.2.66 show the
microstructure of these overstrained specimens after certain numbers
of overstraining. The microscopic structure of these specimens after
the first overstraining is not shown here. since it is identical to

the case of initial overstrain.

The microstructures of specimen 8.8.5. which was subjected to
.093 percent strain. after different degrees of overstraining are
shown in Figures 6.2.46 to 6.2.48. The slip bands within the grains

of this specimen after the third. seventh. and sixteenth overload can

 

Figure 6.2.47 Microstructure of B.S.5 After Seventh Overstrain

(20001)

 

figure 6.2.48 Microstructure of B.S.5 After Sixteenth Overstrain

(30001)

139

be seen clearly in these figures. These micrographs were taken at
relatively low magnification in order to show more grains. As can be
seenclearly in these photos. slip bands are evenly distributed over
the ferrite grains. and. as the number of overstrain blocks increase.

in some grains they get denser. especially along the grain boundaries.

Figures 6.2.49 to 6.2.51 show the microstructure of specimen
8.8.23. which was tested at 0.0102 percent strain. after the second.
fourth and sixth overstraining. The extremely dense slip band struc-
ture of this specimen is clearly evident from these pictures. Similar
results were also observed from the specimen 8.8.3 which was tested at

0.095 percent strain. Photographs of this specimen are not shown.

The microstructure of specimen T.S.23 after different numbers of
overstraining appears in Figures 6.2.52 to 6.2.56. As can be seen
from these photos most slip bands are coarse. Furthermore. as the
number of overstrain blocks is increased. the number of these slip
bands and their length also increases. Very few fine slip bands can
be found in any of these pictures. However. after the second over-
straining. well developed fatigue slip bands and microcracks can be
seen in most areas of the gage sections. Since specimen T.S.21 had a
life which was much shorter than what was predicted. the data it pro-

vided was not considered here.

Tests with 1030 steel show that this material is highly sensitive

to overstrain. In particular. the fatigue life is shortened by over-

140

 

Figure 6.2.49 Microstructure of B.S.23 After Second Overstrain

(30001)

 

Figure 6.2.50 Microstructure of 8.8.23 After Fourth Overstrain

(20001)

141

 

Figure 6.2.52 Microstructure of T.S.23 After Second Overstrain

(45001)

142

 

Figure 6.2.53 Microstructure of T.S.23 After Fourth Overstrain

(45001)

 

Figure 6.2.54 Microstructure of T.S.23 After Sixth Overstrain (30001)

143

 

Figure 6.2.55 Microstructure of T.S.23 After Seventh Overstrain

(30001)

 

figure 6.2.56 Microstructure of T.S.23 After Failure ((45001)

144

 

Figure 6.2.57 Microstructure of F.S.l7 After Second Overstrain

(70001)

 

Figure 6.2.58 Microstructure of F.S.17 After Tenth Overstrain (45001)

145

 

Figure 6.2.60 Microstructure of F.S.18 After Second Overstrain

(45001)

146

strain. Figures 6.2.57-6.2.59. show the microstructure of F.S.17
after second. and tenth overstraining. and failure (2.336.000 rever—
sals). Comparison of these micrographs reveals the damages (slip
bands and microcracks) that were caused by successive overstraining.
Figures 6.2.60 - 6.2.62 show microstructures of specimen F.S.18.
Successive growth of slip bands and fatigue microcracks are clearly
evident in these photographs. Figures 6.2.63 - 6.2.65 display the
microstructure of specimen F.S.12 after the second and third over-
strain. Figure 6.2.65 shows a magnified section of the micrograph
shown in Figure 6.2.64 (upper left portion). In this micrograph
simultaneous interpenetration of two different slip bands is shown.
This phenomenon was not observed for the other two materials.
Comparison of the micrographs taken between two successive overstrains
during the fatigue test shows that the appearance of slip bands for

this material was faster than those for 1018 and 1020.

Another interesting feature of the 1030 specimens is that speci-
mens which were subjected to initial overstraining had a longer life
compared with specimens subjected to periodic overstraining. This may

be because of non-uniformity of the grain size of this material.

Examination of replicas taken from the gage section of over-
strained specimens after a certain period (usually after each
overstraining) reveals that overstraining gives rise to a large number
of well-developed slip bands. Slip bands first started to appear on

the coarse grains. and the density in these grains was higher. A sim-

147

 

Figure 6.2.62 Microstructure of F.S.18 After Failure (70001)

148

 

Figure 6.2.63 Microstructure of F.S.12 After Second Overstrain

(30001)

 

Figure 6.2.64 Microstructure of F.S.12 After Third Overstrain (30001)

149

a

V _ _...rflr If ..
a... -

s - .. a)...
.94... fig ...
xv. fit.» 1 I
.4. . .

. ..JII. . 1 .

i
l. . ..
.4 ,

. 1 .

.‘
.

a

_ x , 1 . . /. Id
. a I | l .l .
a . m _, . r. . n
_ . ... ..w ‘
.. . . 4‘
z . . 1. . 1 ...z
5.
. V .
; .. x u u. .
.. V , . . . v . . , . .
J ., . ,. , 1.. u, .
V ,. . 4. . x t ... ...
. . , , ,. n
.. . . . V a
. a v.» v. (

Mn.

4
...v

u...

 

Figure 6.2.65 The same as 6.2.64 but higher Magnification (70001)

 

Figure 6.2.66 Microstructure of F.S.12 After Failure (30001)

150

ilar phenomenon.was observed in the case of initial overstraining. As
can be seen in Figures 6.2.46 - 6.2.66. a large number of
well-developed slip bands were present in some grains. At the begin-
ing of overstraining. the density of these slip bands was low. but

increased as the cycling continued.

'hile an increase in the number of overstrains during a test
resulted in an increase in the slip band density. it seems reasonable
to conclude that the deve10pment of the slip bands is solely due to
overstraining. and cycling between two overstrains seems only to elim-

inate the hardening which is caused by overstraining.

Overstraining results in the hardening of the specimens. It also
causes coarse slip bands in the weak grains of the specimens.
Periodic overstraining prevents the deve10pment of fine slip bands.
which usually appear when a specimen is cycled with a small amplitude.
Moreover. it results in an increase in the number of coarse slip bands

and microcracks as well as the extension of existing microcracks.

In general. it can be said that continued cyclic loading leads to
an increased slip band activity resulting in microcracks which. in
turn. propagate until the specimen fails. An increased strain ampli-
tude accelerates the development of slip hands. it also makes them

denser and coarser. If the specimen experiences an initial over-

151

straining the formation of slip bands occurs at a faster rate which
causes a large number of coarse slip bands to form. The susceptibili-
ty to overstrain for 1030 specimens is higher than for the other two
materials. Both the periodic overstraining itself and a rise in its
frequency increase the density of the slip bands. 'hile the formation
of slip bands can be attributed to overstraining only. the hardening
caused by it is neutralized by cycling between the overstrains. For
all three types of loading. grain boundaries serve as the sources of

blockage within each grain.

As mentioned in the previous section. the extent of the effect of
overloading differs for different materials. Changes which occured in
microstructures due to cycling were very much dependent on the history

of the specimens and the materials.

The following recommendations resulted from this study: first.
tests (either initial or periodic overstraining) should be performed
on pure materials. second. it could be useful to study the structural
damage in layers close to the surface of specimens. This should be
done on thin enough specimens to enable the making of thin foil sam-
ples for electron microscOpy examination without the need of slicing

the gage section or any other usage of a mechanical device.

CHAPTER 7

SUMMARY AND CONCLUSIONS

In this investigation more than 75 plain carbon stool specimens
of three different geometries were tested under one of the following
conditions: no overstrain. initial overstrain. and periodic over-

strain.

Each overstrain block consisted of 20 decreasing cycles with a
maximum strain 0f *1 percent. All tests were performed under com-
pletely reversed strain control. For thin sheet specimens. axial
strain was calculated from the axial stress and transverse strain. and
then used to control the test. During each fatigue test. hysteresis
loops were recorded to show cyclic behavior'and for correlation with
microstructural data. Among these loops the stable ones were chosen
as representative loops and cyclic stress-strain properties were
determined from them. Fatigue properties of each material were deter-
mined from the same stress-strain data that were used to determine the

cyclic stress-strain properties.

To study the microstructure of the specimens and to detect slip

bands and fatigue microcracks. some of the specimens of each kind were

152

153

polished and then etched to obtain a fine smooth surface. Plastic
replicas were then made from the whole gage sections of these speci-
mens after every 100.000 cycles and after each overstraining. A
series of replicas formed a permanent record of the (surface) micros-

tructure of the specimen during its fatigue life.

These three steels exhibited cyclic softening at low strain
amplitudes and cyclic hardening at higher amplitudes. Furthermore
they never become completely stable under any strain amplitude. The
instability observed seems to be cycle dependent. In general the

fatigue test results showed the pattern characteristic of mild steels.

For all of these steels. cyclic overstraining resulted in a small
amount of hardening which in turn reduced the amount of plastic
strain. When the specimen was cycled continuously at a constant
amplitude it softened and returned to its stable condition. For 1018
cylindrical specimens. periodic overstraining resulted in a fatigue
life which was appreciably higher than when the specimens received
only an initial overstrain. This can be attributed to the strain har-
dening of the material during the overstrain and also the uniform
microstructure of the material. (Recall that the 1018 steel has finer
and more uniform grains.) 0n the other. hand constant amplitude
cycling of specimens of this material yielded a fatigue life only

slightly higher than that of periodically overstrained specimens.

Overstreining of the 1020 thin sheet specimens did not produce

154

any significant change in the fatigue life. whereas periodic cyclic
overstrain had a noticeable effect. Initial overstraining of 1030
sheet specimens was found to have no appreciable effect on fatigue
life of these specimens. whereas periodic overstraining caused a sharp
decrease in the fatigue life. This is almost entirely due to the

nonuniformity of the grains of this material.

For all the materials which were used. the structural deformation
(i.e. the appearance of slip bands. initiation of microcracks. etc.)
was found to be inhomogeneous and history dependent. As expected.
slip bands appeared in weaker grains (coarse ferrite grains) first.
No slip bands were observed in the pearlite grains. As for micro-
cracks. in all cases they initiated within the grains and not along

the grain boundaries as has sometimes been reported.

In general the mechanical prOperties of the material seemed to be
affected by local plastic strain and fatigue damage resulting from the

application of cyclic strain.

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