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

Transcription

1 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 (Nominal Pipe Size), stainless steel 3L, schedule 1, 9 elbows. Such elbows are widely used in industries such as nuclear power generation and chemical manufacturing. Under seismic events or thermomechanical 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. MPa (1 psi) and.7 MPa (3 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 35 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 curves of the ASME code.

2 Copyright 1 by Matthew Allen Fenton All Rights Reserved

3 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 15 APPROVED BY: Dr. Christopher Bobko Dr. Mohammad Pour-Gauz Dr. Tasnim Hassan Committee Chair

4 This thesis is dedicated to my family. DEDICATION ii

5 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 towards a PE. iii

6 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 items and for general help around the Mann 1 lab. iv

7 TABLE OF CONTENTS LIST OF TABLES... viii LIST OF FIGURES... ix Chapter 1 Introduction Background Pipe Elbows Objectives Motivation Scope Organization of Thesis... 5 Chapter Literature Review....1 Introduction.... Room Temperature Tests....3 High Temperature Tests...3. Summary of Previous Work...1 Chapter 3 Room Temperature Experimental Program Introduction Elbow Test Specimens Experimental Setup Data Acquisition Experimental Loadings...53 v

8 3. Short Radius Experimental Results SR1 Results SR Results SR3 Results SR Results SR5 Results SR Results SR7 Results SR8 Results SR9 Results Fatigue Life Results Long Radius Experimental Results LR1 Results LR Results LR3 Results LR Results LR5 Results LR Results LR7 Results Fatigue Life Results Discussion on Short and Long Radius Elbow Results Pressure Influence Discussion...9 vi

9 3.. Bend Radius Influence Discussion Chapter High Temperature Experimental Program Introduction Experimental Setup Data Acquisition High Temperature Experimental Results HTLR1 Results Comparison between Room and High Temperature Results Chapter 5 Evaluation of the ASME Code Introduction ASME BPVC Section III Elbow Experimental Results and Code Comparison Bree Diagram Chapter Conclusion Experimental Results Code Analysis Results Future Work REFERENCES APPENDICIES... 1 vii

10 LIST OF TABLES Table 3.1: Loading parameters for both short and long radius (SR and LR) elbows....5 Table 3.: SR1 elbow thickness and diameter measurements Table 3.3: Fatigue lives from the short radius elbow tests....7 Table 3.: Fatigue lives from the long radius elbow tests....9 Table 3.5: Summary of fatigue lives of elbow tests....9 Table.1: Comparison of fatigue lives between room and high temperature tests of long radius elbows viii

11 LIST OF FIGURES Figure 1.1: Detail of NPS long radius elbow, (a) and short radius elbow, (b) showing the bend radii of each as well as the actual diameter Figure.1: Diagram of Markl's testing frame (Markl, 195) Figure.: Test setup for the elbow specimens (Suzuki & Nasu, 1989)...1 Figure.3: In-plane elbow test setup (General Electric Nuclear Energy, 199) Figure.: Test specimen and loading frame diagram (Sakai et al., 1995)....1 Figure.5: Test specimens within loading frame (Yahiaoui et al., 199) Figure.: Elbow test specimen and setup (Suzuki et al., ).... Figure.7: Model test specimen and setup (Suzuki et al., )....1 Figure.8: Line diagram of elbow testing setup (Chen et al., )....3 Figure.9: Overview of the test setup (Karamanos et al., )....5 Figure.1: Image of the elbow test setup (Varelis et al., 13)....7 Figure.11: Image of a pressurized elbow test setup (Varelis & Karamanos, 1)...9 Figure.1: Diagram of the testing frame (Heald & Kiss, 197)....3 Figure.13: Schematic of the loading frame and test specimen (Imazu et al., 1977) Figure.1: Test frame within a safety tank (Bhandari et al., 198) Figure.15: Drawing of the elbow test setup (Hilsenkopf et al., 1988) Figure.1: Diagram of test specimen (Ueda et al., 199).... Figure 3.1: (a) shows a picture of a long radius elbow specimen setup in the MTS and (b) shows a diagram of a long radius elbow specimen with nominal dimensions in millimeters as well as the boundary conditions....5 ix

12 Figure 3.: Diagram of the pressurization system.... 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....8 Figure 3.: Elbow thickness measurement locations along various (a) planes around (b) cross-sections....9 Figure 3.5: (a) DIC camera pointed at the speckle pattern on a test specimen and (b) speckle pattern appearing on screen....5 Figure 3.: SR1 fatigue failure through-wall crack 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 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....5 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 3.1: Problem with obtaining intrados thickness measurements for short radius elbows Figure 3.11: Abridged SR 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, and (f) axial strain at the flank versus displacement....1 x

13 Figure 3.1: SR3 plot showing non-steady pressure.... 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 at the flanks versus cycle, (e) circumferential strain at the flank versus displacement, and (f) axial strain at the flank versus displacement....3 Figure 3.1: Abridged SR 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, and (f) circumferential strain at the other flank versus displacement....5 Figure 3.15: Abridged SR5 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, and (f) axial strain at the flank versus displacement....7 Figure 3.1: SR abridged 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, and (f) circumferential strain at the other flank versus displacement....9 Figure 3.17: SR7 weld failure....7 Figure 3.18: SR7 fatigue failure....7 Figure 3.19: Abridged SR7 results with (a) load versus displacement, (b) load versus cycle, (c) change in diameter at the flanks versus displacement, (d) change in diameter xi

14 at the flanks versus cycle, (e) circumferential strain at the flank versus displacement, and (f) circumferential strain at the other flank versus displacement Figure 3.: SR8 load versus displacement response....7 Figure 3.1: SR9 load versus displacement response Figure 3.: 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 at the flanks versus cycle, (e) circumferential strain at the flank versus displacement, and (f) circumferential strain at the other flank versus displacement (Hassan et al., 15) Figure 3.3: LR abridged 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, and (f) circumferential strain at the other flank versus displacement (Hassan et al., 15) Figure 3.: 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 at the flanks versus cycle, (e) circumferential strain at the flank versus displacement, and (f) circumferential strain at the other flank versus displacement Figure 3.5: 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 at the flanks versus cycle, (e) circumferential strain at the flank versus displacement, and (f) circumferential strain at the other flank versus displacement xii

15 Figure 3.: LR abridged 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, and (f) circumferential strain at the other flank versus displacement (Hassan et al., 15) Figure 3.7: 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 Figure 3.8: DIC tensile peak circumferential strain contour plots (in percent) at the flank for the specified cycles Figure 3.9: 1 tensile peak circumferential strain contour plot with specific points selected Figure 3.3: 1 tensile peak circumferential strain variations along (a) u1-u8 and (b) v1-v5...9 Figure 3.31: DIC and strain gauge comparison for peak tensile circumferential strain values....9 Figure 3.3: LR load versus displacement response Figure 3.33: LR7 load versus displacement response....9 Figure 3.3: Influence of pressure on fatigue life Figure 3.35: Short radius force responses (a) mean (Pm) and (b) amplitude (Pc)....9 Figure 3.3: Short radius change in diameter responses (a) mean (ΔDmx) and (b) amplitude (ΔDax) xiii

16 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 Figure 3.39: Long radius change in diameter responses (a) mean and (b) amplitude. 11 Figure 3.: Long radius circumferential strain responses (a) mean and (b) amplitude Figure 3.1: Load amplitude response comparison between (a) short and (b) long radius elbows Figure 3.: Load mean response comparison between (a) short and (b) long radius elbows Figure 3.3: Change in diameter amplitude response comparison between (a) short and (b) long radius elbows Figure 3.: Change in diameter mean response comparison between (a) short and (b) long radius elbows Figure 3.5: Circumferential strain amplitdue response comparison between (a) short and (b) long radius elbows Figure 3.: Circumferential mean strain response comparison between (a) short and (b) long radius elbows Figure.1: Furnace setup around a test specimen Figure.: Diagram of cooling system Figure.3: Image of test specimen cooling system Figure.: Thermocouple data before and during testing xiv

17 Figure.5: Determining the fatigue life of HTLR1 through (a) load versus time and (b) load amplitude versus cycle Figure.: HTLR1 responses of (a) load verus displacement and (b) load versus cycle Figure.7: HTLR1 cycle 75 DIC circumferential strain Figure.8: Long radius elbow comparison between room and high temperature load (a) mean and (b) amplitude Figure 5.1: Short and long radius design stress fatigue lives (ASME, 13) Figure 5.: Bree diagram of short and long radius experimental results xv

18 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 9 elbow due to the flexibility it grants when designing pipe systems. Historically, the 9 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., 1). 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, 199). The actual reactor structure experienced no failure, instead the supporting elements including the piping 1

19 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, 199). One mechanical-vibration-induced fatigue observed occurred in the splitter plate of stainless steel of type 31 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, 199). An investigation into seismic damages to industrial facilities from earthquakes ranging from 19 to 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., 8) 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 short radius elbow has a bend radius equal to the nominal diameter. Figure 1.1 details

20 both a long radius and short radius NPS (Nominal Pipe Size) elbow with a.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 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 B3.1M for carbon steel and in the B3.19M 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 1 to 1, with many values falling into categories of thin wall, standard weight, and extra strong. In the case of stainless steel, only four schedules are defined: 5, 1,, and 8. 3

21 Steel pipe elbows are not threaded, and are all welded to straight pipe sections to comprise pipe systems. 1. Objectives The main objective of this project is to examine the behavior of NPS, 3L 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 are considered the default elbow when designing piping systems. Short radius elbows

22 are only used when spatial constraints become a concern (Parisher & Rhea, ). 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. 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. (15) 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 well as discusses future work. 5

23 Chapter Literature Review.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 9 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 C to 35 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.. Room Temperature Tests One of the earliest fatigue tests was performed by Markl (195). 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, reducers, forged welding tees, miter bends, fabricated intersections, long radius pipe

24 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.1 shows a line diagram of the testing setup. Figure.1: Diagram of Markl's testing frame (Markl, 195). 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 (Markl, 195). 7

25 Edmunds and Beer (191) 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 9 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, 191). 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 15. mm nominal diameter were loaded by external forces and by a combination of external force and internal pressure. The material included both ASTM A-1 grade B 8

26 carbon steel and ASTM A-31 type 3L stainless steel and the elbow thicknesses were either schedule or schedule 8. 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 57. 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 1.3 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 concluded. (Greenstreet, 1978). 9

27 Suzuki and Nasu (1989) conducted an experiment on larger diameter butt-welded elbows, specifically on one 3.8 mm and one 9. mm outer diameter long radius 9 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.. Figure.: 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 connections of the straight pipe. The loading itself consisted of an in-plane closing 1

28 displacement of 13 mm for the 3.8 mm elbow and mm for the 9. 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 % 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 199s 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 1 different piping components, of which were 15. mm nominal pipe size (NPS) elbows. Of the, 1 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 1 elbows were tested under seismic loading (safe-shutdown earthquake or sine sweep loading). Both carbon steel and stainless steel elbows were included. The elbow thicknesses tested included schedule 1,, and 8 (thin wall, standard, and extra 11

29 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 3. mm schedule 8 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 setup in Figure.3. 1

30 Figure.3: In-plane elbow test setup (General Electric Nuclear Energy, 199). The test fixture itself was mounted on a shake table, where four 11, lb hydraulic actuators could apply dynamic loading. The seismic loading consisted of Hz over.8 seconds for the schedule 8 elbows, and.3 Hz over.7 seconds for most of the schedule elbows, with a 1.3 Hz over 11.3 seconds for the remaining components. The failure mode generally observed was fatigue ratcheting. Two tests did not show signs of failure and one test failed due to ratchet buckling. These results were contrary 13

31 to the prevailing understanding at the time, which was that earthquake loading caused plastic collapse in piping systems (General Electric Nuclear Energy, 199). Boussaa et al. (199) 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 15. mm nominal diameter schedule 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.9 MPa, respectively. An inertia loading sequence was applied on each elbow by a shake table which lasted.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 11. 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 correlation between the analytical and experimental outcomes. The authors reason that 1

32 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., 199). 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 SUS3 1B schedule 5S 9 elbow welded to two straight pipes of equivalent material and diameter. The outer diameter of the model elbow measured 7. 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, which provided the seismic loading as shown in Figure.. 15

33 Figure.: 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 8 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 elbow (Sakai et al., 1995). 1

34 An experiment performed by Yahiaoui et al. (199) focused on the seismic response of pressurized pipe elbows under in-plane bending. The experiment consisted of eight pairs of 5.8 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.5 gives an overview of the test specimens and the test frame. 17

35 Figure.5: Test specimens within loading frame (Yahiaoui et al., 199). Each test was performed by subjecting the elbows to a simulated seismic event over a period of 5 to 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 ±1 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 in the axial direction at the intrados. Most importantly, moments greater than the limit 18

36 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., 199). A report by Tan et al. () 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 15% across the six studies reviewed. The report concludes with updated FEA for both straight pipe and elbows based on a modeling study of 5.8 mm schedule stainless steel elbows and aluminum straight pipe which achieves more accurate results (Tan et al., ). 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. () have reported on a piping component test performed under the program. The component test included tees, nozzles, and reducers, but more relevantly 19

37 included elbow specimens. The specimens consisted of 1.3 mm diameter schedule elbows welded to two pipe extensions. The material included SUS3TP and STS1(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.. Figure.: Elbow test specimen and setup (Suzuki et al., ). 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 pipe with two elbows welded at the ends, facing in the opposite direction. Another pipe

38 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.7. Figure.7: Model test specimen and setup (Suzuki et al., ). 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 formed (Suzuki et al., ). 1

39 While not specifically on elbow components, an experiment performed by Miyazaki et al. () focused on cyclic loading of the carbon steel pipes that the nuclear industry uses which are critical to the overall pipe system. The 11.3 mm outer diameter schedule 8 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., ). Chen et al. () conducted an experiment to study the phenomenon of ratcheting in low carbon steel elbows under reversed bending. The test specimen was composed of a 7 mm low carbon steel # (Chinese code GB159-9) long radius elbow welded to two pipes of 1 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.8, consisted of a load cell at one end of the specimen and a hydraulic actuator at the other which applies the cyclic loading.

40 Figure.8: Line diagram of elbow testing setup (Chen et al., ). 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 MPa at a peak bending load of kn for 5 cycles and then at 5 kn for 3 cycles. Specimen two and three were tested at MPa at 5 kn for cycles and at 3 kn for 5 cycles, respectively. Finally, specimen four was tested at an internal pressure of 8 MPa at 5 kn for 5 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 5 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. Finally, in the last case of a constant internal pressure and a multi-step loading, the 3

41 ratcheting rate increased significantly when the loading was increased from kn to 5 kn at the 51 st cycle of the 8 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., ). Research by Karamanos et al. () 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 1 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.9.

42 Figure.9: Overview of the test setup (Karamanos et al., ). Then, the specimen was pressurized to.11 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 % 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 5 direction with respect to the pipe axis due to a state of stress of a combination of torsion and bending. The ultimate moment capacity is 5

43 higher than the capacity for in-plane closing, but far less than the capacity for in-plane opening (Karamanos et al., ). Takahashi et al. (1) conducted an experiment of pipe elbows with local wall thinning using low-cycle fatigue tests. Four 11.3 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., 1). Experimental work carried out by Varelis et al. (13) focused on investigating the lowcycle 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 3. mm nominal diameter schedule long radius steel elbows. Straight pipes 1.1 m in length have been welded to the ends of each elbow in

44 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 % 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.1. Figure.1: Image of the elbow test setup (Varelis et al., 13). The elbows were pressurized with water to less than.5% of the yield pressure (.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 ±5 mm to ±3 mm while the eighth experienced a variable amplitude loading following the European Convention for Constructional Steelwork recommendations. Experimental results show that for lower displacements, 7

45 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., 13). Based on the previous experimental work, Varelis and Karamanos (1) 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 internal pressure. A picture of the pressurized test setup is shown in Figure.11. 8

46 Figure.11: Image of a pressurized elbow test setup (Varelis & Karamanos, 1). Five elbows were included in the pressure tests, with levels of internal pressure of 1%, %, and 5% of the yield stress which corresponds to 3. MPa, 7 MPa, and 1 MPa respectively. Two elbows were pressurized to the 3. MPa level, two more at the 7 MPa level, and the last specimen was pressurized to the 1 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 ± mm and the other at ±3 mm. The elbow tested at 1 MPa was loaded at ± 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 ±3 mm loading, the fatigue life for both pressurized and unpressurized elbows was 1 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 with the plastic stress and strain concentration factors. The results of the fatigue 9

47 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 ± mm did the predicted result underpredict the actual fatigue life (Varelis & Karamanos, 1)..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 (197) conducted experiments on 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 15. mm and 8. mm diameter long radius elbows. The materials included 3 stainless steel and carbon steel and the elbow thicknesses were all schedule. The fatigue load consisted of cyclic deflection controlled bending at both room temperature and 87.8 C, 3

48 with room temperature 15. mm diameter elbows also subjected to 7.39 MPa constant internal pressure. 8. mm diameter specimens were tested at a range of or MPa. Out of the piping components, seven elbow specimens were tested at room temperature, with three 15. mm elbows being loading under in-plane bending at deflections of 58. mm, 38.3 mm, and respectively. Two 8. mm elbows were given applied deflections of 38.3 mm and 33. mm respectively. The elbow tested at a loading of was a carbon steel elbow while the rest were of stainless steel. The remaining two specimens were tested under out-of-plane loading. Four 15. mm elbow specimens were tested at 87.8 C with two tested under in-plane bending at applied deflections of 3.3 mm and 38.3 mm respectively. The elbow loaded at 3.3 mm was made of stainless steel while the elbow loaded at 38.3 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.8 m pipe that extended to a ram support tower, which held the hydraulic actuator that applied loading to the pipe. An overview of the testing frame with a sample pipe test specimen is shown in Figure.1. 31

49 Figure.1: Diagram of the testing frame (Heald & Kiss, 197). The results of the 15. mm elbow room temperature fatigue tests are that the 58. mm displacement failed at 97 cycles, 38.3 mm failed at 9 cycles, and mm failed at 117 cycles. For the 8. mm elbows, the 38.3 mm failed at 399 cycles and the 33. mm failed at 531 cycles. The results of the high temperature tests are that the 3.3 mm failed at cycles and the 38.3 mm failed at 7 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 more tests. As to the primary goal of the study, the investigators concluded that the 3

50 applicable ASME Section III code was conservative in terms of predicting fatigue life (Heald & Kiss, 197). Another early high temperature test on 9 elbows was undertaken by Griffith and Rodabaugh (1975). A single 11. mm schedule 1 long radius elbow was tested at both room and at C. Heating was achieved by a 1 Ga. Chromel Heating Element on 1.7 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 -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 1.38 kn of weights were applied over a period of 1 seconds. Strain readings were then recorded twice daily for the remainder of the test. After 95 hours, the weights were increased by.5 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 8% of the calculated circumferential strain. The maximum measured longitudinal strain finalized at 3% higher than the calculated strain. These differences were attributed to the non-uniform wall thickness. 33

51 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 3.8 mm schedule, 3 stainless steel elbow pipe assembly loaded under in-plane bending at 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.13 shows a diagram of the test specimen and testing frame. 3

52 Figure.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 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 have proposed the reasons behind the discrepancy as being from a deviation of 35

53 constitutive equations from the actual one as well as a neglect of the end effects (Imazu et al., 1977). Bhandari et al. (198) performed an experiment on a single mm 3L stainless steel elbow subjected to an initial crack and heated with liquid sodium at 55 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 of the testing frame within a protective tank is shown in Figure.1. 3

54 Figure.1: Test frame within a safety tank (Bhandari et al., 198). 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 7, cycles for the first sign of crack growth and then another 1, cycles before the crack depth was great enough to cause sodium leakage. The test was ultimately concluded at 9, cycles. The outer flaw s crack development agreed well with the model s predictions, however, the inner flaw s crack development proved to be hard to predict (Bhandari et al., 198). 37

55 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 1 grade B ferritic steel elbows and fifteen ASME TP 3L 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 1 C. A diagram of the test setup is shown in Figure.15. Figure.15: Drawing of the elbow test setup (Hilsenkopf et al., 1988). 38

56 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-ofplane bending but did not have much effect on in-plane opening (Hilsenkopf et al., 1988). Ueda et al. (199) 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 7. mm 3 stainless steel long radius elbows welded together into a U-shape which is shown in Figure.1. 39

57 Figure.1: Diagram of test specimen (Ueda et al., 199). 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 55 C (hot) and 35 C (cold) sodium flows. The hot and cold flowed for 5 minutes, respectively and the cycle period was 1 minutes. The tensile axial load was increased in a stepwise manner with 1 thermal cycles per step. The sodium flow rate was a constant.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 3 cycles. The authors concluded that the presence of transient ratcheting was due to stress redistribution and work-hardening of the elbow (Ueda et al., 199).

58 . Summary of Previous Work A comprehensive history of experimental studies is described here in seriatim. Markl (195) 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 (191) 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-75/7, 1975) and plastic fatigue analysis (Tagart, 197, Rodabaugh & Wood, 1998). Then, in 199s EPRI (General Electric Nuclear Energy, 199) 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., 199, Yahiaoui et al., 199). This result prompted research into code change recommendations (Tagart et al., 199, 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. (199) conducted a review of three dynamic tests performed at ERPI (199) and completed a fatigue life analysis as set forth by Markl (195). One of the first experiments that focused exclusively on short 1

59 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. () conducted an experiment on piping components including elbows in order to devise a simplified piping model. Also Miyazaki et al. () performed an experiment on a piping system where pipes were subjected to local wall thinning. Chen et al. () published an experiment specifically on examining ratcheting in carbon steel elbows. Additionally Karamanos et al. () 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. (1) conducted an experiment on pipe elbows subjected to local wall thinning under low-cycle fatigue. Experimental work performed by Varelis et al. (13) investigated the low-cycle fatigue under various cyclic loadings. This work was recently continued, where Varelis and Karamanos (1) 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 (197) were concerned with the ASME design code with respect to nuclear power plants and cyclic loading. They carried out an experiment on piping components that included internal pressure and high temperature. Griffith and Rodabaugh (1975) performed an experiment on a long radius elbow under high temperature and loaded over time. Later, Bhandari et al. (198) conducted an

60 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 5 elbows that included an elevated temperature level subjected to in-plane or out-of-plane bending. Finally, Ueda et al. (199) 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., 13). 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 to verify models created using data obtained at room temperatures. 3

61 Chapter 3 Room Temperature Experimental Program 3.1 Introduction This chapter describes the room temperature tests that were conducted in this study. This chapter covers the experimental design and materials used as well as presents the test results Elbow Test Specimens The experiments were performed on 3L stainless steel elbow specimens as shown in Figure 3.1. Each specimen consisted of a NPS (.33 mm outer diameter), schedule 1, 9 degree elbows. Both long and short radius elbows were used. The elbows were buttwelded to 5 mm nominal length straight pipes of the same material as the elbows. The straight pipe ends were welded to end blocks, which allowed for the specimen to be pressurized. The end blocks were designed to act as a pin connection for the specimen Experimental Setup The top end block of the elbow specimen was pin connected to the load cell on the cross bar of the MTS frame. The bottom end block was connected by pin connection to the hydraulic actuator through which the displacement controlled loading was applied. Figure 3.1 shows both an image of a long radius test specimen setup in the MTS as well as a line detail of a test specimen that also displays the boundary conditions and gives

62 nominal measurements in millimeters. The short radius specimens were setup similarly. (a) (b) Figure 3.1: (a) shows a picture of a long radius elbow specimen setup in the MTS and (b) shows a diagram of a long radius elbow specimen with nominal dimensions in millimeters as well as the boundary conditions. In order to provide for crack detection and pressurized states, hydraulic oil was pumped through the end blocks with the use of a pneumatic pump. Constant pressure was maintained during cycling through the use of a hydraulic accumulator. Figure 3. gives an overview of the pressurization system. 5

63 Figure 3.: Diagram of the pressurization system Data Acquisition A National Instruments CompactDAQ with two NI 937 modules and one NI 95 module was used to obtain strain, internal pressure, load, displacement, and change in diameter data. The NI 937 modules acquired data from the strain gauges placed around the elbow specimens. Strain gauges were supplied from Tokyo Sokki Kenkyujo Co., Ltd. and consisted of 1 Ohm quarter bridge gauges with a mm gauge length.

64 Gauges were placed to measure both axial and circumferential strains at the intrados, flank, and extrados. A NI 937 module also recorded data from a Sensotec pressure transducer (Sensotec has since been purchased by Honeywell) during pressure tests. One unfortunate aspect of the pressure transducer was that it prohibited the use of the other remaining channels of the module it was connected to. This affected the quantity of strain gauges available for use on the pressurized test specimens. An additional module was purchased to rectify the problem, but was only received in time for a few remaining tests, after a majority of the testing was completed. The NI 95 module recorded data from the MTS load cell and displacement gauge. In the case of the displacement gauge, positive values were recorded when the hydraulic actuator moved down (elbow opening mode), and negative values were recorded when the actuator moved up (elbow closing mode). In addition, the module recorded data from LVDTs (Linear Variable Differential Transformer) that were used to measure change in diameter across the elbow cross-section. Four LVDTs were placed in a rigid polymer ring that could be fixed around the circumference of an elbow specimen s cross-section through the use of spring loaded screws and felt pads, and a picture and diagram of the contraption, referred to as the ΔD Device, is shown in Figure

65 (a) (b) 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. Two LVDTs were located at the flanks of the elbow and the other two were located at the intrados and extrados. This allowed for the cross-sectional diameter change to be measured across these two axes. A GE (General Electric) DM5E wall thickness gauge coupled with a Model DA51 ultrasonic probe was used to measure the wall thicknesses of each elbow specimen. The probe operates by sending an ultrasonic pulse into the material that it is held against (in this case from the outer surface of an elbow) and then recording the time it takes for the reflected pulse to return after rebounding off the opposite side where the material ends (or the inner surface of the elbow). By calibrating with a reference material of known thickness, in this case a stainless steel block with specially machined 8

66 thicknesses, the gauge can return a thickness measurement of the stainless steel elbows based on the reflection of the ultrasonic pulse. In addition, a Vernier slide caliper was used to measure the actual diameter across the intrados and extrados, and across the flanks. The purpose was to determine the actual geometry of the test specimens for use in future analysis. The various points of thickness measurements are presented in Figure 3.. (a) (b) Figure 3.: Elbow thickness measurement locations along various (a) planes around (b) crosssections. Figure 3.a shows the different cross-sections A though G along the elbow where thickness measurements were taken. Figure 3.b shows the various points 1 through 8 at each plane where the elbow thickness was measured. The thickness data of SR1 is presented in Table 3., with the remainder of the data being located in the Appendix. 9

67 The final data acquisition system implemented was digital image correlation (DIC). DIC is an optical method used to measure displacement and more relevantly, strain fields. Importantly, the non-contact optical nature of the method allows for measurement of strains of specimens at high temperatures. DIC works by comparing digital photographs of a test specimen at differing stages of deformation. The images are taken from an area of the specimen where a high contrast speckle pattern (usually black and white) has been placed. The images can then be loaded into a DIC software where it will ideally create a one-to-one image correspondence between the first, or reference image and the subsequent images. This is done by assigning subsets within the reference image and then determining their relative locations within the subsequent images. In other words, groups of pixels are tracked between images, which can then be used to calculate displacements. In the end, a displacement or strain field is generated for each image (Blaber & Antoniou, 1). Research in the field of DIC remains ongoing, with attempts to expand the usability to images taken outdoors in non-controlled environments and moving beyond optical images to other data sets such as surface roughness maps (McCormick & Lord, 1). In order to place the DIC camera in a position to collect images from the specimen while it was in the MTS, a platform had to be constructed and attached to the MTS. Consisting of two wood boards forming a 9 angle, and braced by triangular stiffeners, the platform was secured by four bolts to the MTS and could hold the camera s adjustable base. A Navistar camera was used for image acquisition. The software 5

68 interface for the camera was called TMVS. For the required speckle pattern, each specimen had one flank painted by a heat-resistant silicone-resin white paint. Before the paint dried, powdered graphite was shaken onto the paint, providing a randomly distributed high-contrast speckle pattern. Figure 3.5 provides a depiction of the DIC test setup. 51

69 (a) (b) Figure 3.5: (a) DIC camera pointed at the speckle pattern on a test specimen and (b) speckle pattern appearing on screen. 5

70 The DIC software used is called Ncorr, developed by Justin Blaber and Antonia Antoniou at the Georgia Institute of Technology. Ncorr is an open source D digital image correlation software contained within a MATLAB environment. Ncorr provides a graphic user interface as well as plotting tools for figure creation (Blaber & Antoniou, 1) Experimental Loadings The room temperature experiments included both displacement controlled loading and internal pressure. The cyclic displacement controlled loading used an amplitude of 11.8 mm in order to compare results with tests presented by Hassan et al. (15). The loading rate was 15.7 mm/sec or 3 sec/cycle where one cycle consisted of a positive displacement up to 11.8 mm from mm, then a negative displacement to mm, and then back to mm. Monotonic loading was also prescribed, at a rate of 1.53 mm/sec. Two levels of internal pressure were tested in addition to the unpressurized tests, 11. MPa and.7 MPa. The tests that were labeled as unpressurized were still filled with oil and slightly pressurized (<.7 MPa) in order to determine the through-wall fatigue crack life. Table 3.1 displays the loading parameters for the test specimens. 53

71 Table 3.1: Loading parameters for both short and long radius (SR and LR) elbows. Test Specimens Applied Displacement Internal Pressure Short Radius Elbows Long Radius Elbows δ a (mm) p (MPa) SR1, SR LR1* SR3, SR, SR5 LR*, LR3 ± SR, SR7 LR*, LR5.7 SR8 LR* Monotonic Open SR9 LR7* Monotonic Close *Hassan et al., Short Radius Experimental Results The experimental results for the short radius tests are presented below. Specifically, each section will report the force-displacement, change in diameter, and strain responses for each short radius elbow SR1 Results The SR1 test was an unpressurized displacement controlled test. The elbow failed due to the formation of a through-wall crack at a flank at cycle 3, which is shown in Figure 3.. The crack width is very small, and therefore the crack was highlighted by a black marker (seen over the two R s in the figure). 5

72 P (kn) P (kn) Figure 3.: SR1 fatigue failure through-wall crack. The force versus displacement and force peak in each cycle versus cycle number plots are shown in Figure SS3L SR1 p = MPa -5 Cycle 3-1 (a) SS3L SR1 p = MPa Peaks Valleys (b) N 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

73 ΔD y (mm) ΔD y (mm) ΔD x (mm) ΔD x (mm) In the case of the force versus applied displacement responses, three cycles are plotted: cycle 1, cycle 51, and the cycle of failure in order to examine how the response changes over the range of cycles. For the case of the force versus cycle number, the peaks of the response are plotted at specific intervals of cycles for clarity. This style will be repeated for subsequent plots of the other types of responses and for the subsequent test results. The force results show a stable response, with little variation as the number of cycles increase. Moving on, the change in diameter results from the ΔD Device are shown in Figure SS3L SR1 p = MPa (a) Cycle SS3L SR1 p = MPa Peaks Valleys (b) N 9 3 SS3L SR1 p = MPa (c) Cycle SS3L SR1 p = MPa Peaks (d) Valleys N 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. 5

74 ε θ (%) ε x (%) ε θ (%) ε x (%) ε θ (%) ε x (%) As with the force response, the change in diameter responses are stable and are basically constant as the cycle number increases. Next, the strain responses are presented in Figure 3.9. SS3L SR1 Flank p = MPa (a) 1 SS3L SR1 Flank p = MPa (b) SS3L SR1 Extrados p = MPa (c) 1 SS3L SR1 Extrados p = MPa Strain Gauge Failure (d) - - SS3L SR1 Intrados p = MPa (e) 1 SS3L SR1 Intrados p = MPa (f) 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

75 For the strains responses, there is a slight deviation in terms of the cycles plotted: cycle 1, cycle 51, and either the cycle of strain gauge failure or test specimen failure, whichever comes first. This format is continued for subsequent strain gauge responses from other tests with one exception being that if a strain gauge fails before cycle 51, the entire response until gauge failure will be plotted. For the strain response at the extrados (Figure 3.9a and b), the circumferential strain shows very little response as the displacement magnitude reaches 11.8 mm. The response of the axial strain is indicative of a strain gauge failure, rather than having no strain response. Moving onto the flanks (Figure 3.9c and d), it is in the circumferential direction where the phenomenon of ratcheting is observed. The axial strain response at the flank (Figure 3.9d), and the intrados circumferential and axial strains show greater strain responses than at the extrados, however the effect of ratcheting is hardly present. Table 3. shows the results of the measurements of the wall thickness gauge and diameter measurements. Table 3.: SR1 elbow thickness and diameter measurements. (mm) 1 3 * 5* * 7 8 Dx Dy A B C D E F G *Probe unable to attain a full-contact surface. 58

76 The table presents the thickness and diameter measurements as previously defined in Figure 3.. Dx is the flank to flank outer diameter while Dy is the intrados to extrados outer diameter. The columns with asterisks indicate the locations where the thickness measurements cannot be fully trusted. Those locations are all on the elbow intrados and given the short bend radius, the measurement probe could not achieve a full-contact surface. The problem is shown in Figure 3.1. Figure 3.1: Problem with obtaining intrados thickness measurements for short radius elbows. The presence of the gap causes wild fluctuations in the measurement reading even if the probe is completely still. In addition, even if the fluctuations were not present, the readings that were obtained must be assumed to be an over prediction of the actual elbow wall thickness. Therefore, while all thicknesses are shown in Table 3., subsequent tables presenting thickness measurements will omit those columns. 59

77 However, a view of the other measurements that could be obtained without a gap problem reveals up to a 15% difference in the thickness of the elbow depending on the location, instead of the prescribed.79 mm uniform schedule 1 thickness. The thicknesses also exhibit a trend where they are larger towards the elbow ends and smaller towards the elbow center. Also, the elbow is thinnest at the extrados and increases in thickness as the location moves to the intrados. The cross-sectional diameters are more constant; however, the diameter across the flanks are slightly greater than the diameter across the intrados and extrados. These geometric properties can be a potential variable in determining the behavior of the elbow in future analysis. As the following test results are similar to in format with the results presented in this section, the subsequent sections will present data of higher importance. Other results, for example fatigue failure images and thickness measurements, will be presented in the appendix. 3.. SR Results SR was a repeated unpressurized short radius elbow test. A repeated test allows for determining how replicable the results are between identical elbows and loading parameters. SR failed at cycle 3, which is comparable to SR1 at 3 cycles. The results of this test are shown in Figure As discussed in the previous section, only important results are shown here, notably the load response, change in diameter between the flanks (ΔDx), and the strain response at the flanks. The full response results are covered in the appendix.

78 ε θ (%) ε x (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L SR p = MPa -5 Cycle 3-1 (a) SS3L SR p = MPa Peaks Valleys (b) N 9 3 SS3L SR p = MPa (c) Cycle SS3L SR p = MPa Peaks Valleys (d) N SS3L SR Flank p = MPa δ = 11.8 mm (e) 1 SS3L SR Flank p = MPa δ = 11.8 mm (f) Figure 3.11: Abridged SR 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, and (f) axial strain at the flank versus displacement. Reviewing the load and change in diameter responses, both are stable, similar to SR1. However, examining the circumferential strain reveals a greater effect of ratcheting. 1

79 3..3 SR3 Results SR3 was the first pressurized test conducted, with the test specimen intended to be pressurized to 11. MPa. However, one problem that occurred during this test was that the hydraulic accumulator connected to the pressure system was mistakenly not engaged. This caused the pressure within the elbow specimen to decrease significantly as well as vary during each cycle as seen in Figure 3.1. p (MPa) SS3L SR3 p = 11. MPa δa = 11.8 mm t (sec) Figure 3.1: SR3 plot showing non-steady pressure. The pressure had to be manually increased each time it was noticed on the analog gauge that the pressure had decreased from 11. MPa. The specimen failed at cycle 1. An additional problem that affects the pressurized elbow tests is the presence of the pressure transducer. Due to limitations of the data acquisition system, the pressure transducer reduced the available strain gauge slots to four. For SR3, the intrados gauges were not connected. The abridged results collected are presented in Figure 3.13.

80 ε θ (%) ε x (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L SR3 p = 11. MPa -5-1 (a) SS3L SR3 p = 11. MPa Peaks Valleys (b) N 9 3 (c) 9 3 SS3L SR3 p = 11. MPa Peaks Valleys (d) SS3L SR3 p = 11. MPa N SS3L SR3 Flank p = 11. MPa δ = 11.8 mm (e) - 3 SS3L SR3 Flank p = 11. MPa δ = 11.8 mm (f) 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 at the flanks versus cycle, (e) circumferential strain at the flank versus displacement, and (f) axial strain at the flank versus displacement. The presence of internal pressure has a noticeable effect on the results. In the load responses seen in Figure 3.13a, the hysteresis loops shift downward and the upper and lower peaks slowly separate as the number of cycles increase. In addition, there is now significant ratcheting in the flank-to-flank change in diameter response (Figure 3.13b 3

81 and d). Finally, the rate of ratcheting of the strain response is clearly at least an order of magnitude greater than in the unpressurized tests (compare Figure 3.13e and f to Figure 3.11e and f). Unfortunately, the early failure of the strain gauges prevent the examination of the highest level of strain reached. 3.. SR Results A repeated test at 11. MPa was preformed, this time taking care that the hydraulic accumulator was utilized. This led to a noticeable effect on the stabilization of the pressure as the test was performed. In this case, the specimen failed at cycle 83, which is a significant divergence from the pressurized but fluctuating pressure test of SR3. The results are shown in Figure 3.1.

82 ε θ (%) ε θ (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L SR p = 11. MPa -5 Cycle 83-1 (a) SS3L SR p = 11. MPa Peaks Valleys (b) 1 3 N 9 3 (c) Cycle SS3L SR p = 11. MPa Peaks Valleys (d) SS3L SR p = 11. MPa N SS3L SR Flank (e) - 11 (f) - p = 11. MPa δ = 11.8 mm - SS3L SR p = 11. MPa - Flank δ = 11.8 mm Figure 3.1: Abridged SR 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, and (f) circumferential strain at the other flank versus displacement. For this pressurized test, the locations of the strain gauges were changed in order to better make use of the four limited slots available. The circumferential and axial strain gauges at the flank remained the same, however, another circumferential strain gauge was added to the other flank. The last gauge was placed to measure the circumferential 5

83 extrados strain. The load and change in diameter responses show the similar downward shift and ratcheting, respectively. In the strain responses, it appears that the presence of pressure causes the greatly increased rate of ratcheting. In addition, the strain gauges were able to last through more cycles, which reveals that the rate slows as the cycles increase SR5 Results SR5 was chronologically the last short radius elbow tested at room temperature and therefore could make use of an additional NI 937, which was not available for the other pressurized elbow tests. The additional data acquisition module removed the limitation caused by the pressure gauge, and as a result, the traditional strain gauge setup used in the unpressurized short radius elbow tests could be used. SR5 represents a final repeated test at 11. MPa, in order to explore the divergent fatigue life results from the previous two tests. In this case, the specimen failed at cycle 1, which continues a divergence in results at 11. MPa. The responses from SR5 are shown in Figure 3.15.

84 ε θ (%) ε x (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L SR5 p = 11. MPa -5-1 (a) SS3L SR5 p = 11. MPa Peaks Valleys (b) N 9 3 SS3L SR5 p = 11. MPa (c) 9 3 SS3L SR5 p = 11. MPa Peaks Valleys (d) N (e) - 3 SS3L SR5 Flank p = 11. MPa δ = 11.8 mm (f) Cycle 3 SS3L SR5 p = 11. MPa - Flank δ = 11.8 mm - Figure 3.15: Abridged SR5 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, and (f) axial strain at the flank versus displacement. In starting with the load versus displacement and load versus cycle plots (Figure 3.15a and b), the downward shift is still present. The effect of ratcheting also is continued to be observed in the change in diameter responses at the flank (Figure 3.15c and d). Finally, great strain ratcheting is observed in the circumferential flank strain results, 7

85 while ratcheting to a lesser extent is seen in the axial flank strain results (Figure 3.15e and f). 3.. SR Results SR was the first elbow specimen tested at.7 MPa. There were no noticeable problems with the test, and the specimen failed at cycle 758. This represents a significant increase in fatigue life when compared to the 11 MPa level, and especially when compared to the unpressurized tests. The responses from the test are presented in Figure

86 ε θ (%) ε θ (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L SR p =.7 MPa -5 Cycle (a) SS3L SR p =.7 MPa Peaks Valleys (b) 8 N 9 (c) 9 Peaks 3 SS3L SR p =.7 MPa Cycle 758 δ -3 a = 11.8 mm 3-3 SS3L SR p =.7 MPa Valleys (d) 8 N SS3L SR Flank (e) - SS3L SR Flank (f) - p =.7 MPa δ - a = 11.8 mm p =.7 MPa - Figure 3.1: SR abridged 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, and (f) circumferential strain at the other flank versus displacement. The load responses show a significant shift downward (Figure 3.1a and b), where the elbow experiences greater compressive loads than in tension. This may be explained by the presence of the internal pressure, which attempts to open up the elbow. The elbow ends then experience a compressive force as the ends are restrained from opening up. 9

87 Ratcheting in the change in diameter response have increased, especially in the early cycles (Figure 3.1c and d). Like the previous pressurized tests, ratcheting continues until fatigue failure occurs. This test shows a divergence in the strain response at the flanks. At one flank, the strain reaches almost 3% at the second cycle, whereas it takes until the sixth cycle at the other flank to reach the same level of strain. Unfortunately, the rapid, cyclic increase in strain caused the gauges to fail early SR7 Results This test was a repeat at.7 MPa in order to confirm the high fatigue life observed in SR. For this test, a failure occurred at cycle 9, but it was a weld failure. Figure 3.17 shows an image of the weld failure of the specimen. Figure 3.17: SR7 weld failure. 7

88 In an attempt to achieve the fatigue life of the elbow, the weld was repaired by simply rewelding over the crack, and essentially placing another strip of weld around the elbow. The procedure was repeated on the other weld even though there was no failure in the attempt to maintain symmetry. After the rewelding was complete, the specimen was placed back into the MTS and repressurized. No additional strain gauges were applied and the ΔD Device was not setup, as the goal was to determine the fatigue life. After the test was restarted, the specimen experienced cracks at an additional eight cycles, which indicates the actual fatigue life of the elbow was 98 cycles. The fatigue crack in this case was also different as seen in Figure 3.18 as compared with all other elbow fatigue failures observed. 71

89 Figure 3.18: SR7 fatigue failure. Instead of the usual axial crack that occurs at the flank, here there are two circumferential cracks, both at around the midpoint between the flanks and intrados. Investigation of this failure will require future analysis as well as an examination as to whether the rewelding in order to repair the crack could be the cause. The responses collected are shown in Figure

90 ε θ (%) ε θ (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L SR7 p =.7 MPa -5 Cycle 9-1 (a) SS3L SR7 p =.7 MPa Peaks Valleys (b) 8 N 9 (c) 9 Peaks (d) 3 SS3L SR7 p =.7 MPa Cycle SS3L SR7 p =.7 MPa Valleys 8 N SS3L SR7 Flank p =.7 MPa (e) - SS3L SR7 Flank (f) p =.7 MPa - Figure 3.19: Abridged SR7 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, and (f) circumferential strain at the other flank versus displacement. The load and change in diameter responses are similar to SR, where the specimen experiences a larger compressive force and larger ratcheting in the diameter (compare Figure 3.19c and d to Figure 3.1c and d). Looking at the strain responses, there is an even greater discrepancy between the two flank circumferential strain responses 73

91 P (kn) (compare Figure 3.19e and f to Figure 3.1e and f). The flank strain in the last test ratchets quicker than those in this test SR8 Results SR8 is the first of the short radius monotonic tests. The specimen was tested under a monotonic opening loading until it reaches a reasonable limit. No pressurization was used in the test. The load versus displacement response is shown below in Figure 3.; the other responses including change in diameter versus displacement and strain versus displacement are presented in the appendix. 3 SS3L SR8 p = MPa.75 kn/mm Figure 3.: SR8 load versus displacement response. The figure shows that the elbow reached about. kn at a displacement of about 11 mm, where the test was stopped. A quick calculation of the elbow opening elastic stiffness gives.75 kn/mm. 7

92 P (kn) 3..9 SR9 Results SR9 is the second short radius monotonic test, and in this case the specimen was tested under a monotonic closing loading until it reaches a reasonable limit, without any pressurization. The load versus displacement response is shown in Figure SS3L SR8 p = MPa.7 kn/mm Figure 3.1: SR9 load versus displacement response. The maximum force reached was.38 kn at a displacement of 1. mm. The test was stopped at about 1 mm of displacement. The elbow closing elastic stiffness was determined to be.7 kn/mm Fatigue Life Results The fatigue lives of the short radius elbows are compiled in Table

93 Short Radius Elbows Table 3.3: Fatigue lives from the short radius elbow tests. Through-Wall Crack Fatigue Life (Nf) SR1, SR 3, 3 δ a (mm) p (MPa) SR3*, SR, SR5 1*, 83, 1 ± SR, SR7** 758, 98**.7 *Constant pressure could not be maintained. **Initial weld failure. The results show that as pressure increases, the fatigue life of a short radius elbow increases as well. In SR3, constant pressure was unfortunately not achieved due to the hydraulic accumulator not being engaged during the test. In SR7, the elbow experienced a weld failure, and the fatigue life had to be determined after rewelding the elbow. 3.3 Long Radius Experimental Results The long radius experimental results are presented below. This section also includes earlier elbow experiments conducted (Hassan et al., 15) for exploring short versus long radius elbow response and fatigue lives. As discussed in the literature review, long radius experimental results are commonplace LR1 Results This test was the unpressurized long radius elbow performed earlier. The elbow failed at cycle 7. The responses are presented below in Figure 3.. 7

94 ε θ (%) ε θ (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L LR1 p = MPa -5 Cycle 7-1 (a) SS3L LR1 p = MPa Peaks Valleys (b) 8 N 9 3 SS3L LR1 p = MPa (c) Cycle SS3L LR1 p = MPa Peaks (d) Valleys N SS3L LR1 Flank p = MPa (e) Cycle 57 SS3L LR1 Flank p = MPa (f) Cycle Figure 3.: 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 at the flanks versus cycle, (e) circumferential strain at the flank versus displacement, and (f) circumferential strain at the other flank versus displacement (Hassan et al., 15). There are no shifts in the response as the cycles increase (Figure 3.a and b). The change in diameter response shows very little ratcheting, primarily at the later cycles when viewing Figure 3.d. Strain gauging were applied on both flanks, and the circumferential strain responses from the flanks are shown in Figure 3.e and f. 77

95 Interestingly, at zero pressure there is much greater strain ratcheting occurring in the long radius elbow than the short radius elbow. There is a discrepancy between the strain responses at the flanks but this may be due to the difference in load, surface conditions, thickness, etc LR Results LR was the pressurized elbow test at 11. MPa that was performed earlier. The cycle of failure of the elbow was 853. The responses are shown in Figure

96 ε θ (%) ε θ (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L LR p = 11. MPa -5 Cycle (a) SS3L LR p = 11. MPa Peaks Valleys (b) 8 1 N 9 3 SS3L LR p = 11. MPa (c) Cycle SS3L LR p = 11. MPa Peaks Valleys (d) N SS3L LR Flank Cycle 777 p = 11. MPa - (e) SS3L LR Flank p = 11. MPa Cycle 89 - (f) Figure 3.3: LR abridged 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, and (f) circumferential strain at the other flank versus displacement (Hassan et al., 15). In the load response, a shift is present as in the short radius test (Figure 3.3a). The last cycle loop has lower peaks for both the tension and compression (compare Figure 3.3b with Figure 3.13b). The change in diameter response shows a similar ratcheting response when compared with the short radius response (compare Figure 3.3c and d 79

97 with Figure 3.13c and d). The strain responses contain a discrepancy between the two flanks. The last cycle of Figure 3.3e extends to nearly the end of the test yet reaches a strain values less than that reported in Figure 3.3f, where the strain gauge fails earlier on LR3 Results LR3 was a repeat of LR to verify the repeatability of the fatigue life and responses. The test was setup with the same loading conditions and long radius elbow specimen. Unfortunately, at cycle 9 the weld joining the elbow to the pipe on one side failed. The data collected up to that point is presented in Figure 3.. 8

98 ε θ (%) ε θ (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L LR3 p = 11. MPa -5 Cycle 9-1 (a) SS3L LR3 p = 11. MPa Peaks Valleys (b) 1 3 N 9 3 SS3L LR3 p = 11. MPa (c) Cycle SS3L LR3 p = 11. MPa Peaks Valleys (d) N SS3L LR3 Flank (e) - (f) p = 11. MPa - SS3L LR3 p = 11. MPa - Flank - 3 Figure 3.: 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 at the flanks versus cycle, (e) circumferential strain at the flank versus displacement, and (f) circumferential strain at the other flank versus displacement. There is a small difference in the load responses between LR and LR3. However, the change in diameter response shows a good correlation, at least for the cycles LR3 was able to provide. Interestingly, the strain gauge response for both LR and LR3 are comparable, even though the gauges failed at a much earlier cycle in LR3. This 81

99 indicates how in both specimens the rate of ratcheting is high in the early cycles but then slows in the later ones. In an effort to salvage the elbow specimen in order to determine its fatigue life, repairs were conducted, similarly to SR7. Unlike SR7, data acquisition was continued, where strain gauging was reapplied and change in diameter responses were collected. However, after restarting the test, the specimen experienced another weld failure at cycle 178 (with the cycle count zeroed before the test was restarted). This results in a cumulative 7 cycles that LR3 experienced without fatigue failure. The results gathered from the restarted test are shown in Figure

100 ε θ (%) ε θ (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L LR3re p = 11. MPa (a) SS3L LR3re p = 11. MPa Peaks Valleys (b) N 9 3 SS3L LR3re p = 11. MPa (c) SS3L LR3re p = 11. MPa Peaks (d) Valleys N SS3L LR3re Flank p = 11. MPa (e) 78 SS3L LR3re Flank p = 11. MPa (f) Figure 3.5: 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 at the flanks versus cycle, (e) circumferential strain at the flank versus displacement, and (f) circumferential strain at the other flank versus displacement. The load response continues to show a stable result, while ratcheting in the change in diameter response at the flank has slowed down. In the strain responses, it can be observed that ratcheting continues to occur. With the advent of the second weld failure, it was decided to discontinue further attempts at achieving the fatigue life of the elbow. 83

101 3.3. LR Results This test was a long radius elbow loaded at a.7 MPa internal pressure level, performed earlier. Interestingly, the fatigue life of the elbow was only 75, a breaking of the trend where an increased pressure leads to a higher fatigue life. The responses are presented in Figure 3.. 8

102 ε θ (%) ε θ (%) ΔD x (mm) ΔD x (mm) P (kn) P (kn) 1 5 SS3L LR p =.7 MPa -5 Cycle 75-1 (a) SS3L LR p =.7 MPa Peaks Valleys (b) N 9 Cycle 75 (c) 9 Peaks (d) 3 3 Valleys SS3L LR p =.7 MPa -3-3 SS3L LR p =.7 MPa N SS3L LR Flank (e) - 15 (f) p =.7 MPa - SS3L LR p =.7 MPa - 1 Flank δ - a = 11.8 mm Figure 3.: LR abridged 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, and (f) circumferential strain at the other flank versus displacement (Hassan et al., 15). The load response shows that the 51 st cycle has a greater tensile and compressive loading than the 1 st cycle, but the 75 th cycle has a lower tensile and compressive loading than the 51 st cycle but remains greater than the 1 st cycle in those loading types (Figure 3.a and b). The change in diameter responses show the expected presence of 85

103 ratcheting, and the ratcheting rate is greater at the beginning of the test (Figure 3.c and d). The flank circumferential strain responses show a significant ratcheting rate with a different rate between the two flanks (Figure 3.e and f) LR5 Results LR5 was chronologically the last room temperature elbow tested and therefore served as both a repeated test at.7 MPa and as an initial exploration into the DIC data acquisition system. As a D DIC system was used, in order to obtain the images needed for DIC, the testing procedure was modified in the beginning. Initial reference pictures were taken before and after pressurization to.7 MPa. However, the initial picture before pressurization could not be used as a reference because of a difference in the brightness between the pictures due to lighting. Therefore, the picture taken after pressurization was used as the reference. Then for the first 11 cycles, the displacement was held at each tensile peak to allow time for the camera to capture a picture. In addition, the ΔD Device had to be omitted in order to provide a clear line of sight to the speckle pattern on the flank for the camera. After the 11 th cycle, the testing continued without holds to failure. The elbow failed at cycle 5, providing additional confirmation as to the reduced fatigue life at this higher pressure. Starting with the standard responses, Figure 3.7 presents the summary. 8

104 ε θ (%) ε x (%) P (kn) P (kn) 1 5 SS3L LR5 p =.7 MPa -5 Cycle 5-1 (a) SS3L LR5 p =.7 MPa Peaks Valleys (b) N - SS3L LR5 Flank p =.7 MPa - 5 (c) - SS3L LR5 Flank p =.7 MPa (d) - Figure 3.7: 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. Starting with the load responses, there is an obvious jump in the first cycle. However, this is caused by load relaxation during the tensile peak hold. The 51 st to 5 nd cycles show little difference in the load response, a difference from the LR results. There were no change in diameter results to collect as the ΔD Device could not be used. Finally, the rate of flank circumferential strain ratcheting is much greater when compared with LR. Moving next to the DIC responses, there is a clear representation of circumferential strain ratcheting as the number of cycles increase, as shown in Figure

105 Cycle Cycle 8 1 Figure 3.8: DIC tensile peak circumferential strain contour plots (in percent) at the flank for the specified cycles. Starting with the first cycle, there is little strain response due to the pressurization. However, at the fourth cycle, there is now a noticeable band of accumulated strain. The band proceeds to increase in magnitude up to the 11 th cycle, where the DIC image capture was halted. The strain contour can be examined more closely in order to obtain strain values at specific points. For instance, cycle 11 and various points are shown in Figure

106 Figure 3.9: 1 tensile peak circumferential strain contour plot with specific points selected. Using these points, the flank circumferential strain can be plotted along the u and v axes. Using a calibration picture with a ruler, the pixel to mm conversion can be implemented, thus determining the actual distance of each point from the u and v origin. The u axis is 1 mm long while the v axis is 1 mm long. The circumferential strain variations along the u and v axes are shown in Figure

107 ε θ (%) ε θ (%) ε θ (%) 1 8 (a) 1 8 (b) SS3L LR5 DIC u axis u (mm) SS3L LR5 DIC v axis v (mm) Figure 3.3: 1 tensile peak circumferential strain variations along (a) u1-u8 and (b) v1-v5. One final investigation with DIC strain data is to compare it with the strain gauge data to see whether the strain data generated at least has some relation to real data. Figure 3.31 presents the comparison. 1 8 SS3L LR5 DIC Strain Gauge N Figure 3.31: DIC and strain gauge comparison for peak tensile circumferential strain values. The DIC values were taken at the point u/v3 for each cycle. The results show that at least for the cycles where the strain gauge was still functioning, the values produced by DIC are reasonable. This is valuable as DIC is not subject to failure as strain gauges are, and can therefore be used to provide data where it would be impossible to use a strain gauge. 9

108 P (kn) 3.3. LR Results This test was a monotonic opening test performed earlier (Hassan et al., 15). The load versus displacement plot is shown in Figure SS3L LR p = MPa.87 kn/mm (a) Figure 3.3: LR load versus displacement response. The maximum load reached was about 3 kn at the maximum displacement of 153 mm, where the test was ended. The elbow opening elastic stiffness was calculated to be.87 kn/mm LR7 Results LR7 was a monotonic closing test performed earlier (Hassan et al., 15). The load versus displacement graph is shown below in Figure

109 P (kn) 3 SS3L LR7 p = MPa.837 kn/mm (a) Figure 3.33: LR7 load versus displacement response. The maximum force experienced was.77 kn at a displacement of about mm. The test was stopped at a displacement of 1 mm where the load was.5 kn. The closing elastic stiffness was determined to be.837 kn/mm Fatigue Life Results The fatigue life results of the long radius elbows are summarized in Table 3.. Long Radius Elbows Table 3.: Fatigue lives from the long radius elbow tests. Through-Wall Crack Fatigue Life (Nf) LR1 7 δa (mm) p (MPa) LR, LR3* 853, >7* ± LR, LR5 75, 5.7 *Weld failure The fatigue life in the case of the long radius elbow increased as the internal pressure was level increased to 11 MPa; however, as the pressure was increased to.7 MPa lower fatigue lives than the unpressurized and 11. MPa tests were observed. This trend is opposite to the short radius elbow, for which the fatigue life initially decreased 9

110 as 11. MPa was applied and then life increased with.7 MPa as compared to both the unpressurized and 11. MPa tests. 3. Discussion on Short and Long Radius Elbow Results This section compares the results between the short and long radius elbows. In order to facilitate such comparisons, the results are converted into amplitude and mean responses. These responses present a clearer picture than what can be obtained from the results presented so far. For example, in the case of strain, the amplitude values will clearly show either strain hardening or softening, when the response either decreases or increases over the cycle numbers. The mean values can show ratcheting or shakedown, when the response increases or decreases over the cycle numbers. The amplitude response calculations for an example strain response is shown in Equation (3.1). ε a = ε max ε min (3.1) The mean response calculations are shown in Equation (3.). ε m = ε max + ε min (3.) The max and min strains refer to the highest peak value and lowest peak value for each given cycle, respectively. Calculations for load and change in diameter amplitude and mean responses are performed similarly. 93

111 3..1 Pressure Influence Discussion The influence of internal pressure on the results of the elbow tests is discussed in this section. An initial examination of the influence of pressure could be observed in the fatigue lives of the elbow specimens. A compilation of both short and long radius specimens are shown in Table 3.5. Table 3.5: Summary of fatigue lives of elbow tests. δa (mm) ±11.8 p (MPa) Short Radius Elbow Crack Fatigue Life (Nf) Long Radius Elbow Crack Fatigue Life (Nf) 3, *, 83, 1 853, >7***.7 758, 98** 75, 5 *Constant pressure not maintained. **Initial weld failure. ***Weld failure. Generally, in the short radius elbows, at each increment in pressure level there is a commensurate increase in the fatigue life, with one exception at 11. MPa. The trend in the long radius elbows is that the fatigue life increases at the 11. MPa level but decreases at the.7 MPa level (unfortunately no information can be drawn from the specimen that experienced weld failure). An inspection of the fatigue cracks show that there is a slight indentation, or collapse inward at the location of the crack. As higher internal pressure exerts a uniform outward force, there could be some mitigating action present in the failure mechanism of the elbow that might explain the increase of fatigue life phenomenon. A visual depiction of the effect of pressure on fatigue life is shown in Figure

112 Through-Wall Crack Fatuge Life (N f ) Pressure Level (MPa) Short Radius Long Radius Figure 3.3: Influence of pressure on fatigue life. In the following plots, the short radius elbows are represented by either a circle or a diamond. A circle will be the default symbol, the diamond will represent a repeated experiment. Long radius elbows will have a similar representation of a square and triangle, respectively. The levels of pressure are distinguished by color, with blue, red, and black representing ~, 11., and.7 MPa, respectively. Next, amplitude values are shown with hollow symbols, while mean values are shown in solid symbols. Finally, the short radius elbow test that failed to maintain constant pressure and the long radius elbow test that failed at the weld (without a reweld and retest) were omitted from the plots. The load amplitude and mean responses for the short radius elbows are presented in Figure

113 Pm (kn) Pc (kn) 1 SS3L SR Flank (a) 1 SS3L SR Flank (b) ~ MPa 11. MPa.7 MPa -3 8 N ~ MPa 11. MPa.7 MPa 8 N Figure 3.35: Short radius force responses (a) mean (Pm) and (b) amplitude (Pc). The load amplitude responses clearly show a sharp increase at the early cycles before settling into a near constant level for the remainder of their tests. As the level of pressure increases, the sharp increase of load amplitude response increase commensurately. This indicates that test specimens under higher internal pressures are stronger than unpressurized specimens. Turning to the mean amplitude response, the unpressurized elbow specimens have a small tensile response; however, the specimens with internal pressure have a mean compressive force. The presence of this force could be explained by the internal pressure forcing the elbow to open up. As the elbow ends were pinned by the MTS, the compressive reactive force grew. In addition, as the internal pressure increased, the mean compressive force increased. 9

114 ΔDmx (mm) ΔDax (mm) Figure 3.3 presents the flank-to-flank change in diameter amplitude (ΔDax) and mean (ΔDmx) responses for the short radius elbows. 8 SS3L SR Flank (a) 3 SS3L SR Flank (b) 1 ~ MPa 11. MPa.7 MPa 8 N ~ MPa 11. MPa.7 MPa 8 N Figure 3.3: Short radius change in diameter responses (a) mean (ΔDmx) and (b) amplitude (ΔDax). The amplitude responses are almost constant throughout the cycles at all levels of pressurization. While there is a spread in the starting values between the elbow tests, the amplitude response behavior is as expected. Looking at the mean responses, there is very little ratcheting observed at the unpressurized level. At the 11. MPa level, the presence of ratcheting is clearly seen. When the internal pressure is set to.7 MPa, there is a sharp increase in early ΔDmx that decreases as the number of cycles increase, but never reaches shakedown. 97

115 ε mθ (%) ε aθ (%) The flank circumferential strain amplitude and mean responses for the short radius elbows are shown in Figure The flank circumferential strain responses are especially important as the general fatigue failure mode of the elbow is a flank crack in the axial direction, which indicates the circumferential strain controls the failure. 5 SS3L SR Flank (a) 1 SS3L SR Flank (b).8 3. ~ MPa 11. MPa.7 MPa N ~ MPa 11. MPa.7 MPa N Figure 3.37: Short radius circumferential strain responses (a) mean (εmθ) and (b) amplitude (εaθ). Examining the strain amplitude responses reveals significant strain hardening. The initial cycles start with high amplitudes for all pressure levels. As the number of cycles increase, the strain amplitudes drop sharply before leveling off. There also appears to be a general trend where, as the pressure level increases, the strain amplitude decreases more quickly and perhaps reaches a lower constant level. However, these responses are 98

116 somewhat erratic, as can be seen by the discrepancy of responses between the two unpressurized elbow tests and the tests at 11. MPa. In addition, there is a problem of early strain gauge failure, which prevents observations across the entire fatigue life of the test specimens. Therefore, more tests are required to confirm the observed trend. If confirmed, however, the strain amplitude behavior could be used in the ultimate explanation of elbow fatigue life failure. Inspecting the circumferential strain mean responses, the discrepancy between the two unpressurized tests are seen again, although both tests show ratcheting. When internal pressure is added to the tests, the rate of ratcheting increases dramatically. Interestingly, the initial ratcheting rates for the 11. MPa and the.7 MPa tests are similar, although strain gauge failure prevents further examination. This ratcheting trend also will be important in describing elbow fatigue life failure and in developing predictive fatigue life models. These results show that there may be a complex interaction between circumferential strain amplitudes and means that ultimately result in fatigue failure under cyclic loading. The load amplitude and mean responses for the long radius elbow tests are shown in Figure To reiterate, these plots include data both from Hassan et al. (15) and the additional long radius tests performed. 99

117 Pm (kn) Pc (kn) 1 SS3L LR Flank (a) 1 SS3L LR Flank (b) ~ MPa 11. MPa.7 MPa 8 1 N ~ MPa 11. MPa.7 MPa 8 1 N Figure 3.38: Long radius force responses (a) mean and (b) amplitude. The long radius elbow load amplitude results show, similar to the short radius elbow amplitude responses, that as the level of pressure increases, the amplitude responses increase. The increase occurs towards the start of the tests, and then the amplitude responses reach an almost constant steady state. The force mean responses show a small tensile response for the unpressurized case, but as internal pressure is added, a mean compressive force results. Figure 3.39 shows the change in diameter responses for the long radius elbows at the flank. 1

118 ΔDmx (mm) ΔDax (mm) 8 SS3L LR Flank (a) 3 SS3L LR Flank (b) 1 - ~ MPa 11. MPa.7 MPa 8 1 N ~ MPa 11. MPa.7 MPa 8 1 N Figure 3.39: Long radius change in diameter responses (a) mean and (b) amplitude. The amplitude responses are all nearly constant and the level of pressure has no influence on the results. The mean responses, however, are clearly influenced by pressure. At the unpressurized level, the presence of ratcheting is limited. However, at the 11. MPa level, after the initial high rate of ΔDm accumulation a steady ratcheting rate persisted. The.7 MPa level responds in a similar manner, although the magnitudes of the results are higher. The circumferential strain amplitude and mean response at the flank are shown in Figure

119 ε mθ (%) ε aθ (%) 5 SS3L LR Flank (a) 1 SS3L LR Flank (b) ~ MPa 11. MPa.7 MPa 8 N ~ MPa 11. MPa.7 MPa 8 N Figure 3.: Long radius circumferential strain responses (a) mean and (b) amplitude. The strain amplitude responses all start at a high value which quickly diminishes as the cycles increase. As with the short radius elbows, there is a general trend where pressure influences the results, although the available data remains scarce with regard to the full fatigue life of the elbows. The 11. MPa amplitude strain results end early due to strain gauge failure but fall beneath the unpressurized amplitude responses. A similar gauge failure also cuts the.7 MPa data short, but both.7 MPa amplitude responses reach lower values than both the 11. MPa and unpressurized responses. However, turning to the mean strain responses, a clear trend from the influence of pressure can be seen. Ratcheting occurs steadily and continuously over the course of the unpressurized test. When 11. MPa of pressure is added, the rate of ratcheting 1

120 increases significantly. Increasing the pressure to.7 MPa further causes an increase in the rate of ratcheting. 3.. Bend Radius Influence Discussion The influence of the elbow bend radius on the responses is discussed in this section. Examining first the fatigue life, there is a clear difference between short and long radius elbows. At the unpressurized and 11. MPa internal pressure level, the fatigue life of the long radius elbows are higher than the short radius elbows. However, at the.7 MPa level, the short radius elbows exhibit greater fatigue life than the long radius elbows. The load amplitude response comparison is shown in Figure

121 Pc (kn) Pc (kn) 1 SS3L SR Flank (a) 1 SS3L LR Flank (b) 8 8 ~ MPa 11. MPa.7 MPa 8 N ~ MPa 11. MPa.7 MPa 8 N Figure 3.1: Load amplitude response comparison between (a) short and (b) long radius elbows. The load responses clearly show a higher amplitude for the long radius results at each comparable pressure level. This indicates that long radius elbows are stronger than short radius elbows. In addition, examining the monotonic tests in Chapter 3 shows that the elastic stiffnesses of the long radius elbow are greater than the short radius elbow. The load mean response comparison is presented in Figure 3.. 1

122 Pm (kn) Pm (kn) 1 SS3L SR Flank (a) 1 SS3L LR Flank (b) ~ MPa 11. MPa.7 MPa N -3 ~ MPa 11. MPa.7 MPa 8 N Figure 3.: Load mean response comparison between (a) short and (b) long radius elbows. While both mean responses at the unpressurized level are comparable in showing a small tensile mean strain, when internal pressure is added there is a noticeable difference between the short and long radius responses. While both elbows experience an increase in compressive mean strain as the pressure increases, the short radius elbows reach higher mean force magnitudes, more so at the.7 MPa level than the 11. MPa level. Figure 3.3 displays the flank change in diameter amplitude response comparison. 15

123 ΔDax (mm) ΔDax (mm) 3 SS3L SR Flank (a) 3 SS3L LR Flank (b) 1 1 ~ MPa 11. MPa.7 MPa 8 N ~ MPa 11. MPa.7 MPa 8 N Figure 3.3: Change in diameter amplitude response comparison between (a) short and (b) long radius elbows. Both elbow responses show a similar constant response at each pressure level. It is also difficult to determine if a trend is present. For instance, in the short radius elbow tests, the 11. MPa amplitude response is below both of the unpressurized responses but the.7 MPa response is clearly between the two. In the long radius elbow tests, the unpressurized and 11. MPa responses overlap but the.7 MPa response is slightly less in magnitude. Figure 3. shows the change in diameter mean response comparison at the flank. 1

124 ΔDmx (mm) ΔDmx (mm) 8 SS3L SR Flank (a) 8 SS3L LR Flank (b) ~ MPa 11. MPa.7 MPa ~ MPa 11. MPa.7 MPa 8 N 8 N Figure 3.: Change in diameter mean response comparison between (a) short and (b) long radius elbows. The mean responses exhibit some differences in magnitudes. In the short radius elbows, the.7 MPa test and the two 11. MPa tests accumulate ΔDm quickly to high values compared to the unpressurized tests. However, while the long radius elbows experience an influence in pressure at the two levels of pressure, the rate of ratcheting is much slower and at the.7 MPa level, the long radius mean response does not reach the short radius mean response. This indicates that at pressurized states, short radius elbows more easily deform at the flank as opposed to long radius elbows overall. The flank circumferential strain amplitude response comparison is presented in Figure

125 ε aθ (%) ε aθ (%) 1 SS3L SR Flank (a) 1 SS3L LR Flank (b) ~ MPa 11. MPa.7 MPa N ~ MPa 11. MPa.7 MPa N Figure 3.5: Circumferential strain amplitdue response comparison between (a) short and (b) long radius elbows. In the unpressurized case, the long radius response is similar to one of the short radius responses. However, the amplitude response in the initial cycles are only slightly elevated as compared to the short radius initial response. Moving to the 11. MPa case, the long radius response now exhibits the high amplitude at the early cycles similar to the short radius elbow response. The long radius response falls faster than the short radius response; however, early strain gauge failure prevents the knowledge of the behavior in the later cycles. In addition, the long radius response is clearly below the unpressurized response, which is not the case in the short radius response. Finally, in the.7 MPa case, there was an higher initial amplitude response for the long radius than the short radius response in the initial cycles and both elbow responses appear to decrease at approximately the same rate but again, early strain gauge failure prevents 18

126 ε mθ (%) ε mθ (%) examination of whether the long radius elbow response could decrease enough to match the magnitude shown by the short radius response. One final point to draw from the comparison is that the long radius response generally continues the trend discussed in Section 3..1 for the short radius elbows section, where a lower strain amplitude corresponds with a longer fatigue life. The mean flank circumferential strain response comparison is presented in Figure SS3L SR Flank (a) 5 SS3L LR Flank (b) 3 3 ~ MPa 11. MPa.7 MPa 1 1 ~ MPa 11. MPa.7 MPa N N Figure 3.: Circumferential mean strain response comparison between (a) short and (b) long radius elbows. The long and short radius elbow responses correspond reasonably. At the unpressurized level, the long radius elbow correlates well with one of the short radius elbow results 19

127 (the same short radius elbow, N = 3, as in the strain amplitude comparison). At the next 11. MPa pressure level, for the cycle range where both elbow responses are shown, the results overlap, indicating another good correlation. At the.7 MPa level, the long radius elbow response displays an even greater ratcheting rate than the short radius response, and the strain gauge fails before the point where the ratcheting rate begins to slow. 11

128 Chapter High Temperature Experimental Program.1 Introduction This chapter describes the high temperature tests conducted. This chapter covers the experimental design and materials used as well as presents the test results..1.1 Experimental Setup The elbow specimens are identical to those described in Chapter 3. Therefore, the experimental setup was similar in that the test specimen was placed in the MTS with pin connections at the load cell and hydraulic actuator. The difference comes in with the furnace, which is used to heat the test specimen during applied loading. The furnace is able to open up and enclose the majority of the test specimen while it is setup in the MTS. In addition, a platform was constructed in order to hold the DIC (Digital Image Correlation) camera in position. Finally, in order to protect the MTS load cell and actuator from excess heat from the furnace, a cooling system was designed. Due to the high temperature involved, pressurization with hydraulic oil could not be used. The furnace used was a custom designed Series 31 built by ATS (Applied Test Systems, Inc.). The furnace is capable of sustaining a maximum temperature of 1 C. The furnace itself contains three holes, at the top, front, and bottom. The top and front holes allow the test specimen pipes to exit the furnace and to be set up for testing, while 111

129 the bottom hole allows for test monitoring and for thermocouple wire management. When the test specimen is setup in the MTS, the furnace is placed on a frame that holds the furnace at a 5 angle, allowing for proper encasement of the specimen. Insulation is also placed to seal the open gaps in order to allow for controlled heating. Figure.1 shows the furnace setup around a specimen in the MTS. Figure.1: Furnace setup around a test specimen. In order to protect the MTS load cell and actuator from heat levels that could cause damage, a cooling system was implemented. A diagram of the system is shown in Figure.. 11

130 Figure.: Diagram of cooling system. The cooling system consists of a plastic drum, an extended-life sealless plastic centrifugal pump, two custom designed cooling collars, a fan-cooled heat sink, and silicone tubing. The drum serves as a reservoir of water and is located on a movable cart. The pump is on the cart beneath the drum as it is gravity fed by a tube from the drum. The two cooling collars, which consist of an aluminum collar of a diameter of the test specimen pipes with copper tubing threaded through it, are attached to the top and bottom specimen pipe sections that extend out of the furnace. Silicone tubing runs from the pump to the collars through which cold water runs. From the top collar, tubing goes 113

131 to a heat sink, set on a platform on top of the drum, which receives heated water. After removing excess heat from the water, a tube runs from the heat sink back into the drum, recycling the water. Figure.3 shows a picture of the cooling system. Figure.3: Image of test specimen cooling system..1. Data Acquisition Data acquisition in this section again makes use of the National Instruments CompactDAQ and associated modules discussed in Chapter 3 to measure and record 11

132 data from the MTS displacement gauge and load cell. However, due to the high temperature nature of the test, the ΔD Device was not used and conventional strain gauges could not be applied. In an effort to obtain some sort of strain information, the method of DIC was implemented by taking an initial reference picture at the flank before heating and testing, and then taking another image after testing was completed with the hope of at least being able to capture the final strain value. Temperature information about the test specimens was collected through two Type K thermocouples, capable of measuring temperatures between -5 to 1 C, placed at the intrados and flank. The two thermocouples were connected to a Fluke 5 II Dual Input Digital Thermometer. An Extech IR (Infra-Red) Thermometer was used in an initial furnace heating test and to check the temperature of the end blocks during testing. The purpose of the initial test was to check the effectiveness of the cooling system. This testing revealed that insulation was needed to maintain a more uniform heating. In addition, it showed that the cooling collars could prevent excess heat from being transmitted to the end blocks.. High Temperature Experimental Results The high temperature experiment was performed by preparing the elbow specimen by applying a speckle pattern to a flank and welding thermocouples to the intrados and other flank. The elbow specimen was then placed into the MTS as done in the room 115

133 temperature tests. Next, the furnace was maneuvered to encase the elbow. The cooling collars were then fastened and silicone tubing attached. As mentioned previously, a reference picture of the flank was taken for DIC purposes. Finally, power was provided to the furnace in order to start the heating process. Once the flank of the specimen reached 35 C, the test was performed. After the furnace was left to cool down, a final picture was taken of the flank speckle pattern...1 HTLR1 Results HTLR1 was the first elbow specimen tested at high temperatures. The test specimen, as denoted by its name, was a long radius elbow. As it was the first elbow, the initial heating to 35 C was undertaken carefully, so as to not overshoot the specified temperature. After spending some time on incrementally increasing the furnace temperature such that the elbow flank temperature slowly increased to 35 C, the testing could begin. The carefulness was warranted due to the fact that if the temperature of the flank exceeded 35 C and therefore had to be cooled down, the material properties could change. In the end, a furnace temperature of 1 C produced a steady C at the flank and C at the intrados. The use of insulation has been affirmed with a more reasonably close flank and intrados temperature values, as compared to the initial temperature test on the shake table. Figure. shows the history of heating the elbow, both before and during testing. 11

134 T ( C) SS3L HTLR1 Test Started Test Stopped Flank Intrados 8 1 t (min) Figure.: Thermocouple data before and during testing. At the time the test was started, there was an increase in temperature in the elbow. This temperature is probably indicative of the fatigue damage accumulation that was occurring within the elbow while it is undergoing cyclic loading. Since with the test setup it was not possible to determine the fatigue crack initiation of the elbow (the furnace prevented any manual observation of the elbow), the elbow was tested to cycle 75, to at least reach the cycle of failure of the unpressured elbow tested at room temperature. However, post-test examination of the load response gave some indication to the fatigue crack initiation of the elbow. 117

135 (a) SS3L HTLR1 8 SS3L HTLR1 T = 35 C δa = 11.8 mm Pc (kn) P (kn) 1 5 (b) -5 T = 35 C δa = 11.8 mm -1 5 Cycle t (sec) N 8 Figure.5: Determining the fatigue life of HTLR1 through (a) load versus time and (b) load amplitude versus cycle. Figure.5 details the method of determining the fatigue life. After testing, a prominent fatigue crack was present on a flank, suggesting that the elbow had failed long before cycle 75 and that the crack had simply grown as the loading continued after failure. Viewing Figure.5a shows early on in the testing, the load increases then decreases over time before leveling off. However, at around 13 seconds, the peak loads start decreasing at a faster rate. Plotting the load amplitude versus cycle as shown in Figure.5b, a line can be drawn across where the force values have stabilized. Then, it is simple to determine where the amplitude values diverge, which should correspond to the cycle of significant cracking. Using this method, the cycle of crack initiation of HTLR1 is. The load responses are shown in Figure.. 118

136 P (kn) P (kn) 1 5 SS3L HTLR1 T = 35 C (a) 1 5 SS3L HTLR1 Peaks (b) -5 Cycle T = 35 C Valleys N Figure.: HTLR1 responses of (a) load verus displacement and (b) load versus cycle. The first cycle in the load versus displacement plot shows an initial compressive force of about.9 kn. This is due to the heating of the elbow while the actuator is held at its initial zero point. This shows the significance of this force as it is almost one-fourth of the peak force values. Turning to the plot displaying the peak force values versus the number of cycles, it shows the increase in magnitude during the first cycles and then softening effects occur until a stable 3.9 kn is maintained. As previously mentioned, no change in diameter or strain responses could be obtained through the ΔD Device or strain gauges. In the attempt to at least obtain the final strain state, the DIC method was employed. The result from the DIC analysis is presented in Figure

137 Figure.7: HTLR1 cycle 75 DIC circumferential strain. A quick examination shows that the DIC method failed in producing a reasonable result. While a band of concentrated strain appears like in LR5, the magnitude of strains are far below what is expected. In addition, the maximum tensile strain of ~1.5% appears at the lower left of the image, rather than in the middle of the band, where it would be expected. Also, the analysis shows a compressive circumferential strain of over % at the right-hand edges. In contrast, turning to the room temperature long radius test, LR1, the flank strain gauge showed strains reached over %. The primary potential cause of this problem could be the fact that interval of image capturing was too large. In the previous DIC analysis in LR5, the interval of the image was each tensile displacement peak. Here, one image was taken before testing, and one more was taken after 75 cycles. Other potential causes could be due to changes in 1