1、 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 ASM
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8、y 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 Fa
9、tigue STP-PT-031 TABLE OF CONTENTS Foreword . iv Abstract v 1 INTRODUCTION . 1 2 PREVIOUS EXPERIMENTAL RESULTS 2 3 ASME SECTION VIII DIV 3 FATIGUE ANALYSIS. 5 4 ASME SECTION VIII DIV 2 FATIGUE ANALYSIS. 7 4.1 Numerical Stress Analysis Results (Calculated Values of ip) . 7 5 LIFE PREDICTION RESULTS 8
10、 6 MARKL ANALYSIS APPROACH TO THE OBSERVED DATA. 12 7 DISCUSSION14 8 CONCLUSION 18 References 19 Acknowledgments 20 LIST OF TABLES Table 1 - Summary of Fatigue Test Results . 3 Table 2 - Section VIII Div 3 Design Life Analysis Results . 10 Table 3 - Section VIII Div 2 Design Life Analysis Results .
11、11 Table 4 - Comparison of Measured Results with Equation (7) as the Design Curve. 15 Table 5 - Comparison of Safety Factors for Various Design Curves. 16 LIST OF FIGURES Figure 1 - Comparison of Measured Fatigue Lives and Section VIII, Div. 3 Design Curves 9 Figure 2 - Comparison of Measured Fatigu
12、e Lives and Section VIII, Div. 2 Analysis Method 9 Figure 3 - Analysis of the Measured Data Using a Markl Power Law Equation . 13 Figure 4 - 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
13、 project which resulted from ASME Pressure Technology Codes D/T (ratio of main pipe diameter to main pipe thickness) between 20 and 250; and d/D less than t/T (ratio of nozzle thickness to main pipe thickness) less than or equal to 3.0. In all, 75 models were run. A great deal of stress analysis res
14、ults were given in the report. Of interest to this study are the maximum tangential stress that was calculated and the equation that was fit to the results. The equation appears as equation (6.5R) on page 43 of the report. We reproduce the equation here and replace Wideras and Weis term for stress c
15、oncentration with ip: 2.04.08.03.03.08.02984.25326.19270.0+=TtTDDdTtTDDdip(5) 7 STP-PT-031 Pressure Induced Fatigue 5 LIFE PREDICTION RESULTS Using the Section VIII, Div 3 approach with Equation (5) for the stress concentration factor, we can generate Salteqfor all of the experimental results found.
16、 These calculations are summarized in Table 2. Also shown in the table is the design life that would have been allowed if the Section VIII, Div 3 design life rule were invoked. The comparison between the actual measured life and the allowed design life is also visually made in Figure 1. All of the d
17、ata 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 3 would have produced safe designs for the specimens tested. The results obtained using the methods outlined in Secti
18、on VIII, Div 2 are given in Table 3 and plotted in Figure 2. As with the case for the Section VIII, Div 3 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
19、safety factor on life in Table 3 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
20、data. The Div 2 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 1 indicates that the sense of the Div 3 design curves follow the sense of the measured data over the complete ra
21、nge of stress and life measured. Therefore, although the Div 2 approach would result in safe designs, we do not believe that the Div 2 approach correctly models the pressure induced fatigue behavior that we are studying. 8 Pressure Induced Fatigue STP-PT-031 11010010001.E+01 1.E+02 1.E+03 1.E+04 1.E
22、+05 1.E+06 1.E+07CyclesSalteq(ksi)De sig n Curve UTS 80 KsiMayers Report DataKobe Steel DataWRC Bulletin 135 DataDesign Curve UTS 115- 130 ksiFigure 1 - Comparison of Measured Fatigue Lives and Section VIII, Div. 3 Design Curves 101001000100 1000 10000 100000 1000000CyclesStress RangeDiv 2 Des ign C
23、ur veMeas ured DataFigure 2 - Comparison of Measured Fatigue Lives and Section VIII, Div. 2 Analysis Method 9 STP-PT-031 Pressure Induced Fatigue Table 2 - Section VIII Div 3 Design Life Analysis Results Specimen No. Pressure Range (psi) d/D D/T t/T ipPD/2T pmin(psi) pmax(psi) Sa(ksi) Salteq(ksi) De
24、sign 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 5 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 0 3000 20.6 24.0 48571 3000
25、00 T13-F 6382 0.152 22.723 0.815 1.962 72509 0 6382 68.0 134.1 283 2982 T13-D 5657 0.152 22.723 0.815 1.962 64269 0 5657 60.3 107.1 494 9102 T13-C 5222 0.152 22.723 0.815 1.962 59326 0 5222 55.6 93.3 705 28286 F13-F 5512 0.152 22.723 1.000 1.837 62622 0 5512 55.0 91.0 752 6518 F13-D 5222 0.152 22.72
26、3 1.000 1.837 59326 0 5222 52.1 83.3 952 7553 F13-C 4932 0.152 22.723 1.000 1.837 56030 0 4932 49.2 76.2 1222 9772 F13-B 4351 0.152 22.723 1.000 1.837 49438 0 4351 43.4 63.1 2110 15553 T*13-4 7252 0.233 22.723 1.000 2.207 82397 0 7252 86.9 239.6 74 4360 T*13-2 5802 0.233 22.723 1.000 2.207 65917 0 5
27、802 69.5 141.9 247 9502 T*13-3 5077 0.233 22.723 1.000 2.207 57678 0 5077 60.8 109.8 463 9116 T*13-1 4351 0.233 22.723 1.000 2.207 49438 0 4351 52.2 84.4 919 21135 F13-1 7252 0.233 22.723 1.000 2.207 82397 0 7252 86.9 239.6 74 2781 F13-4 5802 0.233 22.723 1.000 2.207 65917 0 5802 69.5 141.9 247 8586
28、 F13-2 5222 0.233 22.723 1.000 2.207 59326 0 5222 62.6 115.6 407 14805 F13-3 4351 0.233 22.723 1.000 2.207 49438 0 4351 52.2 84.4 919 20505 T20-D 7977 0.233 14.700 1.040 1.928 58634 0 7977 52.7 82.0 995 4376 T20-A 6962 0.233 14.700 1.040 1.928 51172 0 6962 46.0 66.8 1780 6145 T20-C 6382 0.233 14.700
29、 1.040 1.928 46908 0 6382 42.1 59.0 2591 9455 T20-B 5802 0.233 14.700 1.040 1.928 42643 0 5802 38.3 51.8 3918 19032 F20-E 7252 0.233 14.700 1.040 1.928 53304 0 7252 47.9 71.0 1494 3462 F20-F 6382 0.233 14.700 1.040 1.928 46908 0 6382 42.1 59.0 2591 6398 F20-A 5802 0.233 14.700 1.040 1.928 42645 0 58
30、02 38.3 51.8 3918 14288 F20-C 4932 0.233 14.700 1.040 1.928 36247 0 4932 32.6 41.8 7306 20890 V-1-1 4325 0.266 18.000 0.297 3.276 38925 0 4325 60.2 108.9 473 7223 V-1-6 4325 0.266 18.000 0.297 3.276 38925 0 4325 60.2 108.9 473 7516 V-1-11 4325 0.056 18.000 0.094 1.910 38925 0 4325 35.1 46.6 5502 517
31、4 V-2-6 2650 0.266 18.000 0.297 3.276 23850 0 2650 36.9 50.8 4162 85868 V-2-2 2650 0.266 18.000 0.297 3.276 23850 0 2650 36.9 50.8 4162 123618 V-3-1 4400 0.266 18.000 0.297 3.276 39600 0 4400 61.3 112.4 437 8990 V-4-6 3460 0.266 18.000 0.297 3.276 31140 0 3460 48.2 75.0 1276 40041 V-4-11 3460 0.056
32、18.000 0.094 1.910 31140 0 3460 28.1 35.0 13104 48437 V-6-2 4400 0.266 18.000 0.297 3.276 39600 0 4400 61.3 112.4 437 19272 V-7-9B 2650 0.395 18.000 0.403 3.773 23850 0 2650 42.5 62.4 2187 23908 V-7-2B 2650 0.278 18.000 1.094 2.157 23850 0 2650 24.3 29.4 23786 135600 V-7-2N 2650 0.278 18.000 1.094 2
33、.157 23850 0 2650 24.3 29.4 23786 375357 V-8-1 4400 0.266 18.000 0.297 3.276 39600 0 4400 61.3 112.4 437 21070 V-8-2 4400 0.266 18.000 0.297 3.276 39600 0 4400 61.3 112.4 437 26311 10 Pressure Induced Fatigue STP-PT-031 Table 3 - Section VIII Div 2 Design Life Analysis Results Specimen No. P (psi) d
34、/D D/T t/T ipSmax(ksi) Smin(ksi) Stress Range (ksi) Corrected Neuber (ksi) Corrected for R (ksi) Design Life (Cycles) Actual Life (Cycles) Safety Factor N Safety Factor Stress T-11 6900 1.000 10.243 1.000 3.676 118.9 1.7 117.2 93.3 91.6 946 2975 3.1 1.4 T-12 1795 0.417 34.934 1.000 3.445 105.2 0.3 1
35、04.9 88.9 66.5 2583 76620 29.7 3.0 T-13 6900 0.417 10.243 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
36、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 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 1.3 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 F1
37、3-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
38、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 F13-1 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 F13-4 5802 0.233 22.723 1.000 2.207 13
39、9.1 0.0 139.1 99.3 72.7 1951 8586 4.4 1.6 F13-2 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 F13-3 4351 0.233 22.723 1.000 2.207 104.3 0.0 104.3 88.6 64.9 2783 20505 7.4 1.9 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
40、 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
41、-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 89.4 102
42、1 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 V-2-6 2650 0.266 18.000 0.297 3.276 73.8 0.0 73.8 71.4 67.7 2435 85868 35.3 3.1 V-2-2 2650 0.266 18.000 0.297 3.276 73.8 0
43、.0 73.8 71.4 67.7 2435 123618 50.8 3.5 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 18.0
44、00 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.
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 6 MARKL ANALYSIS APPROACH TO THE OBSERVED DATA The conclusions we draw fro
46、m 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 enginee
47、r. 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 3 analysis, above, that we must account for the influence of mean stress and multiaxial stresses to
48、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 ipfrom Widera and Wei are adequate approximations to the experimentally determined values of ip. 2
49、) 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 2 for most of the samples reported. There are a few samples that had a small m
