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The Pennsylvania State University
The Graduate School
College of Engineering
CREEP-FATIGUE-RATCHETING BEHAVIOR OF HAYNES 230
VIA ISOTERMAL MULTIAXIAL EXPERIMENTATION
A Thesis in
Engineering Science and Mechanics
by
Gloria W. Choi
© 2013 Gloria W. Choi
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science
December 2013
ii
The thesis of Gloria W. Choi was reviewed and approved* by the following:
Clifford J. Lissenden
Professor of Engineering Science and Mechanics
Thesis Advisor
Bernhard R. Tittmann
Schell Professor of Engineering Science and Mechanics
Ivica Smid
Associate Professor of Engineering Science and Mechanics
Judith A. Todd
Professor of Engineering Science and Mechanics
Head of the Department of Engineering Science and Mechanics
*Signatures are on file in the Graduate School.
iii
Abstract
Haynes 230 is a Ni-Cr-W-Mo-C alloy with a good combination of mechanical properties
and oxidation resistance at high temperatures. It is one of the materials in consideration for the
intermediate heat exchanger (IHX) tubing of the very high temperature reactor design, which is
one of the next generation nuclear plants (NGNPs) and is intended to be operated around 800-
1000ºC. At such high temperatures with this application, the structure will experience creep and
low cycle fatigue damage interaction. Two corresponding material responses of interest are the
ratcheting damage (cyclic strain accumulation) and cyclic hardening-softening responses with
nonproportional multiaxial loading. Ratcheting is the progressive plastic deformation that occurs
with certain cyclic loading until failure. Cyclic stress hardening-softening responses can reveal
changes in the resistance to material deformation due to cyclic strain loading, and are generally
influenced by loading history, loading amplitudes, and microstructure. Varying these loading
conditions and temperature can result in different dominant damage mechanisms. After
understanding the material responses and damage mechanisms, operating conditions can be
established for routine maintenance to occur prior to when predicted failure or excessive
deformation takes place.
Several multiaxial fatigue isothermal experiments were conducted on Haynes 230 thin
wall tubular specimens via axial-torsional loading. Influence of temperature and non-
proportionality of the cyclic loading path is investigated with two types of experiments. Test
temperatures carried out for both sets are the following: 23, 649, 760, 871, 927 and 982°C. One
experiment type (Group A) involves observing the ratcheting-creep-fatigue life, where the
loading path is triangular symmetric shear strain cycling with a steady axial stress. The resulting
axial strain exhibits ratcheting, while the shear stress response exhibits cyclic hardening/softening
due to the shear strain cycling. The second experiment type (Group B) loading path incorporates
the following: (1) axial strain cycles, (2) 90o out-of-phase sinusoidal axial-shear strain cycles, and
(3) axial strain cycles. Both the axial stress and shear stress exhibits cyclic
hardening/softening/stable trends, with the shear stress cyclic response only present during
segment (2). Based on the cyclic stress responses of both experiment types and the ratcheting rate
of Group A experiments, some of the tests can be grouped based on similar trends.
The greatest extent of cyclic stress hardening occurred with the test temperature at 649°C
for Group A and B loading paths. Both test temperatures 649°C and 760°C exhibit low axial
ratcheted strains less than 0.010 m/m for Group A. Higher test temperatures 871°C and 927°C
iv
exhibit ratcheting trends similar to primary and steady-state creep and accumulated ratcheting
strains more than 0.040 m/m. Cyclic stress softening was dominant in test temperatures 871°C
and 927°C in Group A and in test segments (1) and (3) with Group B experiments. On the other
hand, initial cyclic stress hardening was apparent in Group A and B experiments for test
temperatures 649°C and 760°C. To understand the diverse failure modes exhibited in the Group
A experiments microscopy should be performed in the future.
v
TABLE OF CONTENTS
List of Figures .......................................................................................................................... .vii
List of Tables ........................................................................................................................... .xiii
Acknowledgement………………………............................................................................… xiv
Nomenclature…………………………………………………………………………………xv
Chapter 1 .................................................................................................................................. 1
1.1 Objectives................................................................................................................... 2
1.2 Literature review ......................................................................................................... 2
1.2.1 Related Damage Mechanisms ........................................................................ 2 1.2.2 Brief Review of Constitutive Modeling ......................................................... 13 1.2.3 Literature Review for on Haynes 23 ............................................................... 16
Chapter 2 .................................................................................................................................. 21
2.1 Specimen Description .............................................................................................. 21 2.2 Equipment and Instrumentation ............................................................................... 23 2.3 Test Matrix ............................................................................................................... 25
2.3.1 Group A (GA) [Bi-axial Ratcheting Loading Type ........................................ 25 2.3.2 Group B (GB) [90° Out of Phase Strain Cycles] Loading Type ..................... 26
2.4 Experimental Setup and Details ................................................................................. 29
Chapter 3 .................................................................................................................................. 34
3.1 Group A ( Bi-axial Ratcheting) Loading ................................................................... 34 3.1.1 Test GA-1:23°C .............................................................................................. 35 3.1.2 Test GA-2: 649°C............................................................................................ 41 3.1.3 Test GA-3: 760°C............................................................................................ 48 3.1.4 Test GA-4: 871°C............................................................................................ 52 3.1.5 Test GA-5: 927°C............................................................................................ 59 3.1.6 Test GA-6: 982°C............................................................................................ 68 3.1.7 Test GA-7: 927°C ; Higher Strain Amplitude ................................................. 73 3.1.8 Comparison of Group A tests .......................................................................... 76
3.2 Group B (90°Out of Phase Strain Cycles) Loading Type ........................................... 86 3.2.1 Test GB-1: 23°C .............................................................................................. 87 3.2.2 Test GB-2: 649°C ............................................................................................ 90 3.2.3 Test GB-3: 760°C ............................................................................................ 91 3.2.4 Test GB-4: 871°C ............................................................................................ 94 3.2.5 Test GB-5: 927°C ............................................................................................ 95 3.2.6 Test GB-6: 982°C ............................................................................................ 97 3.2.7 Test GB-7: 927°C ; Higher Strain Amplitude ................................................. 99 3.2.8 Comparison of Group B Loading Type ........................................................... 101
Chapter 4 .................................................................................................................................. 106
vi
4.1 Conclusion ................................................................................................................. 106 4.2 Future Work ............................................................................................................. 110
Bibliography ............................................................................................................................ 111
vii
List of Figures
Figure Page
No. No.
1.1 Deformation mechanism map for cast nickel base superalloy MAR-M200 with a
grain size of 0.1 mm. (Webster 1994).
5
1.2 Input signal of the fatigue cycling of stress (left) and corresponding typical
diagram of stress amplitude to fatigue life curve (right)
6
1.3 Uniaxial ratcheting strain (right) resulting from cyclic axial stress with nonzero
mean (left).
7
1.4 Ratcheting strain (right) resulting from multiaxial stresses, where one direction is
constant stress and another cyclic stress (left).
8
1.5 Axial and shear strain cycling in-phase on the left for proportional loading, and
cycling φ° out of phase on the right as nonproportional loading.
8
1.6 Cyclic strain loading paths with varying degrees of nonproportional
loading. (Tanaka 1985).
9
1.7 Fatigue life as a function of total strain range at different temperatures (760°C–
982°C). (Chen 2000).
17
1.8 Fatigue life as a function of strain hold time. (Chen 2000). 18
1.9 Oxidation process in air of Haynes 230 at 900ºC (a) initially and at the steady-
state stage. (Kim 2009).
19
2.1 Thin-wall tubular specimen with typical dimensions in mm. 22
2.2 (Left) Side view of MTS high temperature biaxial extensometer probes mounted
on thin wall tubular specimen. (Right) Heat shield arm fixtures secured
the extensometer against the specimen.
24
2.3 Control test path for Group A experiment as axial load versus shear strain. 25
2.4 On the left, is a schematic of the (a) axial force control as a function of time. On
the right side is a diagram of (b) shear strain control versus time.
26
2.5 Control test path for Group B experiments. High degree of non-proportionality
with segment (2) consisting of 90° out-of-phase strain cycles.
27
2.6 Axial strain (above) and shear strain (below) control for Group B experiments, as
a function of time.
28
2.7 Geometry of a section of a cylindrical specimen under torsion within gage
section.
29
viii
Figure
No.
Page
No.
2.8 Schematic of the numbering of thermocouples used to verify the temperature
profile.
31
2.9 Another schematic of the placement of some thermocouple placements with two
different cross-sectional views of the specimen.
32
3.1 Control of axial stress versus shear strain for Test GA-1. 35
3.2 Control modes as a function of time for axial stress (left) and shear strain (right)
for Test GA-1 (F-09).
35
3.3 Axial strain response of Test GA- 1 for two specimens. 37
3.4 Zoom in view of axial strain response of Test GA-1 for two specimens, for the
first 100 cycles. The smaller window shows the response for the first 10
cycles.
37
3.5 Shear stress peak and valleys of the response to Test GA-1 for two specimens. 38
3.6 Peak values of the shear stress versus cycle numbers plot, for both specimens of
Test GA-1. Smaller window shows peak values for first 100 cycles.
39
3.7 Shear hysteresis loops for specimen F-09, with only cycles 1, 5000, and 10000
shown.
39
3.8 Post-test photograph of specimen F-09 (Test GA-1) 40
3.9 Post-test photograph of specimen F-03 (Test GA-1) 40
3.10 Control of axial stress versus shear strain for Test GA-2. 41
3.11 Axial strain response of Test GA-2 for two specimens. 42
3.12 Zoom in view of axial strain response of specimen F-20 (Test GA-2) for cycles
2000 to 2050.
43
3.13 Zoom in view of axial strain response of specimen F-20 (Test GA-2) for cycles
3750 to 3800.
43
3.14 Zoom in view of axial strain response of specimen F-20 (Test GA-2) for cycles
4250 to 4300.
43
3.15 Shear stress peak and valleys of the response to Test GA-2 for 2 specimens. 44
3.16 Peak values of the shear stress versus cycle numbers plot, for both specimens of
Test GA-2. Smaller window shows peak values for first 150 cycles.
44
3.17 Shear stress and strain hysteresis for F-20, with cycles 1, 2, 5, 10, 20, 50, …2000,
4324 shown.
45
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Figure
No.
Page
No.
3.18 Post-test photograph of Specimen F-16 (Test GA-2) 46
3.19 Combined post-test photographs of longitudinal crack for specimen F-16 (Test
GA-2).
46
3.20 Post-test photograph of specimen F-20 (Test GA-2). 47
3.21 Post-test photograph of surface crack for specimen F-20 (Test GA-2) under low
magnification.
47
3.22 Low magnification photograph of small longitudinal and circumferential cracks
near control thermocouple for specimen F-20 (Test GA-2).
47
3.23 Control of axial stress versus shear strain for Test GA-3 (specimen F-18). 48
3.24 Axial strain response of Test GA-3 for specimen F-18. 49
3.25 Zoom in view of axial strain response of specimen F-18 (Test GA-3) for cycles
2000 to 2050.
49
3.26 Zoom in view of axial strain response of specimen F-18 (Test GA-3) for cycles
3124 to 3174.
50
3.27 Shear stress peak and valleys of the response to specimen F-18 (Test GA-3). 50
3.28 Shear stress and strain hysteresis Test GA-3, with cycles 1, 2, 5, 10, 20, 50,
…2000, and 3174 shown.
51
3.29 Post-test photograph of Specimen F-18 (Test GA-3). 51
3.30 Control of axial stress versus shear strain for Test GA-4 (specimen F-10). 52
3.31 Axial strain response of Test GA-4 for two specimens. 53
3.32 Zoom in view of axial strain response of restart portion of specimen F-14 (Test
GA-4) for cycles 1700 to 1750.
54
3.33 Zoom in view of axial strain response of restart portion of specimen F-14 (Test
GA-4) for cycles 2240 to 2290.
55
3.34 Zoom in view of axial strain response of restart portion of specimen F-14 (Test
GA-4) for cycles 2775 to 2825.
55
3.35 Shear stress peak and valleys of the response to two specimens of Test GA-4. 56
3.36 Shear stress and strain hysteresis for specimen F-14 with cycles 1, 2, 5, 10, 20,
50, …1665 shown. Unusual warping of hysteresis on the left was due to
improper control of the cyclic shear strain signal.
57
3.37 Post-test photograph of specimen F-10 (Test GA-4). 57
x
Figure
No.
Page
No.
3.38 Specimen F-10. Small cracks within gage section. 58
3.39 Post-test photograph of specimen F-14 (Test GA-4). 58
3.40 Control of axial stress versus shear strain for specimen F-11 (Test GA-5). 59
3.41 Axial strain response of Test GA-5 for two specimens. 60
3.42 Zoom in view of axial strain response of specimen F-19 (Test Ga-5) for cycles
300 to 350.
61
3.43 Zoom in view of axial strain response of specimen F-19 (Test GA-5) for cycles
1950 to 2000.
61
3.44 Zoom in view of axial strain response of specimen F-19 (Test GA-5) for cycles
3175 to 3225.
61
3.45 Zoom in view of shear strain signal of specimen F-19 (Test GA-5) for cycles 300
to 350.
62
3.46 Zoom in view of shear strain signal of specimen F-19 (Test GA-5) for cycles
1950 to 2000.
62
3.47 Zoom in view of shear strain signal of specimen F-19 (Test GA-5) for cycles
3175 to 3225.
63
3.48 Screen shot of MPT oscilloscope for specimen F-19 for cycles 335-338. 63
3.49 Screen shot of MPT oscilloscope for specimen F-19 for cycles 1947-1950. 63
3.50 Screen shot of MPT oscilloscope for specimen F-19 for cycles 3188-3191. 64
3.51 Screen shot of MPT oscilloscope for specimen F-19 for cycles 3506-3509. 64
3.52 Shear stress peak and valleys of the response to Test GA-5 for two specimens. 65
3.53 Peak values of the shear stress versus cycle numbers for both specimens of Test
GA-5.
65
3.54 Shear stress and strain hysteresis for specimen F-19, with cycles 1, 2, 5, 10, 20,
50, …3252 shown.
66
3.55 Post-test photograph of specimen F-11 (Test GA-5), with an arrow indicating the
location of the control thermocouple junction prior to unintended
removal.
67
3.56 Post-test photograph of specimen F-11 (Test GA-5) via low magnification. 67
3.57 Post-test photograph of specimen F-19 (Test GA-5). 67
xi
Figure
No.
Page
No.
3.58 Control of axial stress versus shear strain for specimen F-21 (Test GA-6). 68
3.59 Axial strain response of Test GA-6 for two specimens. 69
3.60 Zoom in view of axial strain response of restart portion of specimen F-13 (Test
GA-6) for cycles 500-550.
70
3.61 Zoom in view of axial strain response of restart portion of specimen F-13 (Test
GA-6) for cycles 1000-1050.
70
3.62 Zoom in view of axial strain response of specimen F-13 (Test GA-6) for cycles
1230 to 1280.
70
3.63 Shear stress peak and valleys of the response to Test GA-6 for two specimens. 71
3.64 Shear stress and strain hysteresis for specimen F-13 (Test GA-6), with cycles 1,
2, 5, 10, 20, 50, …1030 shown.
72
3.65 Post-test photograph of specimen F-21 (Test GA-6). 72
3.66 Post-test photograph of specimen F-13 (Test GA-6). 73
3.67 Control of axial stress versus shear strain for specimen F-15 (Test GA-7). 74
3.68 Axial strain response of specimen F-15 for Test GA-7. 75
3.69 Shear stress peak and valley curves of specimen F-15 for Test GA-7. 75
3.70 Post-test photograph of specimen F-15 (Test 7), low magnification of the surface
within the gage section.
76
3.71 Combined plot of axial strain accumulation within first 4500 cycles for Test GA
1 to GA-6, which includes temperatures from 23 to 982 .
79
3.72 Zoom in view of axial strain accumulation within first 4500 cycles versus number
of cycles for general comparison of response for specimen F-18 (Test
GA-3), specimens F-16 and F-20 (Test GA-2).
79
3.73 Combined plot of shear stress peak curves within first 4500 cycles for Test GA 1
to GA-6, which includes temperatures from 23 to 982 .
81
3.74 Control of axial strain versus shear strain for Test GB-1. 87
3.75 Axial stress-strain hysteresis for cycles 1, 10, 20, 41, and 45, which are curves
corresponding to some axial strain cycles of Test GB-1.
88
3.76 Axial stress-strain hysteresis for selected cycles for Test GB-1. 88
3.77 Shear stress-strain hysteresis loops for Test GB-1. 89
3.78 Control of axial strain versus shear strain for Test GB-2 (649°C). 90
xii
Figure
No.
Page
No.
3.79 Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding
to some axial strain cycles of Test GB-2.
90
3.80 Control of axial strain versus shear strain for Test GB-3 (760°C). 91
3.81 Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding
to some axial strain cycles of Test GB-3.
92
3.82 Zoom in view of a section of the axial hysteresis for cycles 1, 20, 41 and 45 of
Test GB-3.
92
3.83 Axial hysteresis for cycles 21 and 40 of segment (2) for Test GB-3. 93
3.84 Control of axial strain versus shear strain for Test GB-4 (871°C). 94
3.85 Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding
to some axial strain cycles of Test GB-4.
95
3.86 Control of axial strain versus shear strain for Test GB-5 (927°C) 96
3.87 Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding
to some axial strain cycles of Test GB-5.
96
3.88 Control of axial strain versus shear strain for Test GB-6 (982°C). 97
3.89 Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding
to some axial strain cycles of Test GB-6.
98
3.90 Control of axial strain versus shear strain for Test GB-7 (927°C). 99
3.91 Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding
to some axial strain cycles of Test GB-7 (larger strain range). Same cycle
numbers from Test GB-5 (smaller strain range) were plotted in green.
100
3.92 Combined plots of axial stress peaks for Tests GB-1 to GB-6. 101
3.93 Combined plots of shear stress peaks for segment (2) for Tests GB-1 to GB-6. 102
3.94 Combined plots of axial stress peaks for Tests GB-5 and GB-7. 104
3.95 Combined plots of shear stress peaks for segment (2) for Tests GB-5 and GB-7. 104
xiii
LIST OF TABLES
Table Page
No. No.
1.1 Possible basic aspects of viscoplastic behavior invoked by 3 general loading cases. 3
1.2 Cyclic hardening mechanisms for low cycle fatigue (LCF) noted from literature
regarding nickel base superalloys
10
1.3 Cyclic softening mechanisms for LCF noted from literature regarding nickel base
superalloys
11
1.4 Limiting chemical composition of Haynes 230 16
2.1 Average inner and outer diameter dimensions for tested specimens. 22
2.2 Test Matrix for Group A experiments. 26
2.3 Test Matrix for Group B experiments, 90° out of phase strain cycles. 28
2.4 Inner diameters of the center 2-turn coil used for Group A and Group B
experiments. The upper and lower coils remained the same for all tests.
32
3.1 Test parameters for Test GA-1 36
3.2 Test parameters for Test GA-2 41
3.3 Test parameters for Test GA-3 49
3.4 Test parameters for Test GA-4 52
3.5 Test parameters for Test GA-5. 59
3.6 Test parameters for Test GA-6. 69
3.7 Test parameters for Test GA-7. 74
3.8 Summary results of axial strain at failure and shear stress softening for Group A
tests.
77
3.9 Surface damage of each Group A specimen and reasons for ending each test. 82
3.10 Summary results of axial strain at failure and shear stress softening for Group A
tests.
84
3.11 Test Parameters for Group B experiments. Cycle period was fixed at 160 seconds
for all tests.
86
3.12 Summary results of axial and shear stress peak responses for Group B experiments. 102
xiv
Acknowledgement
I sincerely thank Dr. Clifford Lissenden for his guidance and support during my
research. His time and effort in guiding the direction of this research and related work was
indispensable. I wish to thank Dr. Tasnim Hassan, Professor at North Carolina State University,
for his cooperation and for helping me understand this field better.
Special thanks to Dr. Bernhard Tittmann and Dr. Ivica Smid for agreeing to review my
thesis and be on my thesis committee.
In addition, I would like to also thank Mr. Ardell Hosterman and Mr. Scott Kralik, for
their prompt assistance with instrument repairs, maintenance and troubles. Mechanical
experimentation was finished very smoothly with their help and advice.
The work was made possible with the support of Honeywell, Inc. and the Department of
Energy, Next Generation Nuclear Program Grants 09-288 and 10-915.
xv
Nomenclature:
List of Symbols/Abbreviations
Symbol/Abbreviation Description
VHTR Very high temperature reactor
(maximum temp. of about 1000°C)
IHX Intermediate Heat Exchanger
TPV Torque peak and valley acquisitioned data
MPT Multipurpose Testware Software (of MTS)
MTS MTS Systems Corporation
0.2% YS Stress at the intersection of the tensile stress and strain curve
with the elastic linear portion 0.2% offset.
GA Group A loading type test
GB Group B loading type test
Δ Ls Arc length formed by the angle of twist
Lg Gage length of 25.4 mm for extensometer and specimen
T Torsional moment
Shear stress at outer diameter
do Outer diameter of specimen within gage section
di Inner diameter of specimen within gage section
ID Inner diameter of center induction coils
θ Shear angle of twist for specimen-extensometer
σx Axial stress
σxm
Applied axial stress mean
σa Applied axial stress amplitude
Δεa Axial strain test range
Δεa /2 Axial strain amplitude
γxy
≈ do θ/ (2Lg), Shear strain
Δγc Shear strain test range
Δγc/2 Shear strain amplitude
θ Shear angle of twist (measured/controlled instead of shear
strain mode)
1
Chapter 1
Introduction
There has always been a drive to obtain engineering structural components capable of
operating more efficiently, which requires the structure to withstand more extreme conditions
such as higher temperatures and pressures. The development of such designs for the desired
operating parameters involves a thorough process of material selection, determining suitable
operating conditions, and planning of routine maintenance and systems checks. Current pending
power plant designs are the Generation IV and small modular reactors, each with generally
different operating temperature ranges. Generation IV reactor proposals have aimed for greater
efficiency through design and incorporation of special alloys capable of withstanding high
temperatures of about 850-950°C, a range higher than current nuclear reactors operation
temperatures. The Very High Temperature Reactor (VHTR) is one of several types of the
generation IV reactors and includes components that require materials that are able to withstand
the thermal and environmental conditions. Structural integrity issues of high concern within
elevated temperatures for reactors such as VHTR, involves the following: environmental effects,
creep-rupture and fatigue damage, simplified bounds for creep ratcheting, creep-rupture damage
due to forming and welding, thermal aging effects, elevated temperature database for mechanical
properties, basis for leak-before-break at elevated temperatures, etc. Steel and nickel based alloys
are common types of materials selected for such applications due to their ability to retain creep
resistance under higher operating temperature to melting temperature ratios. (Webster 1994).
The Intermediate Heat Exchanger (IHX) is one of the VHTR components that would
experience the most extreme conditions. Within the design lifetime of 60 years for the VHTR,
repairs and replacement of parts for the IHX are expected to be conducted routinely. The
maximum temperature experienced by the IHX, determined by the helium-cooled reactor gas
outlet temperature, is expected to be between 850°C and 950°C. Nickel-based superalloys, such
as Haynes 230 and Inconel 617, are considered potential alloys for IHX tubing due to their range
of advantageous mechanical properties. These superalloys have applications involving extreme
conditions due to their high corrosion resistance, creep resistance and strength at elevated
temperatures. Compared with Inconel 617, there is very limited research and information
regarding creep-fatigue-ratcheting behavior for Haynes 230. Unified constitutive modeling of the
2
degradation of the material due to the environment and temperature is crucial in defining tentative
operating parameters within the nuclear reactor life service and material loading limits.
1.1 Objectives
The objective of this research is to explore and characterize the material response of
Haynes 230 under nonproportional loading and torsional fatigue experimental conditions that
induce creep-fatigue-ratcheting behavior. Experimental results are intended to be used by our
colleague Dr. Tasnim Hassan at North Carolina State University in the determination of material
parameters necessary for constitutive modeling the viscoplastic behavior of Haynes 230 and for
verification of the model.
1.2 Literature review
1.2.1 Related Damage Mechanisms (Polycrystalline Material) at High Temperatures
Modeling of metal plasticity relations are mainly divided two general classes, rate
independent and rate dependent plasticity. Rate independent plasticity is more dominant with
deformation of metals at temperatures lower than half the corresponding material‟s melting point
and low strain rates of about 0.01 per second to 10 per second. Rate dependent plasticity, or
viscoplasticity, is invoked for metals deforming at high strain rates greater than 100 per second or
due to stresses at temperatures above half of the melting temperature. (Bower 2012). Viscoplastic
materials, are usually polycrystalline metals, exhibit the time or applied load rate dependence of
inelastic deformation due to corresponding microscopic mechanisms. Basic viscoplasticity
phenomena can be observed through several experimental procedures, examples shown in Table
1.1.
3
Table 1.1 Possible basic aspects of viscoplastic behavior invoked by 3 general loading cases.
Row Input (or applied mode) Resulting viscoplastic behavior
aspects (Neto 2008)
A Strain rate
dependence
observed
with
uniaxial
tension
experiment
B Stress
Relaxation
C Creep
One aspect of strain-rate dependence on viscoplastic materials is demonstrated within the
two figures of row A from Table 1.1. With uniaxial tension tests, time-dependence effects are
more apparent with higher temperature and the hardening observed with stress-strain curves
strongly depends on the rate of straining. Generally, if three specimens of the same viscoplastic
material were deformed at different constant strain rates, larger values of applied strain rates
allows for more plastic flow to take place within a given time period and will exhibit higher yield
strength due to further dislocation formations. The initial duration of dislocation accumulation
serves as obstacles and impedes further dislocation motion.
4
Stress relaxation, another phenomenon of viscoplasticity, is demonstrated by the figures
in row B from Table 1.1. When the strain is held at a constant value, the induced stress in the
viscoplastic material will decrease over time and can eventually stabilize to a constant low value.
While stress relaxation can be investigated with creep and fatigue under complex loadings, the
relaxation phenomenon is not incorporated and not reported in this work.
Creep damage, present with viscoplastic materials, refers to the progressive strain
accumulation as a result of a constant stress. Understanding creep is crucial because sudden
associated failures are possible with applied stress values lower than the material‟s yield strength
and at temperatures above half the melting temperature. There are three main different strain
accumulation curves possible with varying progressive creep damage as a function of time, which
are shown in the figures of row C from Table 1.1. (Neto 2006). There are three main possible
creep damage accumulation trends that can result depending on the applied constant stress. The
creep curve resulting from a moderate stress value, compared with the yield strength, is usually
most desirable for engineering applications. Typically there is an initial section of progressively
decreasing strain rate or slope. Secondary or steady-state creep follows the primary creep stage,
where there is a very long duration of constant strain accumulation. The last and final stage is
called tertiary creep, which occurs immediately prior to rupture and where the measured creep
rate increases for a short duration. Operating temperatures and stresses, with known
corresponding constant creep strain rate and typical rupture life, can be utilized to result with a
long stage of plastic deformation before proceeding to a small duration of slow and gradual
fracture. However, a creep curve of a material loaded with a constant sufficiently high stress
results with a dominant primary creep stage and significantly short steady-state creep duration
before sudden rupture. Low stresses, with respect to the yield strength of the material, can result
in minimal creep damage accumulation and stabilize for a long duration without exhibiting
rupture. Secondary and tertiary creep is more predominate at temperatures more than half the
melting temperature. Primary creep state becomes more apparent typically with temperatures
below half the melting temperature and applied stress higher than yield stress. (Webster 1994).
As a result of the drive to operate at extreme environment conditions with improved
efficiency, there has been focus on developing new alloys with improved properties. Nickel-based
superalloys are often used because they are typically more resistant to creep at higher
temperatures and stresses than other alloys. Figure 1.1 includes two deformation mechanism
maps for nickel base superalloy MAR-M200 with grain size of (a) 100 µm and (b) 1 cm. The
larger grain size requires higher stresses and temperatures to activate power-law creep, where
5
Figure 1.1 Deformation mechanism maps for nickel base superalloy MAR-M200 with grain size of (a) 100 µm and (b)
1 cm. (Gittus 1975).
constant strain rates are proportional to a power relation to stress and are highly dependent on
dislocation glide and climb. The combination of stresses and temperatures lower than power-law
creep results in deformation governed by diffusional flow, where diffusion of vacancies occurs
within and along grain boundaries. Dislocation glide dominates with sufficiently high stresses
compared to the shear strength and occurs as plastic deformation. Within the mechanism maps,
contour lines are labeled with constant strain rates for steady-state creep. With an average grain
size of 100 µm, constant strain rates higher than 10-5
occurred as power-law creep and lower
constant strain rates were regulated by diffusional flow. When the average grain size was
increased to 1 cm, higher stresses and temperatures were required to activate the lower constant
strain rates. The lower creep rates had shifted and became regulated by power-law creep. As a
result, the larger grain size of 1 cm of MAR-M200 would not accumulate significant creep
damage within the stress and temperature conditions utilized for typical turbine operations.
Since the heat treatment, microstructure and composition is different between MAR-
M200 and Haynes 230, the boundaries within the deformation mechanism map for Haynes 230
are shifted and vary slightly from Figure 1.1. Alloying additions of solid solution strengthened
and precipitation hardened alloys will hinder dislocation motion and change diffusion rates. All of
various factors influence the general mechanisms of deformation for crystalline materials such as
6
diffusional flow (formation and migration of vacancies), grain boundary sliding, and dislocation
movements.
In reality, engineering components present in nuclear plants do not continuously operate
with constant loading and temperature states. Under fatigue or cyclic loading, structural
components will develop macroscopic fracture or cracks from microscopic damage and their
ability to support load will degrade. Fatigue damage can be classified into two groups depending
on required number of cycles for failure to occur. Typical failures that occur within 10,000 cycles
are deemed as low-cycle fatigue (LCF) and the loading involves a plastic strain component. With
high cycle fatigue (HCF), failure occurs more than 10,000 cycles after cycling within the elastic
range. Often, higher cyclic stress amplitudes will shorten the fatigue life, or number of cycles to
failure. Commonly observed with several aluminum alloys, sufficiently high stress amplitudes of
cyclic loading produced a low fatigue life, as observed in Figure 1.2. After decreasing the cyclic
stress amplitude below a sufficient value, the fatigue life has increased and may far exceed the
service life of the structure (Dowling 1999).
Figure 1.2 Input signal of the fatigue cycling of stress (left) and corresponding typical diagram of stress amplitude to
fatigue life curve (right).
At high temperatures, cyclic loading with high frequencies, consideration of pure fatigue
is sufficient. However, creep damage is more apparent and must be analyzed when dealing with
fully reversed cyclic loading with low frequencies, due to the sufficient time allowing for creep
damage to accumulate. (Shang 2007). Creep-fatigue and ratcheting mechanisms interacting is
applicable to components such as the intermediate heat exchanger.
More research has been conducted on the two general types of damage (creep and
fatigue) than the interaction between them. Multiple loading paths are possible to induce creep
and fatigue interaction, some are suggested by ASTM E2714-09: Standard Test Method for
Creep-Fatigue Testing, and proposed by a text published by ASM International called Fatigue
and Durability of Metals at High Temperature (Manson 2009). Depending on the testing method
7
and loading path, investigations can be made on the material response through the (a) cyclic stress
strain deformation curve, (b) cyclic creep or relaxation deformation, (c) cyclic
hardening/softening, (d) number of cycles required for single or multiple crack formation, and (e)
cyclic strain accumulation (ratcheting or cyclic creep behavior).
Ratcheting is a phenomenon that can occur and refers to the progressive plastic
deformation or damage associated with cyclic loading. A consequence of ratcheting can be
excessive deformations up to the plastic shakedown state, where plastic flow continues despite
the presence of boundary conditions limiting the displacement. (Maier 2003). For structural
components without limitation on plastic strain accumulation, ratcheting can occur until failure.
One method to induce uniaxial ratcheting is cycling the axial stress about a non-zero mean. As
shown in Figure 1.3, progressive deformation is characterized by the accumulated strain, which
Figure 1.3 Uniaxial ratcheting strain (right) can be induced from a cyclic axial stress with nonzero mean (left).
can cycle with the same frequency as the cyclic load. Ratcheting have been noted to occur with
the early investigations of creep-fatigue experiments and was briefly investigated in the 1960s.
Only within the last two decades, there has there been more emphasis on studying and modeling
uniaxial and multiaxial ratcheting (Lissenden 2007, Chen 2005, Kang 2002, Bari 2002, Hassan &
Kyriakides 1992, etc). Ratcheting can be generated in a material through several loading paths for
thin-walled pipes, involving two of the following: axial stress, shear stress, and pressure. A
common loading path is with a constant axial stress and cyclic shear stress to observe progressive
accumulation of axial strain ratcheting (Wood & Bendler 1962, Moyar & Sinclair 1963). Another
widely used method is associated with enforcing an internal pressure with symmetric cycling of
axial strain, which causes circumferential strain ratcheting, (Hassan 1992, and Ruiz 1967). Both
loading paths can be represented by Figure 1.4, where the multiaxial stresses on the (right)
8
Figure 1.4 Ratcheting strain (right) resulting from multiaxial stresses, where one direction is constant stress and another
cyclic stress (left).
produce ratcheting strain in a particular direction. While stress (σ2) is held constant and another
stress (σ1) cycles, and the accumulation of ratcheting strain occurs in the direction of σ2.
Alternatively, ratcheting can be induced when the stress cyclic loading (σ1) from Figure 1.4 is
replaced with cyclic loading within fixed strain limits with the secondary controlled mode (σ2) is
held constant.
When dealing with cyclic multiaxial loading, nonproportionality can result in greater
damage accumulation than expected when only considering proportional paths. Structural
components often experience a nonproportional component, where there are changes in the
directions of applied principal stresses or strains, which can severely decrease fatigue life. Figure
1.5 demonstrates the difference between proportional and nonproportional loading for cyclic axial
Figure 1.5: Axial and shear strain cycling in-phase on the left for proportional loading, and cycling φ° out of phase on
the right as nonproportional loading.
and shear strain paths. When the phase angle (φ°) is equivalent to zero, the shear strain cycles
start at the same time as the axial strain cycles and retain the same period. Nonproportional
loading occurs by increasing the phase angle (φ°) to a nonzero value and the node of the shear
strain cycles will lag behind the nodes of the axial strain cycles.
9
Tanaka et al 1985 compared the cyclic plasticity response of various strain path shape
loading on Type 316 stainless steel at room temperature. They investigated the influence of
varying degrees of non-proportionality observed in Figure 1.6. Two simple proportional paths
were
Figure 1.6: Cyclic strain loading paths with varying degrees of nonproportional loading. (Tanaka 1985).
were (a) cycling axial strain and (b) cycling shear strain. Nonproportional path (c) cruciform (I)
involved cycling alternatively axial strain and shear strain. Form (d) and (e) were acquired by
following the outline in a counter-clockwise fashion. Both the (f) square path and the (g) circular
path involved cycling the axial strain and shear strain signals 90° out of phase, respectively, via a
triangular wave form and with a sinusoidal wave form. Circular nonproportional loading was
reported to result in the highest amount of cyclic hardening and produced 1.7 times the extent of
cyclic hardening of the two simplest paths. Tanaka et al had categorized the test paths with
increasing severity of cyclic hardening behavior into three groups: (1) simple or proportional
paths of tension-compression and torsion, (2) cruciform and stellate, lastly with (3) square and
circular strain paths. Development of a highly immobilized dislocation structure through
interaction of active slip systems, contributes to the higher cyclic hardening for nonproportional
loadings, when compared to the more stable state with proportional cycles. (Kanazawa 1979, and
McDowell 1983).
Depending on the specific loading conditions involving constant strain amplitude cycling,
nickel base superalloys have exhibited either cyclic hardening, softening, or a stable constant
maximum or minimum stress regime. Some literature reports specific microstructure features
corresponding to the cyclic stress response, which typically involve interactions between
dislocations, precipitates, and grains that cause the specific mechanical responses.
10
Several articles have reported precipitate hardened superalloys (Mar-M247LC, Inconel
617, Rene 80, etc) with either cyclic hardening or softening behavior for room and elevated
temperatures for solely LCF. Under specific loading conditions, some alloys have also shown
initial hardening, which was followed by a duration of cyclic softening (Singh 1991, Stoltz 1978,
Xiao 2008, etc).
Table 1.2 indicates some literature sources that have noted these microstructural
interactions to be the cause of cyclic hardening for low cycle fatigue. Most of these authors have
observed some initial hardening, which was followed by a section of cyclic softening, but offer
Table 1.2: Cyclic hardening mechanisms for low cycle fatigue (LCF) noted from literature
regarding nickel base superalloys, where RT refers to room temperature. Mechanism Literature Material Temperature
coherent strain hardening due
to dislocation-dislocation
(work hardening)
Singh 1991 Nimonic
PE16
RT
order hardening associated
with precipitate shearing
mechanisms that interact with
dislocations
Valsan 1992 Nimonic Pe-
16
650°C
Stoltz Pineau
1978
Waspaloy RT
Choe 1995 directionally
solidified
Mar-
M247LC
760°C, 871°C, and 982°C
increasing slip band density Stoltz Pineau
1978
Waspaloy RT
Buckson Ojo
2012
Haynes 282 RT
pinning and accumulation of
Orowan dislocation loops at
gamma prime precipitates
Choe 1995 directionally
solidified
Mar-
M247LC
760°C, 871°C, and 982°C
(RT = Room Temperature)
insight on the possible causes of cyclic hardening for the nickel base superalloys noted.
Mechanisms found to be related to cyclic hardening include: coherent strain hardening due to
dislocation-dislocation (work hardening) or dislocation-grain boundary interactions (Singh 1991),
order hardening associated with precipitate shearing mechanisms that interact with dislocations
(Valsan 1992), and increasing slip band density (Ye Zheng 2008). An example of coherency is
when the lattice of the precipitate and grain interfaces match, while incoherency implies the
lattices exhibit nonmatching. Order hardening occurs when a dislocation propagates through an
ordered particle, i.e. Ni3Al, and the lattice distortion and antiphase boundaries requires greater
amount of stress to cause further change or deformation.
11
Buckson and Ojo (2012) have observed an initial stress cyclic hardening, which was
followed by duration of cyclic softening for Haynes 282 at room temperature under axial low
cycle fatigue tests. They have concluded for Haynes 282, as a face centered cubic alloy, cyclic
stress hardening was due to the increased dislocation formation within slip bands at room
temperature. Similarly, such initial cyclic hardening was noted to be present with the slip band
density increase.
Mechanisms reported to be found as associated with cyclic softening in several nickel-
based superalloys are listed in Table 1.3. As for cyclic softening, mechanisms correlated with
Table 1.3: Cyclic softening mechanisms for LCF noted from literature regarding nickel base
superalloys. Mechanism Literature Material Temperature
Loss of coherency due to
particle coarsening or
interaction with dislocations
( misfit dislocations)
Antolovich 1981 Rene 80 871°C, 982°C
Hwang 1989
Not named* 760°C, 871°C, 982°C
Lower two were resistant to precipitate
coarsening
Gabb & Welsch
1988
PWA 1480
Single
crystal
1050°C (temperatures above 850°C)
Disordering of precipitates
within deformation/slip bands
Stoltz &Pineau
1978
Waspaloy
Precipitate
size 8nm
RT
shearing of precipitates
Stoltz & Pineau
1978
Wastaloy;
with
precipitate
size of 25
nm and
smaller
RT
Hwang et al
1989
Not named* 760°C, 871°C, 982°C
Gabb & Welsch
1988
PWA 1480
Single
crystal
1050°C (temperatures above 850°C)
Choe et al 1995 directionally
solidified
Mar-
M247LC
760°C, 871°C, and 982°C
Dislocations bypass
precipitates and networks are
formed at γ- γ‟ interface
(localization)
(Orowan mechanism)
Stoltz & Pineau
1978
Waspaloy
Precipitate
size 8 nm
RT
Rao 1988 IN 617 950°C
Gabb & Wlsch
1988
PWA 1480
Single
crystal
1050°C (temperatures above 850°C)
* Hwang et al provided low cycle fatigue results for a nickel base superalloy with the following compositon: 0.17 pct
C-14.1 pct Cr-9.5 pct Co-4.0 pct Mo-4.0 pct W-3.0 pct A1-5.0 pct Ti-0.015 pct B-0.03 pct Zr-balance Ni.
12
nickel-base precipitation strengthened alloys have been hypothesized to be due to the dissolution
of precipitates, disordering of precipitates within deformation bands (Stoltz 1978), growth of
precipitates, and shearing of precipitates (Hwang 1989), or particle coarsening leading to
coherency loss (Antolovich 1981), or dislocation annihilation.
Singh et al 1991 claimed initial hardening with softening following afterward would
result when the dominant mechanism is precipitate shearing, based on TEM observations of a
high density of deformation bands of Nimonic PE 16 samples that experienced low cycle fatigue
at room temperature. Based on their results, they also deduced when cyclic hardening or softening
is only present for a small duration, corresponding microscope state has been observed to have a
high uniform density of Orowan loops and precipitate shearing. Xiao et al 2008 demonstrated that
cyclic behavior have depended on the cyclic strain loading amplitudes through low cycle fatigue
experiments on Inconel 718 at room temperature and 652°C. With cyclic strain amplitude at ΔεA
/2 = 0.6&, only cyclic softening was noted. However, increasing to a higher cyclic strain
amplitude of ΔεA /2 ≥0.8%, resulted in an initial cyclic hardening period, which was succeeded
by cyclic softening. Choe et al 1995 had concluded that the cyclic hardening of directionally
solidified Mar-M247LC superalloy present with low cycle fatigue tests at 760°C, 871°C, and
982°C was due to the pinning and accumulation of Orowan dislocation loops at gamma prime
precipitates, while cyclic softening had correlations to the shearing of gamma prime particles by
dislocations.
Stoltz et al deducted the cyclic softening/hardening behavior dependence on precipitate
size for Waspaloy. Cycle hardening will occur for specimens retaining precipitates larger than the
required size for dislocation bowing, approximately 50 nm to 90 nm. With a smaller size of about
25 nm, initial hardening followed by a slight softening behavior. As for smaller precipitates of
8nm, greater extent of softening follows a short duration. Dependence of temperature on cyclic
softening is apparent with the LCF experiments conducted 760°C, 871°C, 982°C, where further
thermal activation promoted the process of γ‟ precipitates losing coherency, where the
precipitates exhibit a shape change where there is a mismatch with the lattice of neighboring
grains.
There are no softening and hardening mechanisms that have been universally agreed
upon, due to the difficulty in considering the microscale interactions with dislocations and
microstructure. Observed mechanisms are often dependent on the material composition,
microstructure, testing conditions, microscopy surface preparation, and the focus of metallurgist
13
conducting the microstructure analysis. For example, Gabb et al (1989) noted that at temperatures
above 850°C , precipitates are usually not sheared under cyclic loading, but the precipitates
would be restricted to γ- γ‟ interfaces and rearrangement and network formation would result.
However, Gabb et al (1989) conducted research on single crystal PWA 1480, while the
precipitate shearing was observed for polycrystalline nickel based superalloy through Choe (1995)
and Hwang (1989).
Further thorough investigation of the microstructure is required to determine the
underlying dislocation dynamics related to cyclic softening and hardening for the Haynes 230
alloy and the associated temperature dependence.
1.2.2 Brief Review of Constitutive Modeling
Depending on the geometry and operation conditions of a structural component,
multiaxial cyclic stresses and strains are experienced and contribute to failures that occur before
low fatigue crack formation. Cyclic creep responses include cyclic hardening (& softening),
ratcheting and cyclic relaxation. Influencing these material behaviors are various factors such as
degree of loading path non-proportionality, rate of loading and temperature. Ultimately, the
deformation mechanisms involve interactions between lattice and dislocations. Constitutive
modeling is the mathematical description of the response of materials due to specified loading
conditions. Often, these mathematical descriptions require material properties obtained from
mechanical experimentation, which considers the overall interactions of the microstructure and
dislocations under loading. Values of the material properties vary between alloys, and are similar
for alloys of similar class. Validation of the model is obtained through comparison with the
experimental responses and modifications can improve accuracy of modeling a specific
phenomenon.
Within the last 50 years, there have been attempts at developing sufficiently accurate
constitutive models for the interaction of low cycle fatigue (LCF), creep, and ratcheting responses
for viscoelastic materials. For a thorough multiaxial plastic model to be developed, behavior
mechanisms such as cyclic creep, ratcheting, mean stress relaxation, non-proportioning
influences, isotropic hardening, non-linear and linear kinematic must be considered. (Marquis
2003). Isotropic or kinematic hardening material models are often sufficient to provide analytical
solutions of boundary value problems of simple loading histories of uniaxial tension. Isotropic
14
hardening results in expansion of the yield surface with no translation, while kinematic hardening
refers to translation of the yield surface with no deformation. Mixed hardening considers
contribution of both isotropic and kinematic hardening, where the yield surface exhibits both
deformation and translation when material is plastically loaded. However, more complicated
loading histories involving plastic behavior, i.e. cyclic loading, the involved constitutive laws
must include at least two main features: flow and hardening rules. The flow rule is the
incremental plastic stress-strain relation, which accounts for the material response dependence on
the loading history. Typically, the construction of the rules require an assumption of being
independent of loading rate and a plastic potential that coincides with the yield or loading surface.
The changes of the yield surface, due to the plastic flow and cyclic hardening (or softening)
properties, are represented by the hardening rule as a function of the plastic modulus. (Dafalias
1975).
However, often constitutive models are limited in accurately simulating a wide range of
involved mechanical behaviors. Generally, constitutive models are based on different
assumptions relating to the yield surface and plastic flow, hence, their representation of material
behavior may not include some considerations such as that yield surfaces deform during loading,
coupling effects of the two rules, and etc. Bari and Hassan have evaluated models proposed by
Prager, Armstrong and Frederick, Chaboche, Ohno-Wang and Guionnet (Bari and Hassan 2002).
They have reported that Chaboche and Ohno-Wang models have reasonable simulated uniaxial
responses, but not biaxial ratcheting. As for Guionnet‟s model, only one type of biaxial ratcheting
experiment type was accurately modeled. As a result of these comparisons, Bari and Hassan have
proposed a modified Chaboche model with focus on parameters relating to multiaxial ratcheting,
such as kinematic hardening rules and yield surface consistency condition. (Bari and Hassan
2002). The following includes basic mathematical expressions within their modified Chaboche
model described by Krishna and Hassan (2009).
Deformation independent of rate and temperature can be considered with the von-Mises
yield criteria and flow rule. The expression for equivalent stress is
, (eq 1.1)
based on variables including normal and shear stresses. Equivalent strain is
15
, (eq 1.2)
in terms of normal strains and shear strains. The von-Mises yield criteria states plastic flow
initiates when the equivalent stress is equal to the material yield strength. The yield surface of the
von-Mises criteria have been commonly used as an assumption for the yielding boundary and
plastic potential surface. Assuming yield surface to be independent of rate, using von Mises yield
criteria, the yield function appears as
( ) *
( ) ( ) +
( ) (eq. 1.3)
Thus, a yield criterion can be established where the total stress space is equivalent to
( ) *
( ) ( ) +
( ) (eq. 1.4)
and the corresponding deviatoric df = 0 when plastic flow occurs. Within these expressions, is
the stress tensor and is the current center of the yield surface in the total stress space. In
addition, refers to the deviatoric stress tensor, is the current yield surface center in the
deviatoric space, and is the initial size of the yield surface. The R function is the drag
resistance and is considered to be the isotropic hardening variable, which is function of the
accumulated plastic strain p. The elastic domain is where f < 0, where no plastic flow is present
A flow rule is defined where the incremental plastic strain tensor is given by
(eq.1.5)
Where is a plastic multiplier and is magnitude of the plastic strain increment, where the
latter is given by
| | *
+
(eq.1.6)
Incorporating yield surface shape change was their method to improve the modeling of ratcheting
behavior. The kinematic and isotropic hardening variables were a and R respectively, and their
deviators were considered. The deviator of the isotropic hardening variable is given by
[ ] , (eq.1.7)
16
where is the rate constant and maximum yield surface evolution. Expressions for and
can be decomposed further to include influence of nonproportionality of strain-controlled
experiments.
The kinematic hardening rule is represented as
∑ , where (eq. 1.8)
(eq. 1.9)
the variable a refers to the current center of a yield surface in a stress space., with da as an
increment of a and considered as a deviator of dα. are some variables that were
calculated from experimental data and used in modeling the cyclic hardening (and softening),
ratcheting and cyclic relaxation responses, typically with additional relations.
1.2.3 Literature on Haynes 230 Research
The chemical composition of Haynes 230 mainly involves nickel, chromium, tungsten
and molybdenum. Table 1.4 lists the limiting chemical composition of Haynes 230 provided by
Haynes, International.
Table 1.4: Limiting chemical composition of Haynes 230 (Haynes, Int.).
Ni Cr W Mo Fe Co Mn Si Al C La B
57.0
(min)
22.0 14.0 2.0 3.0
(Max)
5.0
(Max)
0.5 0.4 0.3 0.10 0.02 0.015
(Max)
Haynes 230 is an example of an advantageous nickel-based superalloy that has the ability to
retain its ductility and strength after exposure to high temperatures for long durations. More
specifically, Haynes 230 does not form a deleterious phase after 16,000 hours of exposure from
649°C to 871°F. Unlike other solid-solution strengthened alloys, the main precipitated phases in
Haynes 230 are all carbides (primarily M6C). After a duration of high temperature exposure,
tensile ductility and impact strength do not decrease as significantly as these other alloys, such as
Haynes 188, Haynes 625 and the Hastelloy® X alloy. After annealing at 1232°C, typical grain
size of Haynes 230 is ASTM 5 grain size. At exposure to temperatures as high as 1177°F and
17
1204°F up to 24 hours, the grain size can remain relatively unchanged. The good mechanical
strength remains consistent for long durations of heating can be accounted for by the general
stable microstructure (grain size and precipitate phases). Whereas, most other iron-, nickel-, or
cobalt-based alloys and stainless steels would show greater grain size growth and properties that
degrade over time at elevated temperatures. (Haynes Int).
Several experimental studies have been conducted on Haynes 230 by other researchers,
involving fracture toughness (with the interaction of cyclic creep), pure low cycle-fatigue, and
oxidation behavior. Low-cycle fatigue and creep interactions for Haynes 230 have been
investigated by L. J. Chen et al (2000). They have conducted low cycle fatigue through axial
strain range control. The fully reversed strain cycles were limited to 1.0% and 0.7%. A servo-
hydraulic Material Test System was used to cycle with a 1 Hz frequency at test temperatures
between 760-982ºC. Figure 1.7 shows their results for LCF within this temperature range. With
Figure 1.7. Fatigue life as a function of total strain range at different temperatures (760°C – 982°C). (Chen 2000).
additional tests, creep was induced with several different hold times of 120, 600 seconds, or an
“infinite” period at the peak tensile strain of each cycle. Results of number of cycles to failure as
a function of hold time were shown in Figure 1.8. Their results indicated the LCF-creep life
18
Figure 1.8. Fatigue life as a function of strain hold time. (Chen 2000).
exhibited dependence on both temperature and applied strain range for the experimented
temperature range. For an applied strain range smaller than 0.7%, decreasing the test temperature
had prolonged the fatigue life. For the higher test strain range of 1.0%, test temperature did not
shorten or prolong the number of cycles to failure. Further work was done by Chen and Lu to
investigate the transgranular or intergranular fracture modes of crack-growth and low cycle
fatigue-axial strain controlled experiments with hold times at 649, 816, 927, and 982ºC on
Haynes 230. (Chen 2000, Lu 2005, and Lu 2006). Crack initiation was observed as a
transgraunular type at 816 ºC regardless of presence of hold times and at 927 ºC under no hold
time and a 2 minute hold time. However, under a 10 minute hold time with a test temperature at
927 ºC, there was an intergranular fracture mode, which was concluded to be due to the influence
of oxidation on significantly decreasing fatigue life. They have reported the influence of strain
ranges and cyclic hardening/saturation trends. The existence of the dynamic process involving
dislocation annihilation and rearrangement, resulting in dislocation recovery was noted.
In a recent study, Chen et al (2013) conducted experiments and modeling of creep-fatigue
interactions for Haynes 230 and Inconel 617. These experiments were controlled and limited
based on the following total axial strain ranges of 0.5%, 1.0%, and 1.5%, and showed Inonel 617
had shorter creep-fatigue lives than Haynes 230. The creep-fatigue interaction had produced
significantly shorter life of both materials when compared to their low cycle fatigue behavior.
Hold times were also implemented at the maximum tensile strain, under 3, 10, and 30 minute
durations. The linear damage summation and frequency-modified tensile hysteresis energy
models were compared with their tests on creep-fatigue behavior, and the latter had exhibited a
greater accuracy in modeling both material than the former.
19
The following are summaries of some other work conducted on Haynes 230. Vecchio et
al (1995) has conducted low-cycle fatigue tests via strain-controlled in air at elevated
temperatures at 760, 871, 982ºC. They determined that the additional thermomechanical
processing at 1121ºC, below the carbide solvus temperature, had a produced a longer LCF life
compared to the samples that were completely fully solution annealed at 1232°C.
With the Haynes 230 material specification sheet, various mechanical properties such as
metal loss due to oxidation, hydrogen, corrosion resistance, can be found. (Haynes, Inc.).
However, further details are often required to understand the mechanical behavior with elevated
temperatures. Oxidation resistance at 900 and 1100ºC on Haynes 230 and Alloy 617, both main
candidates for the IHX tubing, were considered by Kim et al (2009). Oxidation was analyzed for
air and helium environments. Through several material characterization techniques, they have
identified the continuous formation of MnCr2O4 over the Cr2O3 layer on Haynes 230 has led to
a lower oxidation rate than the steady-state oxidation rate present in Alloy 617 for their lower test
temperature of 900ºC. While both alloys exhibit good oxidation and carburization resistance;
higher elevated temperatures can degrade the material due to the evaporation and “spallation” of
the protective Cr2O3 layer. With EDS, XRD, and XPS, Kim et al concluded the initial rapid
growth of the MnCr2O4 would prevent exposure of the Cr2O3 layer, whose slow growth
becomes more dominant, as shown in Figure 1.3. Their results have indicated the oxide scale had
developed to a thickness of ~ 3µm in Haynes 230 and a Ni-rich oxide thickness of ~17 µm in
Alloy 617 at 900 ºC.
Figure 1.9: Oxidation process in air of Haynes 230 at 900ºC (a) initially and at the steady-state stage. (Kim 2009).
However, oxidation behavior at 1100 ºC is generally similar for Haynes 230 and Alloy
617, where the outer layer above the Cr2O3 would experience spallation, respectively the
MnCr2O4 and the TiO2. Since the inner Cr2O3 becomes exposed, CrO3 volatilized in both
20
materials, and resulting rates are only slightly different in an environment with 1.4 ppm O2 and
1.8 ppm H2O. An earlier study by Jian et al (2006) was conducted on the oxidation behavior of
Haynes 230 for the elevated temperatures between 650 and 850ºC in air. They have determined
there are mainly three stages in oxidation involving the MnCr2O4 and Cr2O3 layers.
There has been various limited work involving the oxidation composition, creep-fatigue
interaction through fracture toughness approach, low cycle fatigue, and etc. However, there has
been no literature regarding nonproportional loading and ratcheting of Haynes 230. Careful
planning of combinations of mechanical experiments and constitutive modeling the creep-fatigue-
ratcheting behavior of Haynes 230 can result in an efficient process to determine the service life
and proper operating conditions.
21
Chapter 2
Experimentation
To support constitutive modeling of viscoplastic behavior of Haynes 230, there are three
main steps: exploration, characterization and validation. Exploration guides the development of
equations, characterization sets the material parameters and validation demonstrates the
correctness of the modeling. The work reported here covers the exploration and characterization
of the cyclic creep deformation (ratcheting strain) and cyclic stress hardening (and softening)
behavior. Since the material parameters related to the hardening and plastic flow rules are unique
to particular alloys, mechanical experiments are required with the induced cyclic plasticity
mechanisms. Analyzing the ratcheting-creep-fatigue mechanical behavior of Haynes 230 and the
cyclic hardening-softening trends based on test path nonproportionality is the objective of this
research. The following are details of the setup involved with these isothermal-multiaxial
experiments for the test range between 23°C and 982°C.
2.1 Specimen Description
Tubular specimens were machined from bars of Haynes 230 stock received from
Honeywell, with the axis of the tube aligned with the rolling direction. These specimens were
machined by Westmoreland Mechanical Testing & Research, Inc, through drilling and honing the
inner diameter of the specimens. Lathing, low stress grinding and longitudinal polishing was
performed to obtain the proper reduced outer diameter within the gage section and surface finish.
The tubular dimensions at the gage section were chosen for appropriate material characterization
experimentation. These dimensions allow the stress, strain, and temperature fields within the gage
section to be as uniform as possible and to ensure buckling would not occur. It is also helpful that
these dimensions match the IHX tubing for the “Next Generation Nuclear Plant Intermediate Heat
Exchanger Acquisition Strategy” prepared by R.E. Mizia in April of 2008. Tubular specimens
used within the experiments reported here have an outer diameter of 21 mm and a wall thickness
of approximately 1.5 mm within the gage section. Other notable dimensions are represented in
Figure 2.1. Originally, the outer diameter of the grip ends were uniformly 30.0 mm for about
22
Figure 2.1: Tubular specimen with typical dimensions in mm.
three of the specimens due to machining error. Since this minor machining error prevented the
specimens from sliding into the grips of the MTS rig, about 60 mm of the ends were slightly
lathed by the Penn State Engineering Services Shop to a diameter about 29.9 mm. Average inner
(di) and outer diameter (do) dimensions within the gage section are provided in Table 2.1.
Specimen F-07 was used to check the temperature distribution within the gage section.
Table 2.1 Average inner and outer diameter dimensions for tested specimens.
Specimen name Test Name
Temp.
(°C)
Avg di
(mm)
Avg do
(mm)
F-01 Test GB-4 871 17.93 21.06
F-02 Test GB-5 927 17.97 21.06
F-03 (Dummy) Test GA-1 23 17.92 21.05
F-04 Test GB-6 982 17.93 21.05
F-05 Test GB-7 927 17.95 21.05
F-06 Test GB-1 23 17.96 21.05
F-07 Temperature n/a 17.95 21.05
F-09 Test GA-1 23 17.95 21.02
F-10 Test GA-4 871 17.91 21.04
F-11 Test GA-5 927 17.97 21.05
F-12 Test GB-3 760 17.93 21.03
F-13 Test GA-6 982 17.92 21.05
F-14 Test GA-4 871 17.95 21.05
F-15 Test GA-7 927 17.97 21.06
F-16 Test GA-2 649 17.97 21.06
F-17 Test GB-2 649 17.97 21.07
F-18 Test GA-3 760 17.95 21.06
F-19 Test GA-5 927 17.93 21.06
F-20 Test GA-2 649 17.95 21.05
F-21 Test GA-6 982 17.93 21.06
23
2.2 Equipment and Instrumentation
A closed loop servohydraulic test system, Axial Torsional Material Test System (MTS)
model 319.25, was used to conduct the multiaxial experiments. It has a force capacity of 250 kN
and a torque capacity of 2200 N-m. In addition, water cooled 646 hydraulic round collet grips
were used to grip the tubular specimen ends. The rig was operated through the MultiPurpose
TestWare (MPT) software through a connecting computer and a MTS Flextest 20 controller, both
contributing to the data acquisition process. The axial channel can be controlled through three
different modes: displacement, force, and strain. Likewise, the torsional channel has the following
modes: angle, torque, and strain. Through the MTS bi-axial high temperature extensometer, the
shear strain was controlled and measured as shear angle of twist, which is proportional to shear
strain. Data were acquired from each of the six modes, while controlling one mode of each
channel. Most of these experiments used a timed data acquisition rate of 10 Hz for the following
signals: axial force, torque, axial displacement, torque angle, axial strain, shear angle of twist, and
running time. Experimental data obtained from a timed acquisition rate of 1 Hz were inadequate
in fully representing the shear stress-strain hysteresis curve and were repeated with an appropriate
rate of 10 Hz. Acquisition of data was also conducted at axial force and torque peak and valley
values during the cyclic loading. Control and monitoring through these modes were possible with
load cells and linear variable displacement transducers and extensometers.
A high temperature bi-axial extensometer, MTS 632.68B-08, was used to control and
measure axial strain and the shear angle of twist of a specimen. It is operational up to
temperatures as high as 1200°C (2200°F). The possible axial strain range is 10%, while the shear
angle of twist limit is ± 2.5 degrees. A standard 25.4 mm indenter from MTS was used to
“punch” two indents with the standard spacing on the surface of the specimen. After the specimen
was gripped, the extensometer was mounted onto the specimen by placing the ceramic
extensometer probe tips through the gap between the induction coils and upon the specimen‟s
indents, as shown in the left photograph of Figure 2.2. The extensometer was secured in place
with the fixture arms of the heat shield, as seen in the photograph on the right of Figure 2.2.
24
Figure 2.2. (Left) Side view of MTS high temperature biaxial extensometer probes mounted on thin wall tubular
specimen. (Right) Heat shield arm fixtures secured the extensometer against the specimen.
The induction heating power unit was manufactured by Superior, model number SI-
12KW, allowed the remote head to output high-frequency current into the three sets of hollow
copper coils to heat the test specimen. The copper tubing was insulated with a glass-fiber mesh
and was attached to adjustable aluminum blocks. The three sets of coils formed a closed circuit
with the remote head and induction power supply unit. This adjustable work coil fixture is of
similar design to that used by Ellis and Bartolotta to conduct thermo-mechanical experiments on
Hastelloy-x. (Ellis 1997).
A type K thermocouple was spotwelded to each specimen at the midpoint of the gage
section and connected to an Omega temperature controller, model CN77554. With a set point
temperature, the temperature controller regulated the Superior induction heater output based on
the measured temperature from the gage section thermocouple. In addition, the temperature at the
shoulder between the top grip end and reduced diameter of the gage section was also monitored
for each specimen. A second thermocouple (type K) was spotwelded 38.1 mm above the gage
section midpoint on the upper shoulder and monitored through a temperature switch (Omega
DP7001). A water coolant pump Dynaflux R1100V had supply lines leading to the induction
copper coils and to the MTS coolant supply system serial No. 320, where the latter provides
filtered water to the extensometer.
25
2.3 Test Matrix
2.3.1 Group A (GA) [Bi-axial ratcheting] Loading Type
The Group A set of experiments involved cycling the shear strain while the axial force was held
steady at a specific value, as seen in Figure 2.3. The two control modes were individually plotted
as a function of time in Figure 2.4. The constant applied axial stress (σxm
) was equivalent to 10%
of the 0.2% offset yield strength of the material for each test temperature. Isothermal Group A
(GA) experiments were conducted at six different temperatures: 23, 649, 760, 871, 927, & 982ºC.
Applied axial loads were determined for each temperature based on specimen geometry and
values of the 0.2% offset yield strength, the latter provided by Dr. Hassan for the corresponding
temperatures. Dr. Hassan had also provided the shear strain (γxy
) test amplitudes, which were
extrapolated from uniaxial isothermal low cycle fatigue (LCF) results on Haynes 230. For each
test temperature, Δγc/ was set to be equivalent to the total axial strain range that produced a
fixed plastic strain range of 0.002 m/m at half the total uniaxial fatigue life before fracture
occurred, where Δγc was the shear strain test range of Group A experiments. Test control
parameters for Group A are listed in Table 2.2. For all Group A tests, the cycle period was fixed
at 3 seconds. An additional test was conducted for 927ºC, to observe the influence of a slightly
higher shear strain amplitude on material response. As noted earlier, the shear strain mode was
controlled as shear angle of twist in degrees and the relationship is shown in section 2.4.
Figure 2.3: Control test path for Group A experiment as axial load versus shear strain.
26
(a) (b)
Figure 2.4 On the left, is a schematic of the (a) axial force control as a function of time. On the right side is a diagram
of (b) shear strain control versus time.
Table 2.2. Test Matrix for Group A experiments.
Test
Temperature 0.2% Y.S.
σxm
Δγc
---------
0.5Δγ
c
0.2% offset
yield
strength
Applied
Axial
Stress
Applied
shear
strain
amp.
Units
Name °C MPa MPa % %
GA-1 23 403.3 40.33 0.60 0.520
GA-2 649 294.4 29.44 0.76 0.658
GA-3 760 280.6 28.06 0.64 0.554
GA-4 871 190.3 19.03 0.53 0.459
GA-5 927 190.3 19.03 0.46 0.398
GA-7 927 190.3 19.03 0.60 0.520
GA-6 982 137.2 13.72 0.39 0.3377
2.3.2 Group B (GB) [90° out of phase strain cycles] Loading Type
The Group B (GB) experiments were conducted in axial and shear strain control. The
three path segments of GB are shown in Figure 2.5. As individual plots, the control modes are
plotted as a function of time in Figure 2.6. Segment (1) entailed symmetric axial strain cycling
with a triangular wave form. Segment (2) encompassed a 90° out-of-phase axial and shear strain
cycling with sinusoidal waveforms, as seen in Figure 2.4. Following afterward was segment (3),
27
which was a repeat of segment (1). The purpose of these experiments was to impose cyclic
hardening-softening behavior under the highest practical degree of non-proportionality with
segment (2) after stabilizing the material with segment (1). Test parameters used for isothermal
Group B experiments are shown in Table 2.3. Cycle period for Group B experiments were fixed
to 160 second. 20 cycles were induced for each of the first two segments and each test was
concluded with 5 axial strain cycles for the last path segment (3). Shear strain amplitudes and test
temperatures from Group A were used in Group B. For each test temperature, the axial strain
range (ΔεA) for Group B were taken to be equivalent to the total axial strain that produced a
plastic strain range of 0.002 m/m at half the fracture life of isothermal uniaxial LCF experiments.
For test temperature 927°C, an additional GB was conducted with slightly higher axial and shear
strain amplitude.
Figure 2.5: Control test path for Group B experiments. High degree of non-proportionality with segment (2) consisting
of 90° out-of-phase strain cycles.
28
Figure 2.6: Axial strain (above) and shear strain (below) control for Group B experiments, as a function of time.
Table 2.3. Test Matrix for Group B experiments, 90° out of phase strain cycles.
Test Name
Temperature
ΔεA ΔεA
2 0.5*Δγc
---------
0.5*Δγc
Axial
strain
range
Applied
axial strain
amp.
Applied
shear
strain
amplitude
Units
Name °C °F % %
% %
GB-1 23 75 0.6 0.30 0.30 0.520
GB-2 649 1200 0.76 0.38 0.38 0.658
GB-3 760 1400 0.64 0.32 0.32 0.554
GB-4 871 1600 0.53 0.27 0.27 0.459
GB-5 927 1700 0.46 0.23 0.23 0.398
GB-7 927 1700 0.6 0.30 0.30 0.520
GB-6 982 1800 0.39 0.195 0.195 0.3377
29
2.4 Experimental Setup and Details
Multi-axial experiments were conducted using standards ASTM E2714-09 (Standard
Testing Method for Creep-Fatigue Testing), ASTM E2207-08 (Standard Practice for Strain-
Controlled Axial-Torsional Fatigue Testing with Thin-Walled Tubular Specimens) and ASTM
E606 (Standard Practice for Strain-Controlled Fatigue Testing) as guidelines. Several portions of
these standards overlap. Both standards required the temperature within the gage section to be
within 1% of the nominal test temperature in Celsius. Standard ASTM E2207 also provided basic
guidelines on specimen dimensions, recommended test protocols, data analysis, and failure
determination.
The MPT software was programed to control one mode from each channel
(axial/torsional), and the Flextest controller would implement the specified data acquisition of all
six modes: displacement, force (P), axial strain (εx), angle, torque (T), and shear angle of twist
(θ). A Matlab program was written to use the force, torque and shear angle of twist acquisitioned
values with the additional input of the inner and outer specimen diameter to calculate the
corresponding axial stress for the tube cross-section, shear stress and shear strain at the outer
diameter.
Figure 2.7: Geometry of a section of a cylindrical specimen under torsion within gage section.
The engineering shear strain (γ) is equivalent to the tangent function of angle Ψ, which is defined
by Δ Ls/ Lg . The Δ Ls is the arc length formed by the angle of twist θ and Lg is the
30
extensometer gage length of 25.4 mm as seen in Figure 2.7. For small angles the tangent can be
approximated by the angle Ψ, since the arc length Δ Ls can be computed as (do/2)θ, where do is
the outer diameter of the tubular specimen. Thus, shear strain will have the following relationship
γxy = do θ/ (2Lg), (eq 2.1)
with shear angle of twist (θ). For tubular specimens, the shear stress ( ) is maximum at the
surface of the outer diameter and is given by
( (
)) , (eq 2.2)
where T is the torsional moment, is the outer gage section diameter, and is the inner
diameter of the gage section. This term incorporates the polar moment of inertia for a tubular
specimen. The shear stress is calculated at the outer diameter because the shear strain is measured
at this surface. For thicker walled tubular specimens, the maximum shear stress is present on the
outer surface, would have a significant difference from the shear stress at the inner diameter
surface. As fatigue cracks typically initiate at free surfaces, the stresses at the specimen surface is
the main necessary location of these values. (Brown 1978).
Axial stress is equivalent to dividing the applied load (P) by the area of the tubular
specimen, where
σx =
(
). (eq 2.3)
Group A and Group B test types had a fixed cycle period of 3 seconds and 160 seconds
respectively. Thus, strain rates were different for each test. Since these were fully reversed cycles,
the axial or shear strain rates can be determined by the following,
Strain rate =
(eq 2.4)
This equation used to determine the strain rate was restricted to ramp shape loading path, since
the strain rate varied along the sinusoidal shaped path for segment (2) of Group B experiments.
31
Before each high temperature experiment was conducted, the temperature profile within
the gage section was verified to be within 1% of the test temperature, as required by ASTM
E2207-08 and ASTM E606. Specimen F-07 was set aside for the sole purpose of measuring the
temperature profile after approximately 20-30 minutes of heating to the test temperature, the gage
section temperature was typically stable within 10 minutes. A “control” thermocouple (TC) was
spot-welded to the midpoint of the gage section and connected to the Omega temperature
controller. To check the temperature distribution, there were 9 additional thermocouples spot-
welded within the gage section with TC # 2, 3, 5, 6, and 8-12. Thermocouple # 1 and 7 were each
spot-welded 6.36 mm from the edge of the gage section and were monitored with the 2-channel
HH506RA Multilogger. There was also an upper shoulder thermocouple located 38.1 mm above
the control TC and connected to a temperature switch. The other ten thermocouples were
monitored with the 10-channel Omega K-type temperature indicator. Figure 2.8 indicates the
general placement and numbering of these thermocouples around the circumference of the
specimen. The small circular markers within Figure 2.9 represent the spot-welded locations for
the thermocouples corresponding to most of the ones from Figure 2.8. The shaded ring of Figure
2.9 is a cross-sectional view of the specimen containing the control thermocouple and TC # 10,
12, and 11.
Figure 2.8 Schematic of the numbering of thermocouples used to verify the temperature profile.
32
Figure 2.9 Another schematic of the placement of some thermocouple placements with two different cross-sectional
views of the specimen.
For the multiaxial Group A and B experiments, only the control TC and upper shoulder TC were
spot-welded to each specimen. In this report, locations of cracks were described around the
circumference as a quantity of degrees starting from the line indicated by initial placement of the
two indents and going counterclockwise.
Due to the wide range of temperatures that were of interest, the center 2-turn coil was
sometimes replaced with a different inner diameter coil. The center coil used for each temperature
test is provided in Table 2.4, with the corresponding inner diameter to obtain the appropriate
temperature distribution to be within 1% of the test temperature within the gage section. The
upper and lower 3-turn coils were used for all tests without replacement, as shown earlier in
Figure 2.2.
Table 2.4: Inner diameters of the center 2-turn coil used for Group A and Group B experiments.
The upper and lower coils remained the same for all tests.
Coil Name Inner diameter
(mm)
Test Name
Coil A 40.5 GA-4 to GA-7
GB-4 to GB-7
Coil B 45.3-45.7 GA-3,
GA-2 (specimen F-20)
GB-3
Coil C 57.4-57.7 GA-2 (specimen F-16)
GB-2
According to standard ASTM E2207-08, failure can be defined when either (1) a 5% or
10% percent peak stress drop method, (2) periodic interruptions for replication of the specimen
surface in observing for when cracks are first visible. Standard E21714-09 had only
33
recommended utilizing the percent peak stress drop method. For the second method, periodic
interruptions would involve undesirable events of cooling and reheating the specimen. The room
temperature experiments with Test GA-1 were interrupted after at least 10,000 cycles were
completed. The higher temperature Group A experiments often resulted in hydraulic instability
and proper control was not possible. Typically, these tests were restarted when macrocracks or
fracture were not visible. Reported in Chapter 3.1.8 are the varying values of percent peak stress
drop obtained by the end of each Group A experiment. Based on these results, it was appropriate
to designate a 5% peak stress drop as when failure occurred for the GA experiments at 649°C and
a 10% peak stress drop for the higher test temperatures, to approximate when the material had
accumulated sufficient damage to have a decrease in load carrying capacity.
34
Chapter 3
Results and Discussion
The results and observable trends for the two isothermal test types Group A and B at
different temperatures (ranging from 23°C to 982°C) are presented. Group A isothermal
experiments involved constant axial stress with cyclic shear strain at a cycle period of 3 seconds.
Included are general test details, material response plots for different signals and details involving
cracks or fracture surface in section 3.1. Details for Group B (GB) experiments, composed of
three-part loading path segments, are reported in section 3.2. Segments (1) and (3) involve axial
strain cycling with shear strain dwell, unless otherwise noted. Segment (2) contains 90° out of
phase cycling of the axial strain and shear strain signals. 20 cycles were conducted for each of the
first two segments and the test was concluded with 5 axial strain cycles for the last path segment
(3). Group A isothermal experiments were conducted to investigate the creep-fatigue interaction
and ratcheting accumulation for a wide range of temperatures. As for Group B isothermal
experiments, the influence of highest degree of nonproportional loading on cyclic stress
hardening and softening for different temperatures is the main concern.
3.1 Group A (Bi-axial Ratcheting) Loading
These tests exhibited a small degree of non-proportionality in loading, where the
principal stresses direction changed slightly during the shear strain cycling with a constant axial
stress. With the addition of the cyclic shear strain, ratcheting of the axial strain was induced by
the plastic strain coupling. Each test was conducted until cracks were visible or hydraulic
instability occurred. Test parameters, including cycle period of 3 seconds, were determined to
accelerate the creep-fatigue and ratcheting damage interactions. Material responses compared
between the different temperatures of GA experiments are the following: ratcheting rate as a
function of time, cyclic hardening or softening of peak shear stresses, and ratcheting-creep-
fatigue life.
35
3.1.1 Test GA-1: 23
General Test Details: The control path for Test GA-1 is provided in Figure 3.1 as applied axial
stress versus shear strain. The modes are plotted individually as a function of time with Figure
3.2. The pattern observed with the shear strain versus time signal is due to the periodically
Figure 3.1: Control of axial stress versus shear strain for Test GA-1 (F-09).
sdf Figure 3.2: Control modes as a function of time for axial stress (left) and shear strain (right) for Test GA-1 (F-09).
timed data acquisition. For the room temperature experiments, water was not supplied to the
collet grips and extensometer because the cooling water was below room temperature.
Test GA-1 was conducted on two specimens, F-09 and F-03, with corresponding
parameters defined in Table 3.1. The cyclic shear strain range for Test GA-1 was ±0.00520
radians and the corresponding control parameter of shear angle of twist for each specimen are
shown in Table 3.1. The shear strain in radians was multiplied by 180*2*Lg/(π*do) to obtain the
shear angle of twist in degrees, where do refers to the outer diameter of the specimen within the
gage section and Lg refers to the gage length. The last row of Table 3.1 indicates the timed data
acquisition rate for each specimen. Toque peak and valley acquisition (TPV) was also used for
both specimens.
36
For both experiments, axial stress was initially ramped to 40.34 MPa in load control,
while the shear strain was controlled to dwell at zero. After the target axial stress was reached, the
shear strain was set to cycle with a triangular waveform with the noted parameters. Prior to
running the experiments reported here, tuning of the control modes on the Axial/Torsional MTS
Rig to Alloy 230 was performed on specimen F-03. During this tuning process, the axial stress
and shear stress were respectively limited to ± 13.9 MPa and ± 13.0 MPa. Specimen F-03 was
also assigned to be used for the repeat test, since there were no other available specimens. These
room temperature tests on specimen F-09 and F-03 were respectively interrupted at 10,898th and
12,551th cycle, which was when the shear stress cyclic softening had stabilized to a low and
generally constant rate and axial strain accumulation was minimal.
Table 3.1: Test parameters for Test GA-1
Test Name GA-1 GA-1 (Repeat)
Specimen F-09 F-03
Axial Stress
Ramp time 40.34 MPa
4.0 sec. 40.34 MPa
4.0 sec.
Angle of Twist
Range
& Rate
±0.71947 degrees
0.95930 deg./sec.
±0.71834 degrees
0.95779 deg./sec.
Data Acquisition 1 Hz, TPV 10 & 20 Hz, TPV *Angle of twist given over the extensometer gage length of 25.4 mm.
Material Response: Axial strains versus time plots are presented in Figure 3.3 for two
specimens of Test GA-1. The following plot shows there was a very slow increase in axial strain
for most of the test duration, which was significantly lower than the ratcheting strain
accumulation resulting from the higher temperature tests. The axial strains within the first 100
cycles of Figure 3.3 are shown in Figure 3.4.
37
Figure 3.3: Axial strain response of Test GA- 1 for two specimens.
Figure 3.4: Zoom in view of axial strain response of Test GA-1 for two specimens, for the first 100 cycles. The smaller
window shows the response for the first 10 cycles.
The start of the shear strain cycling was programmed to begin after completion of the 4.0 second
ramp up of the axial stress to 40.34 MPa. The plots that are shown as a function of cycle numbers
based on the recorded run time that included the initial stress ramp up. However, the ramp up
typically occurs within less than two cycles and is insignificant when considering cycle lives of
more than a thousand cycles. The axial strain value immediately prior to the shear strain cycling
was a value slightly higher than 0.0002 m/m for both F-09 and F-03. The green horizontal line,
shown along the axial strain accumulation axes in Figure 3.4, indicates the measured axial strain
value before the shear strain cycling began. Due to the slower rate of timed acquisition for
specimen F-03, the curve may appear as two separate data sets with blue markers. Both curves are
plotted as markers for the timed acquisition, instead of lines, to prevent possible signal aliasing.
38
As seen in Figure 3.4, the axial strain signal exhibited a saw blade shape throughout the test,
which was present with the start of the shear strain cycling. This saw blade pattern of the axial
strain generally repeats with the same frequency as the shear strain cycling. Possible sources of
the coupling of axial and shear strain modes are due to the extensometer and material response.
After the first 50 cycles, the axial strain accumulation rate had decreased. With an additional 300
cycles, the axial strain exhibited the slow but progressive steady-state increase observed in Figure
3.3. The final accumulated axial strain values for specimen F-09 at cycle 10,898 was 0.00167
m/m and for specimen F-03 at cycle 12,551 was 0.00166 m/m.
Figure 3.5: Shear stress peak and valleys of the response to Test GA-1 for two specimens.
Torque peak and valley (TPV) acquisitioned data were used to plot the maximum and minimum
values of cyclic shear stress response as a function of the number of cycles in Figure 3.5. The
material responses between these two specimens for Test GA-1 demonstrate the repeatability.
Peak and valleys of the shear stress signal as a function of cycle of numbers were generally
symmetrical about the x-axis. Only the peak values of the shear stress response are shown in
Figure 3.6 for Test GA-1.
39
Figure 3.6: Peak values of the shear stress versus cycle numbers plot, for both specimens of Test GA-1. Smaller
window shows peak values for first 100 cycles.
A small window in Figure 3.6 depicts the initial cyclic response for the first 60 cycles.
Figure 3.6 shows only a slight difference between the two experiments for the first 3500 cycles,
where F-09 (blue markers) resulted in a slightly higher shear stress peak curve during this initial
period. The mechanical response continued with cyclic softening to 256 MPa by approximately
cycle 7000 and followed with cyclic softening at a slower rate to about 255 MPa by the end of
both experiments. The ripples observed in the axial strain signal (Figure 3.3), for specimen F-03,
coincide with the ripples observed in the shear stress peak curves in Figure 3.6.
The shear stress-strain hysteresis loops for cycles 1, 5000, and 10000 are shown in Figure
3.7, for specimen F-03 of Test GA-1. These loops were plotted from the timed acquisition data.
Hysteresis loops for cycles 5000 and 10,000 are nearly identical.
Figure 3.7: Shear hysteresis loops for specimen F-09, with only cycles 1, 5000, and 10000 shown.
40
Post Test Observation: No deformation was visible for both specimens of Test GA-1, as seen
with Figure 3.8 and 3.9. The dark lines observed on the surface specimen F-09 were made with a
fine tip permanent marker to indicate the location for indentation.
Figure 3.8: Post-test photograph of specimen F-09 (Test GA-1)
Figure 3.9 shows some shallow longitudinal scratch marks near the indents of specimen F-03.
These shallow scratches were caused by the use of a thin metal template as a reference to adjust
the heat shield to the designated distance from the specimen, prior to tuning the Axial/Torsional
MTS system. The heat shield was not moved after this initial setup step was completed.
Figure 3.9: Post-test photograph of specimen F-03 (Test GA-1)
41
3.1.2 Test GA-2: 649
General Test Details: Test temperature 649 was the lowest temperature that required induction
heating for the reported results. Test GA-2 at 649 was first conducted on specimen F-16. The
resulting control path from the acquired data is shown in Figure 3.10, while the test parameters
for Test GA-2 are provided in Table 3.2. The cyclic shear strain range for Test GA-2 was ±
0.00658 radians and the corresponding shear angle of twist for each specimen are included in
Table 3.2. The center 2-turn induction coil C was used for specimen F-16. After 20 minutes of
heating at 649 , the free thermal strain was stable at 0.00896 m/m.
Figure 3.10: Control of axial stress versus shear strain for Test GA-2, specimen F-16.
Table 3.2: Test parameters for Test GA-2
Test Name GA-2 GA-2 (Repeat)
Specimen F-16 F-20
Axial Stress
Ramp time 29.40 MPa
2.9 sec 29.40 MPa
2.9 sec
Angle of Twist
Range
& Rate
± 0.90957 degrees
1.2128 deg./sec
± 0.91012 degrees
1.21350 deg./sec
Data Acquisition 1 Hz, TPV 20 Hz, TPV
After 3545 cycles, both axial and shear strain signals were ringing accompanied by an
increasingly unusual hydraulic noise, which is a sign of hydraulic instability. After the hydraulic
instability had triggered the MPT to cease the test, the specimen was immediately ungripped and
heating was shut off.
Test GA-2 was also conducted on specimen F-20 with a higher data acquisition rate of 20
Hz. Since other experiments were conducted during the pause of the first and second Test GA-2
42
experiment, there were some periods of removal and attachments of the center coil of other
dimensions. While center coil C was used for specimen F-16, a smaller sized center coil B was
found to produce temperatures within the recommended ±1% range from the test temperature for
locations in the gage section of specimen F-20. After the initial 20 minutes of heating, the free
thermal strain was stable at 0.00897 m/m for specimen F-20. The test was manually stopped after
4336 cycles, since the axial stain signal had exhibited progressively increasing ringing in a
similar manner as specimen F-16 (Test GA-2) before hydraulic instability occurred.
Material Response: The axial strain accumulation curves for specimen F-16 and F-20 are shown
in Figure 3.11. Prior to the start of shear strain cycling, the axial strain was 0.0056 m/m for both
specimens. This initial axial strain value is indicated in Figure 3.11 as the green horizontal line,
Figure 3.11: Axial strain response of Test GA-2 for two specimens.
and was only a small portion of the final accumulated strain. The fastest increase of axial strain
accumulation occurred within the first 20 cycles and to 0.0024 m/m for both specimens.
Ratcheting rates were similar with a slightly faster accumulation rate for specimen F-16.
However, specimen F-20 endured 791 cycles more than F-16 before hydraulic instability had
occurred. By the end of each test, the axial strain had exhibited progressive oscillation.
The axial strain ringing slowly progressed, starting at cycle 2993, up to a notable
oscillation width of 0.00024 m/m by cycle 3165 for specimen F-16. The oscillation had increased
to a width of 0.00245 m/m by cycle 3545 when hydraulic instability occurred and the immediate
average axial strain was 0.00563 m/m. Similarly for specimen F-20, the axial strain oscillation
width increase was slow for the first 3900 cycles, as shown in Figure 3.12 and 3.13.
43
Figure 3.12: Zoom in view of axial strain response of specimen F-20 (Test GA-2) for cycles 2000 to 2050.
Figure 3.13: Zoom in view of axial strain response of specimen F-20 (Test GA-2) for cycles 3750 to 3800.
Figure 3.14: Zoom in view of axial strain response of specimen F-20 (Test GA-2) for cycles 4250 to 4300.
The oscillation width increased slightly between cycle 3918 to 4240 and greater increase occurred
until the end of the test, as shown in Figure 3.14. Figures 3.12 – 3.14 were shown with the same
axes scaling to demonstrate the increase in axial strain oscillation width. When Test GA-2 was
manually interrupted for specimen F-20, the oscillation width was 0.00144 m/m.
44
The progressive ringing could be due to presence of macro-cracks formation and
propagation while loading under cyclic shear strain control. The rippling or wave-like pattern of
the axial strain signal observed with Test GA-1was not apparent with Test GA-2. However, the
rippling was observed on a smaller scale than the accumulating axial strain observed in Test GA-
2. On the other hand, the saw blade shape observed with the axial strain signal for F-03 (Test GA-
1) was also observed with F-20 (Test GA-2). This latter feature was related to the coupling of the
shear strain cycling, either through the extensometer or the material response.
The shear stress responses of the two specimens of Test GA-2 were agreeable and similar
according to Figure 3.15. Figure 3.16 includes only a plot of the peak values of the cyclic shear
Figure 3.15: Shear stress peak and valleys of the response to Test GA-2 for 2 specimens.
Figure 3.16: Peak values of the shear stress versus cycle numbers plot, for both specimens of Test GA-2. Smaller
window shows peak values for first 150 cycles.
45
stress response and shows the initial fast rate of cyclic hardening occurred for the first 26 cycles
for both specimens. The rate of cyclic hardening decreased gradually, reaching a maximum value
at cycle 2931 for specimen F-16 and the 3285th cycle for F-20. Afterward, the cyclic shear stress
behavior started to exhibit a slow rate of cyclic softening with a sharper rate present during the
last 30 cycles for both specimens. The start of the notable axial strain oscillation growth did not
coincide with when the shear stress response reached the maximum values but had started
afterward. For specimen F-16, the notable axial strain oscillation increase started 234 cycles after
the shear stress reached the maximum value and 352 cycles before the sudden shear stress peak
curve drop. The oscillation increase for F-20 had begun 955 cycles after the shear stress begun
cyclic softening and 66 cycles before the sudden shear stress peak drop. Thus, the notable
oscillation in axial strain signal could be used only as a rough indicator of sufficient crack
growth, but cannot be used to determine when the load capacity of the material degrades
significantly.
Shear stress strain hysteresis was plotted from the timed acquisitioned data of specimen
F-20 (Test GA-2) in Figure 3.17. As expected, the shape of the hysteresis curve varied with
accumulated damage and trends could be corresponded to the shear stress peak curves.
Figure 3.17: Shear stress and strain hysteresis for F-20,
with cycles 1, 2, 5, 10, 20, 50, …2000, 4324 shown.
Post Test Observation: A thin blue oxide is visible on specimen F-16 (Test GA-2), as seen in
Figure 3.18. After the specimen had cooled and was removed from the test rig, a thin partially
46
closed longitudinal crack was visible with specimen F-16. The longitudinal crack is parallel to the
axes of symmetry of the tubular specimen with some sections slightly jagged.
Figure 3.18: Post-test photograph of Specimen F-16 (Test GA-2)
Figure 3.19: Combined post-test photographs of longitudinal crack for specimen F-16 (Test GA-2), under 32x
magnification.
Figure 3.19 shows a longitudinal crack within the gage section of specimen F-16, extending from
the photograph on the left to the right. Scale bars are equivalent to 0.6 mm. There is a thin oxide
of bluish tint, which had resulted from heating at 649 . The irregular areas without the oxide
coating (Fig. 3.20) originate from the process of spot welding the thermocouple to the specimen,
since the surface was partially cleaned with acetone. Figure 3.20 is a photograph of specimen F-
20 after Test GA-2 was completed.
47
Figure 3.20: Post-test photograph of specimen F-20 (Test GA-2).
Figure 3.21: Combined post-test photographs of a surface (longitudinal) crack between thermocouple and lower indent
for specimen F-20 (Test GA-2) under low magnification.
Figure 3.22: Low magnification photograph of small longitudinal and circumferential cracks near control thermocouple
for specimen F-20 (Test GA-2).
For specimen F-20, one circumferential thin partially closed crack about 8.7 mm long
was present 7 mm below the top indent, within gage section. A longitudinal crack 10.6 mm long,
48
starts 1.2 mm below control TC (within the gage section), and 0.71 mm straight down right of the
lower indent.
Figure 3.21 shows a surface crack starting below the thermocouple and continues on past
the lower indent. The small oval near the thermocouple is not an inclusion but an irregular mark
resulting from the nonhomogeneous oxidation.
3.1.3 Test GA-3: 760
General Test Details: The test temperature of 760 is within the expected operational
temperature for a small modular reactor design, but is lower than the expected temperatures for
the Very High Temperature Reactor (VHTR). The recorded control modes, axial stress and shear
strain, obtained from the timed acquisition data are shown in Figure 3.23. Coil B was used as the
center 3-turn coil for Test GA-3. The input commands that were used for the MPT are provided in
Table 3.3. The cyclic shear strain range for Test GA-3 was ±0.00554 radians and the
corresponding shear angle of twist for specimen F-18 is included in Table 3.3. After 20 minutes
of heating, free thermal strain was stable at 0.01107 m/m. After the torque limit was tripped, the
MPT program was automatically terminated. Cool down and removal of the specimen revealed a
large fracture.
Figure 3.23: Control of axial stress versus shear strain for Test GA-3 (specimen F-18).
49
Table 3.3: Test parameters for Test GA-3
Test # GA-3
Specimen F-18
Axial Stress
Ramp time 28.10 MPa
2.8 sec.
Angle of Twist
Range & Rate
± 0.76605 degrees
1.0140 deg./sec.
Data Acquisition 10 Hz, TPV
Material Response: Figure 3.24 shows the axial strain signal as a function of cycle numbers,
which correspond to run time. Prior to the start of the cyclic shear strain, the axial strain was
0.00018 m/m for specimen F-18. The axial strain accumulation followed a linear trajectory
starting from the 10th cycle to the 3168
th cycle. Test GA-3 commenced with an axial strain of
0.00959 m/m.
Figure 3.24: Axial strain response of Test GA-3 for specimen F-18.
Figure 3.25: Zoom in view of axial strain response of specimen F-18 (Test GA-3) for cycles 2000 to 2050.
50
Figure 3.26: Zoom in view of axial strain response of specimen F-18 (Test GA-3) for cycles 3124 to 3174.
Figures 3.25 and 3.26 are zoom in views of the axial strain response under same axes scalings but
at different intervals during the test. Both figures show that there is a slight increase in axial strain
oscillation that occurred with higher cycle numbers prior to fracture. Each increase and decrease
in the saw blade pattern of the axial strain signal corresponds to a shear strain cycle. The
progressive oscillation of the axial strain could be due to the presence of macro crack growth.
Based on the peak and valley curves of the shear stress shown in Figure 3.27, greater
initial cyclic hardening was observed within the first 30 cycles. The shear stress response
Figure 3.27: Shear stress peak and valleys of the response to specimen F-18 (Test GA-3).
continued with a decreasing rate of cyclic hardening and continued in a similar manner as for Test
GA-2. Gradual softening of the shear stress occurred after a maximum value (251.3 MPa) was
reached at cycle 2015. There was a sudden and slow increase of the peak and valley curves after
cycle 3174 due to an unusual measurement error of the shear strain during fracture. The lower
51
indent was located on a curved section of the specimen near the fracture, which influenced the
control and measurement of the shear strain signal.
From the 10 Hz timed data acquisition, shear stress and strain hysteresis is provided as
Figure 3.28 for cycles 1, 2, 5, 10, 20, 50, …, 2000, and 3174. A greater extent of cyclic hardening
behavior occurred for Test GA-3 than the lower two test temperatures.
Figure 3.28: Shear stress and strain hysteresis Test GA-3,
with cycles 1, 2, 5, 10, 20, 50, …2000, and 3174 shown.
Post Test Observation: Figure 3.29 is a post-test photograph of specimen F-18. After removal of
Figure 3.29: Post-test photograph of specimen F-18 (Test GA-3)
the heat and specimen from the test rig, a large helical crack is visible that extends from the
middle of the gage section to below and out of the gage section. The large fracture is at an angle
of 45º with respect to the specimen axis of symmetry. There were additional smaller 45º cracks
that have branched from the large fracture and scattered around the circumference of the
specimen within the gage section.
52
3.1.4 Test GA-4: 871
General Test Details: Test GA-4 was conducted on specimen F-10. From the timed data
acquisition, the control loading path was plotted as Figure 3.30. As the first Group A experiment
that was conducted, the control of the shear strain was mistakenly set to cycle under a sinusoidal
wave path instead of the intended triangular wave path for specimen F-10.
Figure 3.30: Control of axial stress versus shear strain for Test GA-4 (specimen F-10).
Control test parameters are listed in Table 3.4. The cyclic shear strain range was ±0.00468 radians
and the corresponding shear angle of twist was listed for each specimen in Table 3.4. Coil A,
with an inner diameter of 40.5 mm, was used as the center 2-turn coil for test temperature 871
and higher. Free thermal strain was 0.01312 m/m after 20 minutes of heating specimen F-10.
After about 1930 shear strain cycles, the axial strain had accumulated to 0.0459 m/m and the
specimen was no longer emitting a dull orange glow. After noticing the heating had ceased, the
test was manually stopped and the heater was turned off. The lettering displayed with the external
temperature controller and a low value for the shoulder temperature indicated the control
thermocouple connection was open and had caused the heating to stop.
Table 3.4: Test parameters for Test GA-4
Test Name GA-4 GA-4 (Repeat)
Specimen F-10 F-14
Axial Stress
Ramp time 19.03 MPa
1.9 sec. 19.03 MPa
1.9 sec.
Angle of Twist
Range
& Rate
± 0.64698 degrees
0.86264 deg./sec
± 0.64659 degrees
0.86212 deg./sec
Data Acquisition 1 Hz, TPV 20 Hz, TPV
53
Test GA-4 was also conducted on specimen F-14, where the cyclic shear strain control
used a triangular waveform. Input parameters are also presented in Table 3.4. A third set of
indents were made and used on the specimen, about 0.25” to the right of the prior two. The prior
indents were suspected of being too small for the extensometer tips to settle into properly without
slippage. Free thermal strain of specimen F-14 was 0.01317 m/m after heating for 20 minutes.
During the Group A loading path, the shear angle of twist exhibited ringing of about 0.2 degrees,
mostly during the negative reversals of the ramp wave. This undesired oscillation width was
about 15.5% of the test amplitude and can be cautiously considered to be within acceptable
variations. Near the end of the test, both strain signals were observed to be increasingly unstable
through the oscilloscope. By cycle 1669, hydraulic instability occurred and caused the MPT to
stop the test, but there were no visible cracks. The thermocouple was replaced after polishing a
small section of the surface, which was where the original thermocouple was spot-welded. The
next day, specimen F-14 was reheated and testing continued with a new set of indents. An upper
torque angle limit of 8 degrees was triggered after 1163 cycles. Prior to the interruption of this
test, the shear angle of twist was ringing within a range of ± 2 degrees.
Material Response: Axial strain as a function of time for the two specimens of Test GA-4 are
shown in Figure 3.31. Prior to shear strain cycling, the axial strains for specimen F-10 and F-14
Figure 3.31: Axial strain response of Test GA-4 for two specimens.
were respectively 0.00012 m/m and 0.00013 m/m. The axial strain rate gradually decreased from
the initial rate for the first 916 cycles of specimen F-10. After a slight jump with the axial strain
curve at cycle 917, ratcheting rate was constant for the next 1002 cycles. The sudden drop for 16
Restart for F-14
54
cycles at the end of the axial strain curve, which occurred at cycle 1933 with axial strain at
0.04592 m/m for specimen F-10, was associated with the sudden temperature drop.
With Figure 3.31, the axial strain curve for specimen F-14 appears to be represented as a
bolder line than F-10, but the curve is thicker due to the ringing in the shear strain control with F-
14. Both curves were actually shown as same sized markers. Specimen F-14 exhibited a
gradually decreasing axial strain accumulation rate until cycle 1669, when the instantaneous
average axial strain reached 0.0311 m/m and hydraulic instability occurred. The thinner section of
the axial strain curve for specimen F-14 represents testing conducted after reheating, where
ringing in the strain signals was minimal. Unexpectedly, the axial strain rate accumulation for
specimen F-14 after reheating caused a faster axial strain accumulation than the testing prior to
reheating and exhibited a nearly linear trend. This latter portion was plotted with offsets based on
the last cycle number and average axial strain value prior to when hydraulic instability occurred.
Figures 3.32-3.34 are zoom in views of the axial strain response for specimen F-14 for 50 cycle
increments after reheating, under similar scaling ratios. The width of the oscillation
Figure 3.32: Zoom in view of axial strain response after reheating for specimen F-14 (Test GA-4) for
cycles 1700 to 1750.
55
Figure 3.33: Zoom in view of axial strain response of restart portion of specimen F-14 (Test GA-4) for
cycles 2240 to 2290.
Figure 3.34: Zoom in view of axial strain response of restart portion of specimen F-14 (Test GA-4) for
cycles 2775 to 2825.
observed with the axial strain saw blade pattern varied with cycle numbers. The combined axial
strain was 0.05618 m/m before the severe fracture occurred, which caused the indent spacing to
increase more drastically.
The greater initial axial strain accumulation present with F-10 compared to F-14, could
be due to the influence of the loading wave path. A sinusoidal wave path has a longer duration at
the peaks and valleys than a triangular wave path and can introduce more damage for each cycle.
From the torque peak and valley (TPV) data acquisition, maximum and minimum values
of the cyclic shear stress response were plotted for specimens F-10 and F-14 in Figure 3.35. For
56
Figure 3.35: Shear stress peak and valleys of the response to two specimens of Test GA-4.
both Test GA-4 experiments, there was initial cyclic hardening within the first 30 cycles, which
was followed by gradual shear stress cyclic softening. There was a sudden decrease in the shear
stress peak and valley curves for specimen F-10 at cycle 917, corresponding to the jump in the
ratcheting axial strain curve. Afterward, the peak and valley values of the shear stress response
proceeded with a slightly faster cyclic softening rate than specimen F-14. By cycle 1933, the peak
value was 149.3 MPa, which corresponds to softening by 16.9% from the maximum value.
With specimen F-14, the maximum shear stress value was 177.1 MPa at cycle 25 and the
peak shear stress curve softened by 6.4% to 165.8 MPa. Hydraulic instability occurred after an
additional 1668 cycles. After specimen F-14 was reheated, the testing continued with initial
cyclic shear stress hardening to 179.1 MPa. Following the previous trend, the peak and valley
plots exhibited a similar rate of shear stress cyclic softening. The shear stress peak values
softened to 170.3 MPa by cycle 2735, but had a slight increase followed by a sudden decrease.
This unusual feature could be due to the presence of a significant crack formation or propagation
with strain control cycling.
The shear strain-strain hysteresis plot is shown in Figure 3.36, which originates from the
Restart for F-14
57
Figure 3.36: Shear stress and strain hysteresis for specimen F-14 with cycles 1, 2, 5, 10, 20, 50, …1665 shown.
Unusual warping of hysteresis on the left was due to improper control of the cyclic shear strain signal.
timed acquisition data for specimen F-14 prior to machine instability. The influence of the ringing
in the shear strain signal during the negative reversals caused irregular hysteresis loops for most
cycles. The ringing can be due to at least one extensometer probe not being properly settled
within the indents during the cycling of the shear strain.
Post Test Observation: Upon realizing the connection for the control thermocouple had opened
and had caused the heater to stop supplying sufficient current to retain the test temperature, the
MPT program was manually stopped. The specimen surface had stopped glowing a dull orange,
originally typical for test temperature 871 , and was an indicator of when sufficient heating
ceased. Figure 3.37 is a post-test photograph of specimen F-10, with a grayish oxide layer visible.
The layer of oxide formed at 871 was thicker than the two lower elevated temperatures of Test
GA-2 & GA-3.
Figure 3.37: Post-test photograph of specimen F-10 (Test GA-4).
58
Additional photographs were taken under low magnification, shown in Figure 3.38. Very small
scattered surface cracks are visible within the gage section. Many are oriented at 45 degrees, but
some were also connected to numerous small longitudinal and circumferential cracks.
Figure 3.38: Specimen F-10. Small cracks within gage section, (a) 90 degrees left [20x magnification] and (b) 90
degrees right from indents [10x magnification].
After the upper torque limit was triggered, the removal and cooling of specimen F-14
revealed a large circumferential fracture. This large circumferential fracture had terminated with
45 degree angle splits on both ends, Figure 3.39.
Figure 3.39: Post-test photograph of specimen F-14 (Test GA-4).
59
3.1.5 Test GA-5: 927
General Test Details: For Test GA-5, the axial force applied on specimen F-11 was calculated
for another specimen‟s dimensions and resulted in an additional 0.31 MPa applied. Figure 3.40
shows the control path of axial stress versus shear strain determined from the timed acquisition
Figure 3.40: Control of axial stress versus shear strain for specimen F-11 (Test GA-5).
data. The axial stress during Test GA-5 for specimen F-11 was between 18.84-19.74 MPa. The
axial stress decreased at the extreme values of the shear strain range, but this small variation is
thought to be negligible. Parameters for Test GA-5 are shown in Table 3.5. The cyclic shear
strain range was ±0.00398 radians and the corresponding shear angle of twist for each specimen
is listed in Table 3.5.
Prior to experimentation, there was some lathe scratch marks scattered around the
circumference of specimen F-11 where the surface was not completely polished by the machine
shop. These scratches were approximately 0.51 mm thick and the closest distance of one of these
scratches to the lower indent was 17.07 mm. After 20 minutes of heating at 927 , the thermal
strain accumulated to 0.01418 m/m.
Table 3.5: Test parameters for Test GA-5.
Test name GA-5 GA-5 (Repeat)
Specimen F-11 F-19
Axial Stress
Ramp time 19.34 MPa
1.9 sec 19.03MPa
1.9 sec
Shear Angle of
Twist Range
& Rate
± 0.55093 degrees
0.73457 deg./sec
± 0.55066 degrees
0.73422 deg./sec
Data Acquisition 1 Hz, TPV 10, 20 Hz, TPV
60
Another notable detail is related to the first few cycles conducted on F-11, when there
was a periodic sharp acoustic „pinging‟ noise, which could be due to at least two possible causes.
The extensometer probes were scraping against the material within the indents or the noise was
due to the material response at a relatively short cycle time (3 seconds). After approximately three
hours of testing, the shear strain signal was no longer controlled properly and hydraulic instability
occurred, where the latter was indicated by an audible mechanical noise.
Specimen F-19 was used for Test GA-5 with parameters listed in Table 3.5. After 20
minutes of heating with center coil A, free thermal strain had stabilized at 0.01418 m/m.
Hydraulic instability occurred for specimen F-19 at cycle 3510 and for specimen F-11 at cycle
3509.
Material Response: Axial strain accumulations for the two specimens of Test GA-5 are shown
in Figure 3.41. Specimen F-19 resulted with a slower accumulating axial strain rate than exhibited
Figure 3.41: Axial strain response of Test GA-5 for two specimens.
by specimen F-11. Prior to when the shear strain cycling began, the axial strain value was
0.00014 m/m for specimen F-19 and was 0.00012 m/m for specimen F-11, which are relatively
small values compared to the final value. The ratcheting strain rate was gradually decreasing
throughout both curves, with the greater rate decrease present within the first 1000 cycles. The
general difference in the axial strain curves for the two specimens can be accounted for by
general material variability.
Further investigation of the axial strain curve for specimen F-19 revealed at least three
mainly different degrees of unusual signal ringing shown in Figures 3.42-3.44. The extent of
61
Figure 3.42: Zoom in view of axial strain response of specimen F-19 (Test GA-5) for cycles 300 to 350.
Figure 3.43: Zoom in view of axial strain response of specimen F-19 (Test GA-5) for cycles 1950 to 2000.
Figure 3.44: Zoom in view of axial strain response of specimen F-19 (Test GA-5) for cycles 3175 to 3225.
ringing of axial strain is negligible compared to the final accumulated axial strain measurement,
but prior experiments have shown that axial strain ringing could be influenced by the presence of
cracks. The axial strain curve for specimen F-19 started with the ringing or oscillation observed in
Figure 3.42, where a higher frequency oscillation is associated along the shear strain cycling. By
cycle 943, the higher frequency oscillation in the axial strain signal slightly decreased and the
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width of the ringing had decreased. These changes gradually progressed until cycle 1390, where
the axial strain signal closely resembles the saw tooth pattern observed in Figure 3.43. The width
of the ringing was smaller and a slightly higher frequency oscillation than the shear strain cycling.
By cycle 3115, the width of the axial strain ringing has increased. In addition, the axial strain
exhibited a more evident oscillation with the shear strain cycles. Starting from cycle 3135 until
cycle 3355, the axial strain ringing was similar to the signal within Figure 3.44, where a lower
frequency ringing was also observed. Immediately prior to hydraulic instability, which occurred
at cycle 3509, the frequency and width of the axial strain oscillation had increased.
The shear strain signal shown as a function of cycle numbers, as shown in Figures 3.45-
3.47, exhibited unique patterns that correspond to the changes in the axial strain ringing. The
Figure 3.45: Zoom in view of shear strain signal of specimen F-19 (Test GA-5) for cycles 300 to 350.
Figure 3.46: Zoom in view of shear strain signal of specimen F-19 (Test GA-5) for cycles 1950 to 2000.
63
Figure 3.47: Zoom in view of shear strain signal of specimen F-19 (Test GA-5) for cycles 3175 to 3225.
earlier cycles of the axial strain ringing shown in Figure 3.42 corresponds with the shear strain
signal shown in Figure 3.45, where both the peak and valley values of the shear strain varied
slightly. When the axial strain signal exhibited the smaller width oscillation in Figure 3.43, the
shear strain signal had relatively constant peak and valley values as shown in Figure 3.46. As for
the sections when the axial strain had oscillated with shear strain cycles and an additional lower
frequency, as seen in Figure 3.44, the shear strain valley values varied slightly with the same
lower frequency.
Screenshots of the MPT oscilloscope, Figures 3.48-3.51, during Test GA-5 for specimen
F-19 reveal varying degrees of shear strain ringing accompanied by axial strain ringing.
Figure 3.48: Screen shot of MPT oscilloscope for axial strain (blue), shear angle of twist (red with axis on the right
hand side), and torque (dark red-brown with axis on the left side) for specimen F-19 for cycles 335-338. Axial strain
signal is displayed with an offset of 0.0110 m/m, where y-axis scaling is 0.001 m/m per division.
Figure 3.49: Screen shot of MPT oscilloscope for axial strain (blue), shear angle of twist (red with axis on the right
hand side), and torque (dark red-brown with axis on the left side) for specimen F-19 for cycles 1947-1950. Axial strain
signal is displayed with an offset of 0.0344 m/m, where y-axis scaling is 0.001 m/m per division.
64
Figure 3.50: Screen shot of MPT oscilloscope for axial strain (blue), shear angle of twist (red with axis on the right
hand side), and torque (dark red-brown with axis on the left side) for specimen F-19 for cycles 3188-3191. Axial strain
signal is displayed with an offset of 0.0440 m/m and with y-axis scaling as 0.001 m/m per division.
Figure 3.51: Screen shot of MPT oscilloscope for axial strain (blue), shear angle of twist (red with axis on the right
hand side), and torque (dark red-brown with axis on the left side) for specimen F-19 for cycles 3506-3509. Axial strain
signal is displayed with an offset of 0.0460 m/m and with y-axis scaling as 0.001 m/m per division.
These screenshots show the cyclic control of shear angle of twist in degrees as the red line and the
applied torque as the dark red-brown line on the MPT oscilloscope. The axial strain signal was
shown as the blue line with the scaling as 0.0010 m/m per division, with a different offset for
each screenshot. The earlier durations of axial strain ringing shown in Figure 3.42 are also present
in Figure 3.48, where the axial strain signal is shown at an offset of 0.0110 m/m. The screenshot
in Figure 3.48 shows that the control shear angle of twist signal exhibited varying ringing at
negative reversals, specific regions where the line was bolder, and resulted with a corresponding
degree of axial strain ringing. Since the earlier plots of the shear strain signal were calculated
from timed acquisitioned data, they cannot reveal the presence of ringing for shear strain. The
shear angle of twist signal eventually cycles without ringing or any bolder sections as seen in
Figure 3.49, where the corresponding axial strain signal is shown with an offset of 0.0344 m/m.
The extensometer is highly sensitive to slight misalignment between indents on specimen and
extensometer probes. Control of shear angle of twist can be hindered by misalignment, improper
size of indents, and etc. It is possible that least one of the indents was too small and caused the
MPT to compensate and prevent the extensometer probe from drifting out of the indent. With a
sufficient duration of heating and the necessary applied pressure from the fixture on the
extensometer was enough to widen the indents slightly. As a result, the oscillation or ringing in
65
the angle of twist signal present with the earlier cycles eventually decreased for some duration.
Near the end of the test, both the shear angle of twist and axial strain signal exhibited progressive
oscillations as seen in Figures 3.50 and 3.51. The screenshot of Figure 3.50 indicated cycle 3190
had slightly more shear angle of twist ringing than cycle 1950. The ringing of shear angle of twist
and axial strain by cycle 3509 was greater than the ringing present in cycle 338. The axial strain
signal was shown with an offset of 0.0440 m/m for Figure 3.50 and an offset of 0.0460 m/m for
Figure 3.51. Only the signal ringing prior to hydraulic instability should be a result of a density
increase of macro cracks. The average axial strain value for F-19 was 0.04673 m/m at cycle 3509.
Specimen F-11 had reached a higher axial strain value of 0.06511 m/m by cycle 3509.
The shear stress response agrees well for specimens F-11 and F-19 based on the shear
stress peak and valley curves shown in Figure 3.52. The shear stress peaks are shown in Figure
3.53. Both specimens of Test GA-5 exhibited cyclic hardening within the first 20 cycles and
Figure 3.52: Shear stress peak and valleys of the response to Test GA-5 for two specimens.
Figure 3.53: Peak values of the shear stress versus cycle numbers for both specimens of Test GA-5.
66
continued with a continuous duration of shear stress cyclic softening. After cycle 938 for
specimen F-19 and cycle 961 for specimen F-11, the shear stress peak and valley scattering range
had decreased. This earlier portion of scatter corresponds to the early duration of ringing of the
shear strain and axial strain signals.
A sharper drop occurred with the shear stress peak and valley values after cycle 3310 for
specimen F-19 and cycle 3468 for specimen F-11, which could a result of macro-crack initiation.
The ringing of the axial strain and shear angle of twist signal had begun prior to the drop for
specimen F-19. The shear stress peak and valley curves have exhibited cyclic softening by 20%
from the maximum peak and valley values for both tests.
Figure 3.54 is the shear stress strain hysteresis for cycles 1, 2, 5, 10, 20, 50, …3252 of
specimen F-19.
Figure 3.54: Shear stress and strain hysteresis for specimen F-19,
with cycles 1, 2, 5, 10, 20, 50, …3252 shown.
Post Test Observation: In general, there are many scattered small cracks present within the gage
section around the circumference of specimen F-11. A post-test photograph of F-11 is shown in
Figure 3.55. The control thermocouple was not attached within this photograph and was removed
after post-test handling the specimen. The arrow within Figure 3.55 indicates the location of the
control thermocouple junction. The residue, within the upper region of the gage section,
originates from contact with the thermocouple outer glass braid insulation at high temperature.
Low magnification photographs at two different regions within the gage section of the typical
crack orientations are shown in Figure 3.56. There were many scattered longitudinal and 45°
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angle micro cracks, which are connected. In addition, a few circumferential micro cracks are also
scattered within the gage section. It is likely that these micro cracks occur at grain boundaries.
Figure 3.55: Post-test photograph of specimen F-11 (Test GA-5), with an arrow indicating the location of the control
thermocouple junction prior to removal.
Figure 3.56: Post-test photograph of specimen F-11 (Test GA-5): (a) Left image: a low magnification image of small
cracks located 90 degrees left from the indents (front face), (b) Right image: is an image under low magnification of the
specimen surface within the gage section and between 90- 135 degrees left of the indents.
As for specimen F-19, there were also small 45 degree angle cracks present within the
gage section as shown in Figure 3.57. The arrow in the figure indicates the general location of a
crack composed of several small sections of 45° angle and circumferential cracking.
Figure 3.57: Post-test photograph of specimen F-19 (Test GA-5), with arrows indicating location of circumferential
cracks connected with 45° angle cracks within gage section.
68
3.1.6 Test GA-6: 982
General Test Details: Due to the difficulty in conducting bi-axial experiments at temperatures as
high as 982 very limited literature can be found on the mechanical behavior at such elevated
temperatures. In addition, more focus was oriented towards lower elevated temperatures for
operation. Center coil A provided an appropriate temperature distribution for test temperature
982 after some adjustments to the spacing between the three-set induction coils. Test GA-6
was conducted on specimen F-21 and the experiment control path is shown in Figure 3.58. The
Figure 3.58: Control of axial stress versus shear strain for specimen F-21 (Test GA-6).
axial stress decreased slightly at the higher shear strain values and remained 13.17 – 14.12 MPa.
This small variation is thought to be negligible. Free thermal strain for specimen F-13 reached
0.01537 m/m after 20 minutes of heating. Test parameters are listed in Table 3.6. The intended
cyclic shear strain range was ± 0.00338 radians and the corresponding shear angle of twist range
for each specimen is listed in Table 3.6.
During Test GA-6 of specimen F-21, the angle upper limit interlock of ~7.0 degrees was
tripped and had caused the MPT to stop at cycle 1863. Test GA-6 was also conducted on
specimen F-13 with parameters listed in Table 3.6, with a faster rate of data acquisition. A second
set of indents were made on specimen F-13 and were 7.01 mm to the left of the misaligned first
pair of indents. After 20 minutes of heating, specimen F-21 stabilized with the free thermal strain
as 0.01530 m/m. Hydraulic instability occurred after cycle 1305 and triggered the MPT to stop
the experiment.
69
Table 3.6: Test parameters for Test GA-6.
Test Name GA-6 GA-6 (Repeat)
Specimen F-21 F-13
Axial Stress
Ramp time 13.72 MPa
1.4 sec 13.72 MPa
1.4 sec
Shear Angle of
Twist Range
& Rate
± 0.46687 degrees
0.62249 deg. /sec
0.46692 degrees
0.62256 deg. /sec
Data Acquisition 1 Hz, TPV 10 &20 Hz, TPV
Material Response: Axial strain accumulations during Test GA-6 for two specimens are shown
in Figure 3.59. The measured axial strains prior to the start of shear strain cycling for
Figure 3.59: Axial strain response of Test GA-6 for two specimens.
Specimen F-21 and F-13 were respectively 0.00009 m/m and 0.00012 m/m. The small vertical
line at the end of the axial strain accumulation curve for specimen F-21 corresponds to when
fracture occurred at cycle 1863. As for specimen F-13, the vertical line correlates to when
hydraulic instability occurred. The axial strain accumulation rate for specimen F-13 was slightly
faster than specimen F-21, but these curves are generally agreeable. The accumulated axial strain
values at the end of the tests for specimen F-21 and F-13 were respectively 0.03243 m/m and
0.02711 m/m.
The axial strain accumulation curve for specimen F-13 exhibited a saw tooth pattern, as
seen in Figures 3.60 -3.62. From these figures with axes of similar scaling, it can be observed that
the oscillation in the axial strain curve also included a faster frequency than the shear strain
70
cycling. The frequency of oscillation within the axial strain had decreased with progressive
cycles.
Figure 3.60: Zoom in view of axial strain response of specimen F-13 (Test GA-6) for
cycles 500-550.
Figure 3.61: Zoom in view of axial strain response of specimen F-13 (Test GA-6) for
cycles 1000-1050.
Figure 3.62: Zoom in view of axial strain response of specimen F-13 (Test GA-6) for
cycles 1230 to 1280.
71
Shear stress peak and valley curves are shown for specimens F-21 and F-13. These
curves are also generally agreeable with the initial cyclic softening, which continued with a
longer duration of gradual softening. The wing tips at the end of these curves for both specimens
are due to the influence of a significant crack development outside of the gage section. A
through-wall crack outside of the gage section will require further twisting of the specimen ends
to produce the same shear strain test amplitude within the gage section.
Figure 3.63: Shear stress peak and valleys of the response to Test GA-6 for two specimens.
Hysteresis curves of the shear stress-strain for specimen F-13 (Test GA-6) are shown in
Figure 3.64. The first two cycles of the hysteresis curves exhibit slightly lower shear strain
amplitudes than the other cycles and control of the shear strain improved over time. Tips of the
hysteresis curve reveal that first two cycles reached a slightly less shear strain amplitude than the
other cycles due to the tuning and control that became more consistent with more cycles.
72
Figure 3.64: Shear stress and strain hysteresis for specimen F-13 (Test GA-6), with cycles 1, 2, 5, 10, 20, 50, …1030
shown.
Post Test Observation: Both specimens F-21 and F-13 fractured outside of the gage section,
approximately 8.9 mm below the lower indent, as shown in Figure 3.65 and Figure 3.66. Both
fractures are predominantly circumferential, where both are composed of several short
longitudinal, circumferential and 45° angle cracks spanning part of the circumference of the
specimen.
Figure 3.65: Post-test photograph of specimen F-21 (Test GA-6).
73
Figure 3.66: Post-test photograph of specimen F-13 (Test GA-6).
While the temperature distribution within the gage section was within ±1% of the nominal test
temperature, the location of these fractures suggests additional stresses were induced by the
thermal gradient below the gage section.
3.1.7 Test GA-7: 927 ; Higher Shear Strain Amplitude
General Test Details: An additional Group A and Group B experiment was conducted with
higher shear strain amplitude for 927°C, since Group B exhibited a cyclically stable shear stress
response to the 90° out of phase cycles at elevated temperatures of 871°C and 927°C. The
purpose of increasing the shear strain amplitude to 0.520% is to ascertain whether the slightly
higher strain amplitude would be sufficient to induce cyclic softening or hardening behavior in
test segment (2) of the Group B loading path test at 927°C. The accompanying GA test with the
higher amplitude was conducted on specimen F-15, with test parameters listed in Table 3.7.
After heating for 20 minutes at 927 the free thermal strain had stabilized at 0.01420
m/m. The axial stress was slightly lower at the reversals of the shear strain cycling, due to
coupling of control modes. The axial stress control was drifting between 18.39 and 19.52 MPa,
but the general variation can be considered negligible. The GA-7 loading path was manually
stopped at cycle 1101, because of the increasingly loud unusual hydraulic noise present by the
end of the test.
74
Figure 3.67: Control of axial stress versus shear strain for specimen F-15 (Test GA-7).
Table 3.7: Test parameters for Test GA-7.
Test Name GA-7
Specimen F-15
Axial Stress
Ramp Time
19.03 MPa
1.9 sec
Shear Angle of
Twist Range & Rate
± 0.71826 degrees
0.95768 deg./sec
Data Acquisition 1 Hz, TPV
Material Response: The axial strain accumulation for Test GA-7, the higher shear strain
amplitude 0.0052 radians test with specimen F-15, is shown in Figure 3.68. The axial strain value
prior to shear strain cycling was 0.0001743 m/m. The ratcheting axial strain rate initially
gradually decreased. After cycle 581, the axial strain accumulation was nearly linear. The axial
strain curve for specimen F-11 (Test GA-5), with shear strain amplitude of 0.00398 radians, is
also included in Figure 3.68. As expected, the ratcheting rate was faster for the higher shear strain
amplitude test, when Test GA-5 and Test GA-7 were compared.
75
Figure 3.68: Axial strain response of specimen F-15 for Test GA-7, with shear strain amplitude of
0.0052 radians. The axial strain curve for specimen F-11 (Test GA-5), with shear strain amplitude
of 0.00398 radians, is also included.
Shear stress peak and valley curves for specimen F-15 (Test GA-7) and F-11(Test
Figure 3.69: Shear stress peak and valley curves of specimen F-15 for Test GA-7, with shear strain
amplitude of 0.0052 radians. Curves for specimen F-11 (Test GA-5), with shear strain amplitude
of 0.00398 radians, is also included.
GA-5), respectively with shear strain test amplitudes of 0.0052 radians and 0.00398 radians, are
shown in Figure 3.69. Initial cyclic hardening was present with specimen F-15. The higher shear
strain amplitude test (Test GA-7) resulted in a faster cyclic softening than Test GA-5. The data
acquisition rate of 1 Hz was not sufficient to produce a complete hysteresis shear stress-strain
curves for a three second cycle time.
F-15
F-11
F-15
F-11
76
Post Test Observation: Figure 3.70 shows two photographs of two different regions within the
gage section of specimen F-15. Within the gage section of specimen F-15, there were many small
scattered microcracks, many of which are interconnected.
Figure 3.70: Post-test photograph of specimen F-15 (Test 7), low magnification of the surface within the gage section.
The left image was recorded between 90 to 135 degrees left of the indents & the right hand side image shows the
surface between 135 to 180 degrees left of the indents.
3.1.8 Comparison of Group A (GA) tests
This section focuses on comparing the results of Tests GA-1 to GA-6, which involved
shear strain cycling with constant applied axial stress to induce creep-fatigue-ratcheting. Tests
GA-1 to GA-6 were numbered accordingly in ascending order for the following test temperatures:
23°C, 649°C, 760°C, 871°C, 927°C, 982°C. The applied axial stress was assigned to be equal to
10% of the yield strength corresponding to the 0.2% yield offset strain, which is temperature
dependent. Shear strain amplitudes for the multiaxial experiments were extrapolated from
uniaxial fatigue experimental data, as explained in Chapter 2.
The purpose of Group A experiments was to explore the influence of creep-fatigue-
ratcheting behavior of Haynes 230 via isothermal multiaxial experiments, within a range of 23°C
to 982°C. Resulting accumulation of ratcheting axial strain and stress peak curves are combined
in plots presented in this section.
Axial Strain Accumulation Trends: Specific axial strain values and test summaries for Test
GA-1 to GA-7 are listed in Table 3.8. Free thermal strain refers to the axial strain value after 20
77
Table 3.8: Specific axial strain values and test summary for Group A tests. Test
Name
Specimen
name
Temp.
(°C)
Free
Thermal
Strain (m/m)
Initial
Axial
strain (m/m)
Final
axial
strain (m/m)
Nf
Final
cycle
number
Reason
for
ending
test
GA-1 F-09 23 n/a 0.00022 0.00167 10,898 Stable
response
GA-1* F-03
(Dummy)
23 n/a 0.00023 0.00166 12,551 Stable
response
GA-2 F-16 649 0.00896 0.00019 0.00563 3545 H.I.
MPT
GA-2* F-20 649 0.00897 0.00020 0.00565 4336 Axial
strain
ringing
manual
GA-3 F-18 760 0.01107 0.00018 0.00959 3230 Fracture
GA-4 F-10 871 0.01312 0.00012 0.04592 1933 Heating
Stopped
GA-4* F-14 871 0.01317 0.00013 0.05618 2817 Upper
angle
limit
tripped
GA-5 F-11 927 0.01418 0.00012 0.06511 3509 H.I.
MPT
GA-5* F-19 927 0.01418 0.00014 0.04673 3509 H.I.
MPT
GA-6 F-21 982 0.01530 0.00009 0.03243 1863 H.I.
MPT
GA-6* F-13 982 0.01537 0.00012 0.02711 1305 H.I.
MPT
GA-7 F-15 927 0.01420 0.00017 0.05481 1101 H.I.
noise
manual
*specimens conducted with a data acquisition rate of 20 Hz
H.I. = Hydraulic Instability; by MPT or manually stopping the test.
minutes of heating with axial force and torque set to dwell at zero. Generally, free thermal strain
after 20 minutes of heating were repeatable for the same test temperatures. As expected, higher
test temperatures also resulted in larger free thermal strain. The range of free thermal strain after
20 minutes was 0.00896 m/m to 0.01537 m/m, respectively corresponding to the test temperatures
649°C and 982°C.
Axial strain and shear angle of twist signals were recorded as offset values immediately
prior to the start of each Group A loading path, which occurred after 20 minutes of heating for the
elevated temperature experiments. The column labeled “initial axial strain”, in Table 3.8, refers to
the measured axial strain prior to the start of the shear strain cycling and originated from the axial
stress ramp up. Of the two specimens used for Test GA-1 at room temperature, the highest initial
axial strain value was 0.00023 m/m for specimen F-03. The initial value was 13.9% of final
accumulated axial strain for Test GA-1. However, the elevated temperature tests had produced
78
initial axial strains that were 0.2% to 3.5% percent of the final accumulated axial strain values so
this can be considered negligible.
The room temperature Test GA-1 on specimens F-09 and F-03 were respectively
interrupted at 10,900th and 12,550
th cycle essentially as run-out. Test GA-2 to GA-6 isothermal
experiments ended within 4500 cycles, due to one of the following reasons: hydraulic instability,
unstable axial strain ringing, or via triggered torque and angle detection limit. If the removal of
the specimen did not reveal cracks or a fracture, the specimen was reheated and the test path was
continued. In addition, all Group A experiments were conducted with a second specimen at a
faster data acquisition rate of 20 Hz, with the exception of Test GA-3. Specimens F-16 and F-20
of Test GA-2 had exhibited axial strain ringing, shown as the increasing signal width at end of the
curves. The vertical line at the end of the axial strain accumulation curve for specimen F-18 (Test
GA-3) corresponds to when the specimen fractured. The axial strain accumulation for specimen
F-10 (Test GA-4) was 0.0459 m/m before the thermocouple connection was open and the test was
manually stopped. Specimen F-14 (Test GA-4) was interrupted by hydraulic instability, but was
restarted without visible cracks until the rupture occurred. Specimens F-11 and F-19 of Test GA-
5 were conducted until hydraulic instability occurred. Specimens F-13 and F-21 were used for
Test GA-6 loading path until a sufficient crack network formed outside of the gage section. The
induction coils prevent monitoring of the specimen surface during the test, but some irregularities
with the controls of the strain signals could reflect the influence of the crack formation.
The ratcheting accumulations of the axial strain for Test GA-1 to GA-6 are shown in
Figure 3.71 for the first 4500 cycles. Only the latter cycles of Test GA-1 were not included in
Figure 3.71, but can be found in Figure 3.3. The axial strain accumulation curves were labeled
with the specimen names and were plotted as markers, where the marker color corresponds to the
test temperature indicated by the legend. With Figure 3.72, the complete axial strain accumulation
curves of Tests GA-2 and GA-3 are shown. The horizontal green line overlaid on the axial strain
axis indicates the axial strain values measured prior to the start of shear strain cycling for Tests
GA-1 to GA-3. For higher temperature tests, Tests GA-4 to GA-7, the initial axial strains were
lower than the axial strain indicated by the green horizontal line shown in Figure 3.72.
79
Figure 3.71: Combined plot of axial strain accumulation within first 4500 cycles for Test GA 1 to GA-6, which
involved test temperatures from 23 to 982 .
Figure 3.72: Zoom in view of axial strain accumulation within first 4500 cycles versus number of cycles for general
comparison of response for specimen F-18 (Test GA-3), specimens F-16 and F-20 (Test GA-2).
By the end of each experiment, axial strain accumulation for the lower three temperature tests
(23°C, 649°C, and 760°C) were significantly less than for the higher temperatures and does prove
certain types of dominant ratcheting mechanisms are temperature dependent. A notable trend,
observed within Figure 3.71, is how the nearly constant accumulation rate for these three lower
test temperatures increased with higher temperatures. The steady state was preceded by a
transient state, which involved a faster axial strain accumulation rate that decreased within 50
cycles to the constant rate. The rippling observed in the axial strain curves Test GA-1(23°C) was
not observed in the other tests. Deformation mechanisms governing ratcheting rates for 649°C
(Test GA-2) and 760°C (Test GA-3) should differ from the higher temperatures. Even though
80
ratcheting axial strain accumulation reached less than 0.01 m/m for these two lower elevated
temperatures, each specimen for 649°C had a long longitudinal crack and the specimen for 760°C
had a severe 45° fracture.
While most tests have shown repeatability with two samples, results for Test GA-4
(871°C) and GA-5 (927°C) produced greater variability between specimens. For test temperature
871°C, specimen F-10 had exhibited a faster axial strain accumulation than specimen F-14. The
sinusoidal wave path of the cyclic shear strain for specimen F-10 caused the faster strain
accumulation than the triangular loading wave form for specimen F-14, since the sinusoidal wave
path involved longer durations at the peaks and valleys of the cyclic control path. Starting at the
beginning of the restart for specimen F-14, there was a nearly linear accumulation.
As shown in Figure 3.71, both Test GA-4 (871°C) and GA-5 (927°C) exhibited a
transient period of the axial strain rate gradually decreasing to a constant rate, where the transient
period was longer and had experienced more accumulated ratcheting than the lower temperature
tests. Comparison of the ratcheting axial strain accumulation for experiments with cyclic
triangular loading wave path revealed the transient period for specimen F-14 (871°C) resulted in
a slower accumulation rate than specimen F-19 and F-11 for the higher temperature test at 927°C.
However, the constant rate of the steady-state duration for the restart duration of specimen F-14
and F-10 (871°C) was faster than that of both specimens with test temperature 927°C.
Although Test GA-6 involved the highest test temperature of 982°C, the axial strain
accumulation for specimens F-13 and F-21 were linear and slower than the initial accumulation
observed in specimens tested at a lower temperature of 927°C with Test GA-5. Since experiment
parameters for each test were determined to minimize temperature effects, Test GA-6 cannot be
expected to accumulate at a faster rate than the lower temperature tests. However, if the GA-6
specimens had failed in the gage section, the results would have been different.
Shear stress versus cycle number: The shear stress response for Tests GA-1 to GA-6 had
exhibited different trends involving cyclic stress softening or hardening and the behaviors were
symmetric with respect to shear stress. Only peak values of the shear stress response for Test GA-
1 to GA-6 are shown in Figure 3.73. Shear stress peak curves were plotted as colored markers,
where the test temperatures are indicated by the legend. The similar shear stress responses of a
second specimen were shown in red for experiments excluding test temperature 760°C.
81
Figure 3.73: Combined plot of shear stress peak curves within first 4500 cycles for Test GA 1 to GA-6, which includes
temperatures from 23 to 982 .
Even though the ratcheting axial strain curves slightly varied between specimens for Test
GA-5 and GA-6, the cyclic shear stress response are in agreement. Specimens F-13 and F-21
(Test GA-6), with the highest test temperature of 982°C, are the only tests exhibiting initial cyclic
softening and all others show initial cyclic hardening. Shear stress cyclic softening continued for
both specimens of Test GA-6 until a sufficient fracture below and outside of the gage section
caused a measurement error and the shear stress to suddenly increase. In general, tests with lower
temperatures resulted in higher cyclic shear stress peak curves, with Test GA-2 at 649°C as the
exception. Tests GA-5 and GA-4 show gradual cyclic softening after the initial short duration of
cyclic hardening. At cycle 917, the shear stress peak curve for specimen F-10 (Test GA-4)
showed a sudden decrease, which also corresponded to a jump in the ratcheting axial strain curve.
Following the sudden decrease, there was a slightly faster cyclic softening rate. As for specimen
F-14 (Test GA-4), the sudden increase after cycle 1669 correlated to the initial cyclic hardening
that occurred after hydraulic instability and the reheating of the specimen.
Specimen F-18 (Test GA-3 at 760°C) showed a longer duration of initial cyclic shear
stress hardening than the higher temperature tests and the cyclic hardening rate decreased faster
than the curves for Test GA-2 (at 649°C). The sudden increase at the end of the curve for 760°C
correlated to strain measurement error during fracturing. As a result, the shear stress peak curves
for Test GA-2 intersected the peak curves obtained from Test GA-1, which stabilized within the
first 1500 cycles. Test GA-2 exhibited a greater extent and longer duration of cyclic hardening
than the other tests.
82
Determination of Failure: Table 3.9 lists the causes for the termination of each Group A
Table 3.9. Surface damage of each Group A specimen and reasons for ending each test.
Test
Name
Specimen
name
Temp.
(°C)
Reason
for
ending
test
Surface Damage (with in the gage section, unless noted otherwise)
GA-1 F-09 23 Stable
response
No Fracture
GA-1* F-03
(Dummy)
23 Stable
response
No Fracture
GA-2 F-16 649 H.I.
MPT
Longitudinal crack at least more than 8.94 mm in length and located 45
degrees to the left of indents.
Circumferential crack out of and below gage section at least 7 mm long,
between 45 and 90 degrees left from gage section, appears as white line in
image (other smaller white lines could be small cracks
GA-2* F-20 649 Axial
strain
ringing
manual
Longest longitudinal crack was 9.17 mm and between thermocouple and
lower indent, and connected to a small oval feature. Smaller longitudinal
crack develops slightly to the right.
Circumferential crack 5.16 mm in the middle between the upper indent and
control thermocouple, spanning leftward.
Other cracks not very visible due to discoloration of thin oxide.
GA-3 F-18 760 Fracture 45° angle fracture
(helical extends within and out of gage section)
GA-4 F-10 871 Heating
Stopped
Many small 45° angle cracks, a few scattered circumferential cracks around
the gage section. Largest observable cracks were about 0.96 mm.
GA-4* F-14 871 Upper
angle
limit
tripped
Circumferential fracture with both ends terminated by 45° angle splits, which
extends from 90° to 270° with respect to the indents. Numerous smaller 45°
(x) cracks and longitudinal cracks are located at the lips of the fracture.
GA-5 F-11 927 H.I.
MPT
There were various small 45° angle, circumferential, and longitudinal cracks,
with some connected.
Longest combination of these cracks are located at 225° left of indents and
are at least 5.16 mm.
Other small cracks were mostly isolated throughout the gage section and was
approximately or smaller than 0.71 mm.
GA-5* F-19 927 H.I.
MPT
Numerous crossed (x) 45° cracks of varying length were scattered with a
fewer density of circumferential cracks. They were the most severe between
0 and 90° left of the indents. The longest crossed crack was 3.28 mm, while
the others were at most 1.3 mm within ±90° with respect to the indents.
Small band of crossed (x) 45° angle cracks were located 8.86 mm below the
lower indents and confined to about ±45° with respect to the indents.
GA-6 F-21 982 H.I.
MPT
Circumferential fracture was visible 9.73 mm below the lower indent
(composed of circumferential and longitudinal cracks) extending +45° and -
90° with respect to indents.
No other location exhibited visible cracks.
GA-6* F-13 982 H.I.
MPT
Circumferential fracture was visible 9.35 mm below lower indent (composed
of circumferential and longitudinal cracks) extending about ±90° with
respect to the indents.
No other location exhibited visible cracks.
GA-7 F-15 927 H.I.
noise
manual
Various small 45° angle, circumferential, and longitudinal cracks.
Concentration of the scattered cracks were between 135°to 225° within the
gage section. Span of largest connected crack was 1.73 mm, many others less
than 0.6 mm.
There were 2 small X (connected 45°) about 5.2 mm to the left of 0°.
83
experiment. Details of any surface cracks and fractures are listed with the number of completed
cycles and final total accumulated axial strain for each experiment. The room temperature
experiments with Test GA-1 were conducted to at least 10,000 cycles and interrupted since the
cyclic shear stress and axial strain response were generally showing a stabilized pattern.
Specimens for Test GA-1, F-09 and F03, did not have any cracks or visible deformation.
Hydraulic instability caused the MPT to interrupt Test GA-2 (649°C) for specimen F-16. Since a
long longitudinal crack was present within the gage section, the test was terminated. Another
specimen of Test GA-2, F-20, was manually stopped after the axial strain exhibited progressive
ringing. However, specimen F-20 also exhibited a long longitudinal crack spanning across the
gage section with some additional small circumferential cracks near the control thermocouple.
Specimen F-18 was tested at 760°C as Test GA-3 until a large 45° fracture occurred, which
extended from within to below the gage section. Many small 45° angle, longitudinal and
circumferential cracks were visible for specimens with test temperatures of 871°C and 927°C and
axial strain accumulation between 0.04673 to 0.06511 m/m. These three types of cracks for
871°C and 927°C were generally shorter than the closed longitudinal cracks observed with
649°C. In addition, both experiments at 649°C (Test GA-2) were interrupted at lower
accumulated axial strain than at 871°C and 927°C. The experiments at 927°C resulted in
hydraulic instability and were either stopped manually or by the MPT. However, experiments at
871°C were interrupted due to other reasons. When the control thermocouple of specimen F-10
(Test GA-4) had an open connection, the specimen was no longer being heated at 871°C. In
addition, specimen F-14 had fractured and triggered the upper angle limit, which is a user-setting
of the MPT. Hydraulic instability occurred for both 982°C experiments (Test GA-6), when a
sufficiently large circumferential fracture developed below the lower indent and outside of the
gage section. This fracture occurred for Test GA-6 specimens at lower axial strain accumulation
values than when Test GA-4 and GA-5 were interrupted and resulted with small multi-angle
surface cracks.
ASTM E2207-08 and ASTM 2714-09 had recommended quantifying the amount of
cyclic softening, such as a 5% or 10% stress peak drop from the maximum value, to indicate
when failure occurred. However, the combinations of crack formation and relative degree of
cyclic shear stress softening have varied between tests of different test temperatures. Therefore,
the method for defining when failure occurred should vary with temperature for the Group A
experiments.
84
The maximum value of the shear stress response was recorded along with the
corresponding cycle number for each Group A test in Table 3.10. Generally, each shear stress
Table 3.10. Summary results of axial strain at failure and shear stress softening for Group A tests.
Name
(Test)
Temp
°C
Max.
shear
stress
(MPa)
% drop of Peak Shear stress
(cyclic softening) from
maximum
Minimum
shear
stress
peak
(@cycle)
Reason
for
ending
test
Surface Damage
(with in the gage
section, unless noted
otherwise) 5% 10% 15%
F-09
GA-1
23 270.7
(c56)
257.2
(c4882)
n/a n/a 254.9
(5.8%
c10535)
Stable
response
NF
F-03
GA-1*
23 267.3
(c55)
n/a n/a n/a 254.8
(4.7%
c12437)
Stable
response
NF
F-16
GA-2
649 346.5
(c2931) 329.1
(c3527)
n/a n/a 320.6
(7.4 %
c3544)
H.I.
MPT
Long L. crack
F-20
GA-2*
649 344.8
(c3285) 327.7
(c4324)
n/a n/a 316.9
(8.1%
c4336)
Axial
strain
ringing
manual
Long L. crack, small
circumferential cracks
F-18
GA-3
760 251.3
(c2015) n/a n/a n/a 250.4
(0.4%
c3174)
Fracture 45º angle fracture
(in & out of gage
section)
F-10
GA-4
871 177.5
(c55)
168.1
(c918.9) 159.8
(10%
c1370)
150.9
(15%
c1914)
145.6-
149.4
(16.9%
c1933)
Heating
Stopped
Many small 45º angle
cracks, a few scattered
C. cracks
F-14
GA-4*
871
177.1
(c25)
---------
*179.1
(c1760)
168.245
(c1292)
--------
*170.3
(c2735)
n/a n/a 165.8
(6.4%
c1668) -----------
*170.3
(c2735)
Upper
angle
limit
tripped
Circumferential
fracture with both ends
terminated by 45º
angle splits
F-11
GA-5
927 153.0
(c19.94)
145.4
(c478) 137.7
(10%
c1496)
130.05
(15%
c 2686)
122.2
(20.1%
c3509)
H.I.
MPT
Various 45º angle, C.,
and L. cracks, with
some are connected
F-19
GA-5*
927
150.6
(c17)
143.1
(c865) 135.54
(10%
c2014)
128.01
(15%
c3252)
119
( 21%
c3508)
H.I.
MPT
Small 45º angle and C.
cracks
F-21
GA-6
982 113.9
(c6)
-----------
[120.2
(c1) ]
108.2
(c678.8) 102.51
(10%
c1509)
n/a 102.0
(10.4%
c1760)
H.I.
MPT
Circumferential
fracture below lower
indent (composed of C
and L. cracks)
F-13
GA-6*
982
R
118.8
(c1)
112.9
(c215.8) 106.9
(10%
c1030)
n/a 105.0
(11.6%
c1217)
H.I.
MPT
Circumferential
fracture below lower
indent (composed of
C. and L. cracks)
F-15
GA-7
927 160.9
(c6.9)
152.9
(c370.9) 144.81
(10%
775.8)
136.7
(15%
c1041)
134
(16.7%
c1101)
H.I.
noise
manual
Various small 45º
angle, C. and L cracks.
L = longitudinal, C = circumferential.
peak curve exhibits cyclic stress softening after a maximum value was reached. The minimum
shear stress peak that occurred as a result of cyclic softening from the maximum value was also
85
recorded with a corresponding cycle number designating when it occurred. Only some of these
tests exhibited a 5%, 10%, or 15% drop in shear stress peak values from the maximum values. It
is reasonable to designate the 15% drop in shear stress peak as when failure occurred for most of
the experiments from Test GA-4, GA-5 and GA-7. Except for the specimen F-14 from Test GA-
4, these listed tests exhibited a shear stress drop only slightly more than 15% by the end of the
experiments and had many visible surface cracks. With the highest temperature 982°C, both
specimens exhibited at least a 10% shear stress softening from the maximum value when the
fracture progressed and caused hydraulic instability. However, the fracture occurred outside of
the gage section and the axial strain accumulation was about half of the lower temperature tests at
927°C and 871°C. Since there was a low axial strain accumulation and no cracks were visible
within the gage section for Test GA-7 experiments, the region within the gage section did not
exhibit material failure. Both Test GA-2 and GA-3 exhibited slower ratcheting of the axial strain
and longer duration of initial shear stress cyclic hardening than the higher temperature
experiments. Specimens tested at 649°C as Test GA-2 exhibited a 7.4% to 8.1% shear stress peak
drop from the maximum value before the tests were interrupted. A 5% shear stress peak drop
criteria should be sufficient to designate when the specimens‟ ability to support load decreased
enough to be when failure occurred. However, specimen F-18 (Test GA-3) had unexpectedly
fractured at a relatively low accumulated axial strain of 0.00959 m/m and after a shear stress peak
drop of only 0.4% from the maximum value. Specimen F-18 was an example of how sudden
fracture can occur after very little plastic deformation, which can be a result of operating
conditions or defect in the as-received form.
86
3.2 Group B ( 90° Out of Phase) Loading
Group B experiments consist of three parts: (1) 20 symmetrical axial strain cycles with
triangular wave form, (2) 20 cycles of 90° out-of-phase axial and shear strain cycles with
sinusoidal wave forms, and ending with (3) 5 axial strain cycles with triangular wave form. When
referring to specific cycle numbers of the tests, cycles 1-20 refer to test segment (1), cycles 21-40
refer to segment (2), and cycles 41 – 45 refer to the final segment (3). With test segment (1), the
first cycle started after an initial ramp up to + 0.0030 m/m. Table 3.11 lists the controlled shear
angle of twist range, which was determined for each specimen from the shear strain range values
listed in Table 2.3. Both tables provide the test parameters for Group B, where fixed cycle period
was 160 seconds. The shear angle of twist mode was commanded to dwell at zero for test
segment (1). Only for Test GB-4 (871°C), test segment (1) involved dwelling at zero shear stress.
After the 2nd
part of each test was complete, the shear angle of twist was commanded to dwell at
zero degrees for part 3. The following sections provide general information regarding each Group
B experiment and the axial stress-strain hysteresis loops for test segments (1) and (3). Since the
axial stress and shear stress cyclic response were symmetric, only peak curves of the cyclic shear
stress hardening or softening curves were provided in section 3.2.8. Results from Group B
experiments were intended to enhance the robustness of the developed unified viscoplastic
constitutive model with the incorporation of the highest degree of loading nonproportionality.
Table 3.11. Test Parameters for Group B experiments. Cycle period was fixed at 160 seconds for
all tests.
Test # Specimen
Name
Temp.
(°C)
Axial Strain
Range
Shear
Angle of Twist Range
& Rate
GB-1 F-06 23 ±0.300 %
0.450 %/Min ±0.71843 deg.
1.07760 deg./Min
GB-2 F-17 649 ±0.380 % 0.570 %/Min
±0.90935 deg.
1.3640 deg./Min
GB-3 F-12 760 ±0.320 % 0.480 %/Min
±0.76707 deg.
1.15060 deg./Min
GB-4 F-01 871 ±0.270 % 0.405%/Min
±0.64635 deg.
0.96953 deg./Min
GB-5 F-02 927 ±0.230 % 0.345 %/Min
±0.55060 deg.
0.82590 deg./Min
GB-6 F-04 982 ±0.300 % 0.450 %/Min
±0.46698 deg.
0.70047 deg./Min
GB-7 F-05 927 ±0.195 % 0.2925 %/Min
±0.71834 deg.
1.0077 deg./Min
* rates were determined for cycle time of 160 seconds.
87
3.2.1 Test GB-1: 23°C
General Test Details: Since the temperature for the water supply to the extensometer and collet
grips was cooler than room temperature, the coolant water was not used for Test GB-1. Axial
strain and shear strain signals from timed acquisitioned data are shown in Figure 3.74.
Figure 3.74: Control of axial strain versus shear strain for Test GB-1.
The straight vertical segment in Figure 3.74 corresponded to the control of the cyclic axial strain
with shear strain dwell at zero for test segments (1) and (3). For path segment (2), the 90º out of
phase strain cycling began at the positive axial strain test amplitude of 0.0030 m/m and had traced
the oval in the counter-clockwise direction. The axial and shear stress response due to the
symmetric cyclic strain controls were each nearly symmetric about zero stress. Peak stress curves
of the responses are provided in section 3.2.8.
Axial stress-strain hysteresis loops are plotted as solid blue lines for cycles 1, 10 and 20
of test segment (1) and superimposed with cycles 41 and 45 from test segment (3) as dashed red
lines in Figure 3.75. Axial stress cyclic hardening of 38.5 MPa occurred within the first 20 cycles
88
Figure 3.75: Axial stress-strain hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding to some
axial strain cycles of Test GB-1.
for path segment (1). As a result of the cyclic stress hardening caused by the out-of-phase cycling,
the difference between the maximum axial stress at cycle 20 (segment 1) and cycle 41 (segment
3) was 85.6 MPa. Within the 5 axial strain cycles of path segment (3), cyclic stress hardening of
5.2 MPa had occurred.
Figure 3.76 shows the axial stress-strain response for cycles 21 and 40, which are the
Figure 3.76: Axial stress-strain hysteresis for cycles 21 and 40 (during the 90º out of phase strain cycling segment 2)
and cycle 41 from test segment (3), which involves only axial strain cycles for Test GB-1.
beginning and ending cycle for test segment (2). Cyclic stress hardening of 77.5 MPa occurred
between cycle 21 and 40. Between the path segments (2) and (3), cyclic hardening was also
89
present. Due to the sinusoidal wave form of the 90°axial strain, the reversals of the shear stress-
strain hysteresis were curved. Following immediately after test segment (2) was cycle 41 of
segment (3), which involved triangular wave form of axial strain cycles. Since the sinusoidal
cycling was the prior wave form, the beginning section of the hysteresis curve for cycle 41 had
differed from the hysteresis curves for the remaining cycles of segment (3), which is shown in
Figures 3.75 and 3.76. Both figures showed the cyclic stress hardening present between segments
(1) and (3) were due to the cyclic stress hardening from segment (2). As cyclic stress hardening
occurred, the hysteresis loop generally narrowed.
The shear stress-strain hysteresis loops for Test GB-1 are shown in Figure 3.77. During
Figure 3.77: Shear stress-strain hysteresis loops for Test GB-1.
segment (1), the shear stress and shear strain remained at values close to zero. For the beginning
of the 90° out of phase segment (2), the shear strain was controlled to start cycling in the negative
direction. The resulting shear hysteresis loops were oval-shaped and similar to the axial hysteresis
loops for test segment (2). In addition, cyclic shear stress hardening of 52.1 MPa was observed
between the first and last cycle of segment (2) with Figure 3.77. The cyclic shear stress hardening
was shown with the ends of the oval gradually reaching higher shear stress values.
90
3.2.2 Test GB-2: 649°C
General Test Details: Center coil C and adjustments to the spacing between coil sets resulted
with the proper temperature distribution, which was ± 1% of the nominal test temperature 649°C
within the gage section for Test GB-2. Specimen F-17 was heated at 649°C for 20 minutes, and
the free thermal strain stabilized at 0.0089. Plot of the resulting axial strain versus shear strain
control path is shown in Figure 3.78.
Figure 3.78: Control of axial strain versus shear strain for Test GB-2 (649°C).
The axial stress-strain hysteresis loops are shown as solid lines for cycles 1, 10 and 20 of
test segment (1) in Figure 3.79. By the end of the first 20 axial strain cycles, stress cyclic
hardening of 88.5 MPa had occurred. Superimposed in Figure 3.79 are hysteresis loops of cycles
41 and 45 from test segment (3) as red dashed lines.
Figure 3.79: Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding to some axial
strain cycles of Test GB-2.
91
As a result of the 90° out of phase strain cycling of segment (2), the axial stress-strain curve
exhibited cyclic stress hardening of 148.1 MPa between the end of test segment (1) and the
beginning of segment (3). In addition, the 5 final axial strain cycles of segment (3) resulted in a
smaller degree of cyclic stress hardening of 3.8 MPa. The beginning of the hysteresis loop of
cycle 41 started at a lower axial stress value from the later cycles of segment (3), which was also
present with Test GB-1 and was due to the immediate change from a sinusoidal to a triangular
wave form. The shear stress-strain hysteresis loops for Test GB-2 were similar to those of Test
GB-1 (Figure 3.77). These hysteresis loops were also diagonal oval-shaped hysteresis and the
corresponding cyclic hardening behavior can be deduced from the peak values of the cyclic shear
stress. The peaks of the shear stress for Group B tests are shown in Figures 3.93 and 3.95.
3.2.3 Test GB-3: 760°C
Test Parameters and Observation: For Test GB-3, 20 minutes of heating specimen F-12 at
760°C with center coil B resulted in free thermal strain of 0.01108 m/m. The first attempt of Test
GB-3 on specimen F-12 had triggered the upper limit axial force set by the operator. As a result,
the axial strain value had ramped up to 0.0010 m/m when the MPT had stopped the test. The
upper limit of the axial force was increased accordingly on the MPT. Specimen F-12 was re-
gripped and reheated another 20 minutes at 760°C, where free thermal strain was 0.01040. Figure
3.80 is a plot of the axial and shear strain signal from the timed acquisitioned data. However,
Figure 3.80: Control of axial strain versus shear strain for Test GB-3 (760°C).
92
there was some small variation (±1.6E4 radians) present with the shear strain signal when the
axial strain signal was past ±0.0006 m/m and at the reversals of the cyclic control. Shear strain
variation was not observed with Test GB-2, which had larger axial strain amplitude than Test GB-
3. Variation in the shear strain signal at axial strain reversals were smaller during test segment
(3) than during segment (1), demonstrating better control within these last five axial strain cycles.
For the axial stress-strain hysteresis loops shown in Figure 3.81, blue solid lines indicate
the hysteresis for cycles 1, 10 and 20 from test segment (1). Cycles 41 and 45 from path segment
(3) are shown as red dashed lines.
Figure 3.81: Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding to some axial
strain cycles of Test GB-3.
Figure 3.82: Zoom in view of a section of the axial hysteresis for cycles 1, 20, 41 and 45 of Test GB-3.
93
The nearly horizontal portions of the hysteresis loops during segment (1) were saw tooth shaped
and indicated the axial strain control was not smoothly cycling, as shown in Figure 3.81. Figure
3.82 is a zoom in view of Figure 3.81 and excludes cycle 10. Based on the observed slight
irregularities in the hysteresis loops in Figure 3.82, the axial stress can be concluded to have
exhibited some slight variations to ensure the axial strain would generally cycle according to the
provided test amplitudes and cycle period. Small variation of both axial strain and shear strain
signals from the control path could be due to slight shifting of the extensometer probes within
indents that were large enough to allow this unexpected translation. The slight variation of axial
strain and
Figure 3.83: Axial hysteresis for cycles 21 and 40 of segment (2) for Test GB-3.
stress had decreased for cycle 21, which belongs to segment (2) and was represented as the blue
loop within Figure 3.83. Cycle 40, the last cycle of the 90° out of phase segment (2) and
represented as the red loop in Figure 3.83, did not show any noticeable variation. However, the
test path had continued with cycle 41, of segment (3), where the extent of the variation in the
axial stress-strain hysteresis had decreased compared to cycle 1 and 20 of segment (1). Thus,
segment (2) may have allowed the extensometer probes to settle into the indents more properly
and resulted in less variation in the control.
Cyclic axial stress hardening of 51.2 MPa occurred by the end of segment (1), as a result
of the first 20 axial strain cycles. Due to the out-of-phase cycling segment, comparison of the
axial stress peak for cycle 20 and cycle 41 showed cyclic hardening by 43.9 MPa. Cyclic stress
softening of 15.8 MPa occurred during segment (3) for Test GB-3, while a smaller degree of
cyclic hardening had occurred for segment (3) of Tests GB-1 and GB-2.
94
3.2.4 Test GB-4: 871°C
General Test Details: Center coil A was used to obtain a temperature distribution within ±1% of
the test nominal temperatures 871°C, 927°C, and 982°C. For Test GB-4, after heating specimen
F-01 for 20 minutes, the free thermal strain was 0.0131 m/m. Test GB-4 was the first test
completed from the Group B set of experiments. Figure 3.84 shows a plot of the axial strain and
shear strain, where the shear strain was calculated from the recorded control of shear angle of
twist.
Figure 3.84: Control of axial strain versus shear strain for Test GB-4 (871°C).
Only Test GB-4 had involved the shear stress dwell at zero during the first part of 20 axial strain
cycles. ASTM 2207-08 recommends utilizing shear stress to remain at zero while the axial strain
mode cycled. However, the shear strain was slowly increasing and drifted to 0.82 x 10-3
radians
by the end of segment (1), which was 8.7% of the shear strain test range for segment (2). The
shear strain increase, while the axial strain cycled and shear stress dwelled at zero, demonstrated
the sensitivity to slight misalignment contribution from two sources. Misalignment for the load
train of the Axial-Torsional MTS rig was confirmed to be less than 10%, and thus was within an
acceptable range. Slight misalignment between the extensometer and indents on the specimens
was another source that could have contributed to the accumulative shift of the shear strain as the
axial strain cycled. All other tests conducted after Test GB-4 controlled the shear strain to dwell
at zero during segment (1), to ensure the shear strain would properly cycle 90° out of phase with
the axial strain for segment (2).
In Figure 3.85, the axial stress-strain hysteresis for Test GB-4 is plotted in the same
95
Figure 3.85: Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding to some axial
strain cycles of Test GB-4.
manner as prior GB experiments. Red dashed lines represented cycles 41 and 45 from GB test
segment (3), and cycles 1, 10, 20 were shown as part of segment (1) as blue solid lines. During
test segment (1), the most cyclic softening occurred between the initial ramp up and the first axial
strain cycle. The softening continued very gradually until the end of test segment (1). Thus, there
was an axial stress peak drop of 25.8 MPa between cycle 1 and cycle 20. The most significant
cyclic stress hardening occurred between segment (1) and segment (2), which involved axial
stress cyclic hardening of 40 MPa. Comparing the peak axial stress of cycle 20 and cycle 41,
which respectively corresponded to the beginning of segment (1) and the end of segment (2),
there was an increase of 14.5 MPa due to the 90° out of phase strains cycling. In addition, the
axial stress peaks decreased between segments (2) and (3) and exhibited cyclic axial stress
softening by 9.3 MPa for the rest of segment (3).
3.2.5 Test GB-5: 927°C
General Test Details: With center coil A, the free thermal strain was 0.0141 m/m after 20
minutes of heating specimen F-02. As the second experiment conducted from the Group B test
set, a small timing error with the sequence of the commands caused the MPT program to stop the
loading path after 5 seconds. The heating was not interrupted. Within these 5 seconds, the axial
strain had reached 0.00028 m/m, axial stress increased to 35.8 MPa and shear stress reached -0.8
96
MPa, which were all relatively low values compared to the rest of the test. Without cooling the
specimen, the test was continued with the command correction within 2 minutes. Shear strain was
calculated from the recorded values of the shear angle of twist and plotted with axial strain as
Figure 3.86.
Figure 3.86: Control of axial strain versus shear strain for Test GB-5 (927°C)
Axial stress-strain hysteresis loops are plotted in Figure 3.83 for cycles 1, 10, 20 of test segment
(1) as blue lines. Cycles 41 and 45 for segment (3) are also included in the figure as red
Figure 3.87: Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding to some axial
strain cycles of Test GB-5.
dotted lines. During the initial axial strain ramp up, the axial stress decreased slightly before the
axial strain reached the test amplitude. The hysteresis loops shown from segment (1) and (3), the
97
axial strain cycling, were very similar and did not exhibit a peak stress change equivalent to the
extent of cyclic stress hardening observed with lower temperature Group B experiments. Between
the initial ramp up to axial strain amplitude of + 0.00230 m/m and first cycle of segment (1), axial
stress cyclic softening of 13.2 MPa had occurred. For the rest of segment (1), there was an
additional 3.6 MPa axial stress peak value drop. During the transition between segment (1) and
the 90° out of phase strain cycling segment, the axial stress peak curve showed an increase of
25.9 MPa. The axial stress peak first exhibited cyclic hardening then softening segment (2) and
decreased 19 MPa at the first cycle of segment (3). The axial hysteresis loops within segment (3)
exhibited cyclic axial stress softening of 5.1 MPa. As a result of the 90° out of phase strain
cycles, the difference between the axial stress peak values of cycle 20 and 41 was 6.9 MPa.
3.2.6 Test GB-6: 982°C
General Test Details: After 20 minutes of heating at 982°C, the thermal strain was 0.0151 m/m
for specimen F-05. Figure 3.88 is a plot of the axial strain versus the shear strain, while the axial
and shear stress responses as peak curves were provided in section 3.2.8.
Figure 3.88: Control of axial strain versus shear strain for Test GB-6 (982°C).
Axial stress-strain hysteresis loops for specific cycles are shown in Figure 3.89. Cycles 1, 10, and
20 from the cyclic axial strain segment (1) are represented as blue solid lines. The partially
98
Figure 3.89: Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding to some axial
strain cycles of Test GB-6.
dashed red lines represent cycles 41 and 45 of segment (3). The beginning of cycle 41 was at a
lower axial stress level than the latter cycles, because the material response was recovering from
test segment (2), which had larger oval–shaped hysteresis loops similar to those observed in
Figure 3.76 of Test GB-1. Test GB-6 exhibits the least amount of cyclic stress hardening and
softening compared to lower temperature Group B experiments.
Similar to Test GB-5 (927°C), the axial stress exhibited stress hardening and softening
before the axial strain reached the test amplitude during the first ramp up of test segment (1).
After reaching the axial stress peak value, it softened by 4.4 MPa once the axial strain reached the
amplitude. By the end of segment (1), the axial stress had shown cyclic stress softening of an
additional amount of 3.13 MPa due to the axial strain cycles. Between the end of segment (1) and
beginning of segment (2), the transition from solely axial strain cycles to 90° out of phase cycles
of axial and shear strain, showed cyclic axial stress hardening of 13.32 MPa. The axial stress
peaks remained between 88.4 and 90.4MPa, where there was a slight decrease between the earlier
and latter cycles of test segment (2). However, the extent of cyclic axial stress softening was
significantly smaller than the degree of cyclic axial stress hardening present in Tests GB-1 to GB-
3. After the 90° out of phase strain cycles (segment (2)) were complete, the cyclic axial stress
showed slight cyclic softening of 3.9 MPa with the start of solely axial strain cycles from test
segment (3). The 90° out of phase strain cycling of segment (2), caused the material to exhibit
cyclic axial stress hardening of 13.4 MPa, which was the difference between axial stress peaks
the last cycle of test segment (1) and the first cycle of test segment (3).
99
3.2.7 Test GB-7: 927°C ; higher shear strain amplitude
General Test Details: Axial strain versus shear strain is shown in Figure 3.90. The free thermal
Figure 3.90: Control of axial strain versus shear strain for Test GB-7 (927°C).
strain stabilized at 0.0141 m/m after 20 minutes of heating specimen F-05 at 927°C. During the
preparation procedure prior to the experiment, the top probe of the extensometer was found to be
slightly chipped. The ceramic rod was rotated to a sharper tip and was secured to the
extensometer with the “extensometer-probe” template. The objective of Test GB-7 was to
observe if the designated higher strain amplitude ± 0.00520 radians was sufficient to induce
cyclic hardening or softening for the axial and shear stress responses within test segment (2).
Axial stress-strain hysteresis loops for some of the axial strain cycles are shown in Figure
3.91. Blue lines indicate cycles 1, 10, and 20 from test segment (1) and red dashed lines represent
cycles 41 and 45 from segment (3) for Test GB-7. Results for the same cycle numbers for the
lower strain amplitude test (Test GB-5) are shown as the green hysteresis loops in Figure 3.91.
100
Figure 3.91: Axial hysteresis for cycles 1, 10, 20, 41, and 45, which are curves corresponding to some axial
strain cycles of Test GB-7 (larger strain range). Same cycle numbers from Test GB-5 (smaller strain range) were
plotted in green.
As observed from Figure 3.91, the axial hysteresis between Test GB-5 and larger strain amplitude
Test GB-7 are similar. The larger strain amplitude test resulted in slightly higher stress hardening
than the lower strain amplitude, with a difference of 6 MPa, and also decreased as the initial ramp
up of the axial strain approached the test amplitude. The hysteresis loops of Test GB-7 reached
slightly higher axial stress peak values than Test GB-5.
Disregarding the initial ramp up, the peak values of the cyclic axial stress exhibited a
decrease of 4.6 MPa by the end of the axial strain cycling of test segment (1). The largest extent
of cyclic axial stress hardening was present between the end of test segment (1) and beginning of
segment (2), where there was an increase of 22.8 MPa. From Figure 3.91, the hysteresis loops
between cycles of test segment (1) and (3) were very similar, and did not exhibit the cyclic
hardening present with Tests GB-1 to GB-3 due to segment (2).
101
3.2.8 Comparison of Group B loading type
Since Group B loading paths were composed of three part segments with control modes
involving cycles of axial and shear strain, cyclic stress hardening and softening behavior were
investigated to understand the cyclic deformation that occurs within the range of test
temperatures. Both control and response signals were symmetric about zero. Test segment (1)
involved 20 axial strain cycles with a triangular wave form while the shear angle of twist dwelled
at zero degrees. For test segment (2), the axial and shear angle of twist (or shear strain) were 90°
out-of-phase through 20 cycles with sinusoidal wave forms. Segment (3) involved 5 axial strain
cycles under triangular wave form, while the shear angle of twist was controlled to stay at zero
degrees.
Axial stress peak curves demonstrate cyclic stress hardening, softening, or generally
stable behavior for Tests GB-1 to GB-6 in Figure 3.92. The two vertical solid black lines grouped
Figure 3.92: Combined plots of axial stress peaks for Tests GB-1 to GB-6. These isothermal experiments involved
temperatures from 23 to 982°C with fixed cycle time as 160 seconds.
the axial stress peak values into one of the three test segments for Group B experiments. The
shear stress peak values during test segment (2) are shown in Figure 3.93. The cyclic behavior for
each of the three test segments are summarized for the axial and shear stress responses in Table
102
3.12. Test parameters, maximum axial stress values, maximum shear stress values are also
recorded.
Figure 3.93: Combined plots of shear stress peaks for segment (2) for Tests GB-1 to GB-6. These isothermal
experiments involved temperatures from 23 to 982°C with fixed cycle time as 160 seconds.
Table 3.12. Summary results of axial and shear stress peak responses for Group B experiments.
Test
Specimen
Name
Temp
(°C)
ΔεA
2
(m/m)
0.5Δγc
--------
(rad)
0.5Δγc
(%)
Test
Seg.
(1)
Axial
Stress
Seg.
(2)
Axial
Stress
&
Shear
Stress
Seg.
(3)
Axial
Stress
Maximum
axial stress
(MPa)
Maximum
shear stress
(MPa)
GB-1 F-06 23 0.0030 0.0030 0.0052 H H H 440.4
(P3 @c5)
321
(P2 c20)
298.4
(P2 c20)
GB-2 F-17 649 0.0038 0.0038 0.0066 H H H 456.2
(P3 @c 5)
443.5
(P2 @c20)
332.6
(P2 @c20)
GB-3
F-12 760 0.0032 0.0032 0.0055 H H S 325.4
(P2 @c20)
234.8
(P2 @c20)
GB-4 F-01 871 0.0027 0.0027 0.0046 S H~S S 191.5
(P2 @ c6)
142.1
(P2 @c2)
GB-5 F-02 927 0.0023 0.0023 0.0040 S S~ S 135
(P2
@c7&14)
100.1
(P2 @c3)
GB-6 F-04 982 0.00195 0.00195 0.00338 S S~ S 90.4
(P2 @c2)
66.19
(P2 @c2)
GB-7 F-05 927 0.0030 0.0030 0.0052 S S~
S 137.2
(P2
@c2&4)
100.7
(P2 @c2)
H =cyclic hardening; S = cyclic softening; ~ possibility this behavior
103
According to Figure 3.92, the damage mechanisms associated with the cyclic strain
loading varied between experiments of different temperatures. While the test parameters were
determined to minimize temperature effects, the deformation mechanisms that are active appear
to be temperature dependent. The peak values of the axial stress and shear stress cyclic response
were generally lower for higher test temperatures, except for test temperature 649°C (Test GB-
2), as observed in Figure 3.92. Cyclic axial and shear stress hardening occurred with test segment
(1) and (2) for test temperatures 23°C (Test GB-1), 649°C (Test GB-2), and 760°C (Test GB-3).
The extent of cyclic axial stress hardening for test temperature 649°C was greater than the other
tests of Group B. Within test segment (1), the first 20 axial strain cycles, the axial stress peak
curve for 649°C and 760°C exhibited greater cyclic stress hardening than test temperature 23°C.
However, the deformation mechanisms of the higher test temperatures (871°C, 927°C, and
982°C) contributed in cyclic stress softening during the axial strain cycles of test segment (1).
Within test segment (2), the 90° out of phase cycles of axial strain and shear strain, test
temperature 871°C had exhibited slight cyclic stress hardening and continued with small amount
of cyclic softening with the axial stress peak and shear stress peak curves, in Figure 3.92 and
3.93. The difference between the axial stress peak values for the first and last cycle of test
segment (2) was only 0.4 MPa. The axial and shear stress peak values for the two highest
temperatures (927°C and 982°C) had resulted in cyclic stress softening less than 2 MPa that could
also be considered as generally stable behavior.
After segment (2), the 90° out of phase cycles of axial strain and shear strain, the
specimens of Group B were loaded with 5 additional axial strain cycles, segment (3). As a result
of the out of phase loading, the axial stress peaks of test segment (3) continued at a higher axial
stress value than the peaks of the prior axial strain cycles from segment (1), for all test
temperatures. However, the difference was smaller between the axial stress peak values for the
first cycle of test segment (3) and the last cycle of test segment (1) for the higher three test
temperatures (871°C, 927°C, and 982°C) than the lower temperature experiments. However,
these higher temperature tests also exhibit a smaller degree of change between test segments (1)
and (2). During test segment (3), these three higher test temperatures exhibit cyclic axial stress
softening where the peak values are gradually decreasing to similar values observed at the end of
segment (1). While test temperature 760°C (Test GB-3) were similar to the lower temperatures
during test segments (1) and (2), axial stress cyclic softening occurs during segment (3) at a faster
rate than the higher test temperatures. Due to the out of phase cycles of segment (2), the axial
stress peak values for segment (3) were higher than for segment (1) and (2) for test temperatures
104
23°C and 649°C. In addition, cyclic axial stress hardening was present with the last 5 axial strain
cycles, but at a slower rate than with the earlier axial strain cycles of test segment (1). Thus, the
influence of the 90° out of phase cycles had a more notable change between two test segments of
axial strain cycles for the three lower test temperatures.
During test segment (2), Tests GB-4 to GB-6 resulted in a smaller or no change in cyclic
deformation response when compared with the lower test temperatures. The purpose of Test GB-
7, which was tested at the same temperature as Test GB-5, was to observe if a more significant
cyclic hardening or softening behavior would result with a higher axial and shear strain
amplitudes. The axial stress peaks of Test GB-7 for the three test segments are shown in Figure
3.94, while the peak values of the shear stress from segment (2) are shown in Figure 3.95.
Figure 3.94: Combined plots of axial stress peaks for Tests GB-5 and GB-7, with Test GB-7 conducted at slightly
higher strain amplitudes than GB-5. Both isothermal experiments involved testing at 927°C with fixed cycle period as
160 seconds.
Figure 3.95: Combined plots of shear stress peaks for segment (2) for Tests GB-5 and GB-7, with Test GB-7 conducted
at slightly higher strain amplitudes than GB-5. Both isothermal experiments involved testing at 927°C with fixed cycle
period as 160 seconds.
105
From Figure 3.94, the axial stress peak values for the higher strain amplitude test (Test
GB-7) exhibit cyclic softening at a similar rate as Test GB-5, but were higher than the lower
strain amplitude test by 3.8 to 7.2 MPa. Similar to Test GB-5, Test GB-7 exhibited cyclic
hardening of 22.8 MPa at the transition of segment (1) and (2), the change from axial strain
cycles to the 90° out of phase cycles of axial strain and shear strain. During the 90° out of phase
cycles, the axial stress peaks for the higher strain test were initially higher by 2.7 MPa. By cycle
27, the seventh of segment (2), Test GB-7 exhibited cyclic axial stress softening to similar values
of Test GB-5. Similarly, the shear stress peaks of Test GB-7 were 2.15 MPa higher than the peak
values of Test GB-5 for four of the first five cycles of test segment (2). By the sixth cycle, the
peak values between the two tests nearly coincide and cyclic shear stress softening is more
apparent with Test GB-7 than GB-5. Both experiments resulted in cyclic stress softening for test
segment (3), the final 5 axial strain cycles, with the difference between the axial stress peaks of
the two tests slowly increasing to 2.2 MPa. Both the axial and shear stress cyclic responses
demonstrate a slight change due to a higher applied strain amplitude.
106
Chapter 4
Conclusion and Future Work
4.1 Conclusion
Axial-torsion isothermal experiments were conducted on Haynes 230 through two
different loading path sets. The influence of nonproportionality on the material‟s cyclic stress
hardening (or softening) was investigated for test temperatures: 23°C, 649°C, 760°C, 871°C,
927°C, and 982°C. Group A experiments involved loading with a constant axial stress and cyclic
shear strain to investigate responses involving creep-fatigue and ratcheting behavior. Group A
loading path incorporates a small degree of nonproportionality and were conducted until macro
cracks were observed or hydraulic instability occurred. Group B (GB) loading path involves three
path segments. Segment (1) are 20 axial strain cycles, segment (2) are 20 cycles of axial strain
and shear strain 90° out of phase, and segment (3) are 5 axial strain cycles. The maximum degree
of nonproportionality possible was induced in test segment (2) of GB experiments. Cyclic stress
responses for both test types had differed between higher and lower temperatures. Conclusions
from the resulting mechanical behavior can be summarized as follows:
1. Temperature: Creep-fatigue and progressive ratcheting damage was observed
through the accumulation of axial strain as a function of cycle numbers for Group A
experiments. There were relatively different mechanical responses within the range of
tested temperatures. In general, the ratcheting resulted in a linear axial strain
accumulation rate for 982°C, which was faster than the minimum axial strain rate of
most of the other temperatures. The ratcheting strain for 871°C and 927°C test
temperatures resulted in a short initial duration similar to primary creep, where the
axial strain rate for the 927°C test progressively decreased for more cycles than for
871°C. At these two test temperatures, the axial strain accumulation rate became
constant at a steady-state. It was unusual that the minimum constant axial strain rate for
871°C appeared to be similar to the higher temperature tests at 982°C. In addition, the
steady state rates at 927°C were generally lower than the other two temperatures 871°C
and 982°C. Since the test parameters were established to minimize temperature effects,
107
the ratcheting strain rate was not expected to exhibit large temperature dependence. At
lower temperatures, 760°C and 649°C, axial strain accumulation was significantly
slower than the higher temperature tests before macro-cracks had formed and resulted
in hydraulic instability. Thus, there was a lower ratcheting contribution with the lower
temperatures compared with higher elevated temperatures. However, significant crack
formation and fracture resulted for the 760°C and 649°C test temperatures at
accumulated axial strain values less than 1%, due to the interaction of creep-fatigue
damage mechanisms. At room temperature, fatigue damage is dominant and creep-
ratcheting effects were not expected to be thermally activated.
Just as with the ratcheting axial strain accumulation behavior, the three higher
temperatures (871°C, 927°C, and 982°C) had significantly different shear stress cyclic
curves than the three lower temperatures (23°C, 649°C, and 760°C). Group A test at
982°C was unique compared to the others, where it had exhibited initial softening and
other test temperatures retained initial cyclic hardening. As for the temperatures 649°C
and 760°C, initial shear stress cyclic hardening is more significant than at higher
temperatures.
In the Group B experiments the higher test temperatures resulted in higher cyclic
stress peak values for axial stress and shear stress. Test temperature 649°C was the only
exception, where the cyclic stress hardening extent was more than other tests and
exhibited higher peak values than those of test temperature 23°C. For the three lower
temperatures (23°C, 649°C, and 760°C), the first 20 cycles of axial strain cycles of
Group B test segment (1) resulted in cyclic axial stress hardening. The higher three test
temperatures exhibited small cyclic stress softening for segment (1). With the
additional cycles of test segment (2), axial and shear stress cyclic hardening was more
apparent than the cyclic stress softening of higher temperatures for the 90° out of phase
cycles.
2. Total shear strain amplitude: Test GA-7 and GA-5, involved testing with the same
constant axial stress and test temperature 927°C, where the former used slightly higher
shear strain amplitude than Test GA-5. As expected, the higher shear strain amplitude
resulted in about a two-thirds reduction in creep-fatigue life than the lower shear strain
amplitude test. A faster ratcheting axial strain was observed for the higher test strain
108
amplitude Test GA-7, when compared to the lower amplitude. The lower strain
amplitude exhibited an axial strain accumulation trend similar to a creep curve with a
primary and steady state duration. However, the axial strain accumulation for Test GA-
7 was predominantly linear and exhibited a faster rate of shear stress cyclic softening
than Test GA-5. The faster cyclic shear stress softening for Test GA-7 was because
both tests had a fixed cycle period of 3 seconds. Thus, the shear strain cycling rate was
actually faster for Test GA-7 than GA-5.
Similarly, Test GB-7 included higher axial strain and shear strain test amplitudes than
Test GB-5, but both were conducted at the same test temperature of 927°C. During
segment (1), the axial stress peaks for Test GB-7 were slightly higher than Test GB-5.
The difference in applied amplitudes was sufficient for Test GB-7 to exhibit a more
definite degree of cyclic softening to similar values of Test GB-5, during the 90° out of
phase strain cycles.
3. Failure: For each creep-fatigue-ratcheting Group A experiment, the cause for test
interruption are listed in Table 3.9. The elevated temperature tests were terminated
when the mechanical response indicated a significant change, which was later
associated with cracks. All elevated temperature tests exhibited cyclic shear stress
softening regardless of the initial behavior under the loading path of Group A. This
signified the degradation of the material‟s load carrying capacity due to cyclic plasticity
damage. Failure for Test GB-2 (649°C) can be designated to have occurred with a 5%
cyclic softening, or a decrease in peak shear stress values from the maximum value.
However, Test GB-3 resulted in a 45° fracture extending from within the gage section
to below the lower indent and had only exhibited a 0.4% drop in the shear stress peak
curve from the maximum value. Since the ratcheting axial strain accumulation was
extremely low and below 0.010 m/m and the lower test temperature 649°C had not
resulted in a similar fracture, specimen F-18 of Test GB-3 at 760°C can be considered
an anomaly. A repeat of Test GB-3 could result in a similar damage or types of cracks
with the closer test temperatures 649°C and 871°C. The reheating before continuing
with the Test GA-4 loading path could influence the dislocation and lattice interaction
involved in cyclic softening. All other specimens for test temperatures 871°C, 927°C,
and 982°C have exhibited a peak shear stress drop of at least 10%. The following is a
summary of the surface damage for each temperature test. There were thin lateral
109
cracks at 649°C and no visible cracks at 23°C. At 760°C, the specimen completely
ruptured and separated at a 45° with respect to the longitudinal axis. The specimens
tested at the higher temperatures 871°C and 927°C had multiple angle cracks, with
small longitudinal and small 45 degree angle scattered throughout the gage section. The
specimen at 871°C, whose test had to be restarted after hydraulic instability, resulted in
a large circumferential fracture, which had split on each end into two 45 degree angle
cracks.
4. Loading History: Group A results indicate the creep-fatigue-ratcheting through the
axial strain. For Group B, by comparing the cyclic stress response as a result of the
cycling axial strain segments (1) and (3), the loading history influence of the 90° out of
phase cycles (2) could be explored. Test temperatures 23°C and 649°C exhibited
greater cyclic axial stress hardening between segments (3) and (1). However, the higher
test temperatures (760°C, 871°C, 927°C, and 982°C) showed a smaller degree of axial
stress hardening between (1) and (3). In addition, cyclic axial stress softening occurred
for the rest of segment (3) for the higher temperature tests to axial stress values similar
to segment (1).
Based on these conclusions, the Group A cyclic responses can be generalized into 4
categories where the dominant axial strain ratcheting varied between, (1) 23°C, (2) 649°C and
760°C, (3) 871°C and 927°C, and (4) 982°C. Based on Group B results, with the consideration of
higher non-proportionality loading paths with segment (2), 649°C could be categorized in its own
group. Photographs of fracture and cracks present on the specimen surface have shown the
severity of possible damage. At elevated temperatures many factors influence material failure due
to creep-fatigue and ratcheting contributions, such as temperature, strain amplitude, strain loading
rate, and nonproportionality.
110
4.2 Future Work
There is potential in analyzing the microstructure and fracture modes present with the
crept-fatigued-ratcheted samples, to determine the dominant dislocation mechanisms causing the
range of behaviors exhibited by the varying temperature tests for Haynes 230. Further mechanical
testing would allow further investigations on the influence of strain rate, temperature, strain
amplitudes, mean stresses on the creep-fatigue-ratcheting life and cyclic behavior of the material.
In addition, there is a possibility of using some signal features resulting from propagating
ultrasonic guided waves to be correlated to the localized creep-fatigue and ratcheting damage
within some of these specimens. Attempt in detection of some of these cracks with different
orientation through guided waves would also be an interesting task.
North Carolina State University will use these material responses to further develop a
constitutive model of creep-fatigue-ratcheting behavior of Haynes 230. They will determine the
necessary parameters to produce a more accurate constitutive model to simulate responses and
compare to these experimental results. This will allow a more accurate methodology to predict
the ultimate life of nuclear plant components for Haynes 230 and similar materials, as well as
certain operating conditions that would prolong operational life.
111
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