CREEP-FATIGUE-RATCHETING BEHAVIOR OF HAYNES 230 …

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


3750 to 3800.

43


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

ix

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


2000 to 2050.

49


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


3.32 Zoom in view of axial strain response of restart portion of specimen F-14 (Test

GA-4) for cycles 1700 to 1750.

54



55



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


x

Figure

No.

Page

No.

3.38 Specimen F-10. Small cracks within gage section. 58


3.40 Control of axial stress versus shear strain for specimen F-11 (Test GA-5). 59


3.42 Zoom in view of axial strain response of specimen F-19 (Test Ga-5) for cycles

300 to 350.

61


1950 to 2000.

61


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





3.53 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


xi

Figure

No.

Page

No.




GA-6) for cycles 500-550.

70


GA-6) for cycles 1000-1050.

70


1230 to 1280.

70


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




3.68 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




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




95

3.86 Control of axial strain versus shear strain for Test GB-5 (927°C) 96



96




98



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




3.5 Test parameters for Test GA-5. 59



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


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


* 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.


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.



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.



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


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.


50


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


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.



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


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


Figure 3.34: Zoom in view of axial strain response of restart portion of specimen F-14 (Test GA-4) for


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.


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.


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


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




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

62

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.


63


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.



signal is displayed with an offset of 0.0344 m/m, where y-axis scaling is 0.001 m/m per division.

64



signal is displayed with an offset of 0.0440 m/m and with y-axis scaling as 0.001 m/m per division.



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 3.53: 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°

67

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


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



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


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.


cycles 1000-1050.



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.


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.


73


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



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,


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 3.82: 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.


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



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



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.


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



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


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


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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CREEP-FATIGUE-RATCHETING BEHAVIOR OF HAYNES 230 …