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SOFTENING MECHANISMS AND MICROSTRUCTURAL INSTABILITIES
OF NICKEL DURING HIGH TEMPERATURE LOW CYCLE FATIGUE

By

Shuhrong Chen

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Metallurgy, Mechanics and Materials Science

1989

@OOJSBO

ABSTRACT

SOFTENING MECHANISMS AND MICROSTRUCTURAL INSTABILITIES
OF NICKEL DURING HIGH TEMPERATURE LOW CYCLE FATIGUE

BY

Shuhrong Chen

The microstructural development and its effect on mechanical
properties was investigated during high temperature low cycle fatigue in
Ni. Even at small strain amplitudes (e<0.004) substantial microstruc-
tural changes were observed due to grain growth, grain boundary
positioning with respect to the applied stress and dynamic recrystal-
lization. Dynamic recrystallization during cyclic deformatirnilaven at
strain amplitude as large as 2% was only observed in polycrystals.
Large differences in the dislocation arrangement was observed between
grain interior and grain boundary regions. The introduced changes are
particularly important for control or retention of grain size during
high temperature applications and in the context of intergranular
fatigue crack propagation associated with grain boundary sliding. The
microstructural development is reflected in the mechanical behavior of
the material and correspondingly will affect the performance of parts
during high temperature service. By appropriate selection of deforma-
tion temperature, strain amplitude and cycle frequency the evolution of
the microstructure can be substantially influenced, in particular under

controlled over-straining.

ACKNOWLEDGEMENTS

First and foremost, I would like to thank my advisor, Professor G.
Gottstein, for his patient guidance and beneficial discussions in
making this project a success. Also, I would like to express my
deepest gratitude to my family for their full support in these years.

The financial support of the U.S. Department of Energy, Office of
Basic Science, under grant number DE-FGOZ-8SER45205 is gratefully

acknowledged.

ii

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

I

II

III

IV

INTRODUCTION
LITERATURE SURVEY
2.1 Grain Boundary Migration during LCF
2.2 DRX in Monotonic Tests
2.3 DRX during High Temperature LCF
2.4 Crack Propagation during High Temperature LCF
EXPERIMENTAL PROCEDURE
3.1 Testing Materials
3.2 Specimens Preparation
3.2.1 Mechanical Testing Specimens
3.2.2 Optical Microscopy Specimens
3.2.3 Transmission Electron Microscopy Specimens
3.2.4 Scanning Electron Microscopy Specimens
3.3 Mechanical Testing
3.3.1 Instron Testing Machine
3.3.2 MTS Testing Machine
3.4 The Microhardness Test
EXPERIMENTAL RESULTS
4.1 Mechanical Behavior
4.2 Microstructural Development

4.3 Evidence of DRX under High Temperature LCF

iii

Page

vi

l4

l6

l8
l9
19
26
32
33
34
34
36

43

45
47

62

4.4 Results of High Strain Amplitude Tests
4.5 Results on Cu Single Crystals
4.6 Dislocation Structures
4.7 Effect of DRX on Mechanical Properties
V DISCUSSION
5.1 Mechanical Behavior And DRX
5.2 Grain Boundary Migration and Dislocation Structure
5.3 Crack Propagation and DRX
VI CONCLUSIONS
VII REFERENCES

APPENDIX A : PROGRAMS SOURCE CODES

iv

Page
65
76
84

103

144
148
155
168
173

177

LIST OF TABLES

Table

3-1. Composition of Ni studied.
3-2. Composition of Al studied.

3-3. Jet polishing conditions for Ni, Al and Cu.

4-l. Test conditions and results of low cycle fatigue.

4-2. Summary of test conditions of crack propagation.

Page

18
18
33
46

106

Figure

2-1.

2-2.

2-3.

2-4.

3-1.

3-2.

3-3.

3-4.

3-5.

LIST OF FIGURES

Captions Page
True resolved shear stress vs. true resolved shear strain for
(111) Ni single crystals [6]. (Courtesy of Gottstein). 8
Subgrain coarsening owing to subboundary relaxation, schema-
tically according to Dillamore et a1. [35], (a) unrelaxed; (b)
relaxed [3]. (Courtesy of Gottstein). 10
TEM micrograph of a twin lamella emanating from a subgrain
boundary by consecutive emission of partial dislocations for a
specimen deformed to the start of DRX at T-707°C, fi-4x10-3s-1,

rR-14.2MPa. (a) bright field image g-(lil) (b) dark field

M’
image with (002)T [3]. (Courtesy of Gottstein). 11
Flow curves of a plain 0.25% C steel in the austenite state

(fcc) at llOO°C (0.76 Tm), illustrating the strong influence

of strain rate, drawing after Rossard [36]. 13
Geometry and dimensions of testing samples. 20
Gauge sectional geometry and orientation of the Cu single

crystal. 22
Geometry and dimensions of notches pre-machined for crack
propagation tests. (a) single-edge; (b) double-edge and (c)

circum ferential notches. 23
The microstructure of Ni (first batch of material) after

annealing at 900°C for 5 hours. 24

The microstructure of Ni (second batch of material) after

annealing at 900°C for 5 hours. 25

vi

3-6.

3-7.

3-8.

3-9.

3-10.

3-11.

3-12.

3-13.

3-14.

4-1.

4-2.

4-3.

Engineering stress-strain curve of a Ni bar, which was annealed

at 900°C for 3 hours, elongated at room temperature with an
initial strain rate of 2x10-‘s-1. 27
The microstructure of the elongated Ni after annealing at 850°C
for (a) 20 min.; (b) 1 hour. 28
The microstructure of Al after annealing at 310°C for 5 hours. 30
Geometry and dimension of a Ni specimen with pre-machined

planar side surface. 31
Arrangement of the high temperature mechanical testing setup. 35
Schematic diagram showing the basic elements of the computerized
high temperature high vacuum servohydraulic test system. 37
A drawing showing the design of the pre-load grips for high
temperature tension-compression fatigue test. 39
Schematic diagram of the specimen gripping insert. 40
Final setup inside a vacuum chamber with an extensometer

attached for conducting a strain amplitude control fatigue

test at high temperature. A 42
(a)-(b) Cyclic hardening curves for Ni and A1 at high tempera-
ture with various total strain amplitudes and cycle frequencies;
(c) stress decrease rate vs. number of cycles. (The numbers of

the curves corresponds to the test numbers in Table 4-1). 48
The microstructure of a Ni after 200 cycles with 0.5% total

strain amplitude at 600°C. 51
The microstructures of a Ni in a plane parallel to the loading
direction after cyclic deformation with 0.5% total strain
amplitude at 600°C (a) Annealed at 900°C for 5 hours; (b) after

10 complete cycles at 600°C, slightly polished and etched again

vii

4-8.

4-9.

to reveal the new grain boundary positions; (c) after 10 complete
cycles, positions A,B,C and D indicate inhomogeneous strain
distribution on the surface; (d) etched to reveal the positions

of new and original grain boundaries simultaneously; (e) after

40 cycles; (f) the positions of new and original grain boundaries
after etching again; (g) slightly polished and etched again,

only new grain boundaries can be seen; (h) right after 160 cycles;
(1) after etching; (j) after polishing and etching. 53
Detailed structure of surface markings after 10 cycles. 57
The microstructure on the planar surface of a Ni after cyclic
deformation with 0.5% total strain amplitude at 600°C for

(a) 10; (b) 20 and (c) 40 complete cycles. The arrow indicates

the offset of a scratch across the grain boundary due to grain
boundary sliding. 59
The microstructure of an A1 after 720 cycles with 0.5% total
strain amplitude at 200°C. 61
In Ni (a) serrations of a grain boundary, nuber of cycles N -

200, total strain amplitude ct- 0.5% ; (b) a protrusion and a

new grain at a grain boundary, N - 200, et- 0.5%; a new grain
formed (c) on the grain boundary, N - 510, 6t- 0.5%; (d) near a
twin, N - 200, et- 0.5%; (e) at a twin boundary, N - 310, 6t:
1.7%; (f) in the interior of a grain at the tip of a twin, N -
510, et- 0.5%. 63
The microstructure of a Ni after 510 cycles with 0.5% total
amplitude. The whole cross sectional area perpendicular to the

loading direction is revealed. 64

The microstructure on the planar surface of a Ni after cyclic

viii

4-10.

4-11.

4-12.

4-13.

4-14.

4-15.

4-16.

4-17.

deformation with 0.5% total strain amplitude at 600°C. (a) after
80 cycles; (b) after 120 cycles and slightly etched. The arrow
indicates the position where a twin was created. 66
The microstructure on the planar surface of a Ni after cyclic
deformation with 0.5% total strain amplitude at 600°C. (a) after
80 cycles; (b) after 120 cycles and slightly etched. A new

grain attached to the serrated grain boundary. 67
Cyclic hardening curve of a Ni after 55 cycles with 5% total
strain amplitude at 600°C. 68
The microstructure of a Ni in a plane parallel to the loading
direction after 55 cycles with 5% total strain amplitude

at 600°C. 70
(a) The microstructure of a Ni after 55 cycles with 5% total
amplitude. The whole cross sectional area perpendicular to the
loading direction is revealed; (b) higher magnification of the
structure in (a). 71
Cyclic hardening curves of two Ni hour-glass shape specimens

with 0.3% and 1% total strain amplitudes at 600°C. 73
The microstructure in a plane parallel to the loading direction
of an hour-glass shape Ni fatigued at 600°C with 1% total axial
strain amplitude. 74
The microstructure in a plane perpendicular to the loading
direction and containing the smallest diameter region of an
hour-glass shape Ni fatigued at 600°C with 1% total axial

strain amplitude. 75
The microstructure in a plane parallel to the loading direction

of an hour-glass shape Ni fatigued at 600°C with 0.3% total

ix

4-18.

4-19.

4-20.

4-21.

4-22.

4-23.

4-24.

4-25.

4-26.

4-27.

4-28.

axial strain amplitude. 77
Cyclic hardening curve of a Cu single crystal tested at 400°C
with 1% total strain amplitude. 78
Dislocation structure of a Cu single crystal tested at 400°C

with 1% total strain amplitude for 420 cycles. 80
Cyclic hardening curve of a Cu single crystal tested at room
temperature with 1% total strain amplitude. 81
Surface markings on a Cu single crystal after 110 cycles with

1% total strain amplitude at room temperature. 82
Microhardness during isochronal annealing of a Cu single crystal
fatigued at room temperature with 1% total strain amplitude. 83
Dislocation structure of a Cu single crystal fatigued at room
temperature. (a) as deformed; deformed and then annealed at

(b) 250°C; (c) 552°C and (d) 850°C for 30 min. 85
The dislocation structure inside a Ni grain after (a) 310

cycles with 1.7% total strain amplitude; (b) monotonic tension
test to a strain 6 - 0.15. 89
The dislocation structure in a Ni of a larger area around a

grain boundary after 310 cycles with 1.7% total strain

amplitude. 92
Cyclic hardening curve of a Ni tested at 600°C with 0.5% total
strain amplitude. 93
Microstructure of a Ni after testing at 600°C with 0.5% total
strain amplitude for 10 cycles. (a) grain interior, (b) around

a grain boundary. 95
Microstructure of a Ni after testing at 600°C with 0.5% total

strain amplitude for 40 cycles. (a) and (b) different areas

4-29.

4-30.

4-31.

4-32.

4-33.

4-34.

4-35.

4-36.

4-37.

in the same specimen. Note difference in structure. 97
Dislocation structure in the grain interior of Ni after testing

at 600°C with 0.5% total strain amplitude for 160 cycles. 99
Dislocation structure around a grain boundary of a Ni after
testing at 600°C with 0.5% total strain amplitude for 160

cycles. 100
Dislocation structure around a grain boundary of a Ni tested at
600°C with 1.7% total strain amplitude. 102
(a) True stress vs. true strain curve during cycles 1210—1218

and (b) corresponding dislocation structure of Ni tested at

600°C with 0.5% total strain amplitude. The test was terminated
during the extended tensile cycle number 1219. 104
The microstructure of a prenotched Ni fatigued at room tempe-
rature with 0.5% total strain amplitude. The arrow indicates the
stress direction. 107
The microstructure of a prenotched Ni fatigued at room tempe-
rature with 0.5% total strain amplitude and after annealing at
764°C (0.6Tm) for 1 hour. 109
The microstructure of a prenotched Ni fatigued at room tempe-
rature with 0.5% total strain amplitude and after annealing at
418°C (0.4Tm) for 1 hour. 110
The microstructure of a prenotched Ni fatigued at 600°C with

0.5% total strain amplitude. The arrow indicates the stress
direction. 112
The microstructure of a prenotched Ni fatigued at 600°C with

0.5% total strain amplitude. The arrow indicates the stress

direction. 113

xi

4-38.

4-39.

4-40.

4-41.

4-42.

4-43.

4-44.

4-45.

4-46.

4-47.

4-48.

The microstructure around a branch of a crack of a Ni fatigued

at 600°C with 0.5% total strain amplitude. The arrow indicates

the stress direction. 114
The microstructure of a prenotched Ni fatigued at 600°C with

0.5% total strain amplitude and strain rate of 2x10-3s-1. The
arrow indicates the stress direction. 115
Cyclic hardening curve of a Ni having a circumferential notch
fatigued at 600°C with 1% total strain amplitude for 605

cycles. 117
The microstructure associated with crack propagation corres-
ponding to the test indicated in the Fig. 4-40. 118
A higher magnification micrograph showing part of the structure
around a crack in Fig. 4-41. 120
A higher magnification micrograph showing part of the structure
around a crack in Fig. 4-41. 121
Flow curve of a Ni having a circumferential notch elongated at
600°C with an initial strain rate of 2x10"s-1. 122
The microstructure associated with crack propagation corres-
ponding to the test indicated in the Fig. 4-44. 123
Flow curve of a Ni having a circumferential notch fatigued at
600°C with i0.5% total strain amplitude and occasional over-
straining with +5%, ~1% total strain amplitude. 124
The microstructure associated with crack propagation corres-
ponding to the test indicated in the Fig. 4-46. 125

Flow curve of a Ni having a circumferential notch fatigued at

xii

4-49.

4-50.

4-51.

4-52.

4-53.

4-55.

4-56.

5-1.

600°C alternatively with +5%, -1% total strain amplitude for 20
cycles and i0.5% total strain amplitude for 200 cycles until
fracture at cycle number 1114. 127
The microstructure associated with crack propagation corres-
ponding to the test indicated in the Fig. 4-48. 128
SEM micrographs of the fracture surface after the test indicated
in the Fig. 4-48. 129
Flow curve of a Ni having double edge notches fatigued at 600°C
alternatively with +0.5%, -5% total strain amplitude for 5

cycles and i0.5% total strain amplitude for 500 cycles until
fracture at cycle number 5512. 131
The microstructure associated with crack propagation corres-
ponding to the test indicated in the Fig. 4-51. 132
SEM micrographs of the fracture surface after the test indicated
in the Fig. 4-51. 134
Flow curve of a Ni having double edge notches fatigued at 600°C
with i0.5% total strain amplitude until fracture at cycle

number 10943. 136
The microstructures associated with crack propagation corres-
ponding to the test indicated in the Fig. 4—54. (a) S-3/4; (b)
S-1/2 and (c) S-0. 138
SEM micrographs of the fracture surface after the test indicated
in the Fig. 4-55. 142
(a) Cyclic hardening curve of a Ni tested at 600°C with 0.5%

total strain amplitude; (b) the hysteresis loops corresponding

to the various cycle numbers at curve (a) which is indicated

in the graph. 149

xiii

5-2.

5-3.

5-4.

5-5.

5-6.

5-7.

5-8.

Normalized true stress vs dislocation cell size in Ni for

cyclic deformation at various temperatures, I - current
investigation, 0 - result of Bhat and Laird [14]. 153
Schematic sketch showing the strain induced grain boundary
migration. Loading is in (a) tension; (b) compression and (c)
returning to zero. 156
SEM micrograph of the fracture surface of a Ni fatigued at

600°C with 0.5% total strain amplitude. 160
SEM micrograph of a Ni fatigued at 600°C with 0.5% total strain
amplitude. (a) after polishing; (b) after etching. 161
Schematic sketch showing DRX due to plastic deformation
associated with the crack propagation. 162
Schematic sketch showing three possible cases related to the
effect of DRX on crack propagation. 164
Flow curves of Ni having double edge notches fatigued at

600°C with (curve 1) and without (curve 2) occasional

overstraining. 166

xiv

I INTRODUCTION

Materials for high temperature applications have become progres-
sively in demand for high technology products: turbine blades for jet
engines or structural components in high temperature reactors are
prominent examples. The excellent mechanical properties of advanced
materials are generally achieved by optimizing the microstructure during
the processing to the final product. A change of this microstructure or
even a breakdown, therefore, will cause serious consequences for the

part in service and may introduce premature failure.

One well known high temperature phenomenon is the recrystallization
of the material during deformation, also referred to as dynamic recrys-
tallization (DRX). DRX has been reported in a variety of fcc metals and
alloys in which the degree of dynamic recovery is restricted [1], such
as Cu [2,3]; CuAl [4]; CuZn [5]; Ag [6]; Ni [7,8]; Ni-Fe [8]; Ni super-
alloys [9]; stainless steel [10], etc.. These experimental reports were
based on the tests conducted in monotonic loading conditions, namely in
tension, compression, or torsion.- In a recent paper, DRX was found at
the grain boundaries during low cycle fatigue (LCF) in bicrystals of Ni.
with special grain boundaries [11]. The occurrence of DRX during cyclic
deformation in polycrystals has recently been reported [12]. The
results on DRX were the minor observations in these studies. Eh) far no

systematical research has been done on DRX during LCF.

Most parts under high temperature service conditions, however, are
subjected to cyclic loading conditions due to vibrations or temperature
fluctuations. A major difference between cyclic and monotonic loading
is that the strain amplitude under cyclic conditions is commonly small
compared to the critical strain to set off DRX in monotonic tests.
However, the critical conditions for DRX to occur are determined by the
microstructure, namely by the development of a cell-or subgrain struc-
ture [3,7,13] . The existence of dynamic recrystallization during high
temperature low cycle fatigue is not immediately obvious. It is ex-
pected because the microstructural development during high temperature
low cycle fatigue is similar in character (although different in scale)
to the structure evolution during monotonic loading at high tempera-
tures, namely the build-up of a cell structure that dynamically
transforms (recovers) to a subgrain structure [14,15]. Moteff and
collaborators [16-18] have studied the microstructural evolution of A181
304 stainless steel at different fractions of the fatigue life. Their
results show that at 0.5 Tm (Tm- melting temperature) already in the
first two cycles the dislocations tend to arrange in a cell structure
which becomes progressively pronounced with increasing number of cycles,
and finally will be converted to a subgrain structure with sharply
defined boundaries. In a study on the nucleation of DRX in single
crystals during monotonic deformation [7] it was found that DRX is
triggered by dynamic recovery as a consequence of fluctuations in the
recovery rate. This was attributed to the local appearance of mobile
subboundary segments in an internally highly stressed environment. The
microstructural studies olehat and Laird [14,15] and Nahm et a1. [16]

show exactly this arrangement of dislocations in fatigued specimens, so

that critical conditions for DRX should also exist in cyclic deformation
mode, although stress and instantaneous strain level remain comparably

small in cyclic loading.

Also, extensive grain boundary migration was observed during high
temperature LCF. Quantitative studies on this phenomenon have been
reported on Pb [19-21] and A1 [22,23]. Since the nucleation of DRX in
polycrystals is likely to occur by bulging of existing grain boundaries
[24,25], the grain boundary migration during LCF may be instrumental iJl

the nucleation of DRX.

In ductile materials, fatigue crack propagation is accompanied by a
plastic deformation zone. In the case of metals, plastic deformation
usually takes place by slip which involves the generation and multi-
plication of dislocations and their movement through the lattice.
According to the model proposed by Rice and Thomson [26], (dislocations
can be emitted from crack tips and thereby shield the concentrated
stress field before the stress intensity factor reaches the critical
fracture stress. This highly plastic deformation may recover at high
temperature and set off DRX during crack propagation and reduce stress

concentrations and thus, decelerate or arrest crack prepagation.

In the present study these problems were addressed by investigating

the microstructural development during LCF.

II LITERATURE SURVEY

2.1 Grain Boundary Migration During LCF

It is clear from the data available to date that the movement of
grain boundaries is an important microstructural process in high tem-
perature fatigue. The paper published by Snowden in 1961 [19] indicated
that the effect of the alternating strain in bending fatigue test of
pure lead was the appearance of slip traces and grain boundary migra-
tion. The rate of migration increased with increasing strain amplitude
and was highest in the early part of the life. One or two hundred
microns displacement of the boundary was found to be common. He ob-
served that some boundaries including coherent twin boundaries, did not
move. One more important feature of the migration was that boundaries
tended to migrate to positions at i45° to the specimen axis. This type
of boundary migration resulted in the formation of an orthogonal grain
structure. He explained.this phenomenon on the basis that, in general,
different amounts of deformation were built up on each side of the
boundaries so that the migration is produced by unequal numbers of
dislocations on opposite sides of the boundaries. A possible reason for
the diminished rate of migration after larger numbers of cycles, sug-
gested by Snowden, was that the boundaries moved to align themselves in
the directions of maximum shear stress. The enhanced grain boundary
sliding at orientations in the shear direction, i.e., at i45° to the
specimen axis, would take care of the deformation necessary to respond

the straining imposed by cyclic fatigue.

Quantitative studies on grain boundary migration and grain boundary
sliding have been reported on Pb [20,21] , A1 [22,23,27], Pb-Sn solid
solution alloy [28,29] and Al-Mg solid solution alloy [30]. The results
will be briefly reviewed. Langdon et al. [20,21] conducted experiments
on high purity lead (99.9995%) at room temperature (0.5Tm) using reverse
bending and torsion fatigue. On contrary to Snowden, the strain
amplitude was increased to more than 0.2% and the structural development
was observed from the very first cycle. The results showed that a large
number of the grain boundaries revealed very extensive migration. As a
result of this migration, a series of essentially parallel markings at
many of the boundaries could be easily observed under optical micro-
scope. By detailed inspection that there was a well defined one-to-one
correspondence between the number of grain boundary markings and the
total number of whole cycles imposed on the specimen which Snowden
didn't report due to his observation was taken after a«104 cycles with a
very small strain amplitude such that the markings were too dense to be
distinguished. The exceptional clarity of each separate migration
marking suggested that grain boundary sliding may also occur cyclically
at the interface, giving a small displacement of material perpendicular
to the specimen surface at each marking. Evidence for cyclic grain
boundary sliding was confirmed by using two-beam interferometry. The
cyclic markings are repetitive through each fatigue cycle, and the sharp
discontinuities in the fringes confirm that sliding occur at the grain
boundaries as an alternating process during cyclic deformation. Further
investigation by optical microscopy using Nomarski interference contrast
showed the presence of a fine structure within the migration markings.

An additional observation noted only when examining the longer grain

boundaries in specimens containing a very coarse grain size, was the
formation of a zig-zag pattern of migration markings. The individual
‘boundary segments of the zig-zag pattern were generally fairly close to
45° with respect to the stress axis. A model was proposed by Langdon et
al. to explain the occurrence of markings on the surface due to alterna-
tion of grain boundary migration and sliding. They assumed that the
migratdxnl is stress-induced in response to the cyclic loading which is
different from the explanation Snowden made (strain induced grain bound-
ary migration). The measurements of grain boundary sliding was done by
using a two-beam interference microscope with a resolution of i0.06 pm.
The average sliding offset perpendicular to the surface was measured
after testing for various numbers of cycles. The value of the average
offset perpendicular to the surface, v (in the order of lO-Ipm), in-
creases rapidly over the initial stage, and thereafter the rate of the
increase is reduced and ultimately the value of v essentially stabi-
lizes.

The saturation in v is likely to correspond to the attainment of the
diamond grain configuration after large numbers of cyclic deformation.
The measurements of grain boundary migration was performed by Yavari et
a1. [23] using Al fatigued at 300°C (0.61Tm). The average distance of
grain boundary migration 51 for polycrystalline A1 with strain amplitude

less than a i 0.4% was found to obey the empirical relationship

.0.35 0.5 0.66

m - Af N A6 exp(-62.0/RT)
where f : frequency
N : number of loading cycles

Ac : strain amplitude

R : gas constant in kJ/mol-k
T : absolute temperature

7 0.35
A : = 3.2x10 pms

Also, the occurrence of cyclic migration leads to the disappearance

of grains and thus is a mechanism of grain coarsening.

A change of the grain morphology due to grain boundary migration
during cyclic deformation at 650°C at a low strain rate (é- 4x10 '2 '3
was also reported on OFHC Cu [31]. But this change in grain shape was
found to be strain rate dependent and at high strain rates , no such
change in grain morphology occurred. That impurities or precipitates
slow down or inhibit grain boundary migration explains why type 304
stainless steel does not exhibit any change in grain structure at 760°C

at the lower strain rate [31].

2.2 DRX In Monotonic Tests

DRX has been investigated extensively in monotonic loading. As is
known from previous investigations, the onset of DRX in single crystals
is indicated by a sharp drop in the flow stress (Fig.2-l) [6,32]. It
has already been shown previously [33], the shear stress (rR) rather
than shear strain (7R) is the critical quantity governing the initiation
of DRX. In single crystals, DRX is controlled by nucleation rather than
by growth of recrystallized grains. In the same paper, they also showed

that DRX is not only triggered but is also totally controlled by the

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deformation process. The growth of a nucleus is stopped by a strain
rate increase, and, once stopped, it is not activated again in a sub-
sequent recrystallization event. For a constant deformation path, i.e.,
same material, orientation, strain rate and temperature, DRX is set off

reproducibly at a definite value of flow stress (r From the experi-

R)'
ments on Cu and Ni Gottstein and Rocks [7] came up with a conclusion.
that dynamic recovery rather than a competing process, is a precondition
to occurrence of DRX. Dynamic recovery of dislocations leads tn: rear-
rangement of cell walls on a local scale which give rise to mobile
subboundary segments [34] in an elastically stressed environment and
thus can trigger DRX. Gottstein et a1. [7] also found that two tempera-
ture regimes can be distinguished with a rather sharp transition at 0.75
Tan. The recrystallized structure was composed of discontinuously grown

subgrains at very high temperature (T>0.75Tm, th), or complete families

of annealing twins at medium high temperature (0.4<T/Tm<0.75, th).

For nucleation mechanisms Karduck et a1. [3] suggested

(1) DRX is nucleated at th most likely by discontinuous subgrain growth
originating from kink bands owing to their special subgrain size and

shape (Fig. 2-2 [35]).

(2) The nucleation of DRX.at th is suggested to occur by emission of
twins from subgrain boundaries. Twin formation is probably.assisted by
internal stresses and favourable dislocation arrangements in the sub-

boundaries (Fig. 2-3).

10

 

 

 

]--’ -—- (bl
(cl

 

 

 

 

Fig. 2-2. Subgrain coarsening owing to subboundary relaxation, schema-
tically according to Dillamore et a1. [35], (a) unrelaxed; (b)relaxed
[3]. (Courtesy of Gottstein).

11

 

Fig. 2-3. TEM micrograph of a twin lamella emanating from a subgrain
boundary by consecutive emission of partial dislocations for a specimen
deformed to the start of DRX at T-707'C, fi-4x10-ss-‘, rR-l4.2MPa. (a)
bright field image g-(111)H; (b) dark field image with (002)T [3].

(Courtesy of Gottstein).

12

For polycrystalline materials, as known, the grain boundaries
influence the development of the dislocation structure as well as the
recrystallization behavior. Hence, additional effects can occur in
polycrystals so that the results on single crystals may not be suffi-
cient to understand all recrystallization phenomena in polycrystalline
aggregates. The initiation of DRX in polycrystals is also indicated by
the drop of true stress as seen in Fig. 2-4 [36]. The strain rate has a
strong influence on DRX. At the higher strain rates, the flow curve
exhibits the typical shape for DRX, but at low strain rates, the flow
curve is periodic due to recurrent cycles of recrystallization. Sakai
and Jonas [37] mentioned that there are two basic differences between
single and polycrystal observations. The first is the initiation stress
(1R,0R) in a typical single crystal oriented for multiple slip can be
high as two or more times that in a polycrystal of the same conditions.
The second difference is that nucleation in polycrystals is mostly
restricted to the original grain boundaries, which it occurs in the
grain interiors in single crystals. They explained the difference of
the critical stress (TR’OR) by homogeneous nucleation for single crys-

tals and heterogeneous nucleation for polycrystals.

The effect of grain boundaries on dynamic recrystallization be-
havior of copper isoaxial bicrystals with (001) tilt boundaries was
investigated by Takada et al. [38]. They found that the recrystallized
Brains form on the already present tilt boundary. This indicates that
the boundary is the preferred nucleation site for dynamic recrystalliza-
tion. It was also found in that study that the tilt boundaries migrate

before the onset of dynamic recrystallization.

13

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Cannon mo cosmSHMCH wcouum osu wcfiumuumSHHH .AEH om.ov oaooaa um noomV

oumum muHCoumsm onu CH Hooum o wmm.o chHQ m mo moPHso 30am .elm .wmm

m .Zamem mDmB

 

 

 

c.” #4 m4 0.” 0.6 v.0 v.0 md 05
a T a q i a J a a u a a a u 4 o
1
r . o“
oom\ 32.6 H w .
- 4 il]!\/\. a
- - on
oum\ v.86 H w. .
- . om
- .. on
1 00m\ .VHd "w. L 00
.. - or
b r P P p p P P P n b p p p p on

 

 

 

[9cm] ‘0 ‘ssaals 3021.1.

14

In polycrystalline materials, static recrystallization is known to
nucleate at original boundaries by the buldging mechanism in moderately
deformed materials, by nucleation in regions of strong orientation
gradients such as deformation bands in heavily deformed materials, and
by the single subgrain growth mechanism [39]. Similar mechanism are
also expected to operate during dynamic recrystallization. The bulging
mechanism for the nucleation of DRX were discussed by Ito et a1. [25]

and Roberts et a1. [40].

2.3 DRX During High Temperature Low Cycle Fatigue

The elevated temperature LCF effect on the mechanical behavior of
structural materials has attracted particular attention in recent years.
Most investigations [41-44] focused on macroscopic parameters such as
stress, strain and cycles to failure, rather than on details of the
microstructural evolution. Microstructural developments during LCF have
been extensively studied during deformation at ambient temperature [45-
47], but very few investigators have addressed the microstructural

aspect of LCF at elevated temperatures.

Not much information is available on DRX during HTLCF. In the same
Paper cited in section 2.1 [19] , DRX was observed in Pb which straddled
the original orthogonal grain boundary after 8x108 cycles with i0.092%
Strain amplitude. At a higher strain amplitude, similar structural
instability near grain boundaries was detected earlier (9:10!5 cycles).

But in more recent papers [20,21], no occurrence of DRX under similar

15

test conditions was reported. One reason might be the small number of
cycles imposed on the specimen (<103 cycles). During the duration of
the current project, a few papers on DRX during LCF were published
[11,12,48]. Lim and Raj [11] conducted tests on pure Ni bicrystals with
special orientation relationships between these two grains. They found
that symmetrically strained bicrystals behave differently from those
which are deformed nonsymmetrically. The edge component of the residual
dislocations left in the boundary by reaction of lattice dislocations
was found important for slip induced cavitation, migration and dynamic
recrystallization. Symmetrical reactions which leave a low energy array
of edge dislocations in the boundary are most likely to suffer dynamic
recrystallization. Lim and Raj explained this as follows: the arrange-
ment of the dislocations leads to the compensation of stress fields, and
therefore, to the accommodation of a higher density of dislocations in
the grain boundary. Since the onset of dynamic recrystallization is
likely to occur when the density of grain boundary dislocations exceeds
a critical value, it is conceivable that a low energy dislocation array
is a necessary condition for the nucleation of fresh grains. Raman and
Reiley investigated DRX on a Pb-Sn solid solution alloy [12,48]. They
Observed that the nuclei were most often found at or near existing grain
boundaries, but in some cases were observed in the grain interior ad-
Jacent to a high density of slip bands, and the newly formed grains also
Participated in cyclic migration and eventually developed boundary

markings .

No systematical research has been reported yet on DRX during LCF

and its effect on material properties.

16

2.4 Crack Propagation During High Temperature Low Cycle Fatigue

Extensive grain boundary migration occurs during HTLCF. Grain
boundary sliding will be enhanced when a grain boundary migrates such as
to align under 45° with respect to the stress axis. Grain boundary
sliding will cause cavity formation [49]. An investigation on an Al-Mg
solid solution alloy [50] has demonstrated that numerous microcavities
are formed at the various migratory positions of the boundaries. The
coalescence of these cavities will eventually lead to intergranular

fracture under HTLCF.

According to the crack tip shielding model proposed by Rice and
Thomson [26], an atomically sharp crack will have been blunted by one
atomic plane after the production and emission of a dislocation from the
crack tip due to the external stress field as concentrated by the
presence of the crack. In ductile materials more dislocations will be
emitted from the crack tip and form the plastic deformation zone. The
plastic zone size was calculated by applying fracture mechanics concepts
[51]. A recrystallization technique can be used to reveal the plastic
Zone size of specimens fatigued at room temperature [52-54]. The zone
was clearly identified as the statically recrystallized area when the
Proper annealing temperature and time was selected. The stored energy
associated with the dislocations might be sufficient to set off DRX
during crack propagation. It has been found that most of the deforma-
tion work is converted into heat, which causes the temperature to rise
in the vicinity of a propagating fatigue crack. Birol conducted

tension-tension fatigue tests on Fe-2.6wt%Si at room temperature [55] .

17

He observed that DRX occurred during the latter stages of fatigue crack
propagation. The same phenomenon is likely to also occur during high

temperature fatigue crack propagation.

III EMPERIMENTAL PROCEDURE

3.1 Testing Materials

Very pure Ni polycrystals having the nominal compositions given.irl
Table 3-1 were used. Also Cu single crystals (99.999% pure) and two A1

polycrystals with the composition given in Table 3-2 were tested.

Table 3-1 Composition of Ni studied

 

Element : Ag Al Cu Fe K Li Mg Mo Na Pb
Wt ppm : <10 <10 <10 <10 <10 <10 <10 <10 <10 <10

 

Element : Si Sn Ti V Zr 0 N C Ni
Wt ppm : <10 <10 <10 <10 <10 14 l * Bal.

 

* no information was given by the vendor (Material Research
Corporation). The concentration may be higher than 10 ppm but
less than 130 ppm as typical in commercial Ni (grade 270).

Table 3-2 Composition of A1 studied

 

 

Element : Ca Cu Fe K Mg Na Si Ce
Wt ppm : .22 .25 .32 .22 3.5 <1.0 1.4 .29
Element : C Cl H N O P A1

Wt ppm : 15 1.1 <1.0 <1.0 <5.0 .29 Bal.

 

According to the vendor (Material Research Corporation), Ni and Al
polycrystals are cold extruded into 9.525 mm diameter rods. Two charges

of Ni rods had been received two years apart which resulted in different

18

19

microstructures after annealing. This will explain in the heat treat-

ment section.

3.2 Specimen Preparation

3.2.1 Mechanical Testing Specimens

(1) Ni polycrystal specimens were machined from 9.525 mm diametxn: rods.
The cold extruded material was sufficiently stiff for machining without
destroying the axial alignment. The specimen shape and dimensions are
shown in Fig. 3-1. Specimens with the shape as Fig. 3-l(a) were used in
the previous testing system (Instron equipped with a reduced atmosphere
furnace). Specimens with the shape as shown in Figs. 3-1(b)-(d) were
used in the current testing system (MTS equipped with a high vacuum high
temperature furnace). Because of the limitation of the raw material,
threaded specimens as shown in Figs. 3-1(c)-(d) were used in order to
increase the cross sectional area, which corresponded to an increase in
stiffness and were suitable for a high strain amplitude test. A few
hour-glass shape specimens were used to observe the effect of a strain

amplitude resulted from area gradient along the stress axis.

(2) Two Cu single crystal specimens were machined down the center sec-
tion, using an electric discharge machine. This method confines the
introduced cold work to a thin surface layer which can be removed

chemically. The orientation of the stress axis was determined by the

20

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. 7...-
trite

 

 

 

 

 

EE 3E:

 

ooém

21¢...

 

 

 

 

coéla

 

E

21

back-reflection Laue method. Specimen shape and orientation are shown

in Figs. 3-2.

(3) A1 polycrystal specimens were machined from 9.525 mm diameter rods

to the same shape as described for Ni.(see Fig. 3-1)

(4) For crack propagation tests, a single-edge or double-edge or circum-

ferential notch was introduced to the specimen as shown in Fig. 3-3.

(5) Heat Treatment

All specimens were annealed in a vacuum furnace at a pressure of
approximately 10.3 Pa. The Ni specimens were chemically polished in
the following solution at 70°C for 30 s to remove any surface irregula-

rities,

glacial acetic acid 64 ml
nitric acid 34 ml

hydrofluoric acid 1 m1.

Two batches of Ni material were received two years apart. The specimens
machined from the first batch were annealed at 900°C for 5 hours. 'This
heat treatment resulted in a grain size of 0.3 mm. (Fig.1iJQ. The
specimens machined from the second batch of Ni material were heat
treated in the same condition, but a different microstructure was ob-
served as shown in Fig. 3-5. This difference can be attributed to
different fabrication methods. The second batch of Ni rods probably

were obtained from extruded raw material at medium to high temperature

22

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so mnu mo coHumucoHuo can xuuosoom accoHuoom owsno .N-m .wwh

 

 

 

 

Oz."—
.3pr

23

.monouoc HmwucoumeSUHHo
on can owco-oansop Any umwco-meCwm Adv .mummu cofiumwmdoua xomuo

now pocwfiome-mua mozouoc mo mcowmcoawp can huuoEooo .Mum .mwh

 

scum scum

 

 

 

 

 

\é/

PT
2T—
/°°\

 

 

 

 

 

 

EE ”ES

24

.musoc w you Uoooo um wCHHmwccm

umuum Aamfiuouma mo souun umuwuv #2 mo unauosuumouoaa ash .an .num

 

25

.musos m you 0.00m um wcuunoccu

uwuum AHmHunume mo nouns vcooomv «2 mo eunuuauunououa och .ncn .uuh

 

26

where texture development is apparent and the microstructure was indi-
cated by the large grains containing many small twins. Therefore, a few
Ni rods with 305 mm original length were annealed at 900°C for 3 hours.
These soft rods were elongated at room temperature with an initial
strain rate of 2x10'fls.1 to 10% of engineering strain (Fig. 3-6). The
specimens then were machined from these deformed Ni rods as specified in
3.2.1. Subsequently the specimens were annealed at 850°C for various
length of time. The microstuctures are shown in Fig. 3-7. The anneal-
ing condition was chosen as 850°C for 20 mins.

The Al specimens were annealed at 310°C for 5 hours (Fig. 3-8). The
Cu single crystal specimens were chemically polished to remove 0.1 mm
from.the surface to avoid any potential sites for recrystallization

during annealing, using the following solution

phosphoric acid 33 ml
glacial acetic acid 33 ml

nitric acid 33 ml
Subsequently, it was annealed at 800°C for 12 hours.
3.2.2 Optical Microscopy Specimens

Some of the optical micrographs were taken directly from the planar
side surface of the specimen (Fig. 3-9), when the test was interrupted
after some cycles. The others were taken after the end of the tests.
Specimens were cut from test samples with a very low speed diamond wheel

cutting machine (Buehler Isomet) along a plane either perpendicular or

m cHxN mo oumu
a- v-

Cannon HmHuHCH cm saws mudumuodEmu Eoou um Umumwcoao .muao: m you oooom um

poamoccm mm3 Loans .umn Hz n no o>u50 Camuum-mmouum mafiuoocwwcm .wum .wuh

E 225% azammmzauzm
mg 3 3 a m A. m m a m m H o

 

d u a u u a q q d u q o 3

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- n p p P p p p p . p on”

28

,, .aaoa a lav n.aaa ON ate tau
0.0mm um wcwamoccm nouns “z pmumwcoao osu no uuauuauunouoaa ugh .hun .uuh

\-

.v.

 

29

 

30

 

0.5 mm

D

Fig. 3-8. The microstructure of Al after annealing at 310°C for 5 hours.

31

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 3-9. Geometry and dimension of a Ni specimen with pre-machined

planar side surface.

parallel to the stress axis.

32

Subsequently they were mounted in cold

setting resin before mechanical polishing. All specimens were first

polished on abrasive grit paper and then on a cloth by using aluminum

oxide to get a mirror-like surface.

The etchants were

nitric acid
glacial acetic acid

hydrochloric acid

hydrofluoric acid
water

hydrochloric acid

ammonium hydroxide = 58%
water

hydrogen peroxide a 30%

46.

46.

7.

67

33

2

2

6

50

50

25

ml

m1

m1

ml

ml

m1

ml

for Ni

for Al, and

for Cu.

All optical micrographs were taken with a Neophot 21 Microscope.

3.2.3 Transmission Electron Microscopy Specimens

Slices of approximately 0.3-0.4 mm thickness were sectioned from

testing samples, using an Isomet low speed saw with diamond wheel such

that the foil plane normal is parallel to the direction of loading.

33

These slices were thinned down to 0.1 mm by careful mechanical polish-

ing.

The final jet polishing was done in a Tenupol jet polishing device.

Electrolytes used were A8(*) for Ni, A7(*) for Al and D2(*) for Cu. The

optimal jet polishing conditions are given in Table 3-3.

Table 3-3 Jet polishing conditions for Ni, A1 and Cu

 

 

 

 

Electrolyte Temp (°C) Voltage (V) Current (A)
Ni A8 13 70 0.18
acetic acid 950 ml
perchloric acid 50 m1
Al A7 -5 - -10 12 0.12
perchloric acid 100 ml
glecerol 200 ml
methanol 700 m1
Cu D2 15 8 0.11
distilled water 500 ml
phosphoric acid 250 ml
ethanol 250 ml
Vogel's Sparbeize 2 m1
propanol 50 m1
urea 5 g

 

* A7, A8 and D2 are registered trade marks of Struers Scientific

Instruments, Inc..

.All specimens were examined in a Hitachi H-800 electron microscope

with double tilt stage.

The applied voltage was 200 kV.

3.2.4 Scanning Electron Microscopy Specimens

Some specimens were fatigued until fracture. The fracture surface

was ultrasonically cleaned with acetone before examining. A JEOL 350

34

SEM was adopted to observe the fracture surface. The applied voltage

was 25 kV.

3.3 Mechanical Testing

Two types of machines and setups were used during the process of

the program.

3.3.1 Instron Testing Machine

By July 1988, the tests were conducted on a floor model electro-
mechanical Instron testing machine with a 500 kg tension-compression
reversible load cell.

Pull rods and button head grips were designed and machined out of
AISI 310 heat resistant stainless steel.

To avoid oxidation of the specimen during testing a cylindrical
protective chamber was designed as shown in Fig. 3-10. A stainless
steel ring with a clearance of 0.75 mm to the pull rod was welded at the
top of the tube, while the lower ring which fitted on the lower pull rod
was made of Invar and the dimensions were chosen such that at tempera-
tures in excess of 200°C a tight fit with the lower pull rod was
obtained due to the difference in thermal expansion between Invar ring
and lower pull rod.

With this chamber design a protective atmosphere of 90% N2 + 10% H2
was maintained during the test inside the chamber to minimize oxidation.
A flow rate of 12 liters/hour at 5 psi of this gas mixture was found

sufficient to avoid oxidation. Higher flow rates were avoided since the

35

 

 

 

 

 

 

 

 

 

 

 

 

UPPER
PULL ROD
O O
0 SIAlNLESS STEEL
, m [@237
a _ _
° [ W l
O Q
HEAIERW . Q
0 O
O O
o SPECIMEN @
0 IC O
0 a
O 0
O O
O 0
O ; 0
O O
O O
3 ‘ ‘ ‘ ' °
’ 0
. \
O "WAR
0 O
T

 

 

 

 

O "

LOWER fun
PULL R00 7 W

GAS

 

/ A

 

 

 

 

 

 

 

Fig. 3-10. Arrangement of the high temperature mechanical testing setup.

36

gas started burning at the top of the chamber, also it created an
unwanted back pressure.

Computer codes were developed in house to control the Instron
testing machine by the digital output from an IBM XT personal computer
and for data aquisition by A/D conversion of the load cell signal.
All the load-displacement data from the test then were stored at an
interval chosen properly. The resolution of data aquisition was 4 pm
per data set with an accuracy better than 0.1%. These data were then
further processed to get the relevant information such as true stress-
strain curves and work hardening coefficient vs. true stress

curves,etc..
3.3.2 MTS Testing Machine

.After July 1988, a new system was assembled. A schematic diagram
showing the essential elements of the system is shown in Fig. 3-11.

The system includes a closed loop servohydraulic load frame (MTS
810) with a 10-100 kN (MTS 661.20A-03) or a 0.5—10kN (MTS 661.19) load
cell, a 25.4mm gauge length water cooled high temperature extensometer
with maximum strain range of 30% and minimum strain range of -10%, and
equipped with a Centorr S-60 high vacuum high temperature furnace. The
maximum resolution of the extensometer is 0.1 pm, but due to the limita-
tion of 12 bit analog-digital converter (ADC), the actual resolution is
0.488 pm. The electronic noise arising from furnace further limits the
resolution. To get better results, signal filtering circuit will be

introduced to the system.

37

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pouwuouzasoo mzu mo muCoEoHo onmn onu wCMBOSm Emummfip oHumEozom .HH-n .wuh

SEE
mevnm><>> 32:5.
>m<mtmm< 3 . m

o; MHZ

 

38

For tension-compression fatigue tests, the crucial point is the
grip design, this is especially important in a high temperature environ-
ment. The crossover phenomenon when changing from tension to
compression can be solved by preloading against the bottom area of the
specimen. This is accomplished by applying hydraulic pressure to a
piston residing inside the pull rod. Such a grip assembly is shown in
Fig. 3-12. The specimen gripping insert includes two pairs of collets,
four tungsten pins and two extension pistons which are shown in Fig. 3-
13. All parts inside the hot zone are made of high temperature
molybdenum alloys (TZM). It contains approximately 0.5% Ti, 0.08% Zr
and 0.01-0.04% C. The alloying elements give rise to both solid solu-
tion hardening and dispersion hardening. The current design is good for
test temperatures up to 1000°C, but failed when trying to test at
1500°C, which is the desired temperature for this system. The major
reason is the bonding between tungsten pins and TZM pull rods at high
temperature under high pressure.

A MicroConsole (MTS 458.20), an AC controller (MTS 458.13), two DC
controllers (MTS 458.11) and a MicroProfiler (MTS 458.91) compose the
mechanical test controlling system. The MicroProfiler has 52KB memory
and can be programmed to generate arbitrary waveforms. Ninety nine
programs can be stored in the memory. Remote programability allows the
user to send programs from the computer to the MicroProfiler via an RS
232 interface. Signals from the load cell, the extensometer or an LVDT
can be used to perform load, strain or stroke controlled tests, respec-
tively.

A Centorr Model S-6O furnace is mounted to the load frame of the

MTS machine. Two bellows for 50.8mm diameter rods accommodate the

39

 

 

   
 
  

VACUUM SEAL

COOLING IN

COOLING OUT PRESSURE IN

PRESSURE RETURN

Fig. 3-12. A drawing showing the design of the pre-load grips for
high temperature tension-compression fatigue test.

40

25

D

 

 

 

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ZOhm_d20_mzm._.xm

 

 

 

 

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mhmqqoo

\l]

%

 

 

D

3m; ¥O<m

 

 

 

 

 

 

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3m; #20:“.

41

movements of the actuator up to 150 mm. The hot zone size is 76.2 mm
diameter by 203.2 mm height with two halves of tungsten mesh heating
elements. The radiation is blocked by six layers of heat shields made
of tungsten and molybdenum. The furnace chamber is designed to also
accommodate the MTS extensometer. The final setup for a test is shown
in Fig. 3-14. The maximum operating temperature of the furnace is 2000°C
in vacuum or in controlled inert gas (argon, nitrogen, helium) atmos-
phere. Two thermocouples of type "C" W5%Re/W26%Re are used as the
temperature sensors and a Honeywell Universal digital PID controller
With 20 programable segments controls the temperature. The temperature
was stable within il°C. An over-temperature controller is installed to
protect the system from over heating in case of a broken main ther-
mocouple.

A Zenith AT compatible personal computer using Intel 80286 CPU and
80287 math coprocessors and equipped with 1 MB of main memory is used to
Perform the machine control and data acquisition. A high performance
analog and digital I/O board (Data Translation DT 2818) is plugged into
One of the system expansion slots in the personal computer backplane.
The board can be programmed from the computer's compiled BASIC language
to perform analog to digital (A/D) conversions; digital to analog (D/A)
conversions; and digital input and digital output transfers. The OT
2818 has a 12 bit A/D converter with a maximum data sampling rate of
13.7 kHz. It uses a simultaneous sample and hold A/D converter, which
permits up to four A/D channels to be sampled simultaneously. By using
Direct Memory Access (DMA), the data can be moved directly into or out
of BASIC variable arrays at high speeds. A real-time software package

(PCLAB) containing a number of machine language routines designed to be

"'HL“"

~§

 

Fig. 3-14. Final setup inside a vacuum chamber with an
extensometer attached for conducting a strain amplitude

control fatigue test at high temperature.

43

called from the computer's compiled BASIC language greatly simplify the
programming required to use the DT 2818 board and only high level
routines for data acquisition and control needed to be written.

A lot of efforts were made to develop the software for test control
and data acquisitdxnl. Because of various testing techniques adopted
among the laboratory colleagues, several programs have been written in
MicroSoft QuickBASIC language to meet individual need. Currently,
programs for tension, compression, load controlled fatigue, strain
controlled fatigue and user defined tests are available. Programs for
plotting and printing the data are available, too. It listing of the
programs used in current fatigue tests are included in appendix A.

Total strain amplitude (i.e. elastic + plastic strain) control was

applied to all fatigue tests.

3.4 The Microhardness Test

The microhardness tester (Buehler Micromet) was adopted to measure
the hardness of the microstructure. The diamond-pyramid hardness number

(DPH) was determined from the following equation [56]

—..___L.A_)..-—_
DPH _ 2P51n20 2 _ 1 854P
L L

where P - applied load, kg
L - average length of diagonal, mm

0 - angle between opposite faces of diamond - 136°.

44

The applied load in the test was 0.3 kg; the loading speed was 70 pm/sec

and the loading time was 20 seconds.

IV EXPERIMENTAL RESULTS

4.1 Mechanical Behavior

The test conditions are summarized in Table 4-1. The cyclic hard-
ening curves of the Ni and A1 specimens are shown in Fig. 4-1. These
curves are plotted in terms of the stress amplitude as function of the
number of cycles (Fig. 4-1(a)) or cumulative strains (Fig. 4-1(b)). The
qualitative shape of the cyclic hardening curve is similar for all
specimens. The true stress increases rapidly in the first few cycles due
to the high initial strain hardening. With increasing number of cycles
(N) the work hardening rate (da/dN) (a-true stress) decreases.
Eventually the hardening curve attains a maximum and exhibits continuous
softening thereafter. The stress decrease at large cumulative strains
indicates a strong softening mechanism to occur at large numbers of
cycles. At a smaller total (elastic + plastic) strain amplitude, the
maximum stress is smaller and attained at a higher number of cycles.
With increasing strain rate (or cycle frequency), the stress level
increases and the maximum stress is attained at a higher cumulative
strain. The same result was observed when the test temperature was
increased to 955°C. An increase in deformation temperature lowers the
stress level and shifts the maximum stress to a higher cumulative
strain. In fact, at the chosen test temperature of 955°C (0.71Tl)l the
hardening curve becomes very flat. Raising the total strain amplitude
results in an increase of the stress level and an attainment of the

maximum at a lower number of cycles. A1 qualitatively shows the same

45

46

 

 

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47

behavior as Ni, but at a much lower stress level. Fig. 4-1(c) Shows the
stress decrease rate ((da/G)/dN) (G-shear modulus) as a function of

number of cycles. At the same homologous temperature and the same total
strain amplitude the average rate of stress decrease in A1 (a

-7 -7
1.152x10 ) is much smaller than that of Ni (35.723x10 ).

It is finally noted that at the end of a test the specimen usually
had not failed or would reveal macroscopic cracking, except for two Ni
specimens, one deformed at the higher strain rate and the other with
0.5% total strain amplitude. This is also noticeable on the hardening

curve by a strong softening toward the end of the test.

4.2 Microstructural Development

Substantial microstructural changes due to extensive grain boundary
migration were found when comparing the microstructures before (Fig” 3-
4) and after (Fig. 4-2) the test. For a more quantitative evaluation one
specimen was machined flat on one side surface (Fig. 3-9) such tiuit the
grain structure could be easily examined by optical microscopy.fflua
specimen was deformed to a specific number of cycles, air cooled to room
temperature, dismounted, examined in a microscope, remounted and
reheated at 10°C/min, further deformed etc.. A series of micrographs
taken directly from the planar side surface of the specimen after each
specific stage are shown in Figs. 4-3(a)-(j). All these micrographs show
the same area which was parallel to the loading direction. Fig. 4-3(a)

is the microstructure of the annealed state. There are many small grains

48

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52

embedded between large ones in this annealed state. Fig. 4-3(b) is the
microstructure after 10 complete cycles. Position A, B and D reveal
extensive grain boundary migration. One grain boundary disappeared and a
twin boundary formed at position C. About 25 pm thickness was removed by
polishing in the sequence from Fig. 4-3(a) to Fig. 4-3(b). Comparing
these two microstructures, it is evident that the small grains tend to
shrink. Fig. 4-3(c) is the microstructure taken immediately after 10
cycles. The distribution of migration distance is inhomogeneous in that
some areas show much stronger grain boundary migration than others. The
sample was slightly etched again such that the boundary position before
and after deformation could be seen simultaneously. Fig. 4-3(d) is the
result after etching. The grain boundary at position B in Fig. 4-3(c)
reveals a series of approximately parallel markings in front of this
grain boundary. The new grain boundary position can be seen in Fig. 4-
3(d) . Those markings delineated the positions of the boundaries at the
end of each stress cycle. Evaluation reveals that there is a one-to-one
correspondence between the number of grain boundary markings and the
total number of whole cycles imposed on the specimen. A more detailed
structure of surface markings is shown in Fig. 4-4. The same procedure
was followed for the investigation at higher numbers of cycles. Figs.
4—3(e)-(g) are the microstructures after 40 cycles. They show qualita-
tively the same phenomenon, but the migration rate has decreased
compared to the first 10 cycles. The positions indicated by arrows make
obvious that the grain boundaries tend to migrate such as to align under
45° with respect to the stress axis as has been shown previously by

Langdon and coworkers [20-23]. This will facilitate the grain boundary

sliding and is believed to cause cavity formation [49]. Figs. 4-3(h)-(j)

53

 

(b)

Fig. 4-3. The microstructures of a Ni in a plane parallel to the loading
direction after cyclic deformation with 0.5a total strain amplitude at
600°C (3) Annealed at 900°C for 5 hours; (b) after 10 complete cycles at
600°C, slightly polished and etched again to reveal the new grain

boundary positions;

54

 

Fig. 4-3(c) after 10 complete cycles, positions A,B,C and D indicate

inhomogeneous strain distribution on the surface; (d) etched to reveal

the positions of new and original grain boundaries simultaneously;

55

 

(') damn

 

Fig. 4-3(e) after 40 cycles; (f) the positions of new and original grain
boundaries after etching again; (g) slightly polished and etched again,

orfly'new grain boundaries can be seen;

56

 

Fig. 4- 3. (h) right after 160 cycles; (1) after etching;
(j) after polishing and etching.

57

.moaoxo 0H uwuum mch—ume oomuusm mo undue—spun cosmumo 47¢ .mHh

 

58

are the micrographs after 160 cycles. Although compared to Figs. 4-3(e)-
(g) the sample had deformed another 120 cycles, Fig. 4-3(j) doesn't show
much difference compared to the microstructure in Fig. 4-3(g) , except
most grain boundaries now are aligned under 45° to the stress axis.
Grain boundary sliding was observed even during the early stage of
cyclic deformation. An example is shown in Fig. 4-5. The specimen was
fatigued at 600°C with 0.5% strain amplitude. A scratch was introduced
accidentally during specimen dismounting after 10 cycles of test (Fig.
4-5(a)). Under further deformation to 20 cycles, a small offset can be
seen in Fig. 4-5(b) as indicated by an arrow. The offset distance
increases as numbers of cyclic deformation increase, which corresponds
to higher degree of grain boundary sliding (Fig. 4-5(c), 40 cycles).
Comparing Fig. 4-5(c) with Fig. 4-5(a), some grain boundaries show much
more migration, but some don't, also some grains reveal higher density

of slip bands.

Grain boundary migration was also observed in Al. The micrographs
in Fig. 4-6 were taken after 720 cycles deformation. Actually, the
micrograph reveals the whole cross sectional area perpendicular to the
loading direction. The extent of grain boundary migration can be seen by
comparison of Figs. 3-8 and 4—6. The deformed state (Fig. 4-6) shows
curved grain boundaries instead of perfectly straight ones, as in the

microstructure of the undeformed specimen (Fig. 3-8).

 

Fig. 4-5. The microstructure on the planar surface of a Ni after cyclic
deformation with 0.5% total strain amplitude at 600°C for (a) 10; (b)
20 and (c) 40 complete cycles. The arrow indicates the offset of a

scratch across the grain boundary due to grain boundary sliding.

60

 

.1 mm

0

(C)

61

 

Fig. 4-6. The microstructure of an Al after 720 cycles with 0.5%

total strain amplitude at 200°C.

62

4.3 Evidence Of DRX Under LCF

'The occurrence of DRX in.polycrystals is difficult to evidence,
since the sample remains polycrystalline and the newly formed grains are
rapidly deformed by concurrent deformation. It is particularly difficult
in LCF because of the small driving forces and thus a small boundary
migration rate. The occurrence of DRX, therefore, had to be indirectly
confirmed by microscopic investigations. After deformation, the sample
was cutperpendicular to the loading direction, and the microstucture
was examined in detail under higher magnification. Special attention was
paid to grain boundaries. They reveal serrations (Fig. 4-7(a)), sharp
protrusions (Fig. 4-7(b)) and even new grains (Figs. 4-7(b)-(f)). These
phenomena are characteristic for the nucleation of recrystallization at
grain boundaries [24,36]. Figs. 4-7(b), (d)-(f) show the details near a
twill. It occurs as if the twin in Fig. 4-7(d) and the grain at the twin
boundary in Fig. 4-7(e) were created during deformation. This is impor-
taxu2, since recrystallization twinning was found to be one of the major
nucleation mechanisms of DRX in monotonic tests. In fact these observed
phenomena are nucleation processes. This becomes clear from Fig. 4-8
which reveals that the microstructure contains areas with many small
grains. While the migration processes observed in the beginning of
deformation, are directed towards a coarsening of the microstructure,
this micrograph, in contrast indicates a local refinement of the

microstructure.

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Ac. At.

 

 

  

64

 

.__.__——I
0.5 mm

Fig. 4-8. The microstructure of a Ni after 510 cycles with 0.5%
total amplitude. The whole cross sectional area perpendicular to

the loading direction is revealed.

65

.More evidence of DRX can be seen on the surface of fatigued
specimen. Fig. 4-9 reveals the microstructure on the planar side sur-
face of a specimen tested at 600°C with 0.5% strain amplitude for 80
cycles (Fig. 4-9(a)) and 120 cycles (Fig. 4-9(b)). Fig. 4-9(b) is tin;
microstructure when slightly etching after test. Twins appear on the
surface of the specimen as indicated by an arrow. In the same specimen,
a new grairlattached to the serrated grain boundary can be seen in Fig.

4-10(b) which is absent in Fig. 4~10(a).

.A parallel study was conducted on Al. Due to the high stacking
fault energy Al is not able to recrystallize dynamically. No small
grains were detected in the fatigued structure (Fig. 4-6). Obviously
without DRX the microstructure has a tendency to uniform coarsening.
This further substantiates the conclusion that Ni polycrystals actually

undergo DRX during LCF at high temperature.

4.4 Results of High Strain Amplitude Tests

Local grain refinement was observed during HTLCF with a small
strain amplitude. By increasing the strain amplitude, the driving force
for DRX may increase such that overall microstructural change which is

similar to monotonic test may be possible.

One specimen was fatigued at 600°C with 5% strain amplitude for 55
cycles. The cyclic hardening curve is shown in Fig. 4-11. The stress

becomes a maximum in the early cycles and then decreases. The

 

Fig. 4-9. The microstructure on the planar surface of a Ni after cyclic
deformation with 0.5% total strain amplitude at 600°C. (a) after 80
cycles; (b) after 120 cycles and slightly etched. The arrow indicates

the position where a twin was created.

67

 

(I)

 

(b) 02 «um

Fig. 4-10. The microstructure on the planar surface of a Ni after cyclic
deformation with 0.5% total strain amplitude at 600°C. (a) after 80
cycles; (b) after 120 cycles and slightly etched. A new grain attached

to the serrated grain boundary.

68

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69

microstructure after the test is shown in Fig. 4-12. This micrograph
reveals the structure of the area which is parallel to the stress axis.
The average grain size of the specimen gauge section is much smaller
than that of the specimen shoulder area where at most elastic deforma-
tion occurred. The microstructure shown in Fig. 4-13(a) further
indicates the overall microstructural change. The structure after
annealing (Fig. 3-5) is totally replaced by a finer grain structure.
This substantiates the occurrence of DRX during LCF with high strain
amplitude. A higher magnification micrograph shows the recrystalliza-
tion twins present in the new structure (4-13(b)). An hour-glass shape
specimen with 6.35 mm radius of curvature and 5 mm smallest diameter was
fatigued with 1% total axial strain amplitude at 600°C for 1013 cycles.
The hardening curve also shows the stress to increase up to 100 cycles
and then to decrease continuously (Fig. 4-14). The microstructure
parallel to the stress axis is shown in Fig. 4-15. It is clearly evi-
dent that a finer grain structure in the center region had replaced the
initial coarse grain structure shown in the area of specimen shoulder.
Except for the fine grains, most grain boundaries had moved to a posi-
tion aligned under 45° with respect to the stress axis. The grain

morphology of the cross section near the smallest diameter of the
specimen is shown in Fig. 4-16. It is quite different from the annealing
structure. In this test, the deformation was confined to the very
narrow region where the cross sectional area was small. One hour-glass
shape specimen with 12.7 mm radius of curvature and 5.08 mm smallest
diameter was fatigued at 600°C for 3645 cycles with 0.3% strain

amplitude. The hardening curve is shown in Fig 4-14. The microstruc-

ture along the gauge length is shown in Fig. 4-17. The structure has

70

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mcHomoH onu ou HoHHmuma ocde a :H Hz a mo ousuosuumououa och .Nwre .muh

 

71

 

Fig. 4-13. (3) The microstructure of a Ni after 55 cycles with 5% total

amplitude. The whole cross sectional area perpendicular to the loading

direction is revealed; (b) higher magnification of the structure in (a)

72

  
  

  

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74

 

Fig. 4-15. The microstructure in a plane parallel to the loading

direction of an hour-glass shape Ni fatigued at 600°C with It

total axial strain amplitude.

 

Fig. 4-16. The microstructure in a plane perpendicular to the loading
direction and containing the smallest diameter region of an hour-glass

shape Ni fatigued at 600°C with 1% total axial strain amplitude.

76

changed due to DRX, but not drastically as shown in Fig. 4-15. The
deformation region is wider than in the previous test because of the
smaller gradient of the cross sectional area along the stress axis.
(lrain boundaries migrate to the position aligned under 45° with respect
to the stress axis. A crack has initiated and propagated along grain
‘boundaries. The strain amplitude in the smallest diameter region is
estimated approximately 3 to 5 times of the strain amplitude imposed to

the whole gauge length.

The irregular and large initial grain structure was utilized.to
investigate the effect of a high strain amplitude. From the microstruc-
ture observed after test, DRX and subsequent the grain boundary

migration can be distinguished without ambiguity.

4.5 Results on Cu Single Crystals

Cu single crystals were tested at 400°C (0.5 Tm) and room tempera-
-4 ;1
ture at a strain rate of 1.6x10 3 and total strain amplitudes of 1%

,3
corresponding to a cyclic frequency of 6.2x10 Hz.

The cyclic hardening curve of a <169> oriented Cu single crystal
cycled at 400°C is shown in Fig. 4-18. After initial hardening the flow
stress reaches a maximum and declines thereafter slightly but con-
tinuously. Despite very careful inspection of the specimen, however, no
recrystallized grains could be detected, neither on the surface nor in

the interior of the single crystal. The dislocations are arranged in a

77

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78

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79

well defined cell structure (Fig. 4-19), and the substructure does not
reveal indications of viable recrystallization nuclei. Hence, the flow
stress behavior has to be attributed entirely to the dislocation struc-
ture development and cannot be associated with DRX or grain boundary
motion phenomena. Consequently, the occurrence of DRX during HTLCF in
polycrystals has to be interpreted as a grain boundary effect. Also, the
results confirm that cyclic softening is not necessarily indicative for
DRX. This was shown before for Al polycrystals, where cyclic softening

was associated with grain growth.

It was further studied whether fatigued dislocation structures in
single crystals are at all prone to recrystallization. A single crystal
was deformed at room temperature for 110 cycles with 1% strain
amplitude. After initial hardening the cyclic hardening curve reaches a
plateau stress (Fig. 4-20) as has been established in many previous
investigations [57,58]. Slip lines could clearly be seen on the sur-
face of the fatigued specimen (Fig. 4-21). Upon isochronal annealing
for 30 min between 200°C and 850°C in a vacuum furnace, the microhard-
ness decreases strongly in the temperature range between 500°C and 700°C
(Fig. 4-22). Annealing at temperatures above 800°C essentially restores
the single crystals yield stress. Different slices of specimen cut
perpendicular to the stress axis from the gauge section were used for
different annealing conditions. After each annealing the specimen was
examined using optical microscopy. While the observed kinetics are very
akin to recrystallization behavior, the absence of recrystallized grains
after annealing at different temperatures indicate that no recrystal-

lization occurred. Some specimens were then further prepared for TEM.

80

3pm

 

Fig. 4-19. Dislocation structure of a Cu single crystal tested
at 400°C with 1% total strain amplitude for 420 cycles.

81

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83

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84

A typical dislocation structure which consists of dense multipolar
arrangement of primary edge dislocations, referred to as veins, which
are separated by dislocation poor regions, can be seen in Fig. 4-23(a).
Upon subsequent annealing at 250°C for 30 min, the density of disloca-
tion between veins decreases due to recovery (Fig. 4-23(b)) . Further
annealing at 552°C which is in the region of decreasing microhardness,
reduces the dislocation density inside the veins (Fig. 4-23(c)). The
final state of recovery which was annealed at 852°C leads to the forma-
tion of almost perfect dislocation networks (Fig. 4-23(d)), with

obviously negligible flow stress contribution.

Thus, even deformation at room temperature to a stress level com-
parable to that at 400°C fails to provide viable recrystallization

nuclei upon annealing.

4.6 Dislocation Structures

Transmission electron microscopy was applied to examine the dis-
location arrangement and its development during LCF. Fig. 4-24(a) shows
the dislocation structure of Ni after 310 cycles with 1.7% total strain
amplitude (amax- 54 MPa). The micrograph reveals a well developed cell
structure inside a grain. Compared to a monotonic test prior to the
onset of DRX (amax- 78 MPa) at the same temperature and strain rate
(Fig. 4-24(b)) the structure of cycled specimens appears more strongly

recovered.

C)
U1

 

(a)

Fig. 4-23. Dislocation structure of a Cu single crystal fatigued at

room temperature. (a) as deformed; deformed and then annealed at (b)
250°C; (c) 552°C and (d) 850°C for 30 min.

 

(b)

 

 

89

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Hz m opumcfi ousuosuum coHuooonHv och .ewné .wum

3

 

90

 

91

Because of the observed.extensive grain boundary migration, special
efforts were made to observe the dislocation structure around grain
boundaries. Fig. 4-25 shows the dislocation arrangement in a Ni
polycrystal after 310 cycles with 1.7% total strain amplitude. The grain
boundary seems to migrate down to the right corner. In front of the
grain boundary, dislocations form a distinct cell structure, but are not
as heavily tangled as in large strain monotonic tests (Fig. 4-24(b)),
rather they are loosely arranged in cell walls. Immediately behind the
serrated boundary segment, the dislocation structure is poorly
recovered, the cell interior is not so neat, and the cell walls are more
diffuse. Such an arrangement is more typical for the beginning of cell
formation and the arrangement indicates that it represents the new
formation of a cell structure after the boundary swept the volume and
eliminated the original structure. In contrast, a well recovered cell
structure is observed in front of or a little farther behind the ser-

rated part of the boundary.

The results from single crystals indicate that grain boundaries play
an important role in DRX during HTLCF. Extensive grain boundary migra-
tion also occurred during cyclic deformation. It is interesting to see
how dislocation structures develop during the test, especially around
the grain boundaries. Fig. 4-26 shows the cyclic hardening curve of
samples deformed at 600°C with a total strain amplitude At - 0.5 % and
cycle frequency 1.3x10"2 Hz. The corresponding microstructures are given
in Figs. 4-27 to 4-30. After 10 cycles the development of a cell struc-
ture is evident (Fig. 4-27). The grain boundary in Fig. 4-27(b) reveals

heavy activity in terms of steps, curvature and considerable dislocation

92

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93

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94

content in the boundary. In contrast to the cell interior (Fig. 4-
27(a)), the cell structure in the vicinity of the boundary is only
poorly developed with incomplete cell wall sections and frequent debris
in the cell interior. After 40 cycles, the cell structure in the grain
interior is now very well developed and much more distinct than after 10
cycles, although far from being uniform (Fig. 4-28). There are areas
with narrow, condensed cell walls and essentially dislocation free cell
volumes (Fig. 4-28(a)), but other areas comprise much less orderly

arranged dislocations (Fig. 4-28(b)).

The dislocation structure after 160 cycles (Fig. 4-29) is akin to
the structure after 40 cycles. Most dislocations are arranged in con-
stricted cell walls, enclosing regions completely denuded of
dislocations, but locally patches of less orderly dislocation patterns
are apparent. The area around a grain boundary is shown in Fig. 4-30.
The boundary curvature indicates recent grain boundary motion. Far away
from the grain boundary the cell structure is very pronounced and well
recovered. In close proximity to the boundary, however, the dislocation
structure is quite different, namely very little organized and only

incipient of cell formation.

The dislocation density and arrangement gradients produced by grain
boundary migration during cyclic deformation may actually be the cause
for DRX phenomena during HTLCF. The microstructure in Fig. 4-31 is due
to a Ni polycrystal deformed at a large strain amplitude, namely A6 -
1.7%, to 300 cycles. The cyclic hardening curve (Fig. 4-1 #3) indicates

the occurrence of DRX and grain boundary migration as apparent from the

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LUHB ooooo on wcHuwou uwuum Hz m «0 unauosuumouofiz .NNIQ .muh

3

 

 

 

(a)

Fig. 4-28. Microstructure of a Ni after testing at 600°C with 0.5%

total strain amplitude for 40 cycles. (a) and (b) different areas

irl the same specimen. Note difference in structure.

98

 

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101

distinct maximum of the flow curve. The vicinity of the vertical bound-
ary in Fig. 4-31 comprises areas with more recovered cell arrangements
(left to the boundary, especially at the bottom) and more disorderly
arranged dislocations (to right of boundary, especially at the top). In
the latter area a twin is created at a triple junction - most likely
during the migration of the vertical grain boundary to the left - and
the steps in the twin boundary indicate migration activity. Also inter-
esting is the area next to the junction of the twin boundary with the
horizontal boundary. A small grain seems to have developed there right
adjacent to a heavily tangled dislocation arrangement. The resemblance
of this arrangement with nucleation phenomena observed in dynamically
recrystallizing Ni during HTLCF is obvious (Fig. 4-7(d)), and supports
the hypothesis that DRX phenomena are due to the structure gradients in
the wake of moving grain boundaries. This argument would also comply
with the observation that DRX does not occur during HTLCF of single

crystals.

Of particular interest with regard to the stability of dislocation
structures is their accommodation of strain path changes, especially if
such changes lead to a different steady state dislocation arrangement.
Fig. 4-32 gives an example that dislocation rearrangements due to
changes of strain path can occur without disruption of the previously
established structure. After 1218 cycles at 600°C and Ac - 0.5 % defor—
mation was continued only in tension to e - 8% (actually incidentally
due to malfunction of the machine control). The maximum of the tensile
flow curve indicates the occurrence of large scale DRX at 6% tensile

strain (Fig. 4-32(a)). The dislocation structure after this additional

 

102

 

Fig. 4-31. Dislocation structure around a grain boundary of a Ni

tested at 600°C with 1.7% total strain amplitude.

103

tensile strain (in the unrecrystallized volume, of course) reveals the
superposition of two cell structures. The well recovered cell structure
was produced during cyclic deformation and is still retained, while a
new cell structure, still much less recovered, is generated within the
old structure. The new cell structure tends toward a smaller cell size
than the fatigued structure, because of the higher flow stress [3,14].
No disruptions or discontinuities of the previous structure are ap-
parent, rather both structures seem to be able to coexist, and gradually
the former cell walls become incorporated in a new homogeneous arrange-
ment. Hence, Fig. 4-32(b) reveals actually two different stages of
dislocation cell structure development and indicates that the specimen
actually retains a 'temporal memory' of its strain history in terms of

its dislocation arrangement, until a new structure is fully developed.

4.7 Effect of DRX on Mechanical Properties

In ductile materials, crack propagation is accompanied by plastic
deformation in the wake of the crack tip. Prenotched specimens were
tested at room temperature first to study the crack tip plastic deforma-
tion zone. Table 4-2 lists the test conditions for the samples referred
in this section. The microstructure of a sample which was fatigued for
440 cycles with 0.5% total strain amplitude is shown in Fig. 4-33. The
micrograph shows the microstructure of the deformed state with a crack
extending through about half of the gauge diameter. The micrograph
reveals the structure in the center of the specimen parallel to the

stress axis indicated by an arrow. The crack propagates transgranularly

104

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106

Table 4-2 Summary of the test conditions

 

Test No. Test conditions

 

,4 ,1
CRKOOK é-2x10 s , T-25°C, Ac-i0.5%, N-440
single edge notch specimen.

,4 ,1
CRKOOF é-2x10 s , T-25°C, Ae-i0.8%, N=380
single edge notch specimen.

,4 ,1
CRKOOA é-2x10 s , T=600°C, Ae-i0.5%, N-600
single edge notch specimen.

,4 ,1
CRKOOE é-2x10 s , T-600°C, Ae-i0.5%, N-880
single edge notch specimen.

,3 l
CRKHFOl é-2x10 s , T-600°C, Ae-i0.5%, N-744
single edge notch specimen.

,4 ,1
CRK6001 é=5x10 s , T-600°C, At-i0.5%, occasionally 1%, -5%
for several cycles, single edge notch specimen.

,4 ,1

CRK6011 é-leO s , T-600°C, Ae-i0.75%, for 710 cycles,
occasionally Ae-i5% for several cycles, single edge
notch specimen.

,4 ,1
CRK6021 é-5x10 s , T-600°C, Ae-i0.5% for 425 cycles,
Ae-il% for 619 cycles, circumferential notch
specimen.
,4 ,l
CRK6031 é-5x10 s , T-600°C, Ae-il% for 605 cycles,

circumferential notch specimen.

,4 ,l
CRK6041 é-5x10 s , T-600°C, Ae-l% for 280 cycles,
hour glass shape specimen with an edge notch.

4 1
CRK6051 é-leO' s- , T-600°C, Ae-i0.5% for 4300 cycles,
. +5%, -1% for 31 cycles, Ae-i0.5% for 284 cycles,
+5%, -1% for 13 cycles, Ae-i0.5% for 93 cycles,

circumferential notch specimen.

4 1

CRK6071 é-5x10- s- , T-600°C, +5%, -1% for 20 cycles then
Ae-i0.5% for 200 cycles, repeat this waveform until
fracture at 1114 cycles, circumferential notch
specimen.

,4 ,1

CRK6081 é-5x10 s , T-600°C, +0.5%, -5% for 5 cycles then
Ae-iO.5% for 500 cycles, repeat this waveform until
fracture at 5512 cycles, double edge notch specimen.

,4 ,1
CRK6091 é-5x10 s , T-600°C, Ae-i0.5%, fracture at 10943
cycles, double edge notch specimen.

 

107

 

Fig. 4-33. The microstructure of a prenotched Ni fatigued at room

temperature with 0.5! total strain amplitude. The arrow indicates

the stress direction.

108

and approximately perpendicular to the applied stress. A slice of the
fatigued sample was then annealed at 764°C (0.6Tm) for one hour. Fig. 4-
34 shows the microstructure after annealing. The overall microstructure
has changed due to grain growth, probably owing to strain induced grain
boundary migration. However, the area very close to the crack surface
reveals finer grains as the result of static recrystallization. This
becomes clearer when annealing at a lower temperature. Fig. 4-35 shows
the same crack as in the previous micrograph but after annealing at
418°C (0.4Tm) for one hour. The plastic zone around the crack can now
be easily distinguished by the many small statically recrystallized
grains along crack surface. This micrograph clearly shows the large
plastic deformation zone associated with the crack. This plastic flow
might be sufficient to initiate dynamic recrystallization during high

temperature fatigue.

Several tests with 0.5% total strain amplitude were conducted at
600°C for 600 to 1000 cycles. Fig. 4—36 shows the microstructure paral-
lel to the stress axis of a notched specimen after 880 cycles. The
results of extensive grain boundary migration can be seen in this
micrograph. Most grain boundaries are now oriented under approximately
45° to the stress axis. Structural grain coarsening resulted from grain
boundary migration. In contrast to room temperature deformation, the
crack does not propagate transgranularly, but advances along the grain
boundaries, and the propagation direction is close to 45° with respect
to the stress axis. This crack propagation under 45° should not be
confused with or attributed to the maximum shear stress in this direc-

tion. Rather it is due to the easy crack opening (or small energy

109

  
 

\ .
/ r
\ x /
>V/K’K‘)
2/4 I q . _
Fig. 4-34. The microstructure of a prenotched Ni fatigued at room

temperature with 0.5% total strain amplitude and after annealing
at 764°C (0.6Tm) for 1 hour.

110

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weaamoccm woumm one oosuwaaem cannon Houou wn.o nuua ouaumuoaaou

Eoou um ooswfiumw Hz oesouocoud a mo eunuosuumouowa och .mnue .Muh

 

lll

release rate) along the boundaries, which are aligned under 45° owing to
previous migration, but contain cavities as a result of grain boundary
sliding. This is for instance substantiated by the crack which
propagated under 45° into a grain and got arrested as indicated by an

arrow. That the crack extended into the grain at all is most likely due
to the fact that a grain boundary was previously located in this posi-
tion and produced cavities because of grain boundary sliding. When the
boundary moved on, it left the cavities behind. While the overall
microstructure has undergone substantial grain coarsening due to grain
boundary migration, there is noticeable grain refinement along the crack
surface and near the crack tip area (Figs. 4-36, 4-37). A branch of the
crack is shown in Fig. 4-38. It is obvious that these small grains
attached to the crack were created during test since they appear in-
dividually and separately which is quite atypical for static
recrystallization. The small grains along the cracks in Figs. lr-36 and
4-37 also have to be understood as the product of dynamic recrystalliza-

tion during crack propagation.

A sample was fatigued at higher strain rate (2X10-3S-1) with 0.5%
strain amplitude for 744 cycles. The microstructure is shown in Fig. 4-
39. The crack propagated along the grain boundary for a short distance
compared to Fig. 4-36 which was tested at lower strain rate (2x10-‘s-1)
for 880 cycles with 0.5% strain amplitude. The average grain size is
smaller which corresponds to a small degree of grain boundary migration

and sliding under higher strain rate (i.e., higher cycle frequency).

112

 

Fig. 4-36. The microstructure of a prenotched Ni fatigued at 600°C with

0.5% total strain amplitude. The arrow indicates the stress direction.

113

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Low: 00000 on seawaumm Mz oocouocoua m we unnuosuumouo«a ugh .hnle .wuh

 

114

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sound one .oUSDHHmam :Hmuum Hmuou wm.o cuHB ooooo um oosmfiumw

Hz m mo xomwo a mo nocmun m padoum ousuosHumouuwfi ugh .wnuc .th

 

115

 

Fig. 4-39. The microstructure of a prenotched Ni fatigued at 600°C

.3-
with 0.5% total strain amplitude and strain rate of 2X10 s l. The

arrow indicates the stress direction.

116

Very pure Ni polycrystals were used to perform the current high
temperature fatigue tests. The dislocation storage rate is fairly small
because of easy dislocation movement which means high recovery rate.
This low energy storage will limit the driving force for DRX which has
been shown as the locally microstructural change during crack propaga-
tion. It is reasonable to speculate that it may be possible to retard
crack propagation by a global rebuilding of the microstructure with
dynamic recrystallization, i.e. by creation of new uncavitated bound-
aries. This might be achieved by intermittent overloads that would
trigger global dynamic recrystallization which has been observed in

section 4.4.

Several tests had been tried and are listed in Table 4-2. Fig 4-40
is the hardening curve of a sample tested at 600°C with 1% strain
amplitude for 605 cycles. The curve gives the stress as a function of
the strain amplitude in terms of cumulative displacement. A circum—
ferential crack was used in order to concentrate the deformation within
the area adjacent to the crack. According to previous results, the load
decrease indicates the occurrence of DRX. The microstructure around the
cracks is shown in Fig. 4-41. Owing to the nature of the circumferen-
tial crack and the higher strain amplitude imposed on the specimen, the
stress highly concentrates in front of the crack, and dynamic recrystal-
lization occurred in this area, which is indicated by the many small
grains ahead of the crack tip. DRX most likely causes the initial load
drop. The following load decreasing probably is due to the combination
of DRX and less effective strain amplitude ( part of the strain

amplitude contribute to the crack opening displacement ). The shape of

117

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Cs: 4de +528

 

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119

the crack tip ( Figs. 4-42 6: 4-43 ) suggests that the crack has been
blunted and the stress concentration has been relieved by those newly
formed small grains. This is further substantiated by a sample with a
circumferential notch elongated at 600°C. The corresponding load-

displacement curve is shown in Fig. 4-44. The initial grain structure
can be visualized as the left hand area away from the notch which con-
tains a high density of annealing twins embedded among large grains.
The notch was enlarged and became blunt due to dynamic recrystallization

as shown in Fig. 4-45.

The result on a sample fatigued at 600°C for 605 cycles with 1%
strain amplitude (Test No. CRK6031, Fig. 4-41) indicates that the
microstructural change was limited around the crack tips, therefore,
occasionally higher strain amplitudes are necessary to set off DRX in
the entire cross section. Such a test is listed in Table 4-2 (CRK6051)
and the hardening curve is shown in Fig. 4-46. The peaks in the curve
show the positions where higher strain amplitudes were applied. Thirty
one cycles of +5%, -1% strain amplitude were imposed to the specimen in
the first peak. The load decreases fast and steadily. This unusual
load decrease is due to the occurrence of DRX across the entirely region
and the propagation of cracks because a high tensile strain was applied
for a large number of cycles. The microstructure of the center area
which is parallel to the stress axis is shown in Fig. 4-47. The first
impression about this micrograph is that the overall microstructure has
been changed. Because of stress relief due to DRX, the crack on the
right hand side of the micrograph has been blunted and no main direction

of propagation could be revealed. This test provides the information

  
   

 

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Fig. 4-42. A higher magnification micrograph showing part of ihv
structure around a crack in Fig. 4-41.

121

 

Fig. 4-43. A higher magnification micrograph showing part of the

4-41.

structure around a crack in Fig.

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5

 

Fig. 4-47. The microstructure associated with crack propagation

corresponding to the test indicated in the Fig. 4-46.

126

about the occurrence of DRX if +5%, -1% strain amplitude was applied.
Another specimen was subjected to a more complex waveform, consisting
of +5%, -1% strain amplitude for 20 cycles then followed by i0.5% for
200 cycles. The circumferential notch specimen was tested at 600°C
(Test No. CRK6071) until fracture occurred after 1114 cycles. The flow
curve is shown in Fig. 4-48. The microstructure and fracture surface
observations are seen in Figs. 4-49 and 4-50, respectively. The
microstructure (Fig. 4-49) reveals small grains extending from the
fracture surface downward along the stress axis. The area included by
two arrows indicates the final fracture part. An SEM micrograph shows
the fracture surface of the whole cross sectional area (Fig. 4-50(a)).
A higher magnification of the final fracture area is given in Fig. 4-
50(b). The very clean surface indicates an intergranular fracture mode.

The crack propagation region is imaged in Fig. 4-50(c).

Because of the high tensile strain imposed on the specimen, DRX has
occurred completely along the notched plane, however, the crack propaga-
tion speed is also influenced by the high tensile strain. Therefore, it
is difficult to distinguish the effect of DRX on the crack propagation
under a small symmetrical strain amplitude (e.g. . i0.5%). A waveform
composed of +0.5%, -5% for 5 cycles and then i0.5% for 500 cycles was
applied repeatly to a sample (CRK6081) until fracture occurred at cycle
5512). A double edge instead of circumferential notch specimen was used
to allow defamation to occur along the whole gauge length. The flow
curve is shown in Fig. 4-51. The microstructure (Fig. 4-52) is quite
different from the previous one (Fig. 4-49). Grain boundary migration

had caused grain coarsening. The crack propagated mostly along grain

127

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133

boundaries which can be seen in the fractograph (Fig. 4-53(a), magnified
in Fig. 4-53(b)) near the notches, which is characterized by many facets
on the fracture surface. Subsequently, transgranular crack propagation
takes over which is revealed in Fig. 4-53(c) by the striations on the
fracture surface. A sample with similar notches was tested at 600°C
with i0.5% strain amplitude until fracture at cycle 10943 (CRK6091) for
comparison with the result of the overload test. The flow curve is
shown in Fig. 4-54. After initial strain hardening, the stress reaches
a maximum and then decreases continuously (Fig. 4-54(b)). The fatigue
life of this specimen is about two times longer than that of the pre.
vious specimen. The microstructure is shown in Fig. 4-55. The notation
S is defined as the normalized distance away from the plane parallel to
the stress axis and through the center of the specimen (S-O). The
maximum value of S is 1 which denotes the plane of the surface of the
gauge section. Fig. 4-55(a) shows the microstructure at S-3/4. Besides
the major cracks which propagate along the notches, two other large
cracks can be seen in this micrograph. DRX is clearly revealed by the
many small grains near the fracture surface and around crack tip. Fig.
4-55(b) shows the microstructure at S-l/2. The structure is similar to
Fig. 4-55(a), only the recrystallization phenomenon is not so obvious as
in Fig. 4-55(a). On the interior at S-O (Fig. 4-55(c)), the microstruc-
ture shows only a few large grains. Fig. 4-56 are SEM micrographs of
the fracture surface. The brighter area reveals the final fracture
surface. The microstructures of Figs. 4-55(a) and 4-55(b) correspond to
this area where a high stress due to the small cross sectional area in
final stage induced a high degree of defamation such that DRX is ap-

parent in this area. Fig. 4-56(b) shows the intergranular crack

 

(a)

Fig. 4-53. SEM micrographs of the fracture surface after
the test indicated in the Fig. 4-51.

 

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138

 

Fig. 4-55. The microstructures associated with crack propagation

corresponding to the test indicated in the Fig. 4-54. (a) Sx3/4;
(h) S-l/2 and (c) S-0.

 

(b)

 

141

propagation from the surface in the early stage of crack growth. Fig.
4-56(c) reveals the microstructure in the center region of the fracture
surface. The striations indicate that plastic deformation due a:

transgranular crack propagation has occurred which becomes even clearer

in higher magnification (Fig. 4-56(d)).

142

 

Fig. 4-56. SEM micrographs of the fracture surface after
the test indicated in the Fig. 4-55.

 

V DISCUSSION

5.1 Mechanical Behavior and DRX

All cyclic hardening curves (Fig. 4-l(a)) reveal a maximum followed
by a continuous decrease of the true stress. The number of cycles to the
flow stress maximum is the smaller the larger the cyclic total strain
amplitude. This behavior indicates a strong softening mechanism that
occurs at large cumulative strains. It is proposed to attribute this
softening to grain boundary migration (grain coarsening) and DRX. In
monotonic tests DRX is known to occur at relatively large strains and to
make itself felt by a drastic decrease of the flow stress [7,37]. The
softening observed in the current cyclic tests is much less spectacular,
because the net driving force for DRX in cyclic tests is much smaller
than in monotonic tests. The microstructural observations evidence
extensive grain boundary migration (Fig. 4-3) and the occurrence of new
grains (Figs. 4-7,4-9,h-10) during LCF. Since grain boundaries are known
to absorb dislocations during migration, this process will decrease the
total dislocation density and thus, the flow stress. With increasing
strain the specimen continues to strain harden, but the strain hardening
coefficient decreases owing to dynamic recovery, and DRX becomes in-
creasingly stronger. This will finally lead to a maximum of the flow

stress and a continuous stress decrease at larger accumulated strains.

The stress maximum is not sufficient, however, to infer the occur-

rence of DRX. Al also shows a hardening curve with a stress maximum,

144

145

although the average stress decrease rate is much smaller than that of
Ni. (Note also that a is considerably smaller for A1, under the same
conditions). Al is known not to recrystallize dynamically due to its
high stacking fault energy. In this case the stress maximum has to be
attributed totally to dynamic recovery and grain coarsening during
cyclic deformation. This is evident from the microstructure which
reveals huge grains after cyclic deformation of A1 (Fig. 4-6). In con-
trast, when the materials exhibits DRX, then grain refinement due to DRX
will reduce the softening effect caused by grain coarsening, but even in
this situation Ni still shows a larger stress decrease rate. This

substantiates that DRX is the major softening mechanism in Ni.

High temperature LCF on Ni-ZOO and dispersion strengthened (DS) Ni
was investigated by Bhat and Laird [14,15] . No DRX was found during
cyclic deformation, in contrast to their results in monotonic tests.
This is not in contradiction to the current findings, though. Bhat and
Laird draw their conclusions exclusively from TEM results, where it is
difficult to establish the rather localized occurrence of DRX. Also they
confined their cyclic testing to only 100 cycles, while our specimens
were subjected to 300 cycles and more, and the maximum generally was
attained at cycle numbers in excess of 100. Furthermore their specimens
- even the "pure" nickel - was much less pure than the material used in
the current investigation. This is particularly evident from the dis-
tinctly higher flow stress of the specimens used by Bhat and Laird. It
is a well known fact that recrystallization is delayed by the presence
of impurities, owing to their retarding effect on dislocation recovery

and grain boundary migration [59,60].

146

In monotonic tests, the onset of DRX can be associated with the
drop of the flow stress. In cyclic tests this is doubtful, however,
because the softening due to DRX is much smaller than in monotonic tests
due to the low dislocation density, i.e., the low driving force. Also
the concurrent deformation of the new grains will reduce the softening

effect associated with these newly formed grains.

It is further noted that these results on DRX during cyclic defor-
mation are also relevant for the understanding of DRX under monotonic
conditions. During hot working, high strains and stresses are necessary
to set off_DRX, and it has been argued, whether DRX occurs nucleation or
growth controlled [1,3,7,36]. The current observations show that DRX can
be initiated at very low driving forces but dislocation production rates
comparable to monotonic tests. This suggests that the nucleation is the
triggering process for the initiation of DRX. Once nucleated, the grain
will grow even at very small driving forces and thus, small growth rates
despite concurrent dislocation production. With increasing critical
stress, i.e. increasing dislocation density or, equivalently, driving
force, the growth rate'only controls the grain size in competition with
the nucleation rate so that at very high critical stresses and singular
nucleation events in monotonically deformed single crystals very large

recrystallized grains are obtained [32].

Usually, it was found that a certain critical strain ( in the order
of 15% or so) (or stress), had to be exceeded in order to set off DRX in

monotonic tests. For high strain amplitude (in the order of 5%), an

147

overall microstructural change has been observed (Figs. 4-12, 4-13, h-
15, 4-17) due to the large driving force for DRX which is comparable to
monotonic tests. According to the mechanical test results from current
research, the stress maximum occurs in the order of 100% in terms of
cumulative strain that stands for the sum of the strain (elastic +
plastic, negative + positive) imposed on the specimen, under the strain
rate of 10 4s'l(cycle frequency in the order of 10-2Hz depending on the

strain amplitude) at 0.5Tm.

The results fronltwo hour-glass shape specimens are of particular
interest. The microstructure (Figs. 4-15, 4-17) indicates grain refine-
ment and grain boundary migration. The final grain size is apparently
smaller than the original value. From the Hall-Fetch relation, the
smaller grain size should give rise to a higher flow stress. The stress
decrease in Fig. 4-14, therefore, can be only attributed to softening
owing to the occurrence of DRX. The recrystallized grains contain fewer
dislocations which is the real determinant of the flow stress. From the
results of DRX in monotonic tests, the size of dynamically recrystall-
ized grains will reach a steady state value, i.e. the grain size will
remain constant during progressing deformation. However, the stress is
observed to continually decrease in the current case. This may indicate
a reduction.of the effective strain due to the action of grain boundary
sliding, when the grain boundaries become aligned under 45° with respect
to the stress axis. For instance, in an hour-glass shape specimen (Fig.
4-15) only a small crack was detected which can not cause the high
magnitude of flow stress decrease. Further evidence can be gained by

examining the hysteresis loops at various critical points on the cyclic

148

hardening curve. Fig. 5-1(a) is the hardening curve of a Ni specimen
fatigued at 600°C with 0.5% strain amplitude. The stress reaches a
maximum at about 100 cycles, and then decreases continuously. The
hysteresis loops are plotted in Fig. 5-l(b). These loops share a line
within the elastic region with a common slope quite well. This suggests
the lack of macrocavities within the specimen. The significant stress
decrease, therefore, indicates that the softening phenomena observed are

mainly due to microstructural changes.

5.2 Grain Boundary Migration and Dislocation Structure

From the test results on Cu single crystals, it was concluded that
DRX during HTLCF is a grain boundary effect and, thus, occurs only in
polycrystals. The grain boundary becomes important in the initiation of
DRX. Most grain boundaries in Ni and Al were found to show extensive
migration during the test. Langdon et al. reported the same behavior in
Al and Pb [20-23] and they assumed that the boundary migration is
stress-induced in response to the cyclic loading, since the boundaries
tend to align parallel to the plane of maximum shear stress. Since grain
boundary migration will annihilate the dislocations in the swept volume,
there ought to be a substantial difference in dislocation density in
front of and behind a moving grain boundary. All TEM investigations
failrni to substantiate a drastic gradient in dislocation density across
a boundary. Only qualitative differences in dislocation arrangements

were noticed (Fig. 4-25). This does not mean though, that the grain

149

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151

boundaries do not absorb dislocations. Rather it has to be taken into
account that

(1) Grain boundary migration takes place gradually and continuously, but
the concurrent deformation constantly produces dislocations, and thus,
replaces annihilated dislocations.

(2) DRX progresses very slowly because of a very small driving force
compared to monotonic test where the boundaries of new grains move very
fast that usually dislocation free region can be observed if properly

quenched the specimen at the time DRX occurs.

From the results of dislocation observations during different
number of cycles, it was found that the dislocation structure in grain
interior is quite different from the dislocation structure in the wake
of the boundary (Fig. 4-30). The structure development during the
progress of the fatigue test suggests that the structure close to grain
boundary corresponds to a very early state of cell structure develop-
ment. and thus, has to be interpreted as the rebuilding of a cell

structure which was eliminated during grain boundary migration.

In essence it is concluded that from the observation of the struc-
tural gradient along a path perpendicular to the grain boundary, that
boundary migration leads to the destruction of the previously formed
dislocation cell structure, which subsequently is rebuilt through all
stages of cell development. By analogy, one may conjecture that the
patchwise occurrence of disorderly arranged dislocations in the grain
interior may also be the result of dynamic changes in the microstructure

owing to concurrent deformation.

152

A quantitative measure of the high temperature deformation struc-
ture is the size of the subgrains. The flow stress a is usually found
inversely related to the average subgrain size d [61]

g - K E (b-Burgers vector, K-constant).
Fig. 5-2 gives the relationship between subgrain size and flow stress of
Ni. The data roughly join a straight line with slope -0.75 (Bhat and
Laird) , -O.86 (current study) and -l.03 (all data). In this figure,
Young's modulus (E) was used instead of the shear modulus (G) in order

to compare the current results with data reported by Bhat and Laird

[14].

One of the most important questions in the current investigation is
"What is the driving force for grain boundary migration ?"

The scale of grain boundary migration under HTLCF is extremely
large (a few hundred microns [19]). If the specimens were tested under
the same conditions in monotonic loading, one would not observe grain
boundary migration or at most on a small scale in some special cases
(ex. creep). In contrast to the assumption made by Langdon and
coworkers, I propose adopt the explanation given by Snowden [19];
"Different amounts of deformation were built up on each side of bound-
aries so that the migration is produced by unequal numbers of
dislocations on opposite sides of boundaries", which also corresponds to
the terminology: "Strain induced boundary migration (SIBM)". According
to Taylor [62] five independent slip systems are necessary to maintain
shape compatability at the boundary between grains which can undergo

arbitrary deformation. For simplicity, only one favorable slip system

153

 

10

L 1 11 ll]

1

 

l l 11L]

O'/Eb [pm"]

I

l

 

 

 

()J' I rT’ I I I TIVFI I I I I IIFTI]T’

0.1 1 1o
CELL SIZE d [um]

Fig. 5-2. Normalized true stress vs dislocation cell size in Ni for
cyclic deformation at various temperatures, I - current investigation,

0 - result of Bhat and Laird [14].

154

is shown in Fig. 5-3. During the tensile loading, the grain with higher
resolved shear stress will produce higher density of dislocations,
provided the resolved shear stress is larger than the critical shear
stress. But the difference between the dislocation density is not so
high, and one more important factor is that the stress acting on the
grain boundary is in the same direction as the gradient of dislocation
density. That means the energy difference between both grains due to
dislocation gradient is somehow balanced by the pile-up stress of dis-
location against the grain boundary. Upon changing loading direction
from tension to compression, the dislocation will move toward the center
of grains. Due to higher dislocation density in grain A, the elastic
stress coming from other dislocations will retard the motion of disloca-
tions from moving away from the grain boundary area. However, in grain
B the retarding stress is smaller which means the dislocation will move
toward the center of grain easily. In the same time, more dislocation
will be produced in grain B in order to obtain the overall strain exter-
nally. The difference of dislocation density between grains A and B is
even higher and the stress acting on the grain boundary also changes the
direction from B to A which assists the grain boundary migration. The
new positions of grain boundaries are indicated as dotted lines in Fig.
5-3(b). The dislocation density in the region far away from grain
boundary is similar for both grains after completing a cycle. At high
temperature, recovery takes place and transfers the dislocations into
cell structure as shown in Fig. 4-30. When the cycle finished, the load
returned to zero then the dislocations relax from the external stress
and back to the wake of grain boundary (Fig. 5-3(c)) which explains the

very early state of cell structure development around grain boundary as

155

observed in Fig. 4-30. In conclusion, the driving force for grain
boundary migration is the difference of dislocation density comes from
the unequal amounts of deformation between grains under cyclic loading

condition with a small strain amplitude.

5.3 Crack Propagation and DRX

From the crack propagation test results, it was found that the
dynamically recrystallized zone does not extend to a larger size (Figs.
4-36, 4-37), that is, comparable to the zone observed for room tempera-
ture tests (Fig. 4-35). It was also found that the recrystallized zone
is not contiguous but consists of isolated grains along the crack path
(Fig. 4-38). The important difference between room temperature and
elevated temperature deformation crack propagation is that during room
temperature deformation the crack propagates transgranularly, that is
perpendicular to the direction of the largest principal stress, while
during a high temperature test, the crack propagates intergranularly,
which is usually not perpendicular to the normal stress, but along the
path of weakest resistance to crack growth owing to cavitation in the
boundaries. A larger resistance to crack growth in a ductile material is
equivalent to a large amount of plastic deformation, for instance in
case of transgranular crack growth. Intergranular crack propagation can
occur in two possible ways . Either the cavities grow and coalesce until
they touch the crack, which means the crack advances without major
plastic defamation. Or, the cavities nucleate and grow, but do not

become contiguous. Then plastic deformation has to occur locally to

156

 

 

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159

advance the crack between cavities, but the plastic zone size will be
limited to the dimension of the distance between adjacent cavities. The
SEM micrograph of the fracture surface, clearly reveals the occurrence
of plastic deformation between cavities (Fig. 5-4). The relation of
recrystallized grain size to the spacing of major cavities can be seeni
in Fig. 5-5. A.small grain formed between these two large cavities but
remains attached to the preexisting grain boundary. In terms of deforma-
tion mechanisms, dislocations will be produced and emitted along the
glide plane with the highest resolved shear stress (Fig. 5-6). These
dislocations provide the driving force for nucleation of a viable
recrystallization nucleus which can grow to the size of the plastic
zone. It is also worthy to note that the nucleation of grains is not
symmetric, i.e., grains do not appear equally on both sides of the
boundary. This can be understood from the plastic anisotropy owing to
the difference of orientation on both sides of the boundary. One grain
will usually have a slip system oriented most favorably, i.e. will
experience the largest resolved shear stress and thus, carry the plastic
deformation. This grain will be most liable to recrystallization, as

indeed was observed.

With regard to structural applications, the main question to be
answered is whether and how the occurrence of dynamic recrystallization
affects the crack propagation, that is the toughness of the material.

In this regard there are three cases which should be distinguished:
(a) Dynamic recrystallization is slow compared to crack growth. Then the
newly formed grain will only form behind the crack tip and thus, will

have no effect on crack propagation (Fig. 5-7(a)).

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(a)

 

(b)

Fig. 5—5. SEM micrograph of 8 Ni fatigued at 600°C with 0.5%

total strain amplitude. (a) after polishing; (b) after etching.

162

 

 

 

 

 

 

(C)

Fig. 5-6. Schematic sketch showing DRX due to plastic

deformation associated with the crack propagation.

163

(b) Dynamic recrystallization is fast compared to crack growth. Then the
newly formed grain will form ahead of the crack, although most likely
leave unchanged the original boundary orientation (Fig. 5-7(b)) , along
which the crack advances. However, the new grain changes the orientation
relationship across the boundary and therefore, its structure. This may
change the grain boundary energy and thus, the crack extension force. No
major influence on crack propagation would be expected in this case,
because

(1) The grain boundary energy is substantially changed only for very
few special orientations.

(2) The new grain boundary will not change the density of cavities
already present in the previous boundary. This however
constitutes the major effect on grain boundary strength.

(c) Dynamic recrystallization not associated with crack growth but with
the imposed cyclic deformation, changes the overall microstructure (Fig.
5-7(c)). This unzips the grain boundaries from their cavities which are
left in the new grain interior. This would blunt the crack tip and
temporarily impede crack propagation until new cavities are produced in

the recrystallized grain boundaries.

For small strain amplitude tests (<l%), it has almost always ob-
served case (a), in some instance it is difficult to discriminate
between case (a) and (b). From the discussions about cases (a) and (b),
the DRX will not affect the toughness of the materials. However, oc-
casionally imposing high strain amplitude (35%) test has shown a large
scale or even overall microstructural changes as revealed in Figs. 4-41

and 4-47. The crack tips have been fully blunted as can be seen in

164

 

 

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--------- ' ' |
- ' \ Grain m / Gram
(a)
GrahIl
i/’-‘\

    
 

 

 

  
 

Grain Ill Grain ll

ax grain

 

Cavny

Fig. 5—7. Schematic sketch showing three possible cases
related to the effect of DRX on crack propagation.

165

Figs. 4-42 and 4-43. One may suspect that these newly formed grains are
soft, then the stress field ahead of the blunted crack tip is still
enough to ‘tear' the grains apart and accelerate the crack propagation.
From the pure tensile test of a notched specimen, it was found that the

crack tips were rounded which would not be if tearing mode occurred.

Direct comparison of fatigue life, however, shows the opposite
result. The load - cumulative displacement curves of Test Nos. CRK6081
and CRK6091 were plotted and shown in Fig. 5-8. The test with oc-
casional high compression strain amplitude failed at half of the number
of cycles'which the specimen without over-straining could withstand.
However, when predicting or evaluating the material fatigue life, one
should not neglect the statistical characteristics of fatigue and in
particular flaws on the surface or within the specimen. For both tests,
the final fracture surface is along the prenotched plane which is ex-
pected. But the sample fatigued without occasional over-straining whose
surface along gauge length revealed numerous cracks as can be seen in
Fig. 4-55. lfids indicates that the notch artificially introduced to
this specimen is not as critical to the specimen as the one with oc-
casional over-straining which in return higher fatigue life was
obtained. Also, the over-straining was applied in the compression
direction did not give rise to an overall DRX instead more damage was
accumulated from this compression strain which partially contributed to

the early fracture.

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.For a quantitative comparison, more knowledge about the crack tip
stress and strain field is necessary in order to select optimal test

condition.

IV CONCUUSIONS

The present investigations yield the following results:

(1). Under cyclic deformation the flow stress amplitude as function.of'
the cumulative strain shows a maximum after a large number of cycles,
and subsequently the stress decreases continuously. The cumulative
strain at the maximum increases with decreasing total strain amplitude.
These results indicate that a strong softening mechanism that occurs at
large cumulative strains.

(2). Most grain boundaries show extensive migration. The migration rate
decreases as the number of cycles increases. The grain boundaries move
such as to align under 45° with respect to the stress axis.‘The driving
force for grain boundary migration can be explained as the unequal
amounts of dislocations produced on opposite sides of boundaries which
causes strain induced boundary migration.

(3). Under cyclic deformation, even at a total strain amplitude as small
as (Lfli75%, there is evidence that Ni also undergoes dynamic recrystal-
lization, although very locally and progressing very slowly. Dynamic
recrystallization appears to be the major softening mechanism at large
cumulative strains during low cycle fatigue of Ni at rn4n1 temperature.
With high strain amplitudes (=3-5%), dynamic recrystallization occurs in
a large scale and induces the overall microstructural change. The
microstructural investigations suggest that the nucleation of dynamic
recrystallization during low cycle fatigue can be attributed to grain

boundary bulging and recrystallization twinning.

168

169

(II). The current results support the hypothesis that the initiation of
DRX is controlled by nucleation rather than growth of recrystallized
grains.

(5). With progressing cyclic deformation a cell structure develops; the
cell boundaries become increasingly condensed and the cell interior
become free of dislocations. Dislocation structures near grain bound-
aries indicate that the migration of grain boundaries destroys the
previously established cell structure and that a new cell structure is
generated through all development stages involved. Grain boundary motion
during cyclic deformation leads to a gradient in dislocation density and
arrangement on a path away from the boundary. This gradient seems to
provide potential nucleation sites for DRX during HTLCF.

(6). Strain path changes do not lead to sequential destruction and
rebuilding of the cell structure. Rather the new cell structure is
continuously superimposed to the former structure until a homogeneous
structure is attained.

(7). Cu single crystals reveal that only recovery occurred during HTLCF
as well as during annealing of specimens fatigued at ambient tempera-
ture. No indication of recrystallization was found for strain amplitudes
less than 2%, irrespective of the cumulative strain. Therefore DRX
during HTLCF is a grain boundary effect and thus, occurs only in
polycrystals.

(8). Transgranular crack propagation was found in room temperature
fatigue test, but invariably intergranular crack propagation was ob-

served in high temperature low cycle fatigue test.

170

(9). Dynamic recrystallization was observed to occur along the crack
surface during high temperature low cycle fatigue with prenotched
specimens. The plastic zone associated with crack propagation at
elevated temperature is much smaller than during transgranular crack
growth at room temperature.

(10). The recrystallization phenomena associated with crack growth
during high temperature low cycle fatigue can be described by cavity
formation at the grain boundaries and the development of localized
plastic zones between cavities.

(11). Dynamic recrystallization was in no case found detrimental to
fatigue resistance. Under occasionally overostraining fatigue tests, DRX

was found to occur on a large scale, and crack blunting was observed.

171

Directions For Future Research:

The current study has demonstrated the occurrence of dynamic
recrystallization during high temperature low cycle fatigue with a small
strain amplitude. Since dynamic recrystallization occurs locally and
slowly, also due to concurrent deformation, it is difficult to identify
the dynamically recrystallized grains as well as to prepare specimens
containing DRX grains for TEM observations. The nucleation mechanism
remains unresolved. It is proposed to run tests using large grain
specimens with hour-glass shape in the gauge length for various numbers
of cycles such that the microstructural evolution can be observed. The

initiation of DRX and nucleation mechanisms shall be understood.

The mechanical testing system available in this laboratory is
capable of performing a wide range and precise tests, by changing the
strain rate, test temperature and strain amplitude, it is possible to
derive a constitutive equation for dynamic recrystallization under high

temperature low cycle fatigue.

The diamond structure forms after large number of cyclic deforma-
tion. Most grain boundaries align under 45° with respect to the stress
axis. It will be interesting to develop a computer code to model this
phenomenon by considering a two dimensional hexagonal contiguous grain
subjected to a macroscopic strain that is partially accommodated by

grain boundary sliding. The grain boundary will migrate under the

172

driving of unbalanced energy stored on the opposite sides of boundary as

shown in Fig. 5-3.

'The theoretical understanding about the stress and strain field
around crack tips becomes necessary in order to select an optimal condi«
tion for the investigation of the interaction between DRX and crack
propagation without introducing excessive damage to the specimen which

will affect the quantitative evaluation of the fatigue life.

The high temperature grips design is an important issue in the
current testing system. It is also an intriguing topic to pursue. The
problem due to bonding between tungsten pins and TZM pull rod may be
possible to solve by coating with ceramics onto pins as a diffusion
barrier. The nature and magnitude of the stress experienced by the pins

should be evaluated in order to simulate the test condition.

[10]

[11]

[12]

[13]

[14]

[15]

[15]

VII REFERENCES

H.J. McQueen and J.J. Jonas, in "Recovery and Recrystallization
during High Temperature Deformation" in Treatise on Materials
Science and Technology, 6, 393 (1975).

G. Gottstein, Met. Sci. 17, 497 1983.

P. Karduck, G. Gottstein and H. Mecking, Acta Metall. 31, 1525
(1983).

R. Bromley and C.M. Sellars, in "The Microstructure and Design of
Alloys (ICSMA 3)", 2, Institute of Metals, London, 380 (1973).
B.J. Sunter and N.M. Burman, J. Australian Inst. Metals 17,

91 (1972).

P.J.I. Stuitjie and G. Gottstein, Z. Metallk. 71, 279 (1980).
G. Gottstein and U.F. Kocks, Acta Metall. 31, 175 (1983).

M.J. Luton and C.M. Sellars, Acta Metall. 17, 1033 (1969).

A.A. Cuimaraes and J.J. Jonas, Metall. Trans. 12A, 1655 (1981).
D.R. Barraclough and C.M. Sellars, Met. Sci. 13, 257 (1979).
L.C. Lim and R. Raj, Acta Metall. 33, 2205 (1985).

V. Raman and T.C. Reiley, Scripta Metall. 20, 1343 (1986).

R.E. Cook, G. Gottstein and U.F. Kocks, J. Mat. Sci. 18, 2650
(1983).

S.P. Bhat and C. Laird, Int. J. Fatigue Engng. Mater. Struct.,
1, 59 (1979).

S.P. Bhat and C. Laird, Int. J. Fatigue Engng. Mater. Struct.,
1, 79 (1979).

H. Nahm, J. Moteff and D.R. Dierks, Acta Metall. 25, 107 (1977).

173

[17]
[18]
[19]
[20]

[21]

[22]
[23]

[24]

[25]

[26]
[27]
[28]
[29]
[30]

[31]

[32]

[33]

[34]

[35]

174

A.M. Ermi and J. Moteff, Metall. Trans. 13A, 1577 (1982).
A.M. Ermi and J. Moteff, J. Eng. Mat. Tech. 105, 21 (1983).
K.U. Snowden, Phil. Mag., 6, 321 (1961)

T.C. Langdon and R.C. Gifkins, Acta Metall. 31, 927 (1983).
T.C. Langdon, D. Simpson and R.C. Gifkins, Acta Metall. 31,
939 (1983).

P. Yavari and T.C. Langdon, Acta Metall. 31, 1595 (1983).
P. Yavari and T.C. Langdon, Acta Metall. 31, 1605 (1983).
E. Furubayashi and M. Nakamura, Proc. ICOTOM 6, Iron Steel Inst.
Japan, Tokyo, 619 (1981).

T. Ito, T. Taketani and Y. Nakayama, Scripta, Metall. 20, 1329
(1986).

J.R. Rice and R. Thomson, Phil. Mag. 29, 73 (1974).

V. Raman and T.C. Langdon, J. Mat. Sci. Lett. 2, 180 (1983).
H.S. Betrabet and V. Raman, Metall. Trans. 19A, 1437 (1988).
V. Raman and T.C. Reiley, Scripta Metall. 20, 1343 (1986).

V. Raman and T.C. Langdon, Acta Metall. 37, 725 (1989).

H. Abdel-Raouf, A. Plumtree and T.H. Topper, Metall. Trans.,
5, 267 (1974).

H. Mecking and G. Gottstein, in "Recrystallization of Metallic
Materials" (edited by F. Haessner), 2nd edn., pp. 195-222, Dr.
Riederer Verlag, Stuttgart, 1978.

G. Gottstein, D. Zabardjadi and H. Mecking, Metal Sci. 13, 223
(1979)

T. Hasegawa and U.F. Kocks, Acta Metall. 27, 1705 (1979).

I.L. Dillamore, P.K. Morris, C.J.E. Smith and W.B. Hutchinson,

Proc. R. Soc. Lon. A329, 405 (1972).

175

[36] C. Rossard, Metaux 35, pp. 102-115, 140-153, 190-205, (1960).

[37] T. Sakai and J.J. Jonas, Acta Metall. 32, 189 (1984).

[38] J. Takada, N. Nishino and S. Kikuchi, J. Mat. Sci. 21, 3420
(1986).

[39] G. Gottstein, Proc. 5—th Conf. Textures of Materials, 1, Springer,
Berlin, 73 (1978).

[40] W. Roberts and B. Ahlblom, Acta Metall. 26, 801 (1978).

[41] L.F. Coffin Jr., J. Mat. Sci. 6, 388 (1971).

[42] L.F. Coffin Jr., S.S. Manson, A.E. Carden, L.K. Serverud and W.L.
Greenstreet in "The Dependent Fatigue of Structural Alloys, A
General Assessment", 1975, ORNL-5073, Published Jan. 1977.

[43] 8.8. Manson in "Fatigue at Elevated Temperature", ASTM STP 520,
744 (1973).

[44] D.R. Dierks in "Advances in Design for Elevated Temperature
Environment", ASME, 29 (1975).

[45] H. Mughrabi in "Strength of Metals and Alloys", eds. P. Haasen,
V. Cerold and G. Kostorz, Pergamon Press, 1615 (1980).

[46] L.M. Brown, Met. Sci. 11, 315 (1977).

[47] S.J. Basinski, Z.S. Basinski and A.W. Howe, Phil. Mag. 19,

899 (1969).

[48] V. Raman and T.C. Reiley, Metall. Trans. 19A, 1533 (1988).

[49] T. Saegusa and J. R. Weertman, Scripta Metall. 12, 187 (1978).

[50] V. Raman and T.C. Langdon, Acta. Metall. 37, 725 (1989).

[51] D. Broek, "Elementary Engineering Fracture Mechanics", Noordhoff,
Leyden, 1974.

[52] Y. Birol, J. Mat. Sci. Lett. 6, 46 (1987)

[53] Y. Birol, Metallography 21, 77 (1988).

[54]
[55]

[56]

[57]

[58]
[59]
[60]
[61]

[62]

176

Y. Birol, J. Mat. Sci. 23, 2079 (1988).

Y. Birol, Scripta Metall. 22, 405 (1988).

G.E. Dieter "Mechanical Metallurgy", 2nd edn., McGraw-Hill Inc.,
396 (1976).

C. Laird, 'Cyclic Deformation of Metals and Alloys’ in Treatise
on Materials Science and Technology, 6, Academic Press, 101,
(1975).

H. Mughrabi, Mater. Sci. & Engng. 33, 207 (1978).

C. Messager and O. Dimitrov, Cpt. Rd. Acad. Sc., 251, 88 (1960).
K. Lucke and H. P. Stuwe, Acta Metall. 9, 1087 (1971).

J. E. Pratt, Acta Metall. 15, 319 (1967).

O

1. Taylor, J. Inst. Met. 62, (i) 307 (1938).

APPENDIX A

PROGRAM SOURCE CODES

177

178

MTS.BAS

COMMON user.name$, SPEC.NAME$, TEST.NAME$, CRYSTAL.TYPE, LAMBDA, KAPPA,
SLIP.MODE
COMMON STRAIN.RATE, GAUGE.LEN, CROSS.SEC, VOLUME, test.type, GRIP.SPEED
TEST.TEMP, sum.no

COMMON SAMPLE.RATE.MM, FS.STROKE, FS.LOAD, FS.STRAIN, PAR.FILE$,
DATA.FILE$, CYCLE.FILE$

DIM test.type$(5), CRYSTAL.TYPE$(2), SLIP.MODE$(3)

***********************************************************************

a s * a a a a a a a a a s a a e * a » x » a s a a a a

- MTS -

VERSION 1.0
01-JAN-1988
AUTHOR: SHUHRONG CHEN

This program handles the menu selection and test parameters input
used in the chaining programs for the 458.91 MicroProfiler

Chaining programs

TENSION.EXE - Performs the tensile test and data storage

COMPRESS.EXE Performs the compression test and data storage

STRAINCF.EXE Performs the low cycle fatigue test by strain

amplitude control and stores data

Performs the low cycle fatigue test by stress

amplitude control and stores data

MTSEZ.EXE - Performs the test which is defined by user and
collects data for further process

STRESSCF.EXE

Shelling programs

PRINTMTS.EXE
PLOTMTS.EXE

Prints out the test data
Plots the test result

} AUTHOR : c. GOTTSTEIN

* e a x a a » a $ * » s s a a a s a a » a x a s s x *

***********************************************************************

IF PAR.FILE$ <> "" THEN 530

SCREEN 0, 1: KEY OFF: COLOR l, l: CLS : CLEAR

CHDIR "\MTS": SHELL "DEL *.T": SHELL "DEL *.S"
SHELL "DEL *.CYC": COLOR 15, l: CLS

SHELL "type memo"

90 a$ - INKEY$: IF a$ - "" THEN 90

VERSIONS - "1.0"

DASH$ - STRING$(79, 45)
COSUB 705: COSUB 800

PRINT " --------------- MAIN SPECIFICATION INPUT ---------------- ":
PRINT
COSUB 1000
general specification
PRINT " USER PASSWORD ....... ?": LOCATE 3, 24: COLOR 1, 1: INPUT

passwordS: COLOR 15, 1
IF (password$ - "csr") OR (password$ - "CSR") THEN
user.name$ - "CHEN"

179

MTS.BAS 2

ELSEIF (password$ - "al61") OR (password$ - "A161") THEN

user.name$ - "YUNG"

ELSEIF (password$ - "boss") OR (password$ - "BOSS") THEN

user.name$ - "CG"

ELSEIF password$ - "0202" THEN

user.name$ - "LEE"

ELSE CLS : LOCATE 10, 10: PRINT " Unauthorized user, please see
Shuhrong Chen for instructions": GOTO 600

END IF
100 LOCATE 4, 1: INPUT " SPECIMEN NAME ....... "; SPEC.NAME$
110 INPUT " TEST NAME ........... "; TEST.NAME$

IF TEST.NAME$ - "" THEN PRINT : GOTO 110
' test specification
120 LOCATE 8, 1: PRINT " INDICATE TYPE OF TEST :”

PRINT

PRINT " TENSION ................. l "
PRINT " COMPRESSION ............. 2 "
PRINT " STRESS CYCLE ............ 3 "
PRINT " STRAIN CYCLE ............ 4 "
PRINT " USER DEFINES ............ 5 "
INPUT " TEST TYPE ...... "; test.type

IF test.type <- 0 OR test.type > 5 THEN 120

IF test.type - 1 THEN PRINT : PRINT " Please refer to the compression
test program to update this program ": END

IF test.type - 3 THEN PRINT : PRINT " Please refer to the strain cyclic

test program to update this program ": END
IF test.type - 5 THEN 520
COSUB 800
PRINT : REM specimen specification
130 PRINT " TYPE OF CRYSTAL : ": PRINT
PRINT " POLYCRYSTAL ............. l "
PRINT " SINGLE CRYSTAL .......... 2 "
INPUT " CRYSTAL TYPE ...... "; CRYSTAL.TYPE

IF CRYSTAL.TYPE - 1 THEN 140
IF CRYSTAL.TYPE <> 2 THEN 130
PRINT

PRINT " CRYSTAL ORIENTATION : "
PRINT

INPUT " LAMBDA - "; LAMBDA
INPUT " KAPPA - "; KAPPA

PRINT
PRINT " MODE OF SLIP "
PRINT
PRINT " SINGLE SLIP ............ 1 "
PRINT " DOUBLE SLIP ............ 2 "
PRINT " MULTIPLE SLIP .......... 3 "
INPUT " SLIP MODE ...... "; SLIP.MODE
140 PRINT : PRINT -
INPUT " GAUGE LENGTH ........... [mm] "; GAUGE.LEN
INPUT " GAUGE DIAMETER ......... [mm] "; GAUGE.DIAM

IF GAUGE.LEN - 0 OR GAUGE.DIAM - 0 THEN 140

P1 - 4 * ATN(1): CROSS.SEC - PI * ((GAUGE.DIAM / 2) A 2)

VOLUME - GAUGE.LEN * CROSS.SEC

PRINT : PRINT : IF test.type - 3 THEN 160

150 INPUT " INITIAL STRAIN RATE ...(ex. 2E-4) [l/sec] "; STRAIN.RATE
IF STRAIN.RATE - 0 THEN 150

180

MTS.BAS 3

sum.no - INT(-4 * LOG(STRAIN.RATE))
GRIP.SPEED - GAUGE.LEN * STRAIN.RATE
IF test.type > 2 THEN PRINT : GOTO 160
INPUT " SAMPLING RATE .................. [um/set] "; SAMPLE.RATE
IF SAMPLE.RATE - 0 THEN SAMPLE.RATE - 10
SAMPLE.RATE.MM - SAMPLE.RATE / 1000: PRINT

160 INPUT " FULL SCALE STROKE .......... [mm] "; FS.STROKE
INPUT " FULL SCALE LOAD ............ [kN] "; FS.LOAD

INPUT " FULL SCALE STRAIN .......... [%] "; FS.STRAIN: FS.STRAIN -
FS.STRAIN * .25

INPUT " TEST TEMPERATURE ........... [C] "; TEST.TEMP

IF FS.LOAD - 0 OR FS.STRAIN - 0 THEN PRINT : GOTO 160

' print out of input data

PRINT

GOSUB 800

PRINT " CHECK YOUR INPUT DATA : "

PRINT

PRINT " USER LAST NAME ..................... "; user.name$

PRINT " SPECIMEN NAME ...................... "; SPEC.NAME$

PRINT " TEST NAME .......................... "; TEST.NAME$

PRINT " DATE ............................... "; DATES

PRINT

PRINT " TEST TYPE .......................... "; test.type$(test.type)

PRINT " CRYSTAL TYPE ....................... ";
CRYSTAL.TYPE$(CRYSTAL.TYPE)
IF CRYSTAL.TYPE - 1 THEN 500

PRINT " LAMBDA ............................. "; LAMBDA; " [Degrees]"
PRINT " KAPPA .............................. "; KAPPA; " [Degrees]"
PRINT " SLIP MODE .......................... "; SLIP.MODE$(SLIP.MODE)

500 PRINT

PRINT " GAUGE LENGTH ....................... "; GAUGE.LEN; " [mm]"
PRINT " GAUGE DIAMETER ..................... "; GAUGE.DIAM; " [mm]"
PRINT " CROSS SECTION ...................... "; CROSS.SEC; " [mmA2]"
PRINT

IF test.type - 3 THEN PRINT : GOTO 510

PRINT " INITIAL STRAIN RATE ................ "; STRAIN.RATE; " [1/sec]"
PRINT " CROSS HEAD SPEED ................... "; GRIP.SPEED * 60; "
[mm/min]"

IF test.type > 2 THEN 510

PRINT " SAMPLING RATE ...................... "; SAMPLE.RATE; "

[um/set]"

510 PRINT " FULL SCALE STROKE .................. "; FS.STROKE; " [mm]"
PRINT ” FULL SCALE LOAD .................... "; FS.LOAD; " [kN]"
PRINT " FULL SCALE STRAIN .................. "; FS.STRAIN; " [mm]"
PRINT " TEST TEMPERATURE ................... "; TEST.TEMP; " [C]"

PRINT
INPUT " INPUT DATA OK ---------------------- (Y/N) "; ANSS

IF ANS$ <> "Y" AND ANS$ <> "y" THEN COSUB 800: GOTO 100

LPRINT TAB(1l); CHR$(14); "M T s ": COSUB 1100

LPRINT " *** MAIN DATA INPUT *** "

LPRINT TAB(11); " ------------------------------------------------------

LPRINT
COSUB 900

181

MTS.BAS 4

520 IF test.type - 1 THEN chn$ - "TENSION" ELSE IF test.type - 2 THEN
chn$ - "COMPRESS" ELSE IF test.type - 3 THEN chn$ - "STRESSCF" ELSE IF
test.type - 4 THEN chn$

COLOR l, l: CLS

temp$ - "TEMP"

OPEN "0", #1, temp$

PRINT #1, " ** user ID : "; user.name$
PRINT #1, " test start at : "; DATE$; " "; TIMES
CLOSE #1

SHELL "attrib -r monitor.mts"
SHELL "copy monitor.mts + temp monitor.mts"
SHELL "attrib +r monitor.mts"
KILL temp$: COLOR 15, 1: CLS
IF user.name$ - "CHEN" AND test.type - 4 THEN 523 ELSE 525
523 LOCATE 10, 12: PRINT "1. STRAINCF ": PRINT TAB(l2); "2. SCHEN "
PRINT : INPUT " Your choice ... "; ttype
IF ttype - 2 THEN chn$ - "SCHEN"
525 CHAIN chn$
530 CHDIR user.name$
SHELL "COPY C:\MTS\*.T": IF test.type - 5 THEN 540
SHELL "COPY C:\MTS\*.S": IF test.type < 3 THEN 540
SHELL "COPY C:\MTS\*.CYC"
540 CLS : CHDIR ".."
COLOR 1, 1: CLS
temp$ - "TEMP"
OPEN "0", #1, temp$
PRINT #1, " test finish at : "; DATE$; " "; TIMES
PRINT #1, " "
CLOSE #1
SHELL "attrib -r monitor.mts"
SHELL "copy monitor.mts + temp monitor.mts"
SHELL "attrib +r monitor.mts"
KILL temp$: COLOR 15, 1: CLS
IF test.type - 5 THEN 570
COSUB 1100: LPRINT CHR$(12)
LOCATE 8, 10: INPUT " DO you want to print the data ..... (Y/N) "; C$
IF C$ <> "Y" AND C$ <> "y" THEN 560
SHELL "PRINTMTS"
LOCATE 24, 15: PRINT "Wait until the printer finished printing"
PRINT TAB(lS); "Press any key to continue .... "
550 a$ - INKEY$: IF a$ - "" THEN 550
CLS
560 LOCATE 14, 10: INPUT " Do you want to plot the result .... (Y/N) ";

05
IF D$ <> "Y" AND D$ <> "y" THEN 570
SHELL "PLOTMTS"
570 CLS : LOCATE 9, 20: PRINT " *** Test Complete ***": PRINT : PRINT
LOCATE 14, 14: PRINT " Run another test ? Just type MTS ": PRINT :
PRINT

600 END
' check condition of Micro’s REMOTE and RUN ENABLE
700 OPEN "COMl:9600,e,7,,cs,ds,pe" FOR RANDOM AS #1

PRINT #1, "M"
GOSUB 1200: INPUT #1, status
CLOSE #1

IF status <> -1 THEN 720

182

MTS.BAS

705 CLS
TTLE$ - " Check Machine Status "
LOCATE 1, INT(4O - LEN(TTLES) / 2)
PRINT TTLE$;
PRINT DASH$;
LOCATE 5, 10
PRINT " VERIFY THAT I "
LOCATE 7, 15

PRINT " MicroProfiler is in REMOTE and RUN ENABLE conditions "

LOCATE 9, 15

PRINT " The Error, Upper and Lower Limit are in ENABLE condition "

LOCATE 23, l: PRINT DASH$
LOCATE 24, l

PRINT "
continue";

710 a$ - INKEY$: IF a$ - "" THEN 710
IF LEN(a$) < 2 THEN 710

ANS - ASC(RIGHT$(a$, 1))

IF ANS <> 81 THEN 710

GOTO 700

720 RETURN
800 CLS : LOCATE 25, 15

PRINT " P R O G R A M M T S
LOCATE l, 1

RETURN

900 LPRINT TAB(ll); " TEST NAME ................

TEST.NAME$

LPRINT TAB(ll); " SPECIMEN NAME ...............

LPRINT

LPRINT TAB(ll); " TEST TYPE ...................

test.type$(test.type)

LPRINT TAB(ll); " CRYSTAL TYPE ................

CRYSTAL.TYPES(CRYSTAL.TYPE)
IF CRYSTAL.TYPE - 1 THEN 910

LPRINT TAB(ll); " LAMBDA ......................

[Degrees]"

LPRINT TAB(ll); " KAPPA .......................

[Degrees]"

LPRINT TAB(ll); " SLIP MODE ...................

SLIP.MODE$(SLIP.MODE)
910 LPRINT

LPRINT TAB(ll); " GAUGE LENGTH ................

[mm] It

LPRINT TAB(ll); " GAUGE DIAMETER ..............

[mm]"

LPRINT TAB(ll); " CROSS SECTION ...............

[mm‘2]"
LPRINT
IF test.type - 3 THEN LPRINT : GOTO 93o
LPRINT

LPRINT TAB(ll); " INITIAL STRAIN RATE .........

" [l/secl"

LPRINT TAB(ll); " CROSS HEAD SPEED ............

60; " [mm/minl"
IF test.type > 2 THEN 920

< Page Down > -

version "; VERSIONS

.......... "; CHR$(14);

"; SPEC.NAME$

"; LAMBDA; "

"; KAPPA; "

"; GAUGE LEN; "
"; GAUGE.DIAM; "

"; CROSS.SEC; "

"; STRAIN.RATE;

"; GRIP.SPEED *

183

MTS.BAS 6
LPRINT TAB(ll);_" SAMPLING RATE ...................... "; SAMPLE.RATE;
" [um/set]"
LPRINT
920 LPRINT TAB(ll); " FULL SCALE STROKE .................. "; FS.STROKE;
n [mmlu
930 LPRINT TAB(ll); " FULL SCALE LOAD .................... "; FS.LOAD; "
[kN]"
LPRINT TAB(ll); " FULL SCALE STRAIN .................. ";
FS.STRAIN; " [mm]"
LPRINT
LPRINT TAB(ll); " TEST TEMPERATURE ................... "; TEST.TEMP; "
[C]"
RETURN
1000 test.type$(1) - "TENSION"
test.type$(2) - "COMPRESSION"
test.type$(3) - "STRESS CYCLING"
test.type$(4) - "STRAIN CYCLING"
CRYSTAL.TYPE$(1) - "POLYCRYSTAL"
CRYSTAL.TYPE$(2) - "SINGLE CRYSTAL"
SLIP.MODE$(1) - "SINGLE SLIP"
SLIP.MODE$(2) - "DOUBLE SLIP"
SLIP.MODE$(3) - "MULTIPLE SLIP"
RETURN
1100 LPRINT : LPRINT
LPRINT " "; CHR$(14); DATE$; " "; CHR$(14); TIME$
LPRINT
RETURN

1200 t1 - TIMER

1210 t2 - TIMER
IF ABS(t2 - t1) < .1 THEN 1210
RETURN

184

STRAINCF. BAS 1

COMMON USER.NAME$, SPEC.NAME$, TEST.NAME$, CRYSTAL.TYPE, LAMBDA, KAPPA,
SLIP.MODE
COMMON STRAIN.RATE, gauge.len, CROSS.SEC, VOLUME, TEST.TYPE, grip.speed,
TEST.TEMP, sum.no
COMMON SAMPLE.RATE.MM, fs.stroke, fs.load, fs.strain, PAR.FILE$,
DATA.FILE$, CYCLE.FILE$
' $INCLUDE: 'pcldefs.bi'
' --- STRAINCF ---
' VERSION 2.0
' 27-MAR-1989
' **********************************************************************
DIM analog.val%(10): DIM AX$(20): DIM stop.mode$(3): DIM
digit.val%(200)
DIM digit(5): DIM a#(2, 3): DIM f(lOO, 2)
100 CLS : LOCATE 3, 10
PRINT " Indicate the type Of test "
PRINT : PRINT TAB(lO); " 1. Symmetry +/- strain amplitude test "
PRINT TAB(IO); " 2. Asymmetry +/- strain amplitude test "
LOCATE 8, 11: INPUT " -> Your choice is ..... "; amp.type
IF amp.type <> 1 THEN IF amp.type <> 2 THEN 100
LOCATE 10, 10: INPUT " Are you using the extensometer ? (Y/N) ";
etsm$
IF etsm$ - "y" OR etsm$ - "Y" THEN etsm - 1 ELSE etsm - 2
IF amp.type - 1 THEN 200 ELSE LOCATE 12, 10: GOTO 300
200 LOCATE 12, 10: INPUT " The strain amplitude is ... [%] "; strain.amp
frequency - grip. speed * 100 / (4 * strain. amp * gauge. len)
LPRINT TAB(ll); " STRAIN AMPLITUDE ...................
strain. amp; "[%] OR "; strain.amp * gauge.len * 10; "um": GOTO 400
300 INPUT " The positive strain amplitude ...... [%] "; pos.strain
LOCATE 13, 10: INPUT " The negative strain amplitude ...... [%] ";
neg.strain
neg.strain - ABS(neg.strain)
frequency - grip.speed * 100 / (2 * (pos.strain + neg.strain) *
gauge.len)
LPRINT TAB(ll); " POSITIVE STRAIN AMPLITUDE .......... "; pos.strain; "
[%] OR "; pos.strain * gauge.len * 10; "um"
LPRINT TAB(ll); " NEGATIVE STRAIN AMPLITUDE .......... "; neg.strain; "
[%] OR "; neg.strain * gauge.len * 10; "um"
400 LPRINT TAB(ll); " CYCLE FREQUENCY .................... "; frequency;
" [1/sec]”
IF etsm - 1 THEN LPRINT TAB(ll); " USING THE EXTENSOMETER
............. YES"
LPRINT
period - (1.03 + pos.strain / (2 * (pos.strain + neg strain))) /
frequency
410 LOCATE 15, 10: INPUT " Cycle plot interval ....................
"; plot.int
LOCATE 17, 10: INPUT " Cycle store interval ................... ";

store.int
LPRINT TAB(ll); " CYCLE STORAGE INTERVAL ............. "; store.int
LOCATE 19, 10: PRINT " Cylce print interval { must be different"
LOCATE 20, 10: INPUT " from plot interval } .................. ";
print.int
LPRINT TAB(ll); " CYCLE PRINT INTERVAL ............... "; print.int

IF plot.int - 0 OR store.int - 0 THEN 410
IF print.int - 0 THEN 410

185

STRAINCF.BAS 2

CLS
LOCATE 7, 8: PRINT " Indicate the test terminated condition : "
LOCATE 9, 8: PRINT " 1. After tested certain number Of cycles "
LOCATE 10, 8: PRINT " 2. After fully fractured "
LOCATE 11, 8: PRINT " 3. After stress decreased to certain amount "
LOCATE 13, 8: INPUT " -> Your selection is ......... "; stop.mode
LOCATE 15, 8
IF stop.mode - 1 THEN INPUT " test terminated cycle .......... ";
end.cyc: ec$ - STR$(end.cyc)
IF stop.mode - 3 THEN INPUT " percent of stress decreased .... [%]
"; stress.de: sd$ - STR$(stress.de) + "%"
stop.mode$(l) - "AT CYCLE # " + ec$: stop.mode$(2) - "FULLY FRACTURE":
stop.mode$(3) - "AFTER STRESS DECREASED " + sd$
LPRINT TAB(ll); " STOP MODE .......................... ";
stop.mode$(stop.mode)
LOCATE l8, 8: PRINT " Input the scales for real-time plot "

LOCATE 20, 8: INPUT " Maximum scale of X axis (true strain) ... [ % ]
"; xmax
LOCATE 21, 8: INPUT " Maximum scale of Y axis (true stress) ... [MPa]
n; max
LPRINT
LPRINT " ‘ -----------------------------------------------------
LPRINT CHR$(27); "H"
LPRINT CHR$(27); "G"; " CYCLE SIG[MPa] LOAD[N]
EPSON[%] PLASTIC STRAIN[%]"
LPRINT " <MAXIMUM> <MINIMUM> "

LPRINT : LPRINT CHR$(27); "H"
CLS : IF etsm - 1 THEN fs.scale - fs.strain ELSE fs.scale - fs.stroke
IF amp.type - 2 THEN 500
command.high - strain.amp * gauge.len / fs.scale
command.1ow - -command.high: GOTO 600
500 command.high - pos.strain * gauge.len / fs.scale
command.low - -neg.strain * gauge.len / fs.scale
600 DEF fnfs (X, Y) - (X * 2 / 4096 - l) * Y
ERROR.WORD% - O
error.code% - INITIALIZE%
error.code% - SET.ERROR.CONTROL.WORD%(ERROR.WORD%)
' DI/O variables
PORT.OUT% - 1: PORT.IN% - 0: MASK.OUT% - 255: MASK.HIGH% - 2: PORT1% - O
PORTO% - 0: PORT1.RUN% - 2: PORT1.STOP% - l: PORT1.0FF% - 0
' A/D variables
TIMING.SOURCE% - 0: START.CHAN% - 0: end.chan% - etsm: GAIN% - l
' Initialize Real Time Variables
test.load - 0: strain - 0: SEGMENT.NO - 2: cycle.no - 1: i - O
: DATA.NO - 0
area - 0: MAX.LOAD - -fs.load * 1000: MAX.STRAIN - -fs.sca1e
MIN.LOAD - fs.load * 1000: MIN.STRAIN - fs.scale
' Set up digital I/O
error.code% - ENABLE.FOR.OUTPUT%(PORT.OUT%)
error.code% - OUTPUT.DIGITAL.VALUE%(PORT.OUT%, MASK.OUT%, PORT1%)
error.code% - ENABLE.FOR.INPUT%(PORT.IN%)
error.code% - GET.ERROR.CODE%(error.code%)
IF error.code% <> 0 THEN PRINT "DI/O Setup error "; error.code%: GOTO
3600
DATA.FILE$ - TEST.NAME$ + ".T"

STRAINCF.BAS

CYCLE.FILE
OPEN ”0", #1,
OPEN "0”, #2,
OPEN "COM1:96

' Set
PRINT
COSUB
PRINT
COSUB
PRINT
COSUB
PRINT
GOSUB

RATE - ST
PRINT
GOSUB
PRINT
COSUB
PRINT
COSUB
PRINT
GOSUB
PRINT
COSUB
PRINT
COSUB
PRINT
COSUB
PRINT
GOSUB

186

$ - TEST.NAME$ + ".CYC"

DATA.FILE$

CYCLE.FILE$

00,E,7,,CS,DS,PE" FOR RANDOM AS #3

up the MicroProfiler
#3, "10R"
4000: INPUT #3, echo
#3, "1008"
4000: INPUT #3, echo
#3, "IT"
4000: INPUT #3, echo
#3, "I"
4000: INPUT #3, echo
RAIN.RATE * gauge.len / fs.scale * 100
#3, RATE; "G"
4000: INPUT #3, echo
#3, command.high; "H"
4000: INPUT #3, echo
#3 ’ "Q"
4000: INPUT #3, echo
#3, command.low; "H"
4000: INPUT #3, echo
#3, RATE; "G"
4000: INPUT #3, echo
#3, command.high; "H"
4000: INPUT #3, echo
#3 ’ "Q"
4000: INPUT #3, echo
#3, command.low; "H"
4000: INPUT #3, echo
Set up clock and A/D

TICKS.AD% - 500

error.code%
error.code%

- SET.CLOCK.DIVIDER%(TICKS.AD%)
- GET.ERROR.CODE%(error.code%)

IF error.code% <> 0 THEN PRINT " Clock setup error "; error.code%: GOTO

3600

error.code% - SETUP.ADC§(TIMING.SOURCE%, START.CHAN%, end.chan%,

GAIN%)
error.code%

- GET.ERROR.CODE%(error.code%)

IF error.code% <> 0 THEN PRINT "A/D Setup error "; error.code%: GOTO

3600
number.o
(sum.no + 3)

f.val% - 200: number.data% - 15: 1ast.val% - (1 + etsm) *

Prompt user for start

CLS
LOCATE 6, 19: PRINT " Strain Fatigue Test Execution "
LOCATE 9, 12: PRINT " -------------- Execution Control -----------------
LOCATE 11, 12: PRINT " TO START, RESTART OR END .......
LOCATE 13, 12: PRINT " TO INTERRUPT ...................
LOCATE 15, 12: PRINT " TO CHANGE AMPLITUDE DURING TEST ...
PRINT " -------------------------------------------------

LOCATE 17, 12:

LOCATE 20, 12'

700 LOCATE 21,

'IO: a$ - INKEY$

PRINT "Please remember these function keys

187

STRAINCF.BAS 4

IF a$ <> "+" THEN 700
GOSUB 4500
' Toggle run to on
error.code% - OUTPUT.DIGITAL.VALUE%(PORT.OUT%, MASK.OUT%,
PORT1.RUN%): GOSUB 4000
error.code% - OUTPUT.DIGITAL.VALUE%(PORT.OUT%, MASK.OUT%, PORTl.OFF%)
error.code% - GET.ERROR.CODE%(error.code%)

IF error.code% <> 0 THEN PRINT " Execution error "; error.code%: GOTO
3600
' Start the MicroProfiler
GOSUB 5500
strain.ini - fnfs(analog.val%(etsm), fs.scale)

DD - 1: ti - TIMER

GOSUB 4000: PRINT #3, "J"

COSUB 4000: INPUT #3, echo
GOTO 2150

' Data collection ( max + min for each cycle )

1000 MAX.VAL2% - 0: MIN.VAL2% - 4096: max.va10% - O: min.va10% - 4096
SEGMENT.NO - SEGMENT.NO + 1
cycle.no - INT(SEGMENT.NO / 2)
LOCATE 1, 73: PRINT "->"; USING "#####"; cycle.no
IF cycle.no - plot.int * INT(cyc1e.no / plot.int) THEN 2000
IF cycle.no - store.int * INT(cycle.no / store.int) THEN 2000
1100 GOSUB 5500
IF SEGMENT.NO - 2 * INT(SEGMENT.NO / 2) THEN 1300
IF analog.va1%(end.chan%) > MAX.VAL2% THEN MAX.VAL2% -
analog.val%(end.chan%): max.va10% - analog.val%(0)
IF MAX.VAL2% - analog.va1%(end.chan%) < 12 / etsm THEN 1500
IF analog.val%(0) > (max.va10% + 8192) / 5 THEN 1500
load.max - fnfs(max.va10%, fs.load) * 1000
strain.max - fnfs(MAX.VAL2%, fs.scale) - strain.ini
area - VOLUME / (gauge.len + strain.max)
IF area < 0 THEN 1200
SIGMA.MAX - load.max / area
EPSON.MAX - LOG(1 + strain.max / gauge.len) * 100
IF load.max > MAX.LOAD THEN MAX.LOAD - load.max: ma.strain -
strain.max
IF strain.max > MAX.STRAIN THEN MAX.STRAIN - strain.max
1200 DATA.NO - DATA.NO + 1
PRINT #1, DATA.NO; load.max; strain.max; SIGMA.MAX; EPSON.MAX
' Failure check
IF SEGMENT.NO - 2 * end.cyc + 1 THEN a$ - "+": GOTO 3000
IF ABS(load.max) < fs.load * 20 THEN a$ - "+": GOTO 3000
IF stop.mode - 3 THEN IF load.max < (1 - .01 * stress.de) *
MAX.LOAD THEN a$ - "+": GOTO 3000
IF cycle.no > 2 THEN COSUB 5600
IF cycle.no <> print.int * INT(cyc1e.no / print.int) AND cycle.no >
10 THEN 1000
LPRINT TAB(l2); SIGMA.MAX; TAB(37); load.max; TAB(52); EPSON.MAX;
TAB(67); plastic.strain
GOTO 1000
1300 IF analog.val%(end.chan%) < MIN.VAL2% THEN MIN.VAL2% -
analog.val%(end.chan%): min.va10% - analog.val%(0)
IF ABS(MIN.VAL2% - analog.val%(end.chan%)) < 12 / etsm THEN 1500
IF analog.va1%(0) < (min.va10% + 8192) / 5 THEN 1500
load.min - fnfs(min.va10%, fs.load) * 1000

188

STRAINCF.BAS 5

strain.min - fnfs(MIN.VAL2%, fs.scale) - strain.ini
area - VOLUME / (gauge.len + strain.min)
IF area < 0 THEN 1400
SIGMA.MIN - load.min / area
EPSON.MIN - LOG(1 + strain.min / gauge.len) * 100
IF load.min < MIN.LOAD THEN MIN.LOAD - load.min: mi.strain -
strain.min
IF strain.min < MIN.STRAIN THEN MIN.STRAIN - strain.min
1400 DATA.NO - DATA.NO + l
PRINT #1, DATA.NO; load.min; strain.min; SIGMA.MIN; EPSON.MIN
IF cycle.no > 2 THEN GOSUB 5600
IF cycle.no <> print.int * INT(cyc1e.nO / print.int) AND cycle.no >
10 THEN 1000
LPRINT TAB(3); cycle.no: TAB(24); SIGMA.MIN; TAB(37); load.min; TAB(52);
EPSON.MIN; TAB(67); p1astic.strain
GOTO 1000
1500 a$ - INKEY$: IF a$ <> "" THEN 3000 ELSE 1100
' Plot detail curve and store data
2000 DD - 1
period - 1.01 / frequency
ti - TIMER
i - i + 1: IF i > 17 THEN i - 1
LOCATE 1, 4 * i: PRINT USING "####"; cycle.no: GOTO 2150
2100 GOSUB 5500
2150 test.load - fnfs(analog.va1%(0), fs.1oad) * 1000
strain - fnfs(analog.val%(end.chan%), fs.scale) - strain.ini
area - VOLUME / (gauge.len + strain)
IF area < 0 THEN 2100
TRUE.STRESS - test.load / area
TRUE.STRAIN - LOG(1 + strain / gauge.len) * 100
XX - 346 + TRUE.STRAIN * UX: IF XX > 632 OR XX < 60 THEN 2200
YY - 166 - TRUE.STRESS * UY: IF YY > 304 OR YY < 28 THEN 2200
IF DD - 1 THEN PSET (XX, YY), l4: XXO - XX: YYO - YY: DD - O: GOTO
2200
LINE (XXO, YYO)-(XX, YY), 14: XXO - XX: YYO - YY
2200 IF cycle.no <> 1 AND cycle.no <> store.int * INT(cycle.nO /
store.int) THEN 2290
PRINT #2, TRUE.STRAIN; TRUE.STRESS; p1astic.strain; cycle.no
2290 t1 - TIMER
2300 t2 - TIMER
a$ - INKEY$: IF a$ - "+" THEN 3000
IF ABS(t2 - t1) < l / (75 * frequency) THEN 2300
tf - TIMER
IF tf < ti THEN tf - cf + 86400
IF tf - ti < period THEN 2100
2310 IF SEGMENT.NO - 2 * end.cyc THEN a$ - "+": GOTO 3000
SEGMENT.NO - SEGMENT.NO + l
GOTO 1000
' Stop or Interrupt test
3000 IF a$ - "+" THEN 3100
IF a$ - "-" THEN 3200
IF a$ - "*" THEN 5000 ELSE 1100
3100 GOSUB 5500
IF ABS(analog.va1%(0) - 2048) > 20 THEN 3100
3200 COSUB 4000: PRINT #3, "C"
COSUB 4000: INPUT #3, echo

 

189

STRAINCF.BAS 6

IF a$ - "+" THEN 3400
3300 a$ - INKEY$: IF a$ <> "+" THEN 3300

GOSUB 4000: PRINT #3, "D"

GOSUB 4000: INPUT #3, echo
IF b$ <> ”" THEN b$ - "": GOTO 5620
GOTO 1100

3400 CLOSE
' Toggle stop
error.code% - OUTPUT.DIGITAL.VALUE%(PORT.OUT%, MASK.OUT%,
PORT1.STOP%): GOSUB 4000
error.code% - OUTPUT.DIGITAL.VALUE%(PORT.OUT%, MASK.OUT%,
PORT1.0FF%):
error.code% - GET.ERROR.CODE%(error.code%)
IF error.code% <> 0 THEN PRINT " DI/O Error "; error.code%: GOTO
3600
t1 - TIMER
3500 t2 - TIMER
kk$ - INKEY$: IF kk$ <> "" THEN 3510
IF t2 - t1 < 30 THEN BEEP: GOTO 3500
3510 SCREEN 0: COLOR 15, 1: CLS : COSUB 3700
3600 error.code% - TERMINATE%
CHAIN "MTS"
END
' Store test parameters
3700 PAR.FILE$ - TEST.NAME$ + ".8"
OPEN "0", #2, PAR.FILE$
MAX.ENG.STRAIN - MAX.STRAIN / gauge.len
MIN.ENG.STRAIN - MIN.STRAIN / gauge.len
MAX.TRUE.STRAIN - LOG(1 + MAX.STRAIN / gauge.len)
MIN.TRUE.STRAIN - LOG(1 + MIN.STRAIN / gauge.len)
MAX.ENG.STRESS - MAX.LOAD / CROSS.SEC
MIN.ENG.STRESS - MIN.LOAD / CROSS.SEC
MAX.TRUE.STRESS - MAX.ENG.STRESS * (1 + ma.strain / gauge.len)
_ MIN.TRUE.STRESS - MIN.ENG.STRESS * (1 + mi.strain / gauge.len)
WRITE #2, SPEC.NAME$, TEST.NAME$, DATE$, CRYSTAL.TYPE, LAMBDA, KAPPA,
SLIP.MODE
WRITE #2, gauge.len, CROSS.SEC, TEST.TYPE, grip.speed, SAMPLE.RATE,
fs.load, TEST.TEMP
WRITE #2, DATA.NO, MAX.STRAIN, MAX.LOAD, MAX.ENG.STRAIN, MAX.ENG.STRESS,
MAX.TRUE.STRAIN, MAX.TRUE.STRESS
CLOSE
' Test overview
PRINT : PRINT : LOCATE 3, 15: PRINT "*** TEST OVERVIEW ***"
PRINT " --------------------------------------------------------- "

PRINT

PRINT " SPECIMEN NAME ....................... "; SPEC.NAME$

PRINT " TEST NAME ........................... "; TEST.NAME$

PRINT " DATE ................................ "; DATE$

PRINT " NUMBER OF CYCLE ..................... "; cycle.no

PRINT " MAXIMUM STRAIN ...................... "; MAX.STRAIN; " [mm]"
PRINT " MINIMUM STRAIN ...................... "; MIN.STRAIN; " [mm]"
PRINT " MAXIMUM LOAD ........................ "; MAX.LOAD; " [N]"

PRINT " MINIMUM LOAD ........................ "; MIN.LOAD; " [N]"

PRINT ” MAXIMUM ENGINEERING STRAIN .......... "; MAX.ENG.STRAIN * 100; "

[%]"

190

STRAINCF.BAS 7
PRINT ” MINIMUM ENGINEERING STRAIN .......... "; MIN.ENG.STRAIN * 100; "
[15]"

PRINT " MAXIMUM ENGINEERING STRESS .......... "; MAX.ENG.STRESS; "
[MPa]"

PRINT " MINIMUM ENGINEERING STRESS .......... "; MIN.ENG.STRESS; "
[MPa]"

PRINT " MAXIMUM TRUE STRAIN ................. "; MAX.TRUE.STRAIN * 100;
n [%]n

PRINT " MINIMUM TRUE STRAIN ................. "; MIN.TRUE.STRAIN * 100;
II [%]n

PRINT " MAXIMUM TRUE STRESS ................. "; MAX.TRUE.STRESS; "
[MPa]"

PRINT " MINIMUM TRUE STRESS ................. "; MIN.TRUE.STRESS; "
[MPa]"

PRINT

PRINT " ......................................................... u

LPRINT : LPRINT : LPRINT : LPRINT TAB(23); "*** TEST OVERVIEW ***"
LPRINT TAB(ll); " .......................................................

LPRINT

LPRINT TAB(ll); " NUMBER OF CYCLE .................... "; cycle.no
LPRINT TAB(ll); " MAXIMUM STRAIN ..................... "; MAX.STRAIN; "
[N]"

LPRINT TAB(ll); " MINIMUM STRAIN ..................... "; MIN.STRAIN; "
[N]"

LPRINT TAB(ll); " MAXIMUM LOAD ....................... "; MAX.LOAD; "
[N]"

LPRINT TAB(ll); " MINIMUM LOAD ....................... "; MIN.LOAD; "
[N]"

LPRINT TAB(ll); " MAXIMUM ENGINEERING STRAIN ......... "; MAX.ENG.STRAIN
* 100; " [%]"

LPRINT TAB(ll); " MINIMUM ENGINEERING STRAIN ......... "; MIN.ENG.STRAIN
* 100; " [%]"

LPRINT TAB(ll); " MAXIMUM ENGINEERING STRESS ......... ";
MAX ENG.STRESS; " [MPa]"

LPRINT TAB(ll); " MINIMUM ENGINEERING STRESS ......... ";
MIN.ENG.STRESS; [MPa]"

LPRINT TAB(ll); MAXIMUM TRUE STRAIN ................ ";
MAX.TRUE.STRAIN 100; " [%]"

LPRINT TAB(ll); MINIMUM TRUE STRAIN ................ ";
MIN.TRUE.STRAIN 100; " [%]"

LPRINT TAB(ll); MAXIMUM TRUE STRESS ................ ";
MAX.TRUE.STRESS; " [MPa]"

LPRINT TAB(ll); " MINIMUM TRUE STRESS ................ ";
MIN.TRUE STRESS; " [MPa]"

LPRINT

LPRINT TAB(ll); " -------------------------------------------------------

a $ 3 $ 3 3

t1 - TIMER
3800 t2 - TIMER
IF ABS(t2 - t1) < 3 THEN 3800
CLS
RETURN
' Time relay
4000 t7 - TIMER
4010 t8 - TIMER

191

STRAINCF.BAS 3
IF ABS(t8 - t7) < .001 THEN 4010
RETURN

' Set up screen

4500 CLS

UX - 286 / xmax
UY - 138 / ymax
ymax$ - STR$(ymax): xmax$ - STR$(xmax)
SCREEN 9: COLOR 12, 7: CLS
LINE (60, 28)-(632, 304), 1, BF
LINE (60, 28)-(632, 304), 14, B: LINE (61, 29)-(631, 303), 14, B
LINE (60, 166)—(632, 166), 3: LINE (346, 304)-(346, 28), 3
LINE (60, 97)-(66, 97), 14: LINE (626, 97)-(632, 97), 14
LINE (60, 235)-(66, 235), 14: LINE (626, 235)-(632, 235), 14
LINE (203, 28)-(203, 33), 14: LINE (203, 299)-(203, 304), 14
LINE (489, 28)-(489, 33), 14: LINE (489, 299)-(489, 304), 14
LOCATE l, l: PRINT "N - "
LOCATE 23, 8: PRINT -xmax: LOCATE 23, 44: PRINT "0": LOCATE 23, 54
PRINT "TRUE STRAIN [%]": LOCATE 23, 8O - LEN(xmaxS): PRINT xmax
LOCATE 13, 6: PRINT "0": LOCATE 7, 6: PRINT "+": LOCATE 18, 6: PRINT
LOCATE 3, 7 - LEN(ymaxS): PRINT ymax: LOCATE 22, 7 - LEN(ymaxS): PRINT
ymax
LOCATE 2, 39: PRINT "TEST : "; TEST.NAME$
RESTORE
FOR AA - 1 TO 15
READ AX$(AA)
NEXT AA
DATA T,R,U,E,,S,T,R,E,S,S,,M,P,A
FOR BB - 1 TO 15
LOCATE BB + 4, 3: PRINT AX$(BB)
NEXT BB
RETURN
' Change strain amplitude while holding the test
5000 GOSUB 4000: PRINT #3, "C"
GOSUB 4000: INPUT #3,
echo
b1ank$ - STRING$(80, 32)
LOCATE l, 1: PRINT blank$: LOCATE 1, 1
IF amp.type - 2 THEN 5100
INPUT " Input the strain amplitude ...... [%] "; strain.amp
IF strain.amp - 0 THEN 5200
LPRINT
LPRINT TAB(2); "* The strain amplitude has been changed to"; strain.amp;
"% since cycle #"; cycle.no + l
LPRINT
command.highl - strain.amp * gauge.len / fs.scale
command.lowl - -command.high1
frequency - grip.speed * 100 / (4 * strain.amp * gauge.len): GOTO

5200

5100 INPUT " Input the positive strain amplitude ..... [%] "; pos.strain
LOCATE 1, l: PRINT b1ank$: LOCATE 1, 1
INPUT " Input the negative strain amplitude ..... [%] "; neg.strain
IF pos.strain - 0 AND neg.strain - 0 THEN 5200

LPRINT

LPRINT TAB(2); "* The positive strain amplitude has been changed to”;
pos.strain; "% since cycle #"; cycle.no + 1

192

STRAINCF.BAS 9

LPRINT TAB(2); "* The negative strain amplitude has been changed to";
neg.strain; "%"
LPRINT
command.highl - pos.strain * gauge.len / fs.scale
command.lowl - -ABS(neg.strain) * gauge.len / fs.scale
frequency - grip.speed * 100 / (2 * (pos.strain + ABS(neg strain))
* gauge.len)
5200 LOCATE l, 1: PRINT blank$: LOCATE 1, 1
INPUT " Do you want to start new screen with different scales ? (Y/N)
"; 135
IF a$ <> "Y" AND a$ <> "y" THEN 5300
CLS : LOCATE 10, 8: PRINT " Input the scales for real-time plot : "
5210 LOCATE 12, 8: INPUT " Maximum scale for X axis (true strain) .....
[8] "; xmax

LOCATE 14, 8: INPUT " Maximum scale for Y axis (true stress) ... [MPa]
"; ymax

LOCATE l7, 8: INPUT " Cycle plot interval ............. [ Default 20 ]
"; plot.int

LOCATE l9, 8: INPUT " Cycle stroe interval ........... [ Default lOO ]
"; store.int

LOCATE 21, 8: INPUT " Cycle print interval ........... [ Default 17 ]
"; print.int

IF plot.int - 0 THEN plot.int - 20
IF store.int - 0 THEN store.int - 100
IF print.int - 0 THEN print.int - 17
IF xmax - 0 OR ymax - 0 THEN 5210
COSUB 4500
5300 IF command.highl - 0 AND command.lowl - 0 THEN 5400
IF command.highl - command.high AND command.lowl - command.low THEN
5400
PRINT #3, "V"
COSUB 4000: INPUT #3, echo
IF command.highl - command.high THEN command.highl - command.highl *
1.005
PRINT #3, command.highl; "H"
GOSUB 4000: INPUT #3, echo
PRINT #3, ”Q"
COSUB 4000: INPUT #3, echo
IF command.lowl - command.low THEN command.lowl - command.lowl *
1.005
PRINT #3, command.lowl; "H"
GOSUB 4000: INPUT #3, echo
command.high - command.highl: command.low - command.lowl
5400 LOCATE 1, 1: PRINT blank$: LOCATE 1, l: PRINT "N - "z i - 0
LOCATE 1, 75: PRINT cycle.no

GOSUB 4000: PRINT #3, "D"
GOSUB 4000: INPUT #3, echo
IF b$ <> "" THEN b$ - "": GOTO 5620
GOTO 1100

' Data acquisition routine
5500 error.code% - BEGIN.ADC.DMA(number.Of.val%, digit.val%(0))
error.code% - WAIT.ADC.DMA(digit.va1%(last.va1%))
error.code% - STOP.ADC.DMA
FOR abc - 0 TO sum.no - 1
digit(O) - digit(O) + digit.val%(abc * (l + etsm))
digit(etsm) - digit(etsm) + digit.val%(abc * (l + etsm) + etsm)

193

STRAINCF.BAS 10

NEXT abc
analog.va1%(0) - INT(digit(O) / sum no): analog val%(etsm) -
INT(digit(etsm) / sum.no)
digit(O) - 0: digit(etsm) - 0
RETURN
' Plastic strain amplitude control
5600 LOCATE 2, 1: PRINT " "
cde - 0
FOR mm - 1 TO 2
FOR mmm - 1 TO 3
a#(mm, mmm) - 0
NEXT mmm
NEXT mm
f(0, 1) - 0: f(O, 2) a 0
5610 GOSUB 5500
cde - cde + 1
f(cde, 1) - fnfs(analog.val%(0), fs.1oad) * 1000
f(cde, 2) - fnfs(analog.val%(etsm), fs.scale) - strain.ini
t8 - TIMER
a$ - INKEY$
IF a$ - "+" THEN 3100
IF a$ - "-" THEN b$ - a$: GOTO 3200
IF a$ - "*" THEN b$ - a$: GOTO 5000
5620 t9 - TIMER
IF ABS(t9 - t8) < .0004 / grip.speed THEN 5620
IF f(cde, 1) < load.max / 5 AND f(cde, 1) > load.min / 5 THEN 5610

5630 FOR fg - 1 TO cde
a#(l, 1) - a#(l, 1) + f(fg, 2) A 2
a#(l, 2) - a#(l, 2) + f(fg, 2)
a#(l, 3) - a#(l, 3) + f(fg, 1) * f(fg, 2)
a#(2, 3) - a#(2, 3) + f(fg, 1)

NEXT fg .
IF -cde * a#(l, 1) + a#(l, 2) ‘ 2 - 0 OR a#(l, 1) = 0 THEN
p1astic.strain - -plastic.strain: GOTO 5640
b - (a#(l, 3) * a#(l, 2) - a#(2, 3) * a#(l, 1)) / (-cde * a#(l, l) +
a#(l, 2) A 2) '
a - (a#(l, 3) - b * a#(l, 2)) / a#(l, 1)
IF a - 0 THEN 5640
ba - 1 - b / (a * gauge.len): IF ba < 0 THEN 5640
p1astic.strain - INT(LOG(ba) * 100000) / 1000
5640 LOCATE 2, 1: PRINT " Ep - "; p1astic.strain; "% "; cde
RETURN