Low-Cycle Fatigue Failure and Ratcheting Responses of Short and Long Radius Elbows at Room and High Temperatures.

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ABSTRACT

FENTON, MATTHEW ALLEN. Low-Cycle Fatigue Failure and Ratcheting Responses of Short and Long Radius Elbows at Room and High Temperatures. (Under the direction of Dr. Tasnim Hassan.)

In order to develop a comprehensive set of fatigue and ratcheting data of pipe elbows,

tests were performed on a set of NPS 2 (Nominal Pipe Size), stainless steel 304L,

schedule 10, 90° elbows. Such elbows are widely used in industries such as nuclear

power generation and chemical manufacturing. Under seismic events or

thermo-mechanical operations, elbow components can experience fatigue and ratcheting

damage. However, despite continued ASME Code design provision updates,

understanding of failures caused by ratcheting damage continues to be elusive,

therefore resulting in significantly conservative and costly designs. This thesis presents

displacement controlled testing results of both long and short radius elbows. In addition

to unpressurized tests, experiments were conducted at the 11.0 MPa (1600 psi) and 20.7

MPa (3000 psi) pressure levels. Force, displacement, change in diameters across the

flanks as well as the intrados and extrados data were collected. Moreover, axial and

circumferential strain gauges were placed at the elbow midsection at the extrados,

flank, and intrados. As high temperature conditions are frequently found in nuclear

power plants, a high temperature test at 350 °C was performed on a long radius elbow

specimen. In addition to the standard forms of strain gauge data acquisition, digital

image correlation was evaluated for strain measurement. The results compared the

effect of pressure on the responses, the effect of the elbow bend radius on the responses,

and the effect of high temperature. Finally, the results were compared with the design

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Low-Cycle Fatigue Failure and Ratcheting Responses of Short and Long Radius Elbows at Room and High Temperatures

by

Matthew Allen Fenton

A thesis submitted to the Graduate Faculty of North Carolina State University

in partial fulfillment of the requirements for the degree of

Master of Science

Civil Engineering

Raleigh, North Carolina

2015

APPROVED BY:

______________________________________ ______________________________________

Dr. Christopher Bobko Dr. Mohammad Pour-Gauz

__________________________________________ Dr. Tasnim Hassan

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ii DEDICATION

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iii BIOGRAPHY

Matthew Fenton attended Purdue University in West Lafayette, Indiana for his

undergraduate study. After having developed an interest in both art and science, he

decided to major in civil engineering, with a focus in structural engineering. While at

Purdue, Matthew had the opportunity to perform undergraduate research at the Bowen

Laboratory, where he assisted on a joint American Institute of Steel Construction and

National Science Foundation project on the structural integrity of gravity frame steel

structures under Prof. Judy Liu. This experience, along with having already completed

concrete graduate design courses prompted him to enroll at North Carolina State

University for a Master of Science in Civil Engineering. Under the guidance of Dr.

Tasnim Hassan, Matthew conducted research experiments on the fatigue failure of

stainless steel elbows, as well as served as a teaching assistant for a couple semesters.

After graduation, Matthew plans to begin a career as a structural engineer and work

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iv ACKNOWLEDGMENTS

I would like to thank my advisor, Dr. Tasnim Hassan for all his guidance throughout

the project. I appreciate his willingness to always answer questions as well as his

constant availability for helping with running tests. Another professor I would like to

thank Dr. Andrew Greishop for his ideas on concepting the cooling system. I would also

like to acknowledge Machel Morrison for his assistance in using the Material Test

System. Finally, I would like to thank Jake Rhoads for his help in constructing various

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v TABLE OF CONTENTS

LIST OF TABLES ... viii

LIST OF FIGURES ... ix

Chapter 1 – Introduction ... 1

1.1 Background ... 1

1.1.1 Pipe Elbows... 2

1.2 Objectives ... 4

1.3 Motivation ... 4

1.4 Scope ... 5

1.5 Organization of Thesis... 5

Chapter 2 – Literature Review ... 6

2.1 Introduction ... 6

2.2 Room Temperature Tests ... 6

2.3 High Temperature Tests ...30

2.4 Summary of Previous Work ...41

Chapter 3 – Room Temperature Experimental Program ...44

3.1 Introduction ...44

3.1.1 Elbow Test Specimens ...44

3.1.2 Experimental Setup ...44

3.1.3 Data Acquisition ...46

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vi

3.2 Short Radius Experimental Results...54

3.2.1 SR1 Results ...54

3.2.2 SR2 Results ...60

3.2.3 SR3 Results ...62

3.2.4 SR4 Results ...64

3.2.5 SR5 Results ...66

3.2.6 SR6 Results ...68

3.2.7 SR7 Results ...70

3.2.8 SR8 Results ...74

3.2.9 SR9 Results ...75

3.2.10 Fatigue Life Results ...75

3.3 Long Radius Experimental Results ...76

3.3.1 LR1 Results ...76

3.3.2 LR2 Results ...78

3.3.3 LR3 Results ...80

3.3.4 LR4 Results ...84

3.3.5 LR5 Results ...86

3.3.6 LR6 Results ...91

3.3.7 LR7 Results ...91

3.3.8 Fatigue Life Results ...92

3.4 Discussion on Short and Long Radius Elbow Results ...93

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vii

3.4.2 Bend Radius Influence Discussion ... 103

Chapter 4 – High Temperature Experimental Program ... 111

4.1.1 Experimental Setup ... 111

4.1.2 Data Acquisition ... 114

4.2 High Temperature Experimental Results... 115

4.2.1 HTLR1 Results ... 116

4.3 Comparison between Room and High Temperature Results ... 121

Chapter 5 – Evaluation of the ASME Code... 124

5.2 ASME BPVC Section III ... 124

5.2.1 Elbow Experimental Results and Code Comparison ... 127

5.3 Bree Diagram ... 128

Chapter 6 – Conclusion ... 131

6.1 Experimental Results ... 131

6.2 Code Analysis Results ... 133

6.3 Future Work ... 133

REFERENCES ... 135

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viii LIST OF TABLES

Table 3.1: Loading parameters for both short and long radius (SR and LR) elbows. ...54

Table 3.2: SR1 elbow thickness and diameter measurements. ...58

Table 3.3: Fatigue lives from the short radius elbow tests. ...76

Table 3.4: Fatigue lives from the long radius elbow tests. ...92

Table 3.5: Summary of fatigue lives of elbow tests. ...94

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ix LIST OF FIGURES

Figure 1.1: Detail of NPS 2 long radius elbow, (a) and short radius elbow, (b) showing

the bend radii of each as well as the actual diameter. ... 3

Figure 2.1: Diagram of Markl's testing frame (Markl, 1952). ... 7

Figure 2.2: Test setup for the elbow specimens (Suzuki & Nasu, 1989)...10

Figure 2.3: In-plane elbow test setup (General Electric Nuclear Energy, 1994). ...13

Figure 2.4: Test specimen and loading frame diagram (Sakai et al., 1995). ...16

Figure 2.5: Test specimens within loading frame (Yahiaoui et al., 1996). ...18

Figure 2.6: Elbow test specimen and setup (Suzuki et al., 2002). ...20

Figure 2.7: Model test specimen and setup (Suzuki et al., 2002). ...21

Figure 2.8: Line diagram of elbow testing setup (Chen et al., 2006). ...23

Figure 2.9: Overview of the test setup (Karamanos et al., 2006). ...25

Figure 2.10: Image of the elbow test setup (Varelis et al., 2013). ...27

Figure 2.11: Image of a pressurized elbow test setup (Varelis & Karamanos, 2014)...29

Figure 2.12: Diagram of the testing frame (Heald & Kiss, 1974). ...32

Figure 2.13: Schematic of the loading frame and test specimen (Imazu et al., 1977). ...35

Figure 2.14: Test frame within a safety tank (Bhandari et al., 1986). ...37

Figure 2.15: Drawing of the elbow test setup (Hilsenkopf et al., 1988). ...38

Figure 2.16: Diagram of test specimen (Ueda et al., 1990). ...40

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x Figure 3.2: Diagram of the pressurization system. ...46 Figure 3.3: (a) shows an image of the ΔD Device while mounted on a test specimen and (b) shows a line detail of the ΔD Device and identifies the individual components. ...48

Figure 3.4: Elbow thickness measurement locations along various (a) planes around (b) cross-sections. ...49

Figure 3.5: (a) DIC camera pointed at the speckle pattern on a test specimen and (b) speckle pattern appearing on screen. ...52

Figure 3.6: SR1 fatigue failure through-wall crack. ...55 Figure 3.7: SR1 responses (a) force-displacement (P-δ) hysteresis loops and (b) peak and valley force responses as a function of cycle number. ...55

Figure 3.8: SR1 change in diameter (ΔD) responses across the (a) flanks (ΔDx) versus displacement and (b) ΔDx versus cycle number and across the (c) intrados-extrados (ΔDy)

versus displacement and (d) ΔDy versus cycle number. ...56

Figure 3.9: SR1 strain responses versus displacement for the (a) flank circumferential strain, (b) flank axial strain, (c) extrados circumferential strain, (d) extrados axial

strain, (e) intrados circumferential strain, and (f) intrados axial strain...57

Figure 3.10: Problem with obtaining intrados thickness measurements for short radius elbows. ...59

Figure 3.11: Abridged SR2 results with (a) load versus displacement, (b) load versus cycle, (c) change in diameter at the flanks versus displacement, (d) change in diameter

at the flanks versus cycle, (e) circumferential strain at the flank versus displacement,

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xi Figure 3.12: SR3 plot showing non-steady pressure. ...62 Figure 3.13: Abridged SR3 results with (a) load versus displacement, (b) load versus cycle, (c) change in diameter at the flanks versus displacement, (d) change in diameter

and (f) axial strain at the flank versus displacement. ...63

and (f) circumferential strain at the other flank versus displacement. ...65

and (f) axial strain at the flank versus displacement. ...67

Figure 3.16: SR6 abridged results with (a) load versus displacement, (b) load versus cycle, (c) change in diameter at the flanks versus displacement, (d) change in diameter

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xii at the flanks versus cycle, (e) circumferential strain at the flank versus displacement,

Figure 3.20: SR8 load versus displacement response. ...74 Figure 3.21: SR9 load versus displacement response. ...75 Figure 3.22: LR1 abridged results with (a) load versus displacement, (b) load versus cycle, (c) change in diameter at the flanks versus displacement, (d) change in diameter

and (f) circumferential strain at the other flank versus displacement (Hassan et al.,

2015). ...77

Figure 3.23: LR2 abridged results with (a) load versus displacement, (b) load versus cycle, (c) change in diameter at the flanks versus displacement, (d) change in diameter

2015). ...79

Figure 3.24: LR3 abridged results with (a) load versus displacement, (b) load versus cycle, (c) change in diameter at the flanks versus displacement, (d) change in diameter

Figure 3.25: LR3re abridged results with (a) load versus displacement, (b) load versus cycle, (c) change in diameter at the flanks versus displacement, (d) change in diameter

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xiii Figure 3.26: LR4 abridged results with (a) load versus displacement, (b) load versus cycle, (c) change in diameter at the flanks versus displacement, (d) change in diameter

2015). ...85

Figure 3.27: LR5 abridged results with (a) load versus displacement, (b) load versus cycle, (c) circumferential strain at the flank versus displacement, and (d) axial strain at the flank versus displacement. ...87

Figure 3.28: DIC tensile peak circumferential strain contour plots (in percent) at the flank for the specified cycles. ...88

Figure 3.29: Cycle 11 tensile peak circumferential strain contour plot with specific points selected. ...89

Figure 3.30: Cycle 11 tensile peak circumferential strain variations along (a) u1-u8 and (b) v1-v5...90

Figure 3.31: DIC and strain gauge comparison for peak tensile circumferential strain values. ...90

Figure 3.32: LR6 load versus displacement response. ...91

Figure 3.33: LR7 load versus displacement response. ...92

Figure 3.34: Influence of pressure on fatigue life. ...95

Figure 3.35: Short radius force responses (a) mean (Pm) and (b) amplitude (Pc). ...96

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xiv Figure 3.37: Short radius circumferential strain responses (a) mean (εmθ) and (b)

amplitude (εaθ). ...98

Figure 3.38: Long radius force responses (a) mean and (b) amplitude. ... 100

Figure 3.39: Long radius change in diameter responses (a) mean and (b) amplitude. 101 Figure 3.40: Long radius circumferential strain responses (a) mean and (b) amplitude. ... 102

Figure 3.41: Load amplitude response comparison between (a) short and (b) long radius elbows. ... 104

Figure 3.42: Load mean response comparison between (a) short and (b) long radius elbows. ... 105

Figure 3.43: Change in diameter amplitude response comparison between (a) short and (b) long radius elbows. ... 106

Figure 3.44: Change in diameter mean response comparison between (a) short and (b) long radius elbows. ... 107

Figure 3.45: Circumferential strain amplitdue response comparison between (a) short and (b) long radius elbows. ... 108

Figure 3.46: Circumferential mean strain response comparison between (a) short and (b) long radius elbows. ... 109

Figure 4.1: Furnace setup around a test specimen. ... 112

Figure 4.2: Diagram of cooling system. ... 113

Figure 4.3: Image of test specimen cooling system. ... 114

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xv Figure 4.5: Determining the fatigue life of HTLR1 through (a) load versus time and (b) load amplitude versus cycle. ... 118

Figure 4.6: HTLR1 responses of (a) load verus displacement and (b) load versus cycle. ... 119

Figure 4.7: HTLR1 cycle 675 DIC circumferential strain. ... 120 Figure 4.8: Long radius elbow comparison between room and high temperature load (a) mean and (b) amplitude. ... 123

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1

Chapter 1 – Introduction

1.1 Background

Piping and its various components make up critical internal systems within industrial

structures such as nuclear power plants and chemical installations. They are used to

transport fluids ranging from room to high temperatures. One particular component

used frequently is the 90° elbow due to the flexibility it grants when designing pipe

systems.

Historically, the 90° elbow has been difficult to properly analyze and model. This arises

due to its complex geometry. While being deformed, the cross-section of the elbow

undergoes ovalization. This ovalization can either stiffen or weaken the elbow

depending on the kind of deformation such as opening or closing, as well as causes high

strain concentrations which increase the probability of failure. The result has led to

overcompensation in the design codes and wasteful overdesigning by engineers (Han, et

al., 2012).

Even with such precautions, piping still experience critical failures at both service levels

due to fatigue and thermal gradients. In a review of fatigue failures in Japanese Light

Water Reactor (LWR) nuclear power plants, service level failures have been observed,

some of which resulted in temporary plant shutdowns (Iida, 1992). The actual reactor

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2 systems, pumps, and valves were the areas that saw failure. Two causes were

ascertained: mechanical-vibration-induced fatigue and thermal-fluctuation-induced

fatigue, with vibration-induced fatigue occurring more often than previously believed

(Iida, 1992). One mechanical-vibration-induced fatigue observed occurred in the splitter

plate of stainless steel of type 316 elbows that were part of the primary coolant system

of a power plant. One thermal-fluctuation-induced fatigue recorded involved a crack at

the butt welded joint between an elbow and a straight pipe which resulted in leakage of

the internal fluid. In the end, even though there was no critical damage to the reactor

structure, a shutdown and expensive repairs were still required (Iida, 1992).

An investigation into seismic damages to industrial facilities from earthquakes ranging

from 1960 to 2000 found that while design codes called for damage caused to the piping

systems of general and high pressure gas manufacturing facilities to be limited to

deformations, many installations had piping systems that had either leakage or

complete fluid stoppage within the pipes. Such failures have triggered new provisions

within the design codes as well as research into more advanced damping systems

(Suzuki K. , 2008).

1.1.1 Pipe Elbows

The pipe elbow consists of two standard types, the long radius elbow and the short

radius elbow. The two types are differentiated by the bend radius, as their names imply.

The long radius elbow has a bend radius of 1.5 times the nominal diameter while the

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3 both a long radius and short radius NPS 2 (Nominal Pipe Size) elbow with a 60.33 mm

outer diameter. The NPS dimensions are a North American standard set of pipe sizes

and were defined by ANSI (American National Standards Institute).

(a) (b)

Figure 1.1: Detail of NPS 2 long radius elbow, (a) and short radius elbow, (b) showing the bend radii of each as well as the actual diameter.

The elbow thicknesses are defined in the ANSI B36.10M for carbon steel and in the

B36.19M for stainless steel. Elbow thicknesses are referred to as schedules, which are

numbers derived from a certain ratio of the service pressure to the allowable stress. For

carbon steel, schedules range from schedule 10 to 160, with many values falling into

categories of thin wall, standard weight, and extra strong. In the case of stainless steel,

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4 Steel pipe elbows are not threaded, and are all welded to straight pipe sections to

comprise pipe systems.

1.2 Objectives

The main objective of this project is to examine the behavior of NPS 2, 304L stainless

steel elbows under in-plane bending and cyclic loading both at room and high

temperatures. Both short and long radius elbows are considered and compared with

each other. In order to accomplish this objective, the following tasks were completed:

a. Room temperature tests were performed on elbows using a uniaxial hydraulic

load system from MTS Systems Corporation.

b. Pressurized room temperature tests were performed on the MTS load system.

c. High temperature testing was conducted on the MTS load system. This included

a design and implementation of a heat sink and water cooling system.

1.3 Motivation

As shown in the following chapter, the mechanisms behind low cycle fatigue failures are

still not well understood. Many investigators are still performing experiments on elbow

specimens in order to derive a comprehensive set of data in order to explain and to be

able to predict behavior of elbows experiencing low-cycle fatigue loading. In addition,

many such experiments are focused on long radius elbows and in almost all cases,

exclusively. This purview is not entirely without just cause, as in fact long radius elbows

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5 are only used when spatial constraints become a concern (Parisher & Rhea, 2002).

However, simply because long radius elbows are the default choice does not mean that

short radius elbows are not used at all. For example, certain designs of nuclear power

reactors can have limitations in their size, and therefore short radius elbows are more

versatile in such a setting (Sakai, Yamamoto, & Hagiwara, 1995). Therefore,

understanding the behavior of short radius elbows is important, and especially in

determining if and when their behavior substantially differs from long radius elbows.

1.4 Scope

The scope of this project covers the preparation and testing of the elbow specimens. The

parameters tested include elbow bend radius, displacement amplitude, internal

pressure, and high temperatures. Previous experimental long radius elbow results

presented by Hassan et al. (2015) are also compared with in this project.

1.5 Organization of Thesis

This thesis is organized into chapters. Chapter one consists of the introduction

including background information and the project objectives. Chapter two contains the

literature review. Chapter three discusses the room temperature tests while chapter

four presents the high temperature tests. Finally, chapter five analyzes the results with

respect to the ASME code and chapter six summarizes the results and conclusions as

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6

Chapter 2 – Literature Review

2.1 Introduction

As the function of the piping systems of industrial structures are critical to their

operation, especially with regard to nuclear or chemical plants, research has been

undertaken to understand the behavior of the components that comprise such systems.

Numerous tests have been performed on the 90° elbow component in order to determine

its behavior. However, many of these tests were done at room temperatures. As the real

world application of these components are at high temperatures, ranging from 200 °C to

350 °C for nuclear facilities and at an even greater variability for chemical installations,

high temperature testing is more important. There have been some high temperature

experiments, but due to the difficulty in performing them the quantity available has not

been very comprehensive.

2.2 Room Temperature Tests

One of the earliest fatigue tests was performed by Markl (1952). Seeing the need for

information on the behavior of piping systems subjected to cyclic bending loads from

thermal expansion or contraction, pressure pulses, and vibrations in order to provide

design data for piping engineers, the Product Engineering and Research Department of

Tube Turns, Inc. initiated a full scale fatigue testing program, conducted by Markl. The

testing program included a variety of piping components including straight pipe,

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7 bends, and more relevantly, elbows. A testing frame was devised such that it could test

both straight pipe specimens and L-shaped specimens in both in-plane and out-of-plane

cyclic bending. One end held specimens rigidly while the other consisted of a hinged end

connected to an actuator. Figure 2.1 shows a line diagram of the testing setup.

Figure 2.1: Diagram of Markl's testing frame (Markl, 1952).

After the tests were performed, S-N (stress versus cycle) diagrams were compiled and

analyzed, as specimens were loaded such that the endurance limit, where a stress

amplitude could be sustained in perpetuity, could be determined for each type of piping

component. However, in the conclusion the author notes that the stresses were

estimates, as they were based on many assumptions. Therefore, a design procedure with

conservative piping stress calculations was proposed for fatigue life determinations

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8 Edmunds and Beer (1961) published a paper on fatigue failure due to ratcheting. The

authors investigated the factor concerning the possibility of taking advantage of strains

greater than yield in high strain fatigue endurance of materials when designing for a

certain life span. Specifically, ratchet failure, or incremental collapse as referred to by

the investigators prevents designers from making use of the endurance of the material

in pressure vessels. While a significant portion of the paper is dedicated to analysis of

both incremental shakedown and incremental collapse, other portions included tests on

piping components that had not been done previously. A relevant test was on short

radius pipe bends. Unlike pipe elbows, pipe bends include the straight pipe sections and

the 90° curve all as one piece. The pipe bends were tested at varying levels of internal

pressure, and with each increase in pressure there was also a corresponding increase in

in-plane bending deflections up to four cycles. Using stress analysis, incremental

collapse limits were calculated. In the conclusion, the authors recommend additional

tests to investigate the assumptions made with the analysis performed (Edmunds &

Beer, 1961).

A large scale room temperature experiment on elbow connections with monotonic

loading was performed by Greenstreet (1978). The investigation was concerned with the

plastic collapse failure mode of elbows, and therefore an experiment into determining

allowable loads was performed. Twenty commercial short and long radius elbows with a

152.4 mm nominal diameter were loaded by external forces and by a combination of

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9 carbon steel and ASTM A-312 type 304L stainless steel and the elbow thicknesses were

either schedule 40 or schedule 80. Dial indicators were used to determine limit loads for

the elbows while strain gages were used for verification purposes and to provide details

on the plastic collapse. The final elbow test specimen was comprised of an elbow butt

welded to 457.2 mm pipes at both ends. One pipe end was fixed and the other end was

connected by a roller support to a hydraulic ram, which applied the loading. Loading

was slowly applied through increasing stepwise increments in either in-plane opening,

closing, or out-of-plane loading. In the cases where internal pressure was applied, a

10.34 MPa pressure was used. Load-deflection curves were obtained for all specimens.

The results showed that for a given elbow with a certain wall thickness, bend radius,

and material under external alone, an in-plane closing type loading will have a smaller

collapse moment than the other two types of loading. In the presence of internal

pressure, the collapse moment is generally increased in all loading cases. While the

primary purpose of the experiments was to determine in-plane and out-of-plane limit

loads, the experiments did yield other secondary results. Carbon steel has a higher

collapse load while the transition from linear behavior to plastic behavior for stainless

steel occurs more quickly. The presence of internal pressure provides a higher collapse

load while quickening the movement from linear response to plastic response for both

steel types. Finally, the ovalization in the elbow geometry remained generally small.

Stainless steel exhibited the greatest ovaling, ranging from 9 to 15% after testing was

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10 Suzuki and Nasu (1989) conducted an experiment on larger diameter butt-welded

elbows, specifically on one 304.8 mm and one 609.6 mm outer diameter long radius 90°

elbows by subjecting them to in-plane monotonic bending. The objective of the

experiment was an early attempt to verify a four-node shell element of the program

ADINA in order to develop an alternative to full scale testing of elbows in order to

determine their behavior and flexibility under earthquake induced ground motions.

Therefore data on load-displacement, strain distributions, and the change of elbow

diameters were collected. The bending tests consisted of setting an elbow test specimen,

which was an elbow welded to two pipes, in a pinned end support configuration which is

shown in Figure 2.2.

Figure 2.2: Test setup for the elbow specimens (Suzuki & Nasu, 1989).

Loading was applied through a hydraulic actuator attached as a hinge at one of the pin

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11 displacement of 130 mm for the 304.8 mm elbow and 240 mm for the 609.6 mm elbow.

The model simulation ultimately showed excellent concurrence with collected data

within the linear elastic range, but the model diverges at the onset of the plastic

response. Maximum strains up to 2% were predicted well. However, the testing and

modeling was only done under monotonic loading, and thus neglects the reverse loading

found in earthquakes. (Suzuki & Nasu, 1989).

In the early 1990s a massive undertaking by the Electric Power Research Institute

(EPRI) and the Nuclear Regulatory Commission (NRC) was performed due to a

prevailing industry concern that the current piping design code was extremely

conservative in seismic and other reverse dynamic loadings in nuclear power piping.

Called the Piping and Fitting Dynamic Reliability Program, the overall project goal was

to determine potential changes to the current code in order to improve piping system

safety and reliability. The investigation was comprised of 41 different piping

components, 24 of which were 152.4 mm nominal pipe size (NPS) elbows. Of the 24, 21

elbows were tested under in-plane bending. Two elbows were tested under high

frequency dynamic loading (water hammer conditions), one elbow was tested under mid

frequency dynamic loading (hydrodynamic input), two more elbows were tested under

static collapse (monotonic opening and closing), but more relevantly the remaining 16

elbows were tested under seismic loading (safe-shutdown earthquake or sine sweep

loading). Both carbon steel and stainless steel elbows were included. The elbow

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12 strong, respectively). The elbows were also subjected to various pressure levels, with

two remaining unpressurized. All but one elbow were long radius, with that particular

elbow being a short radius type. The elbow test specimens consisted of an elbow welded

to two pieces of straight pipe. A flanged end block was welded to the end of one pipe,

which could then be bolted onto the test fixture. The other pipe end was welded to a

flange so that an inertia arm could be bolted. The inertia arm consisted of two pieces of

203.2 mm schedule 80 pipe which was welded together in an L-shape. Weights could

then be added at the top of the inertia arm to control the natural frequency of the test

system and to apply inertial load to the test specimen. A line diagram details the test

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13

Figure 2.3: In-plane elbow test setup (General Electric Nuclear Energy, 1994).

The test fixture itself was mounted on a shake table, where four 11,000 lb hydraulic

actuators could apply dynamic loading. The seismic loading consisted of 7.0 – 7.5 Hz

over 20.48 seconds for the schedule 80 elbows, and 6.3 Hz over 22.76 seconds for most of

the schedule 40 elbows, with a 1.3 Hz over 110.3 seconds for the remaining components.

The failure mode generally observed was fatigue ratcheting. Two tests did not show

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14 to the prevailing understanding at the time, which was that earthquake loading caused

plastic collapse in piping systems (General Electric Nuclear Energy, 1994).

Boussaa et al. (1994) examined three of the dynamic tests performed by EPRI and

performed a fatigue life analysis using first a global approach as detailed by Markl and

a local approach based on local fatigue failure criteria with a proposal from Coffin to

account for ratcheting. Predicting fatigue life under general loading paths was an open

problem, and the additional variables of multiaxiality and amplitude variability with

ratcheting was unexplored at the current time. The investigators attempted to perform

an analysis now that experimental data was available. The three elbow tests selected

from the EPRI experimental program were all 152.4 mm nominal diameter schedule 40

long radius elbows. One elbow was of carbon steel, and the other two were made of

stainless steel. Each elbow was pressurized to 11.7 MPa, 11.7 MPa, and 6.9 MPa,

respectively. An inertia loading sequence was applied on each elbow by a shake table

which lasted 22.7 seconds each. Subsequent sequences were performed until failure of

the elbow, which was the formation of a through-wall crack at either flank was

observed. The results of the global analysis showed some reasonableness in fatigue life

predictions. Although Markl’s equation was developed through tests on 101.6 mm

unpressurized carbon steel specimens, the comparison of the analytical results agreed

well with the pressurized carbon steel experimental results, but had varying results

with the stainless steel elbows. The results of the local approach, however, show a poor

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15 due to the sensitivity of fatigue laws, the uncertainty of material properties has a large

influence on the results. The report concludes that in terms of additional investigation,

the global approach requires a look at the effects of internal pressure and the

differences between the fatigue parameters of carbon and stainless steel. The local

approach requires more data on fatigue-ratcheting interactions as well as a better way

to determine best-fit parameters for short lives (Boussaa et al., 1994).

Sakai et al. (1995) carried out an experiment specifically on a short radius elbow. The

investigators were concerned with the seismic response of short radius elbows due to

their exclusive use in a Demonstration Fast Breeder Reactor (DFBD) as a result of

spatial constraints. As Sakai et al. (1995) were unable to find much dynamic strength

test data, an experiment and static FEM analysis was conducted. The single test

specimen consisted of a short radius stainless steel SUS304 10B schedule 5S 90° elbow

welded to two straight pipes of equivalent material and diameter. The outer diameter of

the model elbow measured 267.4 mm. The test setup consisted of placing the elbow test

specimen in a pinned support configuration, with one end connected to a load cell and

the other end connected to a weight. The entire setup was placed upon a shake table,

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16

Figure 2.4: Test specimen and loading frame diagram (Sakai et al., 1995).

The result of the seismic loading was a through-wall crack failure at both flanks of the

elbow within 82 seconds from the start of excitation. The investigators noted that this

result conflicted with the current understanding at the time, which was that the

traditional failure mode of piping systems under earthquake loading was plastic

collapse. The static FEM analysis investigated a case where the elbow is initially closed,

then opened, and then closed again and another case were was elbow was initially

opened, then closed, and then finally opened. The results showed that the hoop strain

distribution was localized at both flanks, which matched the crack locations. However,

the model underpredicted the maximum load when the model was displaced in the

closing direction, which the authors thought could be caused by a difference of thickness

in the elbow or an effect of material hardening during the manufacturing process of the

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17 An experiment performed by Yahiaoui et al. (1996) focused on the seismic response of

pressurized pipe elbows under in-plane bending. The experiment consisted of eight pairs

of 50.8 mm nominal diameter elbows of both carbon and stainless steel and long and

short radii. Straight pipe of four times the outer elbow diameter in length was welded to

one end of an elbow and pipe of twelve times the outer elbow diameter was welded to

the other end. Each elbow pair was tested simultaneously within a symmetric setup and

pressurized by hand pumped oil to their design pressure. The elbows were placed into

vertical frame capable of applying displacement loading through a hydraulic ram on the

top crosshead to the short pipe ends. Constant force springs were attached to

deadweights located on the free long pipe ends of both specimens. Figure 2.5 gives an

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18

Figure 2.5: Test specimens within loading frame (Yahiaoui et al., 1996).

Each test was performed by subjecting the elbows to a simulated seismic event over a

period of 5 to 20 seconds and then consecutively increasing the input level for

subsequent events until the components reached failure. Due to limitations of the

testing frame, the maximum applied displacements were limited to ±10 mm. The results

showed that the dynamic responses of carbon steel elbows differed dramatically from

the stainless steel elbows. The carbon steel elbows exhibited an elastic-perfectly plastic

behavior while the stainless steel elbows showed a strain-hardening type of behavior.

Cyclic strain accumulation was observed to be greatest in the flank hoop direction

rather than the axial direction. For the short radius elbows, ratcheting was significant

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19 moment were observed, indicating that plastic collapse may not have been the ultimate

governing failure mode. Finally, permanent deformation such as ovalization was not

recorded in any of the tests (Yahiaoui et al., 1996).

A report by Tan et al. (2002) compiled significant experimental research along with

finite element analysis (FEA) of in-plane nonlinear monotonic bending of elbow and pipe

components. The purpose was to determine if FEA models could adequately simulate

the nonlinear behavior of straight pipes and elbows well enough for design purposes. A

summary of percent error between experimental results and model calculations ranged

from 6 – 15% across the six studies reviewed. The report concludes with updated FEA

for both straight pipe and elbows based on a modeling study of 50.8 mm schedule 40

stainless steel elbows and aluminum straight pipe which achieves more accurate results

(Tan et al., 2002).

In the fiscal year of 1998, the Nuclear Power Engineering Corporation (NUPEC) in

Japan decided to initiate a research program investigating the elasto-plastic response

and ultimate strength of the nuclear piping system, the seismic safety margins of the

current design code for piping, and new allowable stress rules. This program came about

due to the remaining technical issues related to the understanding of piping behavior

with plasticity, as seen in research done on the failure modes of ratcheting and collapse.

Suzuki et al. (2002) have reported on a piping component test performed under the

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20 included elbow specimens. The specimens consisted of 216.3 mm diameter schedule 40

elbows welded to two pipe extensions. The material included SUS304TP and STS410(A)

stainless steels. The specimen pipe ends were attached to two pin connections, with one

pin connection connected to a mass on a shake table as shown in Figure 2.6.

Figure 2.6: Elbow test specimen and setup (Suzuki et al., 2002).

Two loading types were performed: a quasi-static loading and a dynamic shaking. The

quasi-static consisted of a deflection controlled sine wave while the dynamic shaking

was an input acceleration control of a seismic wave. The results of the quasi-static cyclic

loading showed that the load-deflection curves of all elbow specimens shifted upwards

with increasing cycles. The hoop strain ratcheted the greatest at the mid flank location,

which was also the location of the through-wall crack failure. In the dynamic shaking

tests, the load-deflection curves shifted to the left with increasing cycles, showing a

permanent increase of deformation in the opening direction. Hoop strains show

ratcheting near the crack, but the axial strains do not. The report also included a test on

a simplified piping model. The model that tested elbow specimens consisted of a center

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21 was then welded to the other ends of the elbows. The model itself was tested with a

shake table under dynamic loading which is shown in Figure 2.7.

Figure 2.7: Model test specimen and setup (Suzuki et al., 2002).

The failure mode of the elbows in the simplified piping system were still fatigue cracks

rather than plastic collapse and buckling. However, axial cracks instead of hoop cracks

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22 While not specifically on elbow components, an experiment performed by Miyazaki et al.

(2002) focused on cyclic loading of the carbon steel pipes that the nuclear industry uses

which are critical to the overall pipe system. The 114.3 mm outer diameter schedule 80

pipes were subjected to local wall thinning in order to simulate corrosion. Two pipes

underwent a load controlled test while four pipes were tested under displacement

control. In the results of the load controlled tests, ductility damage from ratcheting

deformation decreases the fatigue strength of the pipe. For the results of the

displacement controlled test, fracture behavior was not accompanied by ratcheting

deformation, allowing the fatigue strength to be determined by the current fatigue

design curve (Miyazaki et al., 2002).

Chen et al. (2006) conducted an experiment to study the phenomenon of ratcheting in

low carbon steel elbows under reversed bending. The test specimen was composed of a

76 mm low carbon steel #20 (Chinese code GB12459-90) long radius elbow welded to two

pipes of 100 mm in length. The pipe ends were welded to a connecting block which

allowed for a pin connection to the loading bar of the test machine. The test machine,

which is shown in Figure 2.8, consisted of a load cell at one end of the specimen and a

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23

Figure 2.8: Line diagram of elbow testing setup (Chen et al., 2006).

Four elbow specimens were tested under force controlled conditions, at a loading rate of

3 kN/s. Specimen one was tested at an internal pressure of 20 MPa at a peak bending

load of 20 kN for 50 cycles and then at 25 kN for 30 cycles. Specimen two and three were

tested at 20 MPa at 25 kN for 20 cycles and at 30 kN for 50 cycles, respectively. Finally,

specimen four was tested at an internal pressure of 28 MPa at 25 kN for 50 cycles. The

results found that in the case of a bending load with constant internal pressure,

ratcheting occurred at the flank and intrados, but not at the extrados. However,

ratcheting was only recorded at the hoop and 45° strain gauges at those locations, and

not in the axial gauges. In the case of ratcheting under different bending loads at

constant internal pressure, it was observed that the ratcheting rate increases with an

increase in bending load. Next, in the case of the same bending load with differing

internal pressure, the ratcheting rate increased with an increase in internal pressure.

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24 ratcheting rate increased significantly when the loading was increased from 20 kN to 25

kN at the 51st_{cycle of the 80 cycle test. The authors also conducted an analytical study}

of attempting to simulate the ratcheting effect observed in the results by using both the

Ohno-Wang model and the Chen-Jiao-Kim model. The later model was shown to

reasonably simulate the ratcheting response for many of the experimental results but

also did exhibit either under or over prediction in the other results (Chen et al., 2006).

Research by Karamanos et al. (2006) focused on the nonlinear elastic-plastic behavior of

pressurized right angle elbows. While the majority of work was done through FEA

modeling, an experiment was performed to compare with the analytical results. The

experiment consisted of one 160 mm diameter elbow butt welded to two straight pipes.

The elbow was first tested by in-plane and out-of-plane bending within the elastic

region at varying levels of pressure. A schematic of the test setup is shown in Figure

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25

Figure 2.9: Overview of the test setup (Karamanos et al., 2006).

Then, the specimen was pressurized to 0.101 MPa and then loaded into the inelastic

range exceeding the ultimate moment capacity. Numerical results correlate well with

the experimental results, with the predicted maximum load falling within 2% of the

experimental result. Finally, a parametric study was also presented with the intent of

determining the effects of diameter-to-thickness ratios and moderate pressure levels on

the ultimate bending strength of elbows. The study found that the ultimate opening

moment significantly exceeds the ultimate closing moment. Failure during opening is

due to inelastic buckling, with thin-walled elbows buckling more at the flanks.

Pressurization for thin wall elbows provides increased strength and mitigates

ovalization. However, for thick-walled elbows, pressurization causes early yielding and

thus reduces the overall strength of the component. With respect to out-of-plane

bending, ovalization occurs at a 45° direction with respect to the pipe axis due to a state

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26 higher than the capacity for in-plane closing, but far less than the capacity for in-plane

opening (Karamanos et al., 2006).

Takahashi et al. (2010) conducted an experiment of pipe elbows with local wall thinning

using low-cycle fatigue tests. Four 114.3 mm outer diameter carbon steel elbows were

tested, with three of the elbows having a local wall thinning machined at the extrados,

flank, and intrados, respectively, and the final elbow being left sound. The experimental

results showed that the sound elbow had a crack that propagated along the longitudinal

direction at the flank. The extrados thinned specimen was similar to the sound

specimen, with a longitudinal crack at the flank as well. The flank thinned elbow

exhibited a longitudinal crack at the location of the local wall thinning. Finally, the

intrados specimen had a crack initiate at the intrados and then move along the hoop

direction. The investigation then proceeded onto a finite element analysis. When

comparing the cycles to failure between the analysis and experimental results there is

good correlation however the model underpredicts the failure of the intrados thinned

wall (Takahashi et al., 2010).

Experimental work carried out by Varelis et al. (2013) focused on investigating the

low-cycle fatigue of pipe elbows and determining an accurate numerical model for pipe

elbows under severe cyclic in-plane bending, simulating earthquake level loading. The

tests consisted of eight 203.2 mm nominal diameter schedule 40 long radius steel

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27 order to make test specimens. At various points on each elbow specimen, the thickness

of the section was measured. It was found that the thickness could vary by up to over

20% of the nominal thickness of the elbow. The variability was presumed to be caused

by the manufacturing process. The elbow test specimen was placed into a loading frame,

with one end pin connected to the frame and the other pin connected to a hydraulic

actuator. A picture is shown in Figure 2.10.

Figure 2.10: Image of the elbow test setup (Varelis et al., 2013).

The elbows were pressurized with water to less than 0.5% of the yield pressure (0.1

MPa) in order to simply provide an indicator for crack formation in order to determine

fatigue life. The first seven specimens were subjected to constant amplitude end

displacements ranging from ±25 mm to ±300 mm while the eighth experienced a

variable amplitude loading following the European Convention for Constructional

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28 the load-displacement hysteresis loops do not change in shape until failure occurs. At

higher displacements, the loop dramatically shifts away from the initial shape, detailing

structural degradation as the number of cycles increase. The failure mode was a

through-wall crack at the flank midsection for all specimens. The numerical model

developed shows good correlation at lower displacements, but loses some correlation at

higher displacements (Varelis et al., 2013).

Based on the previous experimental work, Varelis and Karamanos (2014) continued to

develop numerical models for steel elbow elastic-plastic behavior under cyclic in-plane

bending. In addition, special attention is given to simulating local strain behavior as

well as the constitutive model for describing the material cyclic behavior of steel. The

ultimate goal remains to create a simple methodology for reliable fatigue design for

steel elbows that fail under low-cycle fatigue. In addition to the previous unpressurized

tests, pressurized elbow tests were conducted in order to capture the influence of

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29

Figure 2.11: Image of a pressurized elbow test setup (Varelis & Karamanos, 2014).

Five elbows were included in the pressure tests, with levels of internal pressure of 12%,

26%, and 45% of the yield stress which corresponds to 3.2 MPa, 7 MPa, and 12 MPa

respectively. Two elbows were pressurized to the 3.2 MPa level, two more at the 7 MPa

level, and the last specimen was pressurized to the 12 MPa level. Pressure was applied

first to the desired level, and then kept constant throughout the cyclic loading. The two

elbows at a pressure level were loaded with one at ±200 mm and the other at ±300 mm.

The elbow tested at 12 MPa was loaded at ±200 mm. The results in comparing the

unpressurized tests with the pressurized tests showed that the presence of internal

pressure generally lowers the fatigue life. In case of the ±300 mm loading, the fatigue

life for both pressurized and unpressurized elbows was 10 cycles. In the numerical

model for fatigue life prediction, the premise was to estimate the local strain at the

critical location (elbow flanks) in order to obtain an estimate for fatigue life based on

Neuber’s equation, which correlates the theoretical elastic stress concentration factor

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30 prediction using the model and comparing to the experimental results show some degree

of accuracy, and is generally conservative. In only one test, which was the elbow

pressurized to 7 MPa and loaded at ±200 mm did the predicted result underpredict the

actual fatigue life (Varelis & Karamanos, 2014).

2.3 High Temperature Tests

Concerned with the current ASME Boiler and Pressure Vessel Code for nuclear power

plants at the time (Section III, Nuclear Power Plant Components), Heald and Kiss

(1974) conducted experiments on 26 piping components commonly used in nuclear

power plants. The ASME BPVC Section III design fatigue curves were based on tests of

small uniaxial tensile specimens, which prompted questions in their use for piping

components. For instance, for the failure of the uniaxial test specimen was the point of

crack initiation, resulting in the cycles to crack initiation being the cycles to failure. In

piping components, those two concepts are decoupled. Piping components can

experience long periods of stable crack growth after the formation of a crack before

actual failure occurs. Therefore, simply exceeding the allowable design cycles does not

mean that an imminent failure is about to occur, but simply that fatigue damage is

steadily increasing with a steadily increasing chance of failure. An experimental

program was performed involving girth butt welds, tees, and more relevantly 152.4 mm

and 228.6 mm diameter long radius elbows. The materials included 304 stainless steel

and carbon steel and the elbow thicknesses were all schedule 40. The fatigue load

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31 with room temperature 152.4 mm diameter elbows also subjected to 7.239 MPa constant

internal pressure. 228.6 mm diameter specimens were tested at a range of 0.6895 –

10.17 or 20 MPa. Out of the 26 piping components, seven elbow specimens were tested

at room temperature, with three 152.4 mm elbows being loading under in-plane bending

at deflections of 548.64 mm, 368.3 mm, and 358.14 respectively. Two 228.6 mm elbows

were given applied deflections of 368.3 mm and 330.2 mm respectively. The elbow tested

at a loading of 358.14 was a carbon steel elbow while the rest were of stainless steel.

The remaining two specimens were tested under out-of-plane loading. Four 152.4 mm

elbow specimens were tested at 287.8 °C with two tested under in-plane bending at

applied deflections of 434.34 mm and 368.3 mm respectively. The elbow loaded at 434.34

mm was made of stainless steel while the elbow loaded at 368.3 mm was of carbon steel.

Elbow test specimens were welded to pipe extensions at their ends. One end of the pipe

extension was fixed to a base plate on a testing frame while the other end of the other

pipe extension was welded to a 6.2484 m pipe that extended to a ram support tower,

which held the hydraulic actuator that applied loading to the pipe. An overview of the

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32

Figure 2.12: Diagram of the testing frame (Heald & Kiss, 1974).

The results of the 152.4 mm elbow room temperature fatigue tests are that the 548.64

mm displacement failed at 907 cycles, 368.3 mm failed at 4469 cycles, and 358.14 mm

failed at 1176 cycles. For the 228.6 mm elbows, the 368.3 mm failed at 3990 cycles and

the 330.2 mm failed at 2531 cycles. The results of the high temperature tests are that

the 434.34 mm failed at 2200 cycles and the 368.3 mm failed at 760 cycles. From the

results, it is clear that stainless steel was far more durable than carbon steel in terms of

fatigue life. The magnitude of the applied displacement also negatively affects fatigue

life, which is expected. Unfortunately, the investigators did not choose directly

comparable tests between room and high temperatures, so it is difficult to draw

conclusions on the effect of temperature. In addition, there was no test that included a

specimen without internal pressure, so the effect of pressure on fatigue life also requires

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33 applicable ASME Section III code was conservative in terms of predicting fatigue life

(Heald & Kiss, 1974).

Another early high temperature test on 90° elbows was undertaken by Griffith and

Rodabaugh (1975). A single 101.6 mm schedule 10 long radius elbow was tested at both

room and at 593.3 °C. Heating was achieved by a 12 Ga. Chromel Heating Element on

12.7 mm Silica Material that was located internally within the welded pipes and elbow.

Twenty-four Chromel-Alumel thermocouples measured the temperature which was

recorded on a 24-point Honeywell strip chart recorder. Both room and high temperature

strain gages were used. The room temperature gauge’s purpose was to record the end

effects of the elbow. The high temperature gauges had a resolution of 1% strain. Tests at

room temperature consisted of applying weights in order to produce pure moment and

strains and displacements were recorded. For the high temperature test, the specimen

was heated to the maximum temperature and then 1.382 kN of weights were applied

over a period of 10 seconds. Strain readings were then recorded twice daily for the

remainder of the test. After 295 hours, the weights were increased by 0.445 kN. The

results of the room temperature tests found that the measured displacements averaged

85% less than the calculated displacements, with the difference being attributed to end

effects. The strain results showed that the highest circumferential strain occurred at the

flanks of the elbow. The measured strain was 80% of the calculated circumferential

strain. The maximum measured longitudinal strain finalized at 36% higher than the

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34 At the high temperature however, it was found that the calculated deflections

significantly overpredict the actual deflections. The same held true for the calculated

strains and the measured strains. An empirical adjustment based on the observed end

effects did, however, bring the calculated results more in line with the measured results

(Griffith & Rodabaugh, 1975).

Imazu et al. (1977) performed a high temperature experiment concerning creep in the

piping systems of Liquid Metal Fast Breeder Reactors (LMFBR). Creep is an important

design consideration, and many computer models and simplified analysis were

developed. However, at that point in time, the authors found that there were few data

on elbows at high temperatures and so conducted this experiment in order to help fill

the gap. The test consisted of a single 304.8 mm schedule 20, 304 stainless steel elbow

pipe assembly loaded under in-plane bending at 600 °C. The elbow specimen was placed

into a loading frame that contained both a furnace for heating the specimen as well as a

weight system to apply constant loading. The furnace heated the test specimen by

circulating heated air through the test specimen. Figure 2.13 shows a diagram of the

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35

Figure 2.13: Schematic of the loading frame and test specimen (Imazu et al., 1977).

For the test procedure, after the specimen reached an average temperature of 600 °C

seven different loadings were successively applied with a hold. The specimen was

unloaded between steps. One displacement transducer was used for large

measurements during loading, unloading, and transient creep stages. A second

displacement transducer recorded small displacement during stationary creep. A load

cell recorded force readings from the top of the specimen and temperature was recorded

by 17 thermocouples. Finally, weldable strain gauges were used to measure strains on

both flanks as well as the midsection between the flank and intrados. Once data was

collected, a finite element model using MARC was compared with the results. The

numerical results had some problems simulating the experimental values. The authors

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36 constitutive equations from the actual one as well as a neglect of the end effects (Imazu

et al., 1977).

Bhandari et al. (1986) performed an experiment on a single 558.8 mm 304L stainless

steel elbow subjected to an initial crack and heated with liquid sodium at 550 °C in

order to simulate actual operating conditions. The purpose of the experiment was to

examine the fracture mechanics of the elbow while undergoing a cyclic test. An overview

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37

Figure 2.14: Test frame within a safety tank (Bhandari et al., 1986).

The initial notches were located on the flanks, with one interior and the other on the

exterior. A static pre-test was performed to check the accuracy of the finite element

model stress calculations before the high temperature test was conducted. The results of

the test showed it took 70,000 cycles for the first sign of crack growth and then another

210,000 cycles before the crack depth was great enough to cause sodium leakage. The

test was ultimately concluded at 290,000 cycles. The outer flaw’s crack development

agreed well with the model’s predictions, however, the inner flaw’s crack development

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38 A study of pipe elbow deformation behavior was conducted by Hilsenkopf et al. (1988) A

comprehensive set of tests were performed on ten ASME SA 106 grade B ferritic steel

elbows and fifteen ASME TP 304L stainless steel elbows consisting of in-plane bending

and out-of-plane bending where some tests included either pressure, preliminary

cycling, or an increased temperature to 120 °C. A diagram of the test setup is shown in

Figure 2.15.

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39 The results of the tests showed that the deformations observed did not impact flow

capacity and that the elbows exhibited high ductility. The preliminary cycling was

shown to decrease elbow strength and quicken the transition from elastic to plastic. The

elevated temperature also decreased elbow strength for in-plane closing and

out-of-plane bending but did not have much effect on in-out-of-plane opening (Hilsenkopf et al.,

1988).

Ueda et al. (1990) was concerned with thermal stress ratcheting, where progressive

deformation can be found in situations of cyclic temperature distribution. The specific

area of focus was in LMFBRs, where liquid sodium is used as the coolant in the primary

and secondary piping systems. However, the investigators noted that while there were

some experiments on straight pipes and bars, there were few experimental works on the

ratcheting behavior of piping elbows. The investigators composed a test of an elbow

specimen in order to observe the ratcheting effect under primary and thermal cyclic

loads. The test specimen was comprised of three 76.2 mm 304 stainless steel long radius

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40

Figure 2.16: Diagram of test specimen (Ueda et al., 1990).

The specimen was then welded to a sodium piping loop. A constant axial load was

applied through a dead weight loader. Thermal loading consisted of cycles of 550 °C

(hot) and 350 °C (cold) sodium flows. The hot and cold flowed for 5 minutes, respectively

and the cycle period was 10 minutes. The tensile axial load was increased in a stepwise

manner with 100 thermal cycles per step. The sodium flow rate was a constant 0.7 m/s.

The test results showed a progressive deformation of the elbow cross section which could

be divided into transient ratcheting behavior followed by a steady state ratcheting

behavior at each axial load level. At the lower axial load levels, however, the transient

ratcheting converged to zero ratcheting after about 15 – 30 cycles. The authors

concluded that the presence of transient ratcheting was due to stress redistribution and

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41

2.4 Summary of Previous Work

A comprehensive history of experimental studies is described here in seriatim. Markl

(1952) published a comprehensive study on the fatigue life of a multitude of piping

components under in-plane and out-of-plane cyclic bending. The ASME design code later

incorporated the results and ultimately formed the basis of many design provisions.

Later, Edmunds and Beer (1961) published a paper on ratcheting and shakedown while

investigating fatigue failure. The next few decades saw studies that focused on specific

areas in piping components. Greenstreet (1978) and Suzuki and Nasu (1989) performed

experiments that examined plastic collapse. Other areas included studies on stress

corrosion failure (NUREG-75/067, 1975) and plastic fatigue analysis (Tagart, 1972,

Rodabaugh & Wood, 1998). Then, in 1990s EPRI (General Electric Nuclear Energy,

1994) undertook a massive experimental program examining fatigue failure of piping

components used in nuclear power plants due to seismic or other dynamic loadings. The

failure mode observed in the tests was fatigue ratcheting, instead of plastic collapse as

written in the earlier ASME design code. Testing performed at around the same time by

other investigators also confirmed the EPRI results by investigating the fatigue

ratcheting failure mechanism (Acker et al., 1992, Yahiaoui et al., 1996). This result

prompted research into code change recommendations (Tagart et al., 1990, Garud et al.,

1993, Chen et al., 1995). In addition, the attention prompted further research (Hwan &

Ranaganth, 1995, Zhao et al., 1995). Boussaa et al. (1994) conducted a review of three

dynamic tests performed at ERPI (1994) and completed a fatigue life analysis as set

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42 radius elbows was carried out by Sakai et al. (1995). The authors noted that the

experiment was necessary at the time because of a lack of data on short radius elbows.

Since the advent of the fatigue ratcheting failure mechanism, research has been ongoing

in order to understand the phenomenon. Suzuki et al. (2002) conducted an experiment

on piping components including elbows in order to devise a simplified piping model. Also

Miyazaki et al. (2002) performed an experiment on a piping system where pipes were

subjected to local wall thinning. Chen et al. (2006) published an experiment specifically

on examining ratcheting in carbon steel elbows. Additionally Karamanos et al. (2006)

focused on producing a finite element model to analyze the nonlinear elastic-plastic

behavior of pressurized elbows. An experiment was performed for comparison.

Takahashi et al. (2010) conducted an experiment on pipe elbows subjected to local wall

thinning under low-cycle fatigue. Experimental work performed by Varelis et al. (2013)

investigated the low-cycle fatigue under various cyclic loadings. This work was recently

continued, where Varelis and Karamanos (2014) conducted pressurized elbow tests in

order to compare with the previous unpressurized tests.

In terms of high temperature tests, the number of experiments conducted are far fewer.

Heald and Kiss (1974) were concerned with the ASME design code with respect to

nuclear power plants and cyclic loading. They carried out an experiment on 26 piping

components that included internal pressure and high temperature. Griffith and

Rodabaugh (1975) performed an experiment on a long radius elbow under high

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43 experiment on a stainless steel elbow with an initial crack and filled with liquid sodium

in order to examine the fracture mechanics during cyclic loading. Hilsenkopf et al.

(1988) executed experiments on 25 elbows that included an elevated temperature level

subjected to in-plane or out-of-plane bending. Finally, Ueda et al. (1990) were concerned

with thermal stress ratcheting in elbows used in LMFBRs. They performed a test on

long radius elbows welded together and connected to a liquid sodium loop.

The review of the literature has shown that there are few experimental studies that

address elbow failure due to low-cycle fatigue, especially with respect to short radius

elbows. Such studies have raised the concern of ratcheting and its effect on the fatigue

life of elbow components. In addition, code committees around the world are revisiting

their respective design codes in order to account for ratcheting. An examination of the

piping elbow studies on the topics of ratcheting, including thermal ratcheting and

shakedown, fatigue failure responses, and constitutive modeling have shown that the

effect is still not suitably predicted by advanced finite element models (Chen et al.,

2013). The literature contains even less experimental data on the behavior of elbows at

high temperatures under low-cycle fatigue. Such data is critical in cases such as nuclear

power plants, as their piping systems will be exposed to elevated temperatures during

normal operation. Without experimental data at those temperatures, it will be difficult