STP-PT-031 PRESSURE INDUCED FATIGUE Prepared by: Joseph A Kapp, PhD, PE Elmhurst Research, Inc Date of Issuance: March 16, 2010 This report was prepared as an account of work sponsored by ASME Pressure Technology Codes and Standards and the ASME Standards Technology, LLC (ASME ST-LLC) Neither ASME, ASME ST-LLC, the author, nor others involved in the preparation or review of this report, nor any of their respective employees, members or persons acting on their behalf, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe upon privately owned rights Reference herein to any specific commercial product, process or service by trade name, trademark, manufacturer or otherwise does not necessarily constitute or imply its endorsement, recommendation or favoring by ASME ST-LLC or others involved in the preparation or review of this report, or any agency thereof The views and opinions of the authors, contributors and reviewers of the report expressed herein not necessarily reflect those of ASME ST-LLC or others involved in the preparation or review of this report, or any agency thereof ASME ST-LLC does not take any position with respect to the validity of any patent rights asserted in connection with any items mentioned in this document, and does not undertake to insure anyone utilizing a publication against liability for infringement of any applicable Letters Patent, nor assumes any such liability Users of a publication are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, is entirely their own responsibility Participation by federal agency representative(s) or person(s) affiliated with industry is not to be interpreted as government or industry endorsement of this publication ASME is the registered trademark of the American Society of Mechanical Engineers No part of this document may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher ASME Standards Technology, LLC Three Park Avenue, New York, NY 10016-5990 ISBN No 978-0-7918-3269-1 Copyright © 2010 by ASME Standards Technology, LLC All Rights Reserved Pressure Induced Fatigue STP-PT-031 TABLE OF CONTENTS Foreword iv Abstract v INTRODUCTION PREVIOUS EXPERIMENTAL RESULTS ASME SECTION VIII DIV FATIGUE ANALYSIS ASME SECTION VIII DIV FATIGUE ANALYSIS 4.1 Numerical Stress Analysis Results (Calculated Values of ip) LIFE PREDICTION RESULTS MARKL ANALYSIS APPROACH TO THE OBSERVED DATA 12 DISCUSSION 14 CONCLUSION 18 References 19 Acknowledgments 20 LIST OF TABLES Table - Summary of Fatigue Test Results Table - Section VIII Div Design Life Analysis Results 10 Table - Section VIII Div Design Life Analysis Results 11 Table - Comparison of Measured Results with Equation (7) as the Design Curve 15 Table - Comparison of Safety Factors for Various Design Curves 16 LIST OF FIGURES Figure - Comparison of Measured Fatigue Lives and Section VIII, Div Design Curves Figure - Comparison of Measured Fatigue Lives and Section VIII, Div Analysis Method Figure - Analysis of the Measured Data Using a Markl Power Law Equation 13 Figure - Comparison of Data with Various Design Curves 14 iii STP-PT-031 Pressure Induced Fatigue FOREWORD This document was developed under a research and development project which resulted from ASME Pressure Technology Codes & Standards (PTCS) committee requests to identify, prioritize and address technology gaps in current or new PTCS Codes, Standards and Guidelines This project is one of several intended to establish and maintain the technical relevance of ASME codes & standards products The specific project related to this document is project 07-06 (B31#3), entitled “Pressure Induced Fatigue.” Established in 1880, the American Society of Mechanical Engineers (ASME) is a professional notfor-profit organization with more than 127,000 members promoting the art, science and practice of mechanical and multidisciplinary engineering and allied sciences ASME develops codes and standards that enhance public safety, and provides lifelong learning and technical exchange opportunities benefiting the engineering and technology community Visit www.asme.org for more information The ASME Standards Technology, LLC (ASME ST-LLC) is a not-for-profit Limited Liability Company, with ASME as the sole member, formed in 2004 to carry out work related to newly commercialized technology The ASME ST-LLC mission includes meeting the needs of industry and government by providing new standards-related products and services, which advance the application of emerging and newly commercialized science and technology, and providing the research and technology development needed to establish and maintain the technical relevance of codes and standards Visit www.stllc.asme.org for more information iv Pressure Induced Fatigue STP-PT-031 ABSTRACT The purpose of this study is to begin the process of developing an appropriate and accurate method of predicting fatigue failure due to internal pressure loading in piping components Historically, piping component fatigue has been analyzed using the approach of Markl [1] The results from the cyclic pressure testing of 41 piping intersections have been evaluated The fatigue results were found to follow the Markl type power law relationship with some considerable scatter The scatter observed in the data is attributed to variation due to the nature of fatigue failure in large welded structures It is further concluded that several design curves are appropriate for use as a design rule for pressure induced fatigue v STP-PT-031 Pressure Induced Fatigue INTENTIONALLY LEFT BLANK vi Pressure Induced Fatigue STP-PT-031 INTRODUCTION Several recent failures in welding tees and branch connections in B31.1 piping due to pressure cycling have been brought to the attention of the B31.1 committee In addition, there has been a longstanding agenda item on the B31 Technical Committee on Mechanical Design (MDC) to develop stress multipliers of some sort for fatigue evaluation of piping components due to pressure cycling The fatigue performance of piping components has been well understood in terms of thermal expansion stresses (i.e., secondary stresses), but the fatigue performance due to pressure cycling has been less understood With the relatively high D/t ratios of high temperature power and process piping, fatigue due to pressure cycling is generally less significant than fatigue due to thermal expansion However, as the pressure technology codes and standards use higher and higher strength materials (resulting in thinner components) and operate at higher and higher pressures (e.g., hydrogen for fuel technology), the cycling effect of pressure is expected to be much more pronounced The purpose of this study is to begin the process of developing an appropriate and accurate method of predicting fatigue failure due to internal pressure loading in piping components Historically, piping component fatigue has been analyzed using the approach of Markl [1] Fatigue life is accounted for by using a power law relationship between the applied loading stresses and life in the form: C = iSN 0.2 (1) Where N is the fatigue life of the component, C is a material constant, i is the stress intensification factor and S is the nominal applied stress This equation assumes a linear relationship between Log(S) and Log(N) as has been observed in rotating beam fatigue tests in steels The exponent value of 0.2 was used based on the experimental observation for steel, and Markl suggests an appropriate value for C is 245 ksi for welded carbon steel For pressure-induced fatigue, the nominal applied stress is the tangential stress in the pipe due to internal pressure and the stress intensification factor (now defined as ip) is experimentally determined through actual fatigue testing of piping components It has been thought that experimental development of ip is superior to analytical methods since the actual components are welded engineering structures and the loading actually developed in the welded structure may not be well described by a continuous homogeneous model that could be used to generate theoretical stresses Therefore, ip is determined for a given pipe intersection by performing two fatigue comparative fatigue tests on a welded pipe without the pipe intersection and also on a pipe with the intersection in such a manner to produce the same fatigue life The value of ip is the ratio of the nominal stress in the pipe without the piping intersection to the nominal stress in the pipe with the piping intersection The purpose of this study is to develop a plan and estimate the cost of performing such a test plan that will result in the determination of ip However, based on the findings obtained, it may not be necessary to perform a testing program since there appears to be sufficient existing data and analysis that adequately describe the fatigue performance of pressure loaded pipe intersections STP-PT-031 Pressure Induced Fatigue PREVIOUS EXPERIMENTAL RESULTS Eight references were provided by Everett C Rodabaugh, PE All of the references were based on work performed 40 to 50 years ago and not all of them could be obtained at local technical libraries or even from engineering society sources Mr Rodabaugh is sending copies of those papers that are only in his library and the results from these sources will be included later Those references that were obtained proved valuable in addressing the issue at hand A large experimental program whose purpose it was to establish values of ip in a traditional manner was performed by Decock [2] This program tested 119 vessels of various sizes with piping intersections The vessels were instrumented with strain gages that were used to determine the maximum stress developed at the various pipe intersections Using the experimental stress analysis results, nominal stress concentration factors were developed for the particular vessel, and based on that, were cyclically fatigue tested at that cyclic pressure that would produce a fatigue life of 100,000 cycles In most cases, the vessels did not fail at 100,000 cycles, and the cyclic pressure was subsequently adjusted (in some cases several times) until fatigue failure of the vessel occurred The data reported in Decock [2] is difficult to include in our review since the actual applied pressure was not reported, and it is not clear how to account for the cumulative damage that was produced in the testing Therefore, we are not including these results in our analysis below Picket and Grigory [3] reported cyclic testing results of several 36 in vessels, each with several different nozzles installed Testing was performed until of one of the piping intersections failed through fatigue The failed intersection was then removed, the vessel repaired, and testing continued until the next weakest intersection failed The repair procedure was repeated and testing again continued until the vessel could no longer be repaired The several test vessels were made from materials of different strengths, and the vessels were tested at different pressure levels Fourteen meaningful fatigue test results were developed from this paper Kameoka et al [4] fatigue tested 24 pipe intersections of various dimensions at various test pressures, all of which were used in this analysis Mayers [5] reported the test results from four piping connections, three from an experimental program and one field failure, in his report to the Design Committee of B31 In all, the results from the fatigue failures of 41 piping intersections were reviewed to generate this report STP-PT-031 Pressure Induced Fatigue LIFE PREDICTION RESULTS Using the Section VIII, Div approach with Equation (5) for the stress concentration factor, we can generate Salteq for all of the experimental results found These calculations are summarized in Table Also shown in the table is the design life that would have been allowed if the Section VIII, Div design life rule were invoked The comparison between the actual measured life and the allowed design life is also visually made in Figure All of the data fall above and to the right of the design curves, even though one sample is quite close to the design curve This suggests that the fatigue analysis approach of Section VIII, Div would have produced safe designs for the specimens tested The results obtained using the methods outlined in Section VIII, Div are given in Table and plotted in Figure As with the case for the Section VIII, Div results, all of the measured data fall to the right and above the design curve and thus could have been used to produce safe designs We have reported the safety factor on stress as well as the safety factor on life in Table and observe that the average safety factor on life is 10.6 and the average safety factor on stress is 1.9 However, we believe that this is misleading Examining the plot of the data in Figure 2, it is clear that the trend of the design curve is not the trend of the data The Div results are much closer to the design curve at higher stress and short life than they are at lower stress and long life Comparing this with the plot of the data in Figure indicates that the sense of the Div design curves follow the sense of the measured data over the complete range of stress and life measured Therefore, although the Div approach would result in safe designs, we not believe that the Div approach correctly models the pressure induced fatigue behavior that we are studying Pressure Induced Fatigue STP-PT-031 1000 100 Salteq (ksi) Design Curve UTS < 80 Ksi Mayers Report Data Kobe Steel Data WRC Bulletin 135 Data Design Curve UTS 115-130 ksi 10 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Cycles Figure - Comparison of Measured Fatigue Lives and Section VIII, Div Design Curves Stress Range 1000 Div Design Curve 100 10 100 Measured Data 1000 10000 100000 1000000 Cycles Figure - Comparison of Measured Fatigue Lives and Section VIII, Div Analysis Method STP-PT-031 Pressure Induced Fatigue Table - Section VIII Div Design Life Analysis Results Specimen No Pressure Range (psi) d/D D/T t/T ip PD/2T pmin (psi) pmax (psi) Sa (ksi) Salteq (ksi) Design Life N Measured T-11 6900 1.000 10.243 1.000 3.676 35339 100 7000 58.6 101.0 573 2975 T-12 1795 0.417 34.934 1.000 3.445 31354 1800 52.5 88.4 813 76620 T-13 6900 0.417 10.243 1.000 2.292 35339 100 7000 36.5 48.1 4958 15084 Descale 3000 1.000 8.889 1.000 3.483 13333 3000 20.6 24.0 48571 300000 T13-F 6382 0.152 22.723 0.815 1.962 72509 6382 68.0 134.1 283 2982 T13-D 5657 0.152 22.723 0.815 1.962 64269 5657 60.3 107.1 494 9102 T13-C 5222 0.152 22.723 0.815 1.962 59326 5222 55.6 93.3 705 28286 F13-F 5512 0.152 22.723 1.000 1.837 62622 5512 55.0 91.0 752 6518 F13-D 5222 0.152 22.723 1.000 1.837 59326 5222 52.1 83.3 952 7553 F13-C 4932 0.152 22.723 1.000 1.837 56030 4932 49.2 76.2 1222 9772 F13-B 4351 0.152 22.723 1.000 1.837 49438 4351 43.4 63.1 2110 15553 T*13-4 7252 0.233 22.723 1.000 2.207 82397 7252 86.9 239.6 74 4360 T*13-2 5802 0.233 22.723 1.000 2.207 65917 5802 69.5 141.9 247 9502 T*13-3 5077 0.233 22.723 1.000 2.207 57678 5077 60.8 109.8 463 9116 T*13-1 4351 0.233 22.723 1.000 2.207 49438 4351 52.2 84.4 919 21135 F'13-1 7252 0.233 22.723 1.000 2.207 82397 7252 86.9 239.6 74 2781 F'13-4 5802 0.233 22.723 1.000 2.207 65917 5802 69.5 141.9 247 8586 F'13-2 5222 0.233 22.723 1.000 2.207 59326 5222 62.6 115.6 407 14805 F'13-3 4351 0.233 22.723 1.000 2.207 49438 4351 52.2 84.4 919 20505 T20-D 7977 0.233 14.700 1.040 1.928 58634 7977 52.7 82.0 995 4376 T20-A 6962 0.233 14.700 1.040 1.928 51172 6962 46.0 66.8 1780 6145 T20-C 6382 0.233 14.700 1.040 1.928 46908 6382 42.1 59.0 2591 9455 T20-B 5802 0.233 14.700 1.040 1.928 42643 5802 38.3 51.8 3918 19032 F20-E 7252 0.233 14.700 1.040 1.928 53304 7252 47.9 71.0 1494 3462 F20-F 6382 0.233 14.700 1.040 1.928 46908 6382 42.1 59.0 2591 6398 F20-A 5802 0.233 14.700 1.040 1.928 42645 5802 38.3 51.8 3918 14288 F20-C 4932 0.233 14.700 1.040 1.928 36247 4932 32.6 41.8 7306 20890 V-1-1 4325 0.266 18.000 0.297 3.276 38925 4325 60.2 108.9 473 7223 V-1-6 4325 0.266 18.000 0.297 3.276 38925 4325 60.2 108.9 473 7516 V-1-11 4325 0.056 18.000 0.094 1.910 38925 4325 35.1 46.6 5502 5174 V-2-6 2650 0.266 18.000 0.297 3.276 23850 2650 36.9 50.8 4162 85868 V-2-2 2650 0.266 18.000 0.297 3.276 23850 2650 36.9 50.8 4162 123618 V-3-1 4400 0.266 18.000 0.297 3.276 39600 4400 61.3 112.4 437 8990 V-4-6 3460 0.266 18.000 0.297 3.276 31140 3460 48.2 75.0 1276 40041 V-4-11 3460 0.056 18.000 0.094 1.910 31140 3460 28.1 35.0 13104 48437 V-6-2 4400 0.266 18.000 0.297 3.276 39600 4400 61.3 112.4 437 19272 V-7-9B 2650 0.395 18.000 0.403 3.773 23850 2650 42.5 62.4 2187 23908 V-7-2B 2650 0.278 18.000 1.094 2.157 23850 2650 24.3 29.4 23786 135600 V-7-2N 2650 0.278 18.000 1.094 2.157 23850 2650 24.3 29.4 23786 375357 V-8-1 4400 0.266 18.000 0.297 3.276 39600 4400 61.3 112.4 437 21070 V-8-2 4400 0.266 18.000 0.297 3.276 39600 4400 61.3 112.4 437 26311 10 Pressure Induced Fatigue STP-PT-031 Table - Section VIII Div Design Life Analysis Results Specimen No P (psi) d/D D/T t/T T-11 6900 1.000 10.243 1.000 T-12 1795 0.417 34.934 T-13 6900 0.417 10.243 ip Smax Smin Stress Corrected Corrected Design (ksi) (ksi) Range Neuber for R Life (ksi) (ksi) (ksi) (Cycles) Actual Life (Cycles) Safety Factor N Safety Factor Stress 2975 3.1 1.4 3.676 118.9 1.7 117.2 93.3 91.6 946 1.000 3.445 105.2 0.3 104.9 88.9 66.5 2583 76620 29.7 3.0 1.000 2.292 74.1 1.1 73.1 70.9 69.7 2230 15084 6.8 1.8 Descale 3000 1.000 8.889 1.000 3.483 41.2 0.0 41.2 41.2 34.4 20289 300000 14.8 2.4 T13-F 6382 0.152 22.723 0.815 1.962 136.0 0.0 136.0 98.5 72.2 1998 2982 1.5 1.1 T13-D 5657 0.152 22.723 0.815 1.962 120.6 0.0 120.6 94.3 69.1 2290 9102 4.0 1.6 T13-C 5222 0.152 22.723 0.815 1.962 111.3 0.0 111.3 91.3 66.9 2538 28286 11.1 2.2 1.3 F13-F 5512 0.152 22.723 1.000 1.837 110.0 0.0 110.0 90.8 66.5 2582 6518 2.5 F13-D 5222 0.152 22.723 1.000 1.837 104.2 0.0 104.2 88.6 64.9 2783 7553 2.7 1.4 F13-C 4932 0.152 22.723 1.000 1.837 98.4 0.0 98.4 86.1 63.1 3044 9772 3.2 1.5 F13-B 4351 0.152 22.723 1.000 1.837 86.8 0.0 86.8 80.2 58.8 3801 15553 4.1 1.6 T*13-4 7252 0.233 22.723 1.000 2.207 173.8 0.0 173.8 106.3 77.9 1574 4360 2.8 1.4 T*13-2 5802 0.233 22.723 1.000 2.207 139.1 0.0 139.1 99.3 72.7 1951 9502 4.9 1.7 T*13-3 5077 0.233 22.723 1.000 2.207 121.7 0.0 121.7 94.6 69.3 2267 9116 4.0 1.6 T*13-1 4351 0.233 22.723 1.000 2.207 104.3 0.0 104.3 88.6 64.9 2783 21135 7.6 1.9 F'13-1 7252 0.233 22.723 1.000 2.207 173.8 0.0 173.8 106.3 77.9 1574 2781 1.8 1.2 F'13-4 5802 0.233 22.723 1.000 2.207 139.1 0.0 139.1 99.3 72.7 1951 8586 4.4 1.6 F'13-2 5222 0.233 22.723 1.000 2.207 125.2 0.0 125.2 95.7 70.1 2190 14805 6.8 1.8 1.9 F'13-3 4351 0.233 22.723 1.000 2.207 104.3 0.0 104.3 88.6 64.9 2783 20505 7.4 T20-D 7977 0.233 14.700 1.040 1.928 105.4 0.0 105.4 89.1 68.7 2333 4376 1.9 1.2 T20-A 6962 0.233 14.700 1.040 1.928 91.9 0.0 91.9 83.0 64.0 2907 6145 2.1 1.3 T20-C 6382 0.233 14.700 1.040 1.928 84.3 0.0 84.3 78.7 60.7 3441 9455 2.7 1.4 T20-B 5802 0.233 14.700 1.040 1.928 76.6 0.0 76.6 73.6 56.7 4244 19032 4.5 1.6 F20-E 7252 0.233 14.700 1.040 1.928 95.8 0.0 95.8 84.9 65.5 2709 3462 1.3 1.1 F20-F 6382 0.233 14.700 1.040 1.928 84.3 0.0 84.3 78.7 60.7 3434 6398 1.9 1.2 F20-A 5802 0.233 14.700 1.040 1.928 76.6 0.0 76.6 73.6 56.7 4244 14288 3.4 1.5 F20-C 4932 0.233 14.700 1.040 1.928 65.1 0.0 65.1 64.2 49.5 6496 20890 3.2 1.5 V-1-N-1 4325 0.266 18.000 0.297 3.276 120.4 0.0 120.4 94.3 89.4 1021 7223 7.1 1.9 V-1-N-6 4325 0.266 18.000 0.297 3.276 120.4 0.0 120.4 94.3 89.4 1021 7516 7.4 1.9 V-1-N-11 4325 0.056 18.000 0.094 1.910 70.2 0.0 70.2 68.6 65.1 2760 5174 1.9 1.2 73.8 71.4 67.7 2435 85868 35.3 3.1 3.5 V-2-6 2650 0.266 18.000 0.297 3.276 73.8 0.0 V-2-2 2650 0.266 18.000 0.297 3.276 73.8 0.0 73.8 71.4 67.7 2435 123618 50.8 V-3-1 4400 0.266 18.000 0.297 3.276 122.5 0.0 122.5 94.9 90.0 1001 8990 9.0 2.0 V-4-6 3460 0.266 18.000 0.297 3.276 96.3 0.0 96.3 85.2 80.8 1401 40041 28.6 2.9 V-4-11 3460 0.056 18.000 0.094 1.910 56.2 0.0 56.2 55.9 53.0 5239 48437 9.2 2.0 V-6-2 4400 0.266 18.000 0.297 3.276 122.5 0.0 122.5 94.9 90.0 1001 19272 19.2 2.6 V-7-9B 2650 0.395 18.000 0.403 3.773 85.0 0.0 85.0 79.2 75.1 1764 23908 13.6 2.3 V-7-2B 2650 0.278 18.000 1.094 2.157 48.6 0.0 48.6 48.5 46.0 8171 135600 16.6 2.5 V-7-2N 2650 0.278 18.000 1.094 2.157 48.6 0.0 48.6 48.5 46.0 8171 375357 45.9 3.4 V-8-1 4400 0.266 18.000 0.297 3.276 122.5 0.0 122.5 94.9 90.0 1001 21070 21.0 2.6 V-8-2 4400 0.266 18.000 0.297 3.276 122.5 0.0 122.5 94.9 90.0 1001 26311 26.3 2.8 Average 10.6 1.9 11 STP-PT-031 Pressure Induced Fatigue MARKL ANALYSIS APPROACH TO THE OBSERVED DATA The conclusions we draw from the analysis reported in the previous section indicate that a fatigue analysis that is used in the pressure vessel codes can be applied to the problem of pressure induced fatigue of welded pipe intersections However, the approach is a little cumbersome and foreign to the practicing piping engineer It is of interest to formulate the problem using the simpler approach of Markl, which assumes that there is a power law relationship between the stress range and fatigue life We know from the Div analysis, above, that we must account for the influence of mean stress and multiaxial stresses to determine an equivalent stress amplitude The Markl approach does not account for these factors explicitly, but the approach can be taken by making the following assumptions 1) The calculated value of ip from Widera and Wei are adequate approximations to the experimentally determined values of ip 2) The stresses produced in a pipe intersection that results in a pressure induced fatigue failure are sufficiently uniaxial that the effects of multiaxial loading can be ignored 3) The mean stress effects are incorporated in the design curve The maximum stress produced in the piping intersection is simply twice the value of the stress amplitude calculated as above and reported in Table for most of the samples reported There are a few samples that had a small minimum applied pressure; in those cases, the maximum stress will be slightly larger than twice the stress amplitude reported in Table To account for the mean stress in the design curve, we manipulate Equation (2) Since the loading is uniaxial and the minimum pressure is assumed to be zero, both Saltij and Smnij become Smax/2 The allowable maximum stress is then determined by solving for Smax in terms of Salteq: S max = 1− 2S alteq 0.2 S alteq (6) 12.5 The design curve is generated by plugging the values for Salteq from the design curve in Section VIII, Division for welded material with ultimate strength less than or equal to 85 ksi When the design curve as described in Equation (6) is plotted, a straight line is produced between 103 and 106 cycles as shown in Figure Also shown in Figure is a fit to the design curve that is remarkably similar to the equation that Markl proposed for carbon steel From the figure, the design curve equation is: 269,660 = i p p max D 0.19 N 2T 12 (7) Pressure Induced Fatigue STP-PT-031 Smax (ksi) 1000.00 Markl Approach (No Mean stress Correction) y = 601.14x -0.1896 R2 = 0.4852 Design Curve Corrected for Mean Stress 100.00 Pow er (Markl Approach (No Mean stress Correction)) Pow er (Design Curve Corrected for Mean Stress) y = 269.66x R2 = 0.9992 -0.19 10.00 1000 10000 100000 1000000 Measured Life Cycles Figure - Analysis of the Measured Data Using a Markl Power Law Equation Markl used in his paper a value of 245,000 for the constant and the exponent had a value of 0.2 We are not sure if Markl suggests that his equation is a design rule or the failure curve Nevertheless, Equation (7) is derived from the test results of small laboratory push-pull fatigue samples of welded material and indeed bounds the observed data by a reasonable margin The test results data are also plotted in Figure and these data can reasonably be assumed to fit a power law relationship, which is determined by linear regression and also plotted in the figure The equation for the fit to the measured data is: 601,140 = i p pmax D 0.1896 N 2T (8) This equation indicates that the mean of the measured data fall on a straight line that is essentially parallel to the design curve and offset by a factor of about 2.2 13 STP-PT-031 Pressure Induced Fatigue DISCUSSION The measured data are compared with the design curve in tabular format in Table for all of the measured data obtained Included in the table are values of safety factors on both stress and life for all of the individual life measurements, using Equation (7) as the design curve The average value of safety factor on stress is 2.3, and the average value of safety factor on life is 130 These safety factors may be more conservative than necessary for a design curve Other ASME design curves have had a safety factor of on stress or 20 on life If the mean life curve for all piping intersections loaded by internal pressure is, in fact, Equation (8), then the constant in Equation (7) for a safety factor of on stress would be 300,570 Similarly, the constant for a safety factor of 20 on life is 340,640 Design curves using these values are compared with the measured data in Figure and in Table 1000.00 Markl Approach (No Mean stress Correction) y = 601.14x R2 = 0.4852 Smax (ksi) -0.1 896 Derived f rom Div Design Curve Derived From Measured Data and Saf ety Factor of on Stress 100.00 Derived From Measured Data and Saf ety Factor of 20 on Life Pow er (Markl Approach (No Mean stress Correction)) 10.00 1000 10000 100000 1000000 Me asured Life Cycles Figure - Comparison of Data with Various Design Curves 14 Pressure Induced Fatigue STP-PT-031 Table - Comparison of Measured Results with Equation (7) as the Design Curve Specimen No pmax (psi) d/D D/T t/T ip PD/2T Smax (ksi) N Measured Design Life T-11 7000 1.000 10.243 1.000 3.676 35339 118.9 2975 74 Safety Factor N 40 S for Measured N 59.0 Safety Factor S 2.0 T-12 1800 0.417 34.934 1.000 3.445 31354 105.2 76620 142 541 31.8 3.3 T-13 7000 0.417 10.243 1.000 2.292 35339 74.1 15084 894 17 43.3 1.7 Descale 3000 1.000 8.889 1.000 3.483 13333 41.2 300000 19,652 15 24.6 1.7 T13-F 6382 0.152 22.723 0.815 1.962 72509 136.0 2982 37 81 59.0 2.3 T13-D 5657 0.152 22.723 0.815 1.962 64269 120.6 9102 69 132 47.7 2.5 T13-C 5222 0.152 22.723 0.815 1.962 59326 111.3 28286 105 268 38.5 2.9 F13-F 5512 0.152 22.723 1.000 1.837 62622 110.0 6518 112 58 50.8 2.2 F13-D 5222 0.152 22.723 1.000 1.837 59326 104.2 7553 149 51 49.4 2.1 F13-C 4932 0.152 22.723 1.000 1.837 56030 98.4 9772 202 48 47.1 2.1 F13-B 4351 0.152 22.723 1.000 1.837 49438 86.8 15553 390 40 43.1 2.0 T*13-4 7252 0.233 22.723 1.000 2.207 82397 173.8 4360 10 432 54.9 3.2 T*13-2 5802 0.233 22.723 1.000 2.207 65917 139.1 9502 33 291 47.3 2.9 T*13-3 5077 0.233 22.723 1.000 2.207 57678 121.7 9116 66 138 47.7 2.6 T*13-1 4351 0.233 22.723 1.000 2.207 49438 104.3 21135 148 142 40.7 2.6 F'13-1 7252 0.233 22.723 1.000 2.207 82397 173.8 2781 10 276 59.8 2.9 F'13-4 5802 0.233 22.723 1.000 2.207 65917 139.1 8586 33 263 48.2 2.9 F'13-2 5222 0.233 22.723 1.000 2.207 59326 125.2 14805 57 261 43.5 2.9 F'13-3 4351 0.233 22.723 1.000 2.207 49438 104.3 20505 148 138 40.9 2.6 T20-D 7977 0.233 14.700 1.040 1.928 58634 105.4 4376 141 31 54.8 1.9 1.8 T20-A 6962 0.233 14.700 1.040 1.928 51172 91.9 6145 288 21 51.4 T20-C 6382 0.233 14.700 1.040 1.928 46908 84.3 9455 455 21 47.4 1.8 T20-B 5802 0.233 14.700 1.040 1.928 42643 76.6 19032 752 25 41.5 1.8 F20-E 7252 0.233 14.700 1.040 1.928 53304 95.8 3462 232 15 57.3 1.7 F20-F 6382 0.233 14.700 1.040 1.928 46908 84.3 6398 455 14 51.0 1.7 F20-A 5802 0.233 14.700 1.040 1.928 42645 76.6 14288 752 19 43.8 1.7 F20-C 4932 0.233 14.700 1.040 1.928 36247 65.1 20890 1,769 12 40.7 1.6 V-1-N-1 4325 0.266 18.000 0.297 3.276 38925 120.4 7223 70 104 49.8 2.4 2.4 V-1-N-6 4325 0.266 18.000 0.297 3.276 38925 120.4 7516 70 108 49.5 V-1-N-11 4325 0.056 18.000 0.094 1.910 38925 70.2 5174 1,190 53.1 1.3 V-2-6 2650 0.266 18.000 0.297 3.276 23850 73.8 85868 917 94 31.1 2.4 V-2-2 2650 0.266 18.000 0.297 3.276 23850 73.8 123618 917 135 29.1 2.5 V-3-1 4400 0.266 18.000 0.297 3.276 39600 122.5 8990 64 141 47.8 2.6 V-4-6 3460 0.266 18.000 0.297 3.276 31140 96.3 40041 225 178 36.0 2.7 V-4-11 3460 0.056 18.000 0.094 1.910 31140 56.2 48437 3,851 13 34.7 1.6 V-6-2 4400 0.266 18.000 0.297 3.276 39600 122.5 19272 64 303 41.4 3.0 V-7-9B 2650 0.395 18.000 0.403 3.773 23850 85.0 23908 436 55 39.7 2.1 V-7-2B 2650 0.278 18.000 1.094 2.157 23850 48.6 135600 8,267 16 28.6 1.7 V-7-2N 2650 0.278 18.000 1.094 2.157 23850 48.6 375357 8,267 45 23.5 2.1 V-8-1 4400 0.266 18.000 0.297 3.276 39600 122.5 21070 64 331 40.7 3.0 V-8-2 4400 0.266 18.000 0.297 3.276 39600 122.5 26311 64 414 39.0 3.1 Average 130 15 2.3 STP-PT-031 Pressure Induced Fatigue Table - Comparison of Safety Factors for Various Design Curves S for Safety Design Life Safety S for Safety Design Life Safety S for Safety Specimen Smax N Design Life Safety Factor Measured Factor Factor Measured Factor Factor Measured Factor No (ksi) Measured (Constant= N (Constant= N N S N S (Constant= N N S 300,570) 340,640) 269,660) T-11 118.9 2975 74 40 59.0 2.0 132 22.6 65.8 1.8 254 11.7 74.5 1.6 T-12 105.2 76620 142 541 31.8 3.3 251 305.4 35.5 3.0 485 158.0 40.2 2.6 T-13 74.1 15084 894 17 43.3 1.7 1,582 9.5 48.3 1.5 3,058 4.9 54.7 1.4 Descale 41.2 300000 19,652 15 24.6 1.7 34,791 8.6 27.4 1.5 67,223 4.5 31.0 1.3 T13-F 136.0 2982 37 81 59.0 2.3 65 45.9 65.7 2.1 125 23.8 74.5 1.8 T13-D 120.6 9102 69 132 47.7 2.5 122 74.3 53.2 2.3 237 38.5 60.3 2.0 T13-C 111.3 28286 105 268 38.5 2.9 187 151.5 42.9 2.6 361 78.4 48.6 2.3 F13-F 110.0 6518 112 58 50.8 2.2 199 32.8 56.7 1.9 384 17.0 64.2 1.7 F13-D 104.2 7553 149 51 49.4 2.1 264 28.6 55.1 1.9 511 14.8 62.4 1.7 F13-C 98.4 9772 202 48 47.1 2.1 357 27.4 52.5 1.9 690 14.2 59.5 1.7 F13-B 86.8 15553 390 40 43.1 2.0 690 22.5 48.0 1.8 1,333 11.7 54.4 1.6 T*13-4 173.8 4360 10 432 54.9 3.2 18 244.3 61.2 2.8 34 126.4 69.3 2.5 T*13-2 139.1 9502 33 291 47.3 2.9 58 164.5 52.7 2.6 112 85.1 59.8 2.3 T*13-3 121.7 9116 66 138 47.7 2.6 117 78.1 53.2 2.3 225 40.4 60.2 2.0 T*13-1 104.3 21135 148 142 40.7 2.6 263 80.5 45.3 2.3 507 41.7 51.4 2.0 F'13-1 173.8 2781 10 276 59.8 2.9 18 155.8 66.6 2.6 34 80.6 75.5 2.3 F'13-4 139.1 8586 33 263 48.2 2.9 58 148.6 53.8 2.6 112 76.9 60.9 2.3 F'13-2 125.2 14805 57 261 43.5 2.9 101 147.2 48.5 2.6 194 76.2 54.9 2.3 F'13-3 104.3 20505 148 138 40.9 2.6 263 78.1 45.6 2.3 507 40.4 51.6 2.0 T20-D 105.4 4376 141 31 54.8 1.9 249 17.6 61.1 1.7 481 9.1 69.3 1.5 T20-A 91.9 6145 288 21 51.4 1.8 510 12.1 57.3 1.6 985 6.2 64.9 1.4 T20-C 84.3 9455 455 21 47.4 1.8 806 11.7 52.8 1.6 1,558 6.1 59.8 1.4 T20-B 76.6 19032 752 25 41.5 1.8 1,331 14.3 46.2 1.7 2,572 7.4 52.4 1.5 F20-E 95.8 3462 232 15 57.3 1.7 411 8.4 63.9 1.5 795 4.4 72.4 1.3 F20-F 84.3 6398 455 14 51.0 1.7 806 7.9 56.9 1.5 1,558 4.1 64.4 1.3 F20-A 76.6 14288 752 19 43.8 1.7 1,331 10.7 48.8 1.6 2,572 5.6 55.3 1.4 F20-C 65.1 20890 1,769 12 40.7 1.6 3,132 6.7 45.4 1.4 6,051 3.5 51.5 1.3 V-1-N-1 120.4 7223 70 104 49.8 2.4 123 58.6 55.6 2.2 238 30.3 63.0 1.9 V-1-N-6 120.4 7516 70 108 49.5 2.4 123 61.0 55.1 2.2 238 31.6 62.5 1.9 V-1-N-11 70.2 5174 1,190 53.1 1.3 2,107 2.5 59.2 1.2 4,071 1.3 67.1 1.0 V-2-6 73.8 85868 917 94 31.1 2.4 1,624 52.9 34.7 2.1 3,137 27.4 39.3 1.9 V-2-2 73.8 123618 917 135 29.1 2.5 1,624 76.1 32.4 2.3 3,137 39.4 36.7 2.0 V-3-1 122.5 8990 64 141 47.8 2.6 113 79.8 53.3 2.3 218 41.3 60.4 2.0 V-4-6 96.3 40041 225 178 36.0 2.7 399 100.4 40.1 2.4 771 51.9 45.5 2.1 V-4-11 56.2 48437 3,851 13 34.7 1.6 6,818 7.1 38.7 1.5 13,174 3.7 43.9 1.3 V-6-2 122.5 19272 64 303 41.4 3.0 113 171.2 46.1 2.7 218 88.6 52.3 2.3 V-7-9B 85.0 23908 436 55 39.7 2.1 771 31.0 44.3 1.9 1,490 16.0 50.2 1.7 V-7-2B 48.6 135600 8,267 16 28.6 1.7 14,635 9.3 31.8 1.5 28,277 4.8 36.1 1.3 V-7-2N 48.6 375357 8,267 45 23.5 2.1 14,635 25.6 26.2 1.9 28,277 13.3 29.7 1.6 V-8-1 122.5 21070 64 331 40.7 3.0 113 187.1 45.3 2.7 218 96.8 51.4 2.4 V-8-2 122.5 26311 64 414 39.0 3.1 113 233.7 43.5 2.8 218 120.9 49.3 2.5 Average 130.0 2.3 73.5 16 2.1 38.0 1.8 Pressure Induced Fatigue STP-PT-031 Let us return to a more general discussion of fatigue performance of large welded structures In addition to large piping systems, there are other classes of structures for which much work has been performed on fatigue life prediction Welded ships and offshore platforms are two types of large welded structures that can fail by fatigue and for which much work has been done Usually the fatigue of such structures is considered in a probabilistic manner and attempts are made to estimate the variance for the multiple factors that influence life Those factors that introduce variance in fatigue life prediction include variation in the applied loading; variation in the ability to measure a laboratory fatigue property; variation in the ability to calculate the developed stress for a particular loading; the variation in the ability to model the actual structure; and the variability associated with fatigue of large engineering structures in the real world We are not proposing to perform a probabilistic analysis of pressure induced fatigue of piping intersections, but we can draw guidance from a qualitative discussion of the components of variance to draw some conclusions about the problem First of all, there is little or no variance due to an uncertainty in the loading The applied loaded was controlled in all of the test results and would be controlled in an operating piping system in an operating plant The variation in the ability to measure an accurate fatigue curve is accounted for in our discussion, by applying a safety factor to that curve to generate the design curve The variance associated with the being able to calculate an accurate stress is small because we know that finite element analysis that was used to determine the stress concentrations used in this report are quite accurate Those two components of variance that contribute in a large manner to scatter in the observed data are most likely the variance from being able to accurately model the actual welded structure and the variance associated with the actual fatigue performance of large structures Let us look at the measured results from some identical samples Samples V-1-1 and V-1-6, and V-81 and V-8-2 from Pickett [3] are two pairs of two identical intersections Each pair is of the same design, made from the same material and tested at the same pressure Yet, each sample failed at a different life These are examples of variance that is due to either inability to model the actual problem (for example, each sample may not actually be identical, but there could be some variation in geometry that we are not aware of due to an inability to make identical welded structures) or the variation associated with fatigue of large structures In other words, it would be very difficult to predict, prior to testing, that each specimen in each of these two pairs would have a different fatigue life The purpose of the above discussion is to address the original intended purpose of this study: to develop an experimental program to measure values of ip Replicate samples such as V-1-1 and V-16, and V-8-1 and V-8-2 would be included in such an experimental program Since different lives were obtained, different values of ip for each of the identical samples would have been determined The reason for that is not because ip is different for each sample; it is due to some other variance Therefore, we conclude that the most accurate measure of ip is that which is obtained from Widera [6] 17 STP-PT-031 Pressure Induced Fatigue CONCLUSION The results from the cyclic pressure testing of 41 piping intersections have been evaluated The fatigue results were found to follow the Markl type power law relationship with some considerable scatter: 601,140 = i p pmax D 0.1896 N 2T In the equation, pmax is the maximum applied cyclic pressure, D is the main vessel mean diameter, T is the main vessel wall thickness, N is the measured fatigue life and ip is the pressure stress intensification factor given by the following equation from Widera [6]: 0.8 0.3 ⎛ d ⎞ ⎛ D⎞ ⎛ t ⎞ i p = 0.9270 − 1.5326⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ D⎠ ⎝ T ⎠ ⎝T ⎠ 0.3 0.8 0.4 ⎛ d ⎞ ⎛ D⎞ ⎛ t ⎞ + 2.2984⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ D⎠ ⎝ T ⎠ ⎝T ⎠ −0.2 Where d is the nozzle mean diameter and t is the nozzle wall thickness The scatter observed in the data is attributed to variation due to the nature of fatigue failure in large welded structures We further conclude that several design curves are appropriate for use as a design rule for pressure induced fatigue Based on the design curve from Section VIII, Division 3, the design rule would be: 269,660 = i p allowed pmax D 0.19 N 2T Based on applying a safety factor of two on stress to the mean measured fatigue lives, the design rule would be: 300,570 = i p allowed pmax D 0.1896 N 2T Based on applying a safety factor of 20 on stress to the mean measured fatigue lives, the design rule would be: 340,640 = i p allowed p max D 0.1896 N 2T 18 Pressure Induced Fatigue STP-PT-031 REFERENCES [1] A Markl, “Piping-Flexibility Analysis,” Transactions of the ASME, pp 127-149, Feb 1955 [2] J Decock, “Fatigue Tests on Pressure Vessel Connections,” Proc of the First International Conference on Pressure Vessel Technology, Delft, pp 743-761, 1969 [3] A Pickett and S Grigory, “Cyclic Pressure Tests of Full-Size Pressure Vessels,” Welding Research Council Bulletin 135, Nov 1968 [4] T Kameoka, E Sato, B An and Y Sato, “Low Cycle Fatigue of Pressure Vessels with BittWelded Nozzles,” Proc of the First International Conference on Pressure Vessel Technology, Delft, pp 1291-1301, 1969 [5] G Mayers, “Report on MD 06-818 Pressure Cycling of Piping Components,” Minutes of Meeting No 93 of the Mechanical Design Technical Committee (MDC) of B31 Code for Pressure Piping, Technical Committee, pp 256-273, Sept 21, 2006 [6] G Widera and Z Wei, “Part Parametric Finite Element Analysis of Large Diameter Shell Intersections (Internal Pressure),” Large Diameter Ratio Shell Intersections, WRC Bulletin 497, Dec 2004 19 STP-PT-031 Pressure Induced Fatigue ACKNOWLEDGMENTS The author acknowledges, with deep appreciation, the following individuals for their technical and editorial peer review of this document: • William J Koves • Michael J Rosenfeld • William H Eskridge Jr • Ronald W Haupt • Jimmy E Meyer The author further acknowledges, with deep appreciation, the activities of ASME staff and volunteers who have provided valuable technical input, advice and assistance with review of, commenting on, and editing of, this document 20